### 2013

#### Geosemantic Snapping for Sketch-Based Modeling,

Alex Shtof, Alexander Agathos, Yotam Gingold, Ariel Shamir, Daniel Cohen-Or,
Computer Graphics Forum, Vol.32, No.2, May, 2013.
Modeling 3D objects from sketches is a process that requires several challenging problems including segmentation, recognition and reconstruction. Some of these tasks are harder for humans and some are harder for the machine. At the core of the problem lies the need for semantic understanding of the shape\\\'s geometry from the sketch. In this paper we propose a method to model 3D objects from sketches by utilizing humans specifically for semantic tasks that are very simple for humans and extremely difficult for the machine, while utilizing the machine for tasks that are harder for humans. The user assists recognition and segmentation by choosing and placing specific geometric primitives on the relevant parts of the sketch. The machine first snaps the primitive to the sketch by fitting its projection to the sketch lines, and then improves the model globally by inferring geosemantic constraints that link the different parts. The fitting occurs in real-time, allowing the user to be only as precise as needed to have a good starting configuration for this non-convex optimization problem. We evaluate the accessibility of our approach with a user study.
@Article{CG_0201,
author = {Alex Shtof and  Alexander Agathos and  Yotam Gingold and  Ariel Shamir and  Daniel Cohen-Or},
title = {{G}eosemantic {S}napping for {S}ketch-{B}ased {M}odeling},
journal = {Computer Graphics Forum},
volume = {32},
number = {2},
month = {May},
year = {2013}
}


#### Discrete bending forces and their Jacobians,

Rasmus Tamstorf, Eitan Grinspun,
Graphical Models, Vol.75, No.6, Nov, 2013.
Computation of bending forces on triangle meshes is required for numerous simulation and geometry processing applications. In particular it is a key component in cloth simulation. A common quantity in many bending models is the hinge angle between two adjacent triangles. This angle is straightforward to compute, and its gradient with respect to vertex positions (required for the forces) is easily found in the literature. However, the Hessian of the bend angle, which is required to compute the associated force Jacobians is not documented in the literature. Force Jacobians are required for efficient numerics (e.g., implicit time stepping, Newton-based energy minimization) and are thus highly desirable. Readily available computations of the force Jacobian, such as those produced by symbolic algebra systems, or by autodifferentiation codes, are expensive to compute and therefore less useful. We present compact, easily reproducible, closed form expressions for the Hessian of the bend angle. Compared to automatic differentiation, we measure up to 7× speedup for the evaluation of the bending forces and their Jacobians.
@Article{CG_0216,
author = {Rasmus Tamstorf and  Eitan Grinspun},
title = {{D}iscrete bending forces and their {J}acobians},
journal = {Graphical Models},
volume = {75},
number = {6},
pages = {362--370},
month = {Nov},
year = {2013}
}


#### A discrete geometric approach for simulating the dynamics of thin viscous threads,

B. Audoly, N. Clauvelin, P.-T. Brun, M. Bergou, E. Grinspun, M. Wardetzky,
Journal of Computational Physics, Vol.253, Nov, 2013.
We present a numerical model for the dynamics of thin viscous threads based on a discrete, Lagrangian formulation of the smooth equations. The model makes use of a condensed set of coordinates, called the centerline/spin representation: the kinematic constraints linking the centerlineʼs tangent to the orientation of the material frame is used to eliminate two out of three degrees of freedom associated with rotations. Based on a description of twist inspired from discrete differential geometry and from variational principles, we build a full-fledged discrete viscous thread model, which includes in particular a discrete representation of the internal viscous stress. Consistency of the discrete model with the classical, smooth equations for thin threads is established formally. Our numerical method is validated against reference solutions for steady coiling. The method makes it possible to simulate the unsteady behavior of thin viscous threads in a robust and efficient way, including the combined effects of inertia, stretching, bending, twisting, large rotations and surface tension.
@Article{CG_0214,
author = {B. Audoly and  N. Clauvelin and  P.-T. Brun and  M. Bergou and  E. Grinspun and  M. Wardetzky},
title = {{A} discrete geometric approach for simulating the dynamics of thin viscous threads},
journal = {Journal of Computational Physics},
volume = {253},
pages = {18--49},
month = {Nov},
year = {2013}
}


#### Parsing Sewing Patterns into 3D Garments,

Floraine Berthouzoz, Akash Garg, Danny Kaufman, Eitan Grinspun, Maneesh Agrawala,
SIGGRAPH ( ACM Transactions on Graphics), Jul, 2013.
We present techniques for automatically parsing existing sewing patterns and converting them into 3D garment models. Our parser takes a sewing pattern in PDF format as input and starts by extracting the set of panels and styling elements (e.g. darts, pleats and hemlines) contained in the pattern. It then applies a combina- tion of machine learning and integer programming to infer how the panels must be stitched together to form the garment. Our system includes an interactive garment simulator that takes the parsed re- sult and generates the corresponding 3D model. Our fully automatic approach correctly parses 68% of the sewing patterns in our collection. Most of the remaining patterns contain only a few errors that can be quickly corrected within the garment simulator. Finally we present two applications that take advantage of our collection of parsed sewing patterns. Our garment hybrids application lets users smoothly interpolate multiple garments in the 2D space of patterns. Our sketch-based search application allows users to navigate the pattern collection by drawing the shape of panels.
@InProceedings{CG_0204,
author = {Floraine Berthouzoz and  Akash Garg and  Danny Kaufman and  Eitan Grinspun and  Maneesh Agrawala},
title = {{P}arsing {S}ewing {P}atterns into 3{D} {G}arments},
booktitle = {SIGGRAPH ( ACM Transactions on Graphics)},
month = {Jul},
year = {2013}
}


#### Interactive Localized Liquid Motion Editing,

Zherong Pan, Jin Huang, Yiying Tong, Changxi Zheng, and Hujun Bao,
SIGGRAPH Asia, Vol.32, No.6, Nov, 2013.
Animation techniques for controlling liquid simulation are challenging: they commonly require carefully setting initial and boundary conditions or performing a costly numerical optimization scheme against user-provided keyframes or animation sequences. Either way, the whole process is laborious and computationally expensive. We introduce a novel method to provide intuitive and interactive control of liquid simulation. Our method enables a user to locally edit selected keyframes and automatically propagates the editing in a nearby temporal region using geometric deformation. We formulate our local editing techniques as a small-scale nonlinear optimization problem which can be solved interactively. With this uniformed formulation, we propose three editing metaphors, including (i) sketching local fluid features using a few user strokes, (ii) dragging a local fluid region, and (iii) controlling a local shape with a small mesh patch. Finally, we use the edited liquid animation to guide an of offline high-resolution simulation to recover more surface details. We demonstrate the intuitiveness and efficacy of our method in various practical scenarios.
@InProceedings{CG_0217,
author = {Zherong Pan and  Jin Huang and  Yiying Tong and  Changxi Zheng and Hujun Bao},
title = {{I}nteractive {L}ocalized {L}iquid {M}otion {E}diting},
booktitle = {SIGGRAPH Asia},
volume = {32},
number = {6},
month = {Nov},
year = {2013}
}


#### One-to-Many: Example-Based Mesh Animation Synthesis,

Changxi Zheng,
Symposium on Computer Animation, Jul, 2013.
We propose an example-based approach for synthesizing diverse mesh animations. Provided a short clip of deformable mesh animation, our method synthesizes a large number of different animations of arbitrary length. Combining an automatically inferred linear blending skinning (LBS) model with a PCA-based model reduction, our method identifies possible smooth transitions in the example sequence. To create smooth transitions, we synthesize reduced deformation parameters based on a set of characteristic key vertices on the mesh. Furthermore, by analyzing cut nodes on a graph built upon the LBS model, we are able to decompose the mesh into independent components. Motions of these components are synthesized individually and assembled together. Our method has the complexity independent from mesh resolutions, enabling efficient generation of arbitrarily long animations without tedious parameter tuning and heavy computation. We evaluate our method on various animation examples, and demonstrate that numerous diverse animations can be generated from each single example.
@InProceedings{CG_0208,
author = {Changxi Zheng},
title = {{O}ne-to-{M}any: {E}xample-{B}ased {M}esh {A}nimation {S}ynthesis},
booktitle = {Symposium on Computer Animation},
month = {Jul},
year = {2013}
}


### 2012

#### Micro Perceptual Human Computation for Visual Tasks,

Yotam Gingold, Ariel Shamir, Daniel Cohen-Or,
ACM Transactions on Graphics, Vol.31, No.5, Aug, 2012.
Human computation (HC) utilizes humans to solve problems or carry out tasks that are hard for pure computational algorithms. Many graphics and vision problems have such tasks. Previous HC approaches mainly focus on generating data in batch, to gather benchmarks or perform surveys demanding non-trivial interactions. We advocate a tighter integration of human computation into online, interactive algorithms. We aim to distill the differences between humans and computers and maximize the advantages of both in one algorithm. Our key idea is to decompose such a problem into a massive number of very simple, carefully designed, human micro-tasks that are based on perception, and whose answers can be combined algorithmically to solve the original problem. Our approach is inspired by previous work on micro-tasks and perception experiments. We present three specific examples for the design of Micro Perceptual Human Computation algorithms to extract depth layers and image normals from a single photograph, and to augment an image with high-level semantic information such as symmetry.
@Article{CG_0196,
author = {Yotam Gingold and  Ariel Shamir and  Daniel Cohen-Or},
title = {{M}icro {P}erceptual {H}uman {C}omputation for {V}isual {T}asks},
journal = {ACM Transactions on Graphics},
volume = {31},
number = {5},
pages = {119:1----119:12},
month = {Aug},
year = {2012}
}


#### RigMesh: Automatic Rigging for Part-Based Shape Modeling and Deformation,

Peter Borosan, Ming Jin, Doug DeCarlo, Yotam Gingold, Andrew Nealen,
ACM Transactions on Graphics, Vol.31, Dec, 2012.
The creation of a 3D model is only the first stage of the 3D character animation pipeline. Once a model has been created, and before it can be animated, it must be rigged. Manual rigging is laborious, and automatic rigging approaches are far from real-time and do not allow for incremental updates. This is a hindrance in the real world, where the shape of a model is often revised after rigging has been performed. In this paper, we introduce algorithms and a user-interface for sketch-based 3D modeling that unify the modeling and rigging stages of the 3D character animation pipeline. Our algorithms create a rig for each sketched part in real-time, and update the rig as parts are merged or cut. As a result, users can freely pose and animate their shapes and characters while rapidly iterating on the base shape. The rigs are compatible with the state-of-the-art character animation pipeline; they consist of a low-dimensional skeleton along with skin weights identifying the surface with bones of the skeleton.
@Article{CG_0198,
author = {Peter Borosan and  Ming Jin and  Doug DeCarlo and  Yotam Gingold and  Andrew Nealen},
title = {{R}ig{M}esh: {A}utomatic {R}igging for {P}art-{B}ased {S}hape {M}odeling and {D}eformation},
journal = {ACM Transactions on Graphics},
volume = {31},
month = {Dec},
year = {2012}
}


#### Speculative Parallel Asynchronous Contact Mechanics,

Samantha Ainsley, Etienne Vouga, Eitan Grinspun, and Rasmus Tamstorf,
ACM Transactions on Graphics (SIGGRAPH Asia), Vol.31, No.6, Nov, 2012.
We extend the Asynchronous Contact Mechanics algorithm and improve its performance by two orders of magnitude, using only optimizations that do not compromise ACM’s three guarantees of safety, progress, and correctness. The key to this speedup is replacing ACM’s timid, forward-looking mechanism for detecting collisions—locating and rescheduling separating plane kinetic data structures—with an optimistic speculative method inspired by Mirtich’s rigid body Time Warp algorithm [2000]. Time warp allows us to perform collision detection over a window of time containing many of ACM’s asynchronous trajectory changes; in this way we cull away large intervals as being collision free. Moreover, by replacing force processing intermingled with KDS rescheduling by windows of pure processing followed by collision detection, we tranform an algorithm that is very difficult to parallelize into one that is embarrassingly parallel.
@Article{CG_0199,
author = {Samantha Ainsley and  Etienne Vouga and  Eitan Grinspun and Rasmus Tamstorf},
title = {{S}peculative {P}arallel {A}synchronous {C}ontact {M}echanics},
journal = {ACM Transactions on Graphics (SIGGRAPH Asia)},
volume = {31},
number = {6},
pages = {8},
month = {Nov},
year = {2012}
}


#### Mapping Cardiac Surface Mechanics with Structured Light Imaging,

Jacob I. Laughner, Song Zhang, Hao Li, Connie C. Shao, Igor R. Efimov,
American Journal of Physiology, Heart and Circulatory Physiology, PMID: 22796539, Jul, 2012.
Background: Cardiovascular disease often manifests as a combination of pathological electrical and structural heart remodeling. The relationship between mechanics and electrophysiology is crucial to our understanding of mechanisms of cardiac arrhythmias and the treatment of cardiac disease. While several technologies exist for describing whole-heart electrophysiology, studies of cardiac mechanics are often limited to rhythmic patterns or small sections of tissue. Methods and Results: Here, we present a comprehensive system based on ultrafast three-dimensional (3D) structured light imaging to map surface dynamics of whole-heart cardiac motion. Additionally, we introduce a novel non-rigid motion-tracking algorithm based on an isometry-maximizing optimization framework that forms correspondences between consecutive 3D frames without the use of any fiducial markers. By combining our 3D imaging system with non-rigid surface registration, we are able to measure cardiac surface mechanics at unprecedented spatial and temporal resolution. Conclusions: We demonstrate accurate cardiac deformation at over 200,000 surface points of a rabbit heart recorded at 200 frames per second and validate our results on highly contrasting heart motions during normal sinus rhythm, ventricular pacing, and ventricular fibrillation.
@Article{CG_0191,
author = {Jacob I. Laughner and  Song Zhang and  Hao Li and  Connie C. Shao and  Igor R. Efimov},
title = {{M}apping {C}ardiac {S}urface {M}echanics with {S}tructured {L}ight {I}maging},
journal = {American Journal of Physiology, Heart and Circulatory Physiology, PMID: 22796539},
month = {Jul},
year = {2012}
}


#### Asynchronous Contact Mechanics (CACM Research Highlights),

David Harmon, Etienne Vouga, Breannan Smith, Rasmus Tamstorf, and Eitan Grinspun,
Communications of the ACM, Vol.55, No.4, Apr, 2012.
@Article{CG_0185,
author = {David Harmon and  Etienne Vouga and  Breannan Smith and  Rasmus Tamstorf and Eitan Grinspun},
title = {{A}synchronous {C}ontact {M}echanics ({C}{A}{C}{M} {R}esearch {H}ighlights)},
journal = {Communications of the ACM},
volume = {55},
number = {4},
pages = {102----109},
month = {Apr},
year = {2012}
}


#### Technical Perspective: Building Robust Dynamical Simulation Systems,

Dinesh Manocha,
Communications of the ACM, Vol.55, No.4, Apr, 2012.
@Article{CG_0184,
author = {Dinesh Manocha},
title = {{T}echnical {P}erspective: {B}uilding {R}obust {D}ynamical {S}imulation {S}ystems},
journal = {Communications of the ACM},
volume = {55},
number = {4},
pages = {101},
month = {Apr},
year = {2012}
}


#### Factored Facade Acquisition Using Symmetric Line Arrangements,

Duygu Ceylan, Niloy J. Mitra, Hao Li, Thibaut Weise, Mark Pauly,
Eurographics (Computer Graphics Forum), Vol.31, No.2, May, 2012.
We introduce a novel framework for image-based 3D reconstruction of urban buildings based on symmetry priors. Starting from image-level edges, we generate a sparse and approximate set of consistent 3D lines. These lines are then used to simultaneously detect symmetric line arrangements while refining the estimated 3D model. Operating both on 2D image data and intermediate 3D feature representations, we perform iterative feature consolidation and effective outlier pruning, thus eliminating reconstruction artifacts arising from ambiguous or wrong stereo matches. We exploit non-local coherence of symmetric elements to generate precise model reconstructions, even in the presence of a significant amount of outlier image-edges arising from reflections, shadows, outlier objects, etc. We evaluate our algorithm on several challenging test scenarios, both synthetic and real. Beyond reconstruction, the extracted symmetry patterns are useful towards interactive and intuitive model manipulations.
@Article{CG_0190,
author = {Duygu Ceylan and  Niloy J. Mitra and  Hao Li and  Thibaut Weise and  Mark Pauly},
title = {{F}actored {F}acade {A}cquisition {U}sing {S}ymmetric {L}ine {A}rrangements},
journal = {Eurographics (Computer Graphics Forum)},
volume = {31},
number = {2},
month = {May},
year = {2012}
}


#### Multi-View Hair Capture Using orientation Fields,

Linjie Luo, Hao Li, Sylvain Paris, Thibaut Weise, Mark Pauly, Szymon Rusinkiewicz,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Jun, 2012.
We present a novel shape completion technique for creating temporally coherent watertight surfaces from real-time captured dynamic performances. Because of occlusions and low surface albedo, scanned mesh sequences typically exhibit large holes that persist over extended periods of time. Most conventional dynamic shape reconstruction techniques rely on template models or assume slow deformations in the input data. Our framework sidesteps these requirements and directly initializes shape completion with topology derived from the visual hull. To seal the holes with patches that are consistent with the subject’s motion, we first minimize surface bending energies in each frame to ensure smooth transitions across hole boundaries. Temporally coherent dynamics of surface patches are obtained by unwarping all frames within a time window using accurate inter-frame correspondences. Aggregated surface samples are then filtered with a temporal visibility kernel that maximizes the use of non-occluded surfaces. A key benefit of our shape completion strategy is that it does not rely on long-range correspondences or a template model. Consequently, our method does not suffer from error accumulation typically introduced by noise, large deformations, and drastic topological changes. We illustrate the effectiveness of our method on several high-resolution scans of human performances captured with a state-of-the-art multi-view 3D acquisition system.
@Article{CG_0180,
author = {Linjie Luo and  Hao Li and  Sylvain Paris and  Thibaut Weise and  Mark Pauly and  Szymon Rusinkiewicz},
title = {{M}ulti-{V}iew {H}air {C}apture {U}sing orientation {F}ields},
journal = {IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {Jun},
year = {2012}
}


#### Geometric Numerical Integration of Inequality Constrained Nonsmooth Hamiltonian Systems,

Danny M. Kaufman and Dinesh K. Pai,
SIAM Journal on Scientific Computing, Vol.34, No.5, 2012.
@Article{CG_0203,
author = {Danny M. Kaufman and Dinesh K. Pai},
title = {{G}eometric {N}umerical {I}ntegration of {I}nequality {C}onstrained {N}onsmooth {H}amiltonian {S}ystems},
journal = {SIAM Journal on Scientific Computing},
volume = {34},
number = {5},
year = {2012}
}


#### Interactive Editing of Deformable Simulations,

Jernej Barbič, Fun Shing Sin, Eitan Grinspun,
SIGGRAPH, Vol.31, No.4, Aug, 2012.
We present an interactive animation editor for complex deformable object animations. Given an existing animation, the artist directly manipulates the deformable body at any time frame, and the sur- rounding animation immediately adjusts in response. The auto- matic adjustments are designed to respect physics, preserve detail in both the input motion and geometry, respect prescribed bilateral contact constraints, and controllably and smoothly decay in space- time. While the utility of interactive editing for rigid body and ar- ticulated figure animations is widely recognized, a corresponding approach to deformable bodies has not been technically feasible be- fore. We achieve interactive rates by combining spacetime model reduction, rotation-strain coordinate warping, linearized elasticity, and direct manipulation. This direct editing tool can serve the final stages of animation production, which often call for detailed, direct adjustments that are otherwise tedious to realize by re-simulation or frame-by-frame editing.
@Article{CG_0195,
author = {Jernej Barbič and  Fun Shing Sin and  Eitan Grinspun},
title = {{I}nteractive {E}diting of {D}eformable {S}imulations},
journal = {SIGGRAPH},
volume = {31},
number = {4},
month = {Aug},
year = {2012}
}


#### Design of Self-supporting Surfaces,

Etienne Vouga, Mathias Hobinger, Johannes Wallner, Helmut Pottmann,
SIGGRAPH ( ACM Transactions on Graphics), 2012.
Self-supporting masonry is one of the most ancient and elegant techniques for building curved shapes. Because of the very geometric nature of their failure, analyzing and modeling such strutures is more a geometry processing problem than one of classical continuum mechanics. This paper uses the thrust network method of analysis and presents an iterative nonlinear optimization algorithm for efficiently approximating freeform shapes by self-supporting ones. The rich geometry of thrust networks leads us to close connections between diverse topics in discrete differential geometry, such as a finite-element discretization of the Airy stress potential, perfect graph Laplacians, and computing admissible loads via curvatures of polyhedral surfaces. This geometric viewpoint allows us, in particular, to remesh self-supporting shapes by self-supporting quad meshes with planar faces, and leads to another application of the theory: steel/glass constructions with low moments in nodes.
@Article{CG_0188,
author = {Etienne Vouga and  Mathias Hobinger and  Johannes Wallner and  Helmut Pottmann},
title = {{D}esign of {S}elf-supporting {S}urfaces},
journal = {SIGGRAPH ( ACM Transactions on Graphics)},
year = {2012}
}


#### Energy-based Self-Collision Culling for Arbitrary Mesh Deformations,

Changxi Zheng and Doug L. James,
SIGGRAPH ( ACM Transactions on Graphics), Vol.31, No.4, Aug, 2012.
In this paper, we accelerate self-collision detection (SCD) for a deforming triangle mesh by exploiting the idea that a mesh cannot self collide unless it deforms enough. Unlike prior work on subspace self-collision culling which is restricted to low-rank deformation subspaces, our energy-based approach supports arbitrary mesh deformations while still being fast. Given a bounding volume hierarchy (BVH) for a triangle mesh, we precompute Energy-based Self-Collision Culling (ESCC) certificates on bounding-volume-related sub-meshes which indicate the amount of deformation energy required for it to self collide. After updating energy values at runtime, many bounding-volume self-collision queries can be culled using the ESCC certificates. We propose an affine-frame Laplacian-based energy definition which sports a highly optimized certificate preprocess, and fast runtime energy evaluation. The latter is performed hierarchically to amortize Laplacian energy and affine-frame estimation computations. ESCC supports both discrete and continuous SCD with detailed and nonsmooth geometry. We demonstrate significant culling on various examples, with SCD speed-ups up to 26X.
@Article{CG_0206,
author = {Changxi Zheng and Doug L. James},
title = {{E}nergy-based {S}elf-{C}ollision {C}ulling for {A}rbitrary {M}esh {D}eformations},
journal = {SIGGRAPH ( ACM Transactions on Graphics)},
volume = {31},
number = {4},
month = {Aug},
year = {2012}
}


#### Reflections on Simultaneous Impact,

Breannan Smith, Danny M. Kaufman, Etienne Vouga, Rasmus Tamstorf, Eitan Grinspun,
SIGGRAPH ( ACM Transactions on Graphics), Vol.31, No.4, 2012.
Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.
@Article{CG_0187,
author = {Breannan Smith and  Danny M. Kaufman and  Etienne Vouga and  Rasmus Tamstorf and  Eitan Grinspun},
title = {{R}eflections on {S}imultaneous {I}mpact},
journal = {SIGGRAPH ( ACM Transactions on Graphics)},
volume = {31},
number = {4},
pages = {106:1----106:12},
year = {2012}
}


#### Discrete Viscous Sheets,

Christopher Batty, Andres Uribe, Basile Audoly, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.31, No.4, Jul, 2012.
We present the first reduced-dimensional technique to simulate the dynamics of thin sheets of viscous incompressible liquid in three dimensions. Beginning from a discrete Lagrangian model for elastic thin shells, we apply the Stokes-Rayleigh analogy to derive a simple yet consistent model for viscous forces. We incorporate nonlinear surface tension forces with a formulation based on minimizing discrete surface area, and preserve the quality of triangular mesh elements through local remeshing operations. Simultaneously, we track and evolve the thickness of each triangle to exactly conserve liquid volume. This approach enables the simulation of extremely thin sheets of viscous liquids, which are difficult to animate with existing volumetric approaches. We demonstrate our method with examples of several characteristic viscous sheet behaviors, including stretching, buckling, sagging, and wrinkling.
@Article{CG_0186,
author = {Christopher Batty and  Andres Uribe and  Basile Audoly and  Eitan Grinspun},
title = {{D}iscrete {V}iscous {S}heets},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {31},
number = {4},
pages = {113:1--113:7},
month = {Jul},
year = {2012}
}


#### Precomputed Acceleration Noise for Improved Rigid-Body Sound,

Jeffrey N. Chadwick, Changxi Zheng, and Doug L. James,
SIGGRAPH (ACM Transactions on Graphics), Vol.31, No.4, Aug, 2012.
We introduce an efficient method for synthesizing acceleration noise - sound produced when an object experiences abrupt rigid-body acceleration due to collisions or other contact events. We approach this in two main steps. First, we estimate continuous contact force profiles from rigid-body impulses using a simple model based on Hertz contact theory. Next, we compute solutions to the acoustic wave equation due to short acceleration pulses in each rigid-body degree of freedom. We introduce an efficient representation for these solutions - Precomputed Acceleration Noise - which allows us to accurately estimate sound due to arbitrary rigid-body accelerations. We find that the addition of acceleration noise significantly complements the standard modal sound algorithm, especially for small objects.
@Article{CG_0209,
author = {Jeffrey N. Chadwick and  Changxi Zheng and Doug L. James},
title = {{P}recomputed {A}cceleration {N}oise for {I}mproved {R}igid-{B}ody {S}ound},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {31},
number = {4},
month = {Aug},
year = {2012}
}


#### Temporally Coherent Completion of Dynamic Shapes,

Hao Li, Linjie Luo, Daniel Vlasic, Pieter Peers, Jovan Popović, Mark Pauly, Szymon Rusinkiewicz,
SIGGRAPH (ACM Transactions on Graphics), Vol.31, No.1, 2012.
We present a novel shape completion technique for creating temporally coherent watertight surfaces from real-time captured dynamic performances. Because of occlusions and low surface albedo, scanned mesh sequences typically exhibit large holes that persist over extended periods of time. Most conventional dynamic shape reconstruction techniques rely on template models or assume slow deformations in the input data. Our framework sidesteps these requirements and directly initializes shape completion with topology derived from the visual hull. To seal the holes with patches that are consistent with the subject’s motion, we first minimize surface bending energies in each frame to ensure smooth transitions across hole boundaries. Temporally coherent dynamics of surface patches are obtained by unwarping all frames within a time window using accurate inter-frame correspondences. Aggregated surface samples are then filtered with a temporal visibility kernel that maximizes the use of non-occluded surfaces. A key benefit of our shape completion strategy is that it does not rely on long-range correspondences or a template model. Consequently, our method does not suffer from error accumulation typically introduced by noise, large deformations, and drastic topological changes. We illustrate the effectiveness of our method on several high-resolution scans of human performances captured with a state-of-the-art multi-view 3D acquisition system.
@Article{CG_0193,
author = {Hao Li and  Linjie Luo and  Daniel Vlasic and  Pieter Peers and  Jovan Popović and  Mark Pauly and  Szymon Rusinkiewicz},
title = {{T}emporally {C}oherent {C}ompletion of {D}ynamic {S}hapes},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {31},
number = {1},
year = {2012}
}


#### Tracking Surfaces with Evolving Topology,

Morten Bojsen-Hansen, Hao Li, Chris Wojtan,
SIGGRAPH (ACM Transactions on Graphics), Vol.31, No.4, Jul, 2012.
We present a method for recovering a temporally coherent, deforming triangle mesh with arbitrarily changing topology from an incoherent sequence of static closed surfaces. We solve this problem using the surface geometry alone, without any prior information like surface templates or velocity fields. Our system combines a proven strategy for triangle mesh improvement, a robust multi-resolution non-rigid registration routine, and a reliable technique for changing surface mesh topology. We also introduce a novel topological constraint enforcement algorithm to ensure that the output and input always have similar topology. We apply our technique to a series of diverse input data from video reconstructions, physics simulations, and artistic morphs. The structured output of our algorithm allows us to efficiently track information like colors and displacement maps, recover velocity information, and solve PDEs on the mesh as a post process.
@Article{CG_0192,
author = {Morten Bojsen-Hansen and  Hao Li and  Chris Wojtan},
title = {{T}racking {S}urfaces with {E}volving {T}opology},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {31},
number = {4},
pages = {53:1----53:10},
month = {Jul},
year = {2012}
}


#### Diamonds From the Rough: Improving Drawing, Painting, and Singing via Crowdsourcing,

Yotam Gingold, Etienne Vouga, Eitan Grinspun, Haym Hirsh,
Human Computation Workshop (HCOMP), Jul, 2012.
It is well established that in certain domains, noisy inputs can be reliably combined to obtain a better answer than any individual. It is now possible to consider the crowdsourcing of physical actions, commonly used for creative expressions such as drawing, shading, and singing. We provide algorithms for converting low-quality input obtained from the physical actions of a crowd into high-quality output. The inputs take the form of line drawings, shaded images, and songs. We investigate single-individual crowds (multiple inputs from a single human) and multiple-individual crowds.
@InProceedings{CG_0189,
author = {Yotam Gingold and  Etienne Vouga and  Eitan Grinspun and  Haym Hirsh},
title = {{D}iamonds {F}rom the {R}ough: {I}mproving {D}rawing, {P}ainting, and {S}inging via {C}rowdsourcing},
booktitle = {Human Computation Workshop (HCOMP)},
month = {Jul},
year = {2012}
}


#### Pixelated Image Abstraction,

Timothy Gerstner, Doug DeCarlo, Marc Alexa, Adam Finkelstein, Yotam Gingold, Andrew Nealen,
International Symposium on Non-Photorealistic Animation and Rendering (NPAR), Jun, 2012.
We present an automatic method that can be used to abstract high resolution images into very low resolution outputs with reduced color palettes in the style of pixel art. Our method simultaneously solves for a mapping of features and a reduced palette needed to construct the output image. The results are an approximation to the results generated by pixel artists. We compare our method against the results of a naive process common to image manipulation programs, as well as the hand-crafted work of pixel artists. Through a formal user study and interviews with expert pixel artists we show that our results offer an improvement over the naive methods.
@InProceedings{CG_0197,
author = {Timothy Gerstner and  Doug DeCarlo and  Marc Alexa and  Adam Finkelstein and  Yotam Gingold and  Andrew Nealen},
title = {{P}ixelated {I}mage {A}bstraction},
booktitle = {International Symposium on Non-Photorealistic Animation and Rendering (NPAR)},
month = {Jun},
year = {2012}
}


#### Faster Acceleration Noise for Multibody Animations using Precomputed Soundbanks,

Jeffrey N. Chadwick, Changxi Zheng, and Doug L. James ,
Symposium on Computer Animation, Aug, 2012.
We introduce an efficient method for synthesizing rigid-body acceleration noise for complex multibody scenes. Existing acceleration noise synthesis methods for animation require object-specific precomputation, which is prohibitively expensive for scenes involving rigid-body fracture or other sources of small, procedurally generated debris. We avoid precomputation by introducing a proxy-based method for acceleration noise synthesis in which precomputed acceleration noise data is only generated for a small set of ellipsoidal proxies and stored in a proxy soundbank. Our proxy model is shown to be effective at approximating acceleration noise from scenes with lots of small debris (e.g., pieces produced by rigid-body fracture). This approach is not suitable for synthesizing acceleration noise from larger objects with complicated non-convex geometry; however, it has been shown in previous work that acceleration noise from objects such as these tends to be largely masked by modal vibration sound. We manage the cost of our proxy soundbank with a new wavelet-based compression scheme for acceleration noise and use our model to significantly improve sound synthesis results for several multibody animations.
@InProceedings{CG_0210,
author = {Jeffrey N. Chadwick and  Changxi Zheng and Doug L. James },
title = {{F}aster {A}cceleration {N}oise for {M}ultibody {A}nimations using {P}recomputed {S}oundbanks},
booktitle = {Symposium on Computer Animation},
month = {Aug},
year = {2012}
}


#### Flexible Developable Surfaces,

Justin Solomon, Etienne Vouga, Max Wardetzky, and Eitan Grinspun,
Symposium on Geometry Processing, 2012.
We introduce a discrete paradigm for developable surface modeling. Unlike previous attempts at interactive developable surface modeling, our system is able to enforce exact developability at every step, ensuring that users do not inadvertently suggest configurations that leave the manifold of admissible folds of a flat two-dimensional sheet. With methods for navigation of this highly nonlinear constraint space in place, we show how to formulate a discrete mean curvature bending energy measuring how far a given discrete developable surface is from being flat. This energy enables relaxation of user-generated configurations and suggests a straightforward subdivision scheme that produces admissible smoothed versions of bent regions of our discrete developable surfaces.
@InProceedings{CG_0202,
author = {Justin Solomon and  Etienne Vouga and  Max Wardetzky and Eitan Grinspun},
title = {{F}lexible {D}evelopable {S}urfaces},
booktitle = {Symposium on Geometry Processing},
year = {2012}
}


### 2011

#### Asynchronous Variational Contact Mechanics,

E. Vouga, D. Harmon, R. Tamstorf, and E. Grinspun,
Computer Methods in Applied Mechanics and Engineering, Vol.200, Apr, 2011.
An asynchronous, variational method for simulating elastica in complex contact and impact scenarios is developed. Asynchronous Variational Integrators (AVIs) are extended to handle contact forces by associating different time steps to forces instead of to spatial elements. By discretizing a barrier potential by an infinite sum of nested quadratic potentials, these extended AVIs are used to resolve contact while obeying momentum- and energy-conservation laws. A series of two- and three-dimensional examples illustrate the robustness and good energy behavior of the method.
@Article{CG_0178,
author = {E. Vouga and  D. Harmon and  R. Tamstorf and E. Grinspun},
title = {{A}synchronous {V}ariational {C}ontact {M}echanics},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {200},
pages = {2181--2194},
month = {Apr},
year = {2011}
}


#### Example-Based Elastic Materials ,

S. Martin, B. Thomaszewski, E. Grinspun, M. Gross,
SIGGRAPH (ACM Transactions on Graphics), Vol.30, No.4, Aug, 2011.
We propose an example-based approach for simulating complex elastic material behavior. Supplied with a few poses that characterize a given object, our system starts by constructing a space of prefered deformations by means of interpolation. During simulation, this example manifold then acts as an additional elastic attractor that guides the object towards its space of prefered shapes. Added on top of existing solid simulation codes, this example potential effectively allows us to implement inhomogeneous and anisotropic materials in a direct and intuitive way. Due to its example-based interface, our method promotes an art-directed approach to solid simulation, which we exemplify on a set of practical examples.
@Article{CG_0183,
author = {S. Martin and  B. Thomaszewski and  E. Grinspun and  M. Gross},
title = {{E}xample-{B}ased {E}lastic {M}aterials },
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {30},
number = {4},
pages = {72:1--72:8},
month = {Aug},
year = {2011}
}


#### Sensitive Couture for Interactive Garment Editing and Modeling,

Nobuyuki Umetani, Danny M. Kaufman, Takeo Igarashi, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.30, No.4, Aug, 2011.
We present a novel interactive tool for garment design that enables, for the first time, interactive bidirectional editing between 2D patterns and 3D high-fidelity simulated draped forms. This provides a continuous, interactive, and natural design modality in which 2D and 3D representations are simultaneously visible and seamlessly maintain correspondence. Artists can now interactively edit 2D pat- tern designs and immediately obtain stable accurate feedback on- line, thus enabling rapid prototyping and an intuitive understanding of complex drape form.
@Article{CG_0179,
author = {Nobuyuki Umetani and  Danny M. Kaufman and  Takeo Igarashi and  Eitan Grinspun},
title = {{S}ensitive {C}outure for {I}nteractive {G}arment {E}diting and {M}odeling},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {30},
number = {4},
month = {Aug},
year = {2011}
}


#### Toward High-Quality Modal Contact Sound,

Changxi Zheng and Doug L. James,
SIGGRAPH (ACM Transactions on Graphics), Vol.30, No.4, Aug, 2011.
Contact sound models based on linear modal analysis are commonly used with rigid body dynamics. Unfortunately, treating vibrating objects as “rigid” during collision and contact processing fundamentally limits the range of sounds that can be computed, and contact solvers for rigid body animation can be ill-suited for modal contact sound synthesis, producing various sound artifacts. In this paper, we resolve modal vibrations in both collision and frictional contact processing stages, thereby enabling non-rigid sound phenomena such as micro-collisions, vibrational energy exchange, and chattering. We propose a frictional multibody contact formulation and modified Staggered Projections solver which is well-suited to sound rendering and avoids noise artifacts associated with spatial and temporal contact-force fluctuations which plague prior methods. To enable practical animation and sound synthesis of numerous bodies with many coupled modes, we propose a novel asynchronous integrator with model-level adaptivity built into the frictional contact solver. Vibrational contact damping is modeled to approximate contact-dependent sound dissipation. Results are provided that demonstrate high-quality contact resolution with sound.
@Article{CG_0211,
author = {Changxi Zheng and Doug L. James},
title = {{T}oward {H}igh-{Q}uality {M}odal {C}ontact {S}ound},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {30},
number = {4},
month = {Aug},
year = {2011}
}


#### Dynamic Hair Capture,

Linjie Luo, Hao Li, Thibaut Weise, Sylvain Paris, Mark Pauly, Szymon Rusinkiewicz,
Technical Report, Princeton University, Vol. TR-, Aug, 2011.
The realistic reconstruction of hair motion is challenging because of hair\\\\\\\\\\\\\\\'s complex occlusion, lack of a well-defined surface, and non-Lambertian material. We present a system for passive capture of dynamic hair performances using a set of high-speed video cameras. Our key insight is that, while hair color is unlikely to match across multiple views, the response to oriented filters will. We combine a multi-scale version of this orientation-based matching metric with bilateral aggregation, a MRF-based stereo reconstruction technique, and algorithms for temporal tracking and de-noising. Our final output is a set of hair strands for each frame, grown according to the per-frame reconstructed rough geometry and orientation field. We demonstrate results for a number of hair styles ranging from smooth and ordered to curly and messy.
@Article{CG_0181,
author = {Linjie Luo and  Hao Li and  Thibaut Weise and  Sylvain Paris and  Mark Pauly and  Szymon Rusinkiewicz},
title = {{D}ynamic {H}air {C}apture},
journal = {Technical Report, Princeton University},
volume = { TR-},
month = {Aug},
year = {2011}
}


### 2010

#### Harmonic enrichment functions: A unified treatment of multiple, intersecting and branched cracks in the extended finite element method,

S. E. Mousavi, E. Grinspun, N. Sukumar,
International Journal for Numerical Methods in Engineering, Vol.85, No.10, Aug, 2010.
A unifying procedure to numerically compute enrichment functions for elastic fracture problems with the extended finite element method is presented. Within each element that is intersected by a crack, the enrichment function for the crack is obtained via the solution of the Laplace equation with Dirichlet and vanishing Neumann boundary conditions. A single algorithm emanates for the enrichment field for multiple cracks as well as intersecting and branched cracks, without recourse to special cases, which provides flexibility over existing approaches in which each case is treated separately. Numerical integration is rendered to be simple—there is no need for partitioning of the finite elements into conforming subdivisions for the integration of discontinuous or weakly singular kernels. Stress intensity factor computations for different crack configurations are presented to demonstrate the accuracy and versatility of the proposed technique.
@Article{CG_0175,
author = {S. E. Mousavi and  E. Grinspun and  N. Sukumar},
title = {{H}armonic enrichment functions: {A} unified treatment of multiple, intersecting and branched cracks in the extended finite element method},
journal = {International Journal for Numerical Methods in Engineering},
volume = {85},
number = {10},
pages = {1306--1322},
month = {Aug},
year = {2010}
}


#### Higher-order extended finite elements with harmonic enrichment functions for complex crack problems,

S. E. Mousavi, E. Grinspun, N. Sukumar,
International Journal for Numerical Methods in Engineering, Vol.86, No.4-5, Dec, 2010.
We analyze complex crack problems in elastic media using harmonic enrichment functions in a higher-order extended finite element implementation. The numerically computed enrichment function of a crack is the solution of the Laplace equation with discontinuous Dirichlet boundary condition along the crack, and its interaction with branches or other cracks is realized by imposing vanishing Neumann boundary conditions along those cracks. The classical finite element displacement approximation is enriched by adding the enrichment function of a crack through the framework of partition of unity. A nested subgrid mesh is used in the Laplace solve with a rasterized approximation of a crack, which simplifies the numerical integration—no partitioning of finite elements is required. Harmonic enrichment functions readily permit the extension to handle multiple interacting and branched cracks without any special treatment around the junction points. Several numerical examples are presented that affirm the accuracy and effectiveness of the method when applied to complex crack configurations under mixed-mode loading conditions.
@Article{CG_0176,
author = {S. E. Mousavi and  E. Grinspun and  N. Sukumar},
title = {{H}igher-order extended finite elements with harmonic enrichment functions for complex crack problems},
journal = {International Journal for Numerical Methods in Engineering},
volume = {86},
number = {4-5},
pages = {560--574},
month = {Dec},
year = {2010}
}


#### Discrete Viscous Threads,

Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.29, No.4, Jul, 2010.
We present a continuum-based discrete model for thin threads of viscous fluid based on the Rayleigh analogy to elastic rods, demonstrating canonical coiling, folding, and breakup in dynamic simulations. Our derivation emphasizes space-time symmetry, which ultimately sheds light on the role of time-parallel transport in eliminating—without approximation—all but an O(n) band of entries of the physical system’s force Jacobian. The result is a fast, unified, implicit treatment of viscous threads and elastic rods that closely reproduces a variety of fascinating physical phenomena, including hysteretic transitions between coiling regimes, competition between surface tension and gravity, and the first numerical fluid-mechanical sewing machine. The novel implicit treatment also yields an order of magnitude speedup in our elastic rod dynamics.
@Article{CG_0171,
author = {Mikl{\'{o}}s Bergou and  Basile Audoly and  Etienne Vouga and  Max Wardetzky and  Eitan Grinspun},
title = {{D}iscrete {V}iscous {T}hreads},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {29},
number = {4},
month = {Jul},
year = {2010}
}


#### Rigid-Body Fracture Sound with Precomputed Soundbanks,

Changxi Zheng and Doug L. James,
SIGGRAPH (ACM Transactions on Graphics), Vol.29, No.3, Jul, 2010.
We propose a physically based algorithm for synthesizing sounds synchronized with brittle fracture animations. Motivated by laboratory experiments, we approximate brittle fracture sounds using time-varying rigid-body sound models. We extend methods for fracturing rigid materials by proposing a fast quasistatic stress solver to resolve near-audio-rate fracture events, energy-based fracture pattern modeling and estimation of “crack”-related fracture impulses. Multipole radiation models provide scalable sound radiation for complex debris and level of detail control. To reduce sound model generation costs for complex fracture debris, we propose Precomputed Rigid-Body Soundbanks comprised of precomputed ellipsoidal sound proxies. Examples and experiments are presented that demonstrate plausible and affordable brittle fracture sounds.
@Article{CG_0212,
author = {Changxi Zheng and Doug L. James},
title = {{R}igid-{B}ody {F}racture {S}ound with {P}recomputed {S}oundbanks},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {29},
number = {3},
month = {Jul},
year = {2010}
}


#### Synthesizing Structured Image Hybrids,

Eric Risser, Charles Han, Rozenn Dahyot, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.29, No.4, Jul, 2010.
Example-based texture synthesis algorithms generate novel texture images from example data. A popular hierarchical pixel-based approach uses spatial jitter to introduce diversity, at the risk of breaking coarse structure beyond repair. We propose a multiscale descriptor that enables appearance-space jitter, which retains structure. This idea enables repurposing of existing texture synthesis implementations for a qualitatively different problem statement and class of inputs: generating hybrids of structured images.
@Article{CG_0172,
author = {Eric Risser and  Charles Han and  Rozenn Dahyot and  Eitan Grinspun},
title = {{S}ynthesizing {S}tructured {I}mage {H}ybrids},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {29},
number = {4},
month = {Jul},
year = {2010}
}


#### Unified Simulation of Elastic Rods, Shells, and Solids,

Sebastian Martin, Peter Kaufmann, Mario Botsch, Eitan Grinspun, Markus Gross,
SIGGRAPH (ACM Transactions on Graphics), Vol.29, No.4, Jul, 2010.
We develop an accurate, unified treatment of elastica. Following the method of resultant-based formulation to its logical extreme, we derive a higher-order integration rule, or elaston, measuring stretching, shearing, bending, and twisting along any axis. The theory and accompanying implementation do not distinguish between forms of different dimension (solids, shells, rods), nor between manifold regions and non-manifold junctions. Consequently, a single code accurately models a diverse range of elastoplastic behaviors, including buckling, writhing, cutting and merging. Emphasis on convergence to the continuum sets us apart from early unification efforts.
@Article{CG_0173,
author = {Sebastian Martin and  Peter Kaufmann and  Mario Botsch and  Eitan Grinspun and  Markus Gross},
title = {{U}nified {S}imulation of {E}lastic {R}ods, {S}hells, and {S}olids},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {29},
number = {4},
month = {Jul},
year = {2010}
}


#### Coherent Ray Tracing for Complex Light Transport Effects,

Ryan Overbeck,
PhD Thesis, Department of Computer Science, Columbia University, 2010.
@InCollection{CG_0166,
author = {Ryan Overbeck},
title = {{C}oherent {R}ay {T}racing for {C}omplex {L}ight {T}ransport {E}ffects},
school = {PhD Thesis, Department of Computer Science, Columbia University},
year = {2010}
}


#### Robust, Efficient, and Accurate Contact Algorithms,

David Harmon,
PhD Thesis, Department of Computer Science, Columbia University, May, 2010.
@InCollection{CG_0174,
author = {David Harmon},
title = {{R}obust, {E}fficient, and {A}ccurate {C}ontact {A}lgorithms},
school = {PhD Thesis, Department of Computer Science, Columbia University},
year = {2010}
}


### 2009

#### Affine Double and Triple Product Wavelet Integrals for Rendering,

Bo Sun and Ravi Ramamoorthi,
ACM Transactions on Graphics, Vol.28, No.2, Apr, 2009.
Many problems in computer graphics involve integrations of products of functions. Double- and triple-product integrals are commonly used in applications such as all-frequency relighting or importance sampling, but are limited to distant illumination. In contrast, near-field lighting from planar area lights involves an affine transform of the source radiance at different points in space. Our main contribution is a novel affine double- and triple-product integral theory; this generalization enables one of the product functions to be scaled and translated. We study the computational complexity in a number of bases, with particular attention to the common Haar wavelets. We show that while simple analytic formulae are not easily available, there is considerable sparsity that can be exploited computationally. We demonstrate a practical application to compute near-field lighting from planar area sources, that can be easily combined with most relighting algorithms. We also demonstrate initial results for wavelet importance sampling with near-field area lights, and image processing directly in the wavelet domain.
@Article{CG_0168,
author = {Bo Sun and Ravi Ramamoorthi},
title = {{A}ffine {D}ouble and {T}riple {P}roduct {W}avelet {I}ntegrals for {R}endering},
journal = {ACM Transactions on Graphics},
volume = {28},
number = {2},
pages = {1--17},
month = {Apr},
year = {2009}
}


#### Implicit-Explicit Variational Integration of Highly Oscillatory Problems,

Ari Stern, Eitan Grinspun,
SIAM Multiscale Modeling and Simulation, Vol.7, No.4, 2009.
We derive a variational integrator for certain highly oscillatory problems in mechanics. To do this, we take a new approach to the splitting of fast and slow potential forces: rather than splitting these forces at the level of the diﬀerential equations or the Hamiltonian, we split the two potentials with respect to the Lagrangian action integral. By using a diﬀerent quadrature rule to approximate the contribution of each potential to the action, we arrive at a geometric integrator that is implicit in the fast force and explicit in the slow force. This can allow for signiﬁcantly longer time steps to be taken (compared to standard explicit methods, such as Störmer/Verlet) at the cost of only a linear solve rather than a full nonlinear solve. We also analyze the stability of this method, in particular proving that it eliminates the linear resonance instabilities that can arise with explicit multiple-time-stepping methods. Next, we perform some numerical experiments, studying the behavior of this integrator for two test problems: a system of coupled linear oscillators, for which we compare against the resonance behavior of the r-RESPA method; and slow energy exchange in the Fermi–Pasta–Ulam problem, which couples fast linear oscillators with slow nonlinear oscillators. Finally, we prove that this integrator accurately preserves the slow energy exchange between the fast oscillatory components, which explains the numerical behavior observed for the Fermi–Pasta–Ulam problem.
@Article{CG_0153,
author = {Ari Stern and  Eitan Grinspun},
title = {{I}mplicit-{E}xplicit {V}ariational {I}ntegration of {H}ighly {O}scillatory {P}roblems},
journal = {SIAM Multiscale Modeling and Simulation},
volume = {7},
number = {4},
pages = {1779--1794},
year = {2009}
}


#### An Empirical BSSRDF Model,

Craig Donner and Jason Lawrence and Ravi Ramamoorthi and Toshiya Hachisuka and Henrik Wann Jensen and Shree Nayar ,
SIGGRAPH (ACM Transactions on Graphics), Vol.28, No.3, Jul, 2009.
We present a new model of the homogeneous BSSRDF based on large-scale simulations. Our model captures the appearance of materials that are not accurately represented using existing single scattering models or multiple isotropic scattering models (e.g. the diffusion approximation). We use an analytic function to model the 2D hemispherical distribution of exitant light at a point on the surface, and a table of parameter values of this function computed at uniformly sampled locations over the remaining dimensions of the BSSRDF domain. This analytic function is expressed in elliptic coordinates and has six parameters which vary smoothly with surface position, incident angle, and the underlying optical properties of the material (albedo, mean free path length, phase function and the relative index of refraction). Our model agrees well with measured data, and is compact, requiring only 250MB to represent the full spatial- and angular-distribution of light across a wide spectrum of materials. In practice, rendering a single material requires only about 100KB to represent the BSSRDF.
@Article{CG_0169,
author = {Craig Donner and Jason Lawrence and Ravi Ramamoorthi and Toshiya Hachisuka and Henrik Wann Jensen and Shree Nayar },
title = {{A}n {E}mpirical {B}{S}{S}{R}{D}{F} {M}odel},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {28},
number = {3},
pages = {30:1--30:10},
month = {Jul},
year = {2009}
}


#### Asynchronous Contact Mechanics,

David Harmon, Etienne Vouga, Breannan Smith, Rasmus Tamstorf, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.28, No.3, Aug, 2009.
We develop a method for reliable simulation of elastica in complex contact scenarios. Our focus is on firmly establishing three parameter-independent guarantees: that simulations of well-posed problems (a) have no interpenetrations, (b) obey causality, momentum- and energy-conservation laws, and (c) complete in finite time. We achieve these guarantees through a novel synthesis of asynchronous variational integrators, kinetic data structures, and a discretization of the contact barrier potential by an infinite sum of nested quadratic potentials. In a series of two- and three dimensional examples, we illustrate that this method more easily handles challenging problems involving complex contact geometries, sharp features, and sliding during extremely tight contact.
@Article{CG_0152,
author = {David Harmon and  Etienne Vouga and  Breannan Smith and  Rasmus Tamstorf and  Eitan Grinspun},
title = {{A}synchronous {C}ontact {M}echanics},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {28},
number = {3},
month = {Aug},
year = {2009}
}


#### Enrichment Textures for Detailed Cutting of Shells,

Peter Kaufmann, Sebastian Martin, Mario Botsch, Eitan Grinspun, Markus Gross,
SIGGRAPH (ACM Transactions on Graphics), Vol.28, No.3, Aug, 2009.
We present a method for simulating highly detailed cutting and fracturing of thin shells using low-resolution simulation meshes. Instead of refining or remeshing the underlying simulation domain to resolve complex cut paths, we adapt the extended finite element method (XFEM) and enrich our approximation by custom designed basis functions, while keeping the simulation mesh unchanged. The enrichment functions are stored in enrichment textures, which allows for fracture and cutting discontinuities at a resolution much finer than the underlying mesh, similar to image textures for increased visual resolution. Furthermore, we propose harmonic enrichment functions to handle multiple, intersecting, arbitrarily shaped, progressive cuts per element in a simple and unified framework. Our underlying shell simulation is based on discontinuous Galerkin (DG) FEM, which relaxes the restrictive requirement of C1 continuous basis functions and thus allows for simpler, C0 continuous XFEM enrichment functions.
@Article{CG_0154,
author = {Peter Kaufmann and  Sebastian Martin and  Mario Botsch and  Eitan Grinspun and  Markus Gross},
title = {{E}nrichment {T}extures for {D}etailed {C}utting of {S}hells},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {28},
number = {3},
month = {Aug},
year = {2009}
}


#### Frequency Analysis and Sheared Reconstruction for Rendering Motion Blur,

Kevin Egan, Yu-Ting Tseng, Nicolas Holzschuch, Frédo Durand, Ravi Ramamoorthi,
SIGGRAPH (ACM Transactions on Graphics), Vol.28, No.3, Jul, 2009.
Motion blur is crucial for high-quality rendering, but is also very expensive. Our first contribution is a frequency analysis of motion-blurred scenes, including moving objects, specular reflections, and shadows. We show that motion induces a shear in the frequency domain, and that the spectrum of moving scenes is usually contained in a wedge. This allows us to compute adaptive space-time sampling rates, to accelerate rendering. For uniform velocities and standard axis-aligned reconstruction, we show that the product of spatial and temporal bandlimits or sampling rates is constant, independent of velocity. Our second contribution is a novel sheared reconstruction filter that is aligned to the first-order direction of motion and enables even lower sampling rates. We present a rendering algorithm that computes a sheared reconstruction filter per pixel, without any intermediate Fourier representation. This often permits synthesis of motion-blurred images with far fewer rendering samples than standard techniques require.
@Article{CG_0156,
author = {Kevin Egan and  Yu-Ting Tseng and  Nicolas Holzschuch and  Frédo Durand and  Ravi Ramamoorthi},
title = {{F}requency {A}nalysis and {S}heared {R}econstruction for {R}endering {M}otion {B}lur},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {28},
number = {3},
pages = {93:1--93:13},
month = {Jul},
year = {2009}
}


#### Harmonic Fluids,

Changxi Zheng and Doug L. James,
SIGGRAPH (ACM Transactions on Graphics), Vol.28, No.3, Aug, 2009.
Fluid sounds, such as splashing and pouring, are ubiquitous and familiar but we lack physically based algorithms to synthesize them in computer animation or interactive virtual environments. We propose a practical method for automatic procedural synthesis of synchronized harmonic bubble-based sounds from 3D fluid animations. To avoid audio-rate time-stepping of compressible fluids, we acoustically augment existing incompressible fluid solvers with particle-based models for bubble creation, vibration, advection, and radiation. Sound radiation from harmonic fluid vibrations is modeled using a time-varying linear superposition of bubble oscillators. We weight each oscillator by its bubble-to-ear acoustic transfer function, which is modeled as a discrete Green\'s function of the Helmholtz equation. To solve potentially millions of 3D Helmholtz problems, we propose a fast dual-domain multipole boundary-integral solver, with cost linear in the complexity of the fluid domain\'s boundary. Enhancements are proposed for robust evaluation, noise elimination, acceleration, and parallelization. Examples of harmonic fluid sounds are provided for water drops, pouring, babbling, and splashing phenomena, often with thousands of acoustic bubbles, and hundreds of thousands of transfer function solves.
@Article{CG_0213,
author = {Changxi Zheng and Doug L. James},
title = {{H}armonic {F}luids},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {28},
number = {3},
month = {Aug},
year = {2009}
}


#### Semantic Deformation Transfer,

Ilya Baran, Daniel Vlasic, Eitan Grinspun, Jovan Popovic,
SIGGRAPH (ACM Transactions on Graphics), Vol.28, No.3, Aug, 2009.
Transferring existing mesh deformation from one character to another is a simple way to accelerate the laborious process of mesh animation. In many cases, it is useful to preserve the semantic characteristics of the motion instead of its literal deformation. For example, when applying the walking motion of a human to a flamingo, the knees should bend in the opposite direction. Semantic deformation transfer accomplishes this task with a shape space that enables interpolation and projection with standard linear algebra. Given several example mesh pairs, semantic deformation transfer infers a correspondence between the shape spaces of the two characters. This enables automatic transfer of new poses and animations.
@Article{CG_0155,
author = {Ilya Baran and  Daniel Vlasic and  Eitan Grinspun and  Jovan Popovic},
title = {{S}emantic {D}eformation {T}ransfer},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {28},
number = {3},
month = {Aug},
year = {2009}
}


#### Adaptive Wavelet Rendering,

Ryan S. Overbeck and Craig Donner and Ravi Ramamoorthi,
SIGGRAPH Asia (ACM Transactions on Graphics), Vol.28, No.5, 2009.
Effects such as depth of field, area lighting, antialiasing and global illumination require evaluating a complex high-dimensional integral at each pixel of an image. We develop a new adaptive rendering algorithm that greatly reduces the number of samples needed for Monte Carlo integration. Our method renders directly into an image-space wavelet basis. First, we adaptively distribute Monte Carlo samples to reduce the variance of the wavelet basis\\\\\\\\\\\\\\\' scale coefficients, while using the wavelet coefficients to find edges. Working in wavelets, rather than pixels, allows us to sample not only image-space edges but also other features that are smooth in the image plane but have high variance in other integral dimensions. In the second stage, we reconstruct the image from these samples by using a suitable wavelet approximation. We achieve this by subtracting an estimate of the error in each wavelet coefficient from its magnitude, effectively producing the smoothest image consistent with the rendering samples. Our algorithm renders scenes with significantly fewer samples than basic Monte Carlo or adaptive techniques. Moreover, the method introduces minimal overhead, and can be efficiently included in an optimized ray-tracing system.
@Article{CG_0167,
author = {Ryan S. Overbeck and Craig Donner and Ravi Ramamoorthi},
title = {{A}daptive {W}avelet {R}endering},
journal = {SIGGRAPH Asia (ACM Transactions on Graphics)},
volume = {28},
number = {5},
pages = {1--12},
year = {2009}
}


### 2008

#### A Precomputed Polynomial Representation for Interactive BRDF Editing with Global Illumination,

Aner Ben-Artzi, Kevin Egan, Frédo Durand, Ravi Ramamoorthi,
ACM Transactions on Graphics, Vol.27, No.2, Apr, 2008.
The ability to interactively edit BRDFs in their final placement within a computer graphics scene is vital to making informed choices for material properties. We significantly extend previous work on BRDF editing for static scenes (with fixed lighting and view) by developing a precomputed polynomial representation that enables interactive BRDF editing with global illumination. Unlike previous precomputation-based rendering techniques, the image is not linear in the BRDF when considering interreflections. We introduce a framework for precomputing a multibounce tensor of polynomial coefficients that encapsulates the nonlinear nature of the task. Significant reductions in complexity are achieved by leveraging the low-frequency nature of indirect light. We use a high-quality representation for the BRDFs at the first bounce from the eye and lower-frequency (often diffuse) versions for further bounces. This approximation correctly captures the general global illumination in a scene, including color-bleeding, near-field object reflections, and even caustics. We adapt Monte Carlo path tracing for precomputing the tensor of coefficients for BRDF basis functions. At runtime, the high-dimensional tensors can be reduced to a simple dot product at each pixel for rendering. We present a number of examples of editing BRDFs in complex scenes with interactive feedback rendered with global illumination.
@Article{CG_0146,
author = {Aner Ben-Artzi and  Kevin Egan and  Frédo Durand and  Ravi Ramamoorthi},
title = {{A} {P}recomputed {P}olynomial {R}epresentation for {I}nteractive {B}{R}{D}{F} {E}diting with {G}lobal {I}llumination},
journal = {ACM Transactions on Graphics},
volume = {27},
number = {2},
month = {Apr},
year = {2008}
}


#### Multiscale Texture Synthesis,

Charles Han, Eric Risser, Ravi Ramamoorthi, Eitan Grinspun,
SIGGRAPH ( ACM Transactions on Graphics), Vol.27, No.3, Aug, 2008.
Example-based texture synthesis algorithms have gained widespread popularity for their ability to take a single input image and create a perceptually similar non-periodic texture. However, previous methods rely on single input exemplars that can capture only a limited band of spatial scales. For example, synthesizing a continent-like appearance at a variety of zoom levels would require an impractically high input resolution. In this paper, we develop a multiscale texture synthesis algorithm. We propose a novel example-based representation, which we call an exemplar graph, that simply requires a few low-resolution input exemplars at different scales. Moreover, by allowing loops in the graph, we can create inﬁnite zooms and inﬁnitely detailed textures that are impossible with current example-based methods. We also introduce a technique that ameliorates inconsistencies in the user’s input, and show that the application of this method yields improved interscale coherence and higher visual quality. We demonstrate optimizations for both CPU and GPU implementations of our method, and use them to produce animations with zooming and panning at multiple scales, as well as static gigapixel-sized images with features spanning many spatial scales.
@Article{CG_0145,
author = {Charles Han and  Eric Risser and  Ravi Ramamoorthi and  Eitan Grinspun},
title = {{M}ultiscale {T}exture {S}ynthesis},
journal = {SIGGRAPH ( ACM Transactions on Graphics)},
volume = {27},
number = {3},
pages = {51},
month = {Aug},
year = {2008}
}


#### Discrete Elastic Rods,

Miklós Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.27, No.3, Aug, 2008.
We present a discrete treatment of adapted framed curves, parallel transport, and holonomy, thus establishing the language for a discrete geometric model of thin flexible rods with arbitrary cross section and undeformed configuration. Our approach differs from existing simulation techniques in the graphics and mechanics literature both in the kinematic description — we represent the material frame by its angular deviation from the natural Bishop frame — as well as in the dynamical treatment — we treat the centerline as dynamic and the material frame as quasistatic. Additionally, we describe a manifold projection method for coupling rods to rigid-bodies and simultaneously enforcing rod inextensibility. The use of quasistatics and constraints provides an efficient treatment for stiff twisting and stretching modes; at the same time, we retain the dynamic bending of the centerline and accurately reproduce the coupling between bending and twisting modes. We validate the discrete rod model via quantitative buckling, stability, and coupled-mode experiments, and via qualitative knot-tying comparisons.
@Article{CG_0143,
author = {Mikl{\'{o}}s Bergou and  Max Wardetzky and  Stephen Robinson and  Basile Audoly and  Eitan Grinspun},
title = {{D}iscrete {E}lastic {R}ods},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {27},
number = {3},
pages = {1--12},
month = {Aug},
year = {2008}
}


#### Light Field Transfer: Global Illumination Between Real and Synthetic Objects,

Oliver Cossairt, Shree Nayar, Ravi Ramamoorthi,
SIGGRAPH (ACM Transactions on Graphics), Vol.27, No.3, Aug, 2008.
We present a novel image-based method for compositing real and synthetic objects in the same scene with a high degree of visual realism. Ours is the first technique to allow global illumination and near-field lighting effects between both real and synthetic objects at interactive rates, without needing a geometric and material model of the real scene. We achieve this by using a light field interface between real and synthetic components---thus, indirect illumination can be simulated using only two 4D light fields, one captured from and one projected onto the real scene. Multiple bounces of interreflections are obtained simply by iterating this approach. The interactivity of our technique enables its use with time-varying scenes, including dynamic objects. This is in sharp contrast to the alternative approach of using 6D or 8D light transport functions of real objects, which are very expensive in terms of acquisition and storage and hence not suitable for real-time applications. In our method, 4D radiance fields are simultaneously captured and projected by using a lens array, video camera, and digital projector. We implement a complete system and provide example scene compositions that demonstrate global illumination and lighting effects between dynamic real and synthetic objects.
@Article{CG_0147,
author = {Oliver Cossairt and  Shree Nayar and  Ravi Ramamoorthi},
title = {{L}ight {F}ield {T}ransfer: {G}lobal {I}llumination {B}etween {R}eal and {S}ynthetic {O}bjects},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {27},
number = {3},
month = {Aug},
year = {2008}
}


#### Robust Treatment of Simultaneous Collisions,

David Harmon, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.27, No.3, Aug, 2008.
Robust treatment of complex collisions is a challenging problem in cloth simulation. Some state of the art methods resolve collisions iteratively, invoking a fail-safe when a bound on iteration count is exceeded. The best-known fail-safe rigidifies the contact region, causing simulation artifacts. We present a fail-safe that cancels impact but not sliding motion, considerably reducing artificial dissipation. We equip the proposed fail-safe with an approximation of Coulomb friction, allowing finer control of sliding dissipation.
@Article{CG_0144,
author = {David Harmon and  Etienne Vouga and  Rasmus Tamstorf and Eitan Grinspun},
title = {{R}obust {T}reatment of {S}imultaneous {C}ollisions},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {27},
number = {3},
pages = {1--4},
month = {Aug},
year = {2008}
}


#### A Layered, Heterogeneous Reflectance Model for Acquiring and Rendering Human Skin,

Craig Donner, Tim Weyrich, Eugene d\'Eon, Ravi Ramamoorthi, Szymon Rusinkiewicz,
SIGGRAPH Asia (ACM Transactions on Graphics), Vol.27, No.5, Dec, 2008.
We introduce a layered, heterogeneous spectral reflectance model for human skin. The model captures the inter-scattering of light among layers, each of which may have an independent set of spatially-varying absorption and scattering parameters. For greater physical accuracy and control, we introduce an infinitesimally thin absorbing layer between scattering layers. To obtain parameters for our model, we use a novel acquisition method that begins with multi-spectral photographs. By using an inverse rendering technique, along with known chromophore spectra, we optimize for the best set of parameters for each pixel of a patch. Our method finds close matches to a wide variety of inputs with low residual error. We apply our model to faithfully reproduce the complex variations in skin pigmentation. This is in contrast to most previous work, which assumes that skin is homogeneous or composed of homogeneous layers. We demonstrate the accuracy and flexibility of our model by creating complex skin visual effects such as veins, tattoos, rashes, and freckles, which would be difficult to author using only albedo textures at the skin\\\'s outer surface. Also, by varying the parameters to our model, we simulate effects from external forces, such as visible changes in blood flow within the skin due to external pressure.
@Article{CG_0150,
author = {Craig Donner and  Tim Weyrich and  Eugene d\'Eon and  Ravi Ramamoorthi and  Szymon Rusinkiewicz},
title = {{A} {L}ayered, {H}eterogeneous {R}eflectance {M}odel for {A}cquiring and {R}endering {H}uman {S}kin},
journal = {SIGGRAPH Asia (ACM Transactions on Graphics)},
volume = {27},
number = {5},
month = {Dec},
year = {2008}
}


#### Compressive Structured Light for Recovering Inhomogeneous Participating Media,

Jinwei Gu, Shree Nayar, Eitan Grinspun, Peter Belhumeur, Ravi Ramamoorthi,
Europian Conference on Computer Vision (ECCV), Oct, 2008.
We propose a new method named compressive structured light for recovering inhomogeneous participating media. Whereas conventional structured light methods emit coded light patterns onto the surface of an opaque object to establish correspondence for triangulation, compressive structured light projects patterns into a volume of participating medium to produce images which are integral measurements of the volume density along the line of sight. For a typical participating medium encountered in the real world, the integral nature of the acquired images enables the use of compressive sensing techniques that can recover the entire volume density from only a few measurements. This makes the acquisition process more efficient and enables reconstruction of dynamic volumetric phenomena. Moreover, our method requires the projection of multiplexed coded illumination, which has the added advantage of increasing the signal-to-noise ratio of the acquisition. Finally, we propose an iterative algorithm to correct for the attenuation of the participating medium during the reconstruction process. We show the eﬀectiveness of our method with simulations as well as experiments on the volumetric recovery of multiple translucent layers, 3D point clouds etched in glass, and the dynamic process of milk drops dissolving in water.
@InProceedings{CG_0151,
author = {Jinwei Gu and  Shree Nayar and  Eitan Grinspun and  Peter Belhumeur and  Ravi Ramamoorthi},
title = {{C}ompressive {S}tructured {L}ight for {R}ecovering {I}nhomogeneous {P}articipating {M}edia},
booktitle = {Europian Conference on Computer Vision (ECCV)},
month = {Oct},
year = {2008}
}


#### Large Ray Packets for Real-time Whitted Ray Tracing,

Ryan Overbeck, Ravi Ramamoorthi, and William R. Mark,
IEEE/EG Symposium on Interactive Ray Tracing (IRT), Aug, 2008.
In this paper, we explore large ray packet algorithms for acceleration structure traversal and frustum culling in the context of Whitted ray tracing, and examine how these methods respond to varying ray packet size, scene complexity, and ray recursion complexity. We offer a new algorithm for acceleration structure traversal which is robust to degrading coherence and a new method for generating frustum bounds around reflection and refraction ray packets. We compare, adjust, and finally compose the most effective algorithms into a real-time Whitted ray tracer. With the aid of multi-core CPU technology, our system renders complex scenes with reflections, refractions, and/or point-light shadows anywhere from 4--20 FPS.
@InProceedings{CG_0148,
author = {Ryan Overbeck and  Ravi Ramamoorthi and William R. Mark},
title = {{L}arge {R}ay {P}ackets for {R}eal-time {W}hitted {R}ay {T}racing},
booktitle = {IEEE/EG Symposium on Interactive Ray Tracing (IRT)},
pages = {41--48},
month = {Aug},
year = {2008}
}


#### Analytical, Wavelet and Frequency based Mathematical Models for Real-Time Rendering,

Bo Sun,
PhD Thesis, Department of Computer Science, Columbia University, 2008.
@InCollection{CG_0170,
author = {Bo Sun},
title = {{A}nalytical, {W}avelet and {F}requency based {M}athematical {M}odels for {R}eal-{T}ime {R}endering},
school = {PhD Thesis, Department of Computer Science, Columbia University},
year = {2008}
}


### 2007

#### A First Order Analysis of Lighting, Shading, and Shadows,

Ravi Ramamoorthi, Dhruv Mahajan and Peter Belhumeur,
ACM Transactions on Graphics , Vol.26, No.1, Jan, 2007.
We derive a complete first order or gradient theory of lighting, reflection and shadows, taking both spatial and angular variation of the light field into account. The gradient is by definition a sum of terms, allowing us to consider the relative weight of spatial and angular lighting variation, geometric curvature and bump mapping. Moreover, we derive analytic formulas for the gradients in soft shadow or penumbra regions, demonstrating applications to gradient-based interpolation and sampling.
@Article{CG_0032,
author = {Ravi Ramamoorthi and  Dhruv Mahajan and Peter Belhumeur},
title = {{A} {F}irst {O}rder {A}nalysis of {L}ighting, {S}hading, and {S}hadows},
journal = {ACM Transactions on Graphics },
volume = {26},
number = {1},
month = {Jan},
year = {2007}
}


#### Discrete Quadratic Curvature Energies [CAGD Most Cited Paper Award for 2010],

Max Wardetzky, Miklós Bergou, David Harmon, Denis Zorin, and Eitan Grinspun,
Computer Aided Geometric Design, Vol.24, No.8-9, Nov, 2007.
[This is preprint--not a final copy.] We present a family of discrete isometric bending models (IBMs) for triangulated surfaces in 3-space. These models are derived from an axiomatic treatment of discrete Laplace operators, using these operators to obtain linear models for discrete mean curvature from which bending energies are assembled. Under the assumption of isometric surface deformations we show that these energies are quadratic in surface positions. The corresponding linear energy gradients and constant energy Hessians constitute an efficient model for computing bending forces and their derivatives, enabling fast time-integration of cloth dynamics with a two- to three-fold net speedup over existing nonlinear methods, and near-interactive rates for Willmore smoothing of large meshes.
@Article{CG_0122,
author = {Max Wardetzky and  Miklós Bergou and  David Harmon and  Denis Zorin and Eitan Grinspun},
title = {{D}iscrete {Q}uadratic {C}urvature {E}nergies [{C}{A}{G}{D} {M}ost {C}ited {P}aper {A}ward for 2010]},
journal = {Computer Aided Geometric Design},
volume = {24},
number = {8-9},
pages = {499--518},
month = {Nov},
year = {2007}
}


#### A Theory of Frequency Domain Invariants: Spherical Harmonic Identities for BRDF/Lighting Transfer and Image Consistency,

Dhruv Mahajan, Ravi Ramamoorthi, Brian Curless,
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.30, No.2, Dec, 2007.
This paper develops a theory of frequency domain invariants in computer vision. We derive novel identities using spherical harmonics, which are the angular frequency domain analog to common spatial domain invariants such as reflectance ratios. These invariants are derived from the spherical harmonic convolution framework for reflection from a curved surface. Our identities apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting conditions. One important case we consider is two different glossy objects in two different lighting environments. For this case, we derive a novel identity, independent of the specific lighting configurations or BRDFs, that allows us to directly estimate the fourth image if the other three are available. The identity can also be used as an invariant to detect tampering in the images. While this paper is primarily theoretical, it has the potential to lay the mathematical foundations for two important practical applications. First, we can develop more general algorithms for inverse rendering problems, which can directly relight and change material properties by transferring the BRDF or lighting from another object or illumination. Second, we can check the consistency of an image, to detect tampering or image splicing.
@Article{CG_0128,
author = {Dhruv Mahajan and  Ravi Ramamoorthi and  Brian Curless},
title = {{A} {T}heory of {F}requency {D}omain {I}nvariants: {S}pherical {H}armonic {I}dentities for {B}{R}{D}{F}/{L}ighting {T}ransfer and {I}mage {C}onsistency},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {30},
number = {2},
pages = {197--213},
month = {Dec},
year = {2007}
}


#### Time-Varying BRDFs,

Bo Sun, Kalyan Sunkavalli, Ravi Ramamoorthi, Peter Belhumeur, and Shree Nayar,
IEEE Transactions on Visualization and Computer Graphics, Vol.13, No.3, May, 2007.
The properties of virtually all real-world materials change with time, causing their BRDFs to be time-varying. However, none of the existing BRDF models and databases take time variation into consideration; they represent the appearance of a material at a single time instance. In this work, we address the acquisition, analysis, modeling and rendering of a wide range of time-varying BRDFs. We have developed an acquisition system that is capable of sampling a material’s BRDF at multiple time instances, with each time sample acquired within 36 seconds. We have used this acquisition system to measure the BRDFs of a wide range of time-varying phenomena which include the drying of various types of paints (watercolor, spray, and oil), the drying of wet rough surfaces (cement, plaster, and fabrics), the accumulation of dusts (household and joint compound) on surfaces, and the melting of materials (chocolate). Analytic BRDF functions are fit to these measurements and the model parameters’ variations with time are analyzed. Each category exhibits interesting and sometimes non-intuitive parameter trends. These parameter trends are then used to develop analytic time-varying BRDF (TVBRDF) models. The analytic TVBRDF models enable us to apply effects such as paint drying and dust accumulation to arbitrary surfaces and novel materials.
@Article{CG_0119,
author = {Bo Sun and  Kalyan Sunkavalli and  Ravi Ramamoorthi and  Peter Belhumeur and Shree Nayar},
title = {{T}ime-{V}arying {B}{R}{D}{F}s},
journal = {IEEE Transactions on Visualization and Computer Graphics},
volume = {13},
number = {3},
pages = {595--609},
month = {May},
year = {2007}
}


#### A Theory of Locally Low Dimensional Light Transport,

Dhruv Mahajan, Ira Kemelmacher Shlizerman, Ravi Ramamoorthi, Peter Belhumeur,
SIGGRAPH (ACM Transactions on Graphics), Vol.26, No.3, Aug, 2007.
Blockwise or Clustered Principal Component Analysis (CPCA) is commonly used to achieve real-time rendering of shadows and glossy reflections with precomputed radiance transfer (PRT). The vertices or pixels are partitioned into smaller coherent regions, and light transport in each region is approximated by a locally lowdimensional subspace using PCA. Many earlier techniques such as surface light field and reflectance field compression use a similar paradigm. However, there has been no clear theoretical understanding of how light transport dimensionality increases with local patch size, nor of the optimal block size or number of clusters. In this paper, we develop a theory of locally low dimensional light transport, by using Szego’s eigenvalue theorem to analytically derive the eigenvalues of the covariance matrix for canonical cases. We show mathematically that for symmetric patches of area A, the number of basis functions for glossy reflections increases linearly with A, while for simple cast shadows, it often increases as \\sqrt{A}. These results are confirmed numerically on a number of test scenes. Next, we carry out an analysis of the cost of rendering, trading off local dimensionality and the number of patches, deriving an optimal block size. Based on this analysis, we provide useful practical insights for setting parameters in CPCA and also derive a new adaptive subdivision algorithm. Moreover, we show that rendering time scales sub-linearly with the resolution of the image, allowing for interactive all-frequency relighting of 1024×1024 images.
@Article{CG_0125,
author = {Dhruv Mahajan and  Ira Kemelmacher Shlizerman and  Ravi Ramamoorthi and  Peter Belhumeur},
title = {{A} {T}heory of {L}ocally {L}ow {D}imensional {L}ight {T}ransport},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {26},
number = {3},
month = {Aug},
year = {2007}
}


#### Active Refocusing of Images and Videos,

Francesc Moreno-Noguer, Peter N. Belhumeur, Shree K. Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.26, No.3, Jul, 2007.
We present a system for refocusing images and videos of dynamic scenes using a novel, single-view depth estimation method. Our method for obtaining depth is based on the defocus of a sparse set of dots projected onto the scene. In contrast to other active illumination techniques, the projected pattern of dots can be removed from each captured image and its brightness easily controlled in order to avoid under- or over-exposure. The depths corresponding to the projected dots and a color segmentation of the image are used to compute an approximate depth map of the scene with clean region boundaries. The depth map is used to refocus the acquired image after the dots are removed, simulating realistic depth of field effects. Experiments on a wide variety of scenes, including close-ups and live action, demonstrate the effectiveness of our method.
@Article{CG_0132,
author = {Francesc Moreno-Noguer and  Peter N. Belhumeur and  Shree K. Nayar},
title = {{A}ctive {R}efocusing of {I}mages and {V}ideos},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {26},
number = {3},
month = {Jul},
year = {2007}
}


#### Efficient Simulation of Inextensible Cloth,

Rony Goldenthal, David Harmon, Raanan Fattal, Michel Bercovier, Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.26, No.3, Jul, 2007.
Many textiles do not noticeably stretch under their own weight. Unfortunately, for better performance many cloth solvers disregard this fact. We propose a method to obtain very low strain along the warp and weft direction using Constrained Lagrangian Mechanics and a novel fast projection method. The resulting algorithm acts as a velocity filter that easily integrates into existing simulation code.
@Article{CG_0131,
author = {Rony Goldenthal and  David Harmon and  Raanan Fattal and  Michel Bercovier and  Eitan Grinspun},
title = {{E}fficient {S}imulation of {I}nextensible {C}loth},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {26},
number = {3},
month = {Jul},
year = {2007}
}


#### Frequency Domain Normal Map Filtering,

Charles Han, Bo Sun, Ravi Ramamoorthi, and Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.26, No.3, Jul, 2007.
Filtering is critical for representing image-based detail, such as textures or normal maps, across a variety of scales. While mipmapping textures is commonplace, accurate normal map filtering remains a challenging problem because of nonlinearities in shading¡ªwe cannot simply average nearby surface normals. In this paper, we show analytically that normal map filtering can be formalized as a spherical convolution of the normal distribution function (NDF) and the BRDF, for a large class of common BRDFs such as Lambertian, microfacet and factored measurements. This theoretical result explains many previous filtering techniques as special cases, and leads to a generalization to a broader class of measured and analytic BRDFs. Our practical algorithms leverage a significant body of previous work that has studied lighting-BRDF convolution. We show how spherical harmonics can be used to filter the NDF for Lambertian and low-frequency specular BRDFs, while spherical von Mises-Fisher distributions can be used for high-frequency materials.
@Article{CG_0123,
author = {Charles Han and  Bo Sun and  Ravi Ramamoorthi and Eitan Grinspun},
title = {{F}requency {D}omain {N}ormal {M}ap {F}iltering},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {26},
number = {3},
pages = {28},
month = {Jul},
year = {2007}
}


#### Prakash: Lighting Aware Motion Capture using Photosensing Markers and Multiplexed Illuminators,

Ramesh Raskar, Hideaki Nii, Bert deDecker, Yuki Hashimoto, Jay Summet, Dylan Moore, Yong Zhao, Jonathan Westhues, Paul Dietz, John Barnwell, Shree Nayar, Masahiko Inami, Philippe Bekaert, Michael Noland, Vlad Branzoi, Erich Bruns,
SIGGRAPH (ACM Transactions on Graphics), Vol.26, No.3, Jul, 2007.
In this paper, we present a high speed optical motion capture method that can measure three dimensional motion, orientation, and incident illumination at tagged points in a scene. We use tracking tags that work in natural lighting conditions and can be imperceptibly embedded in attire or other objects. Our system supports an unlimited number of tags in a scene, with each tag uniquely identified to eliminate marker reacquisition issues. Our tags also provide incident illumination data which can be used to match scene lighting when inserting synthetic elements. The technique is therefore ideal for on-set motion capture or real-time broadcasting of virtual sets. Unlike previous methods that employ high speed cameras or scanning lasers, we capture the scene appearance using the simplest possible optical devices - a light-emitting diode (LED) with a passive binary mask used as the transmitter and a photosensor used as the receiver. We strategically place a set of optical transmitters to spatio-temporally encode the volume of interest. Photosensors attached to scene points demultiplex the coded optical signals from multiple transmitters, allowing us to compute not only receiver location and orientation but also their incident illumination and the reflectance of the surfaces to which the photosensors are attached. We use our untethered tag system, called Prakash, to demonstrate methods of adding special effects to captured videos that cannot be accomplished using pure vision techniques that rely on camera images.
@Article{CG_0142,
author = {Ramesh Raskar and  Hideaki Nii and  Bert deDecker and  Yuki Hashimoto and  Jay Summet and  Dylan Moore and  Yong Zhao and  Jonathan Westhues and  Paul Dietz and  John Barnwell and  Shree Nayar and  Masahiko Inami and  Philippe Bekaert and  Michael Noland and  Vlad Branzoi and  Erich Bruns},
title = {{P}rakash: {L}ighting {A}ware {M}otion {C}apture using {P}hotosensing {M}arkers and {M}ultiplexed {I}lluminators},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {26},
number = {3},
month = {Jul},
year = {2007}
}


#### TRACKS: Toward Directable Thin Shells,

Miklós Bergou, Saurabh Mathur, Max Wardetzky, and Eitan Grinspun,
SIGGRAPH (ACM Transactions on Graphics), Vol.26, No.3, Jul, 2007.
We combine the often opposing forces of artistic freedom and mathematical determinism to enrich a given animation or simulation of a surface with physically based detail. We present a process called tracking, which takes as input a rough animation or simulation and enhances it with physically simulated detail. Building on the foundation of constrained Lagrangian mechanics, we propose weak-form constraints for tracking the input motion. This method allows the artist to choose where to add details such as characteristic wrinkles and folds of various thin shell materials and dynamical effects of physical forces. We demonstrate multiple applications ranging from enhancing an artist’s animated character to guiding a simulated inanimate object.
@Article{CG_0124,
author = {Miklós Bergou and  Saurabh Mathur and  Max Wardetzky and Eitan Grinspun},
title = {{T}{R}{A}{C}{K}{S}: {T}oward {D}irectable {T}hin {S}hells},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {26},
number = {3},
pages = {50},
month = {Jul},
year = {2007}
}


#### 4D Compression and Relighting with High-Resolution Light Transport Matrices,

Ewen Cheslack-Potava, Nolan Goodnight, Ren Ng, Ravi Ramamoorthi and Greg Humphreys,
ACM Symposium on Interactive 3D Graphics and Games, 2007.
@InProceedings{CG_0127,
author = {Ewen Cheslack-Potava and  Nolan Goodnight and  Ren Ng and  Ravi Ramamoorthi and Greg Humphreys},
title = {4{D} {C}ompression and {R}elighting with {H}igh-{R}esolution {L}ight {T}ransport {M}atrices},
booktitle = {ACM Symposium on Interactive 3D Graphics and Games},
year = {2007}
}


#### A Real-time Beam Tracer with Application to Exact Soft Shadows,

Ryan Overbeck, Ravi Ramamoorthi, and William R. Mark,
Eurographics Symposium on Rendering, Jun, 2007.
Efficiently calculating accurate soft shadows cast by area light sources remains a difficult problem. Ray tracing based approaches are subject to noise or banding, and most other accurate methods either scale poorly with scene geometry or place restrictions on geometry and/or light source size and shape. Beam tracing is one solution which has historically been considered too slow and complicated for most practical rendering applications. Beam tracing\'s performance has been hindered by complex geometry intersection tests, and a lack of good acceleration structures with efficient algorithms to traverse them. We introduce fast new algorithms for beam tracing, specifically for beam--triangle intersection and beam--kd-tree traversal. The result is a beam tracer capable of calculating precise primary visibility and point light shadows in real-time. Moreover, beam tracing provides full area elements instead of point samples, which allows us to maintain coherence through to secondary effects and utilize the GPU for high quality antialiasing and shading with minimal extra cost. More importantly, our analysis shows that beam tracing is particularly well suited to soft shadows from area lights, and we generate essentially exact noise-free soft shadows for complex scenes in seconds rather than minutes or hours.
@InProceedings{CG_0133,
author = {Ryan Overbeck and  Ravi Ramamoorthi and William R. Mark},
title = {{A} {R}eal-time {B}eam {T}racer with {A}pplication to {E}xact {S}oft {S}hadows},
booktitle = {Eurographics Symposium on Rendering},
month = {Jun},
year = {2007}
}


#### Dirty Glass: Rendering Contamination on Transparent Surfaces,

Jinwei Gu, Ravi Ramamoorthi, Peter Belhumeur, Shree Nayar,
EuroGraphics Symposium on Rendering, Jun, 2007.
Rendering of clean transparent objects has been well studied in computer graphics. However, real-world transparent objects are seldom clean---their surfaces have a variety of contaminants such as dust, dirt, and lipids. These contaminants produce a number of complex volumetric scattering effects that must be taken into account when creating photorealistic renderings. In this project, we take a significant step towards modeling and rendering these effects. We make the assumption that the contaminant is an optically thin layer and construct an analytic model following pre-existing results in radiative transport theory and computer graphics for the net bidirectional reflectance/transmission distribution function. Moreover, the spatial textures created by the different types of contamination are also important in achieving visual realism. To this end, we measure the spatially varying thicknesses and the scattering parameters of a large number of glass panes with various types of dust, dirt, and lipids. We also develop a simple interactive synthesis tool to create novel instances of the measured contamination patterns. We show several results that demonstrate the use of our scattering model for rendering 3D scenes, as well as modifying real 2D photographs.
@InProceedings{CG_0134,
author = {Jinwei Gu and  Ravi Ramamoorthi and  Peter Belhumeur and  Shree Nayar},
title = {{D}irty {G}lass: {R}endering {C}ontamination on {T}ransparent {S}urfaces},
booktitle = {EuroGraphics Symposium on Rendering},
month = {Jun},
year = {2007}
}


#### Material Based Splashing of Water Drops,

Kshitiz Garg and Gurunandan Krishnan and Shree K. Nayar,
EuroGraphics Symposium on Rendering, Jun, 2007.
The splashing of a water drop is a fascinating phenomenon that results from a variety of complex interactions between the drop and the material it impacts. In general, the distribution of droplets of a splash depends on the drop size and velocity; the surface roughness, rigidity, and wetness; and the angle of impact. Given the number of factors involved, it is difficult to develop an analytical model for the splash distribution. Instead, we take an empirical approach. We have measured the splashing behaviors of 22 different materials that are commonly found in the real world. These materials can be broadly classified as rough (e.g., wood and brick), smooth (e.g., marble and glass), flexible (e.g., silk and paper), and miscellaneous (e.g., water and moss). We have developed a stochastic model for splash distribution that builds upon empirical models previously developed in fluid dynamics and meteorology. Our model is simple and only requires 7 coefficients for generating splashes for head-on impact for a material. A more general model for generating splashes for arbitrary impact angles (due to surface inclination or wind) requires 54 coefficients. The models of different materials may be combined to generate physically plausible splashes for novel materials that have not been measured. Our model is applicable for rendering splashes due to rain as well as water drops falling from large heights such as windowsills, trees, and rooftops.
@InProceedings{CG_0135,
author = {Kshitiz Garg and Gurunandan Krishnan and Shree K. Nayar},
title = {{M}aterial {B}ased {S}plashing of {W}ater {D}rops},
booktitle = {EuroGraphics Symposium on Rendering},
month = {Jun},
year = {2007}
}


#### Scene Collages and Flexible Camera Arrays,

Yoshikuni Nomura, Li Zhang, and Shree Nayar,
EuroGraphics Symposium on Rendering, Jun, 2007.
This paper presents an automatic method for creating a collage from a collection of photos of a scene taken from different viewpoints. The collage is constructed by aligning the images (in terms of their positions, rotations and scales) using a least-squares formulation. We have developed a graph-based optimization algorithm for layering the images so as to minimize the fragmentation of the collage. A collage can be displayed with opaque layers, with transparent layers, or with blended image boundaries. A scene collage can be viewed as a piece-wise perspective representation of a scene with visible seams. This representation has not only aesthetic value but also conveys scene structure and camera motion in an intuitive way. To capture live-action collages of dynamic scenes we have developed camera arrays that can be physically flexed by the user to continuously vary the composition of the scene. The design of our camera arrays enables a user to reconfigure them in terms of the spatial arrangement of the cameras in a matter of minutes. We show several still and dynamic examples that demonstrate that scene collages provide a new and interesting way to experience scenes.
@InProceedings{CG_0136,
author = {Yoshikuni Nomura and  Li Zhang and Shree Nayar},
title = {{S}cene {C}ollages and {F}lexible {C}amera {A}rrays},
booktitle = {EuroGraphics Symposium on Rendering},
month = {Jun},
year = {2007}
}


#### Viewpoint-Coded Structured Light,

Mark Young, Erik Beeson, James Davis, Szymon Rusinkiewicz and Ravi Ramamoorthi,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Jun, 2007.
We introduce a theoretical framework and practical algorithms for replacing time-coded structured light patterns with viewpoint codes, in the form of additional camera locations. Current structured light methods typically use log(N) light patterns, encoded over time, to unambiguously reconstruct N unique depths. We demonstrate that each additional camera location may replace one frame in a temporal binary code.
@InProceedings{CG_0126,
author = {Mark Young and  Erik Beeson and  James Davis and  Szymon Rusinkiewicz and Ravi Ramamoorthi},
title = {{V}iewpoint-{C}oded {S}tructured {L}ight},
booktitle = {IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {Jun},
year = {2007}
}


#### SimX meets SCIRun: A Component-based Implementation of a Computational Study System,

Siu-Man Yau, Eitan Grinspun, Vijay Karamcheti, Denis Zorin,
IEEE International Parallel & Distributed Processing Symposium, Mar, 2007.
This paper describes the ongoing implementation of the SimX system for multi-experiment computational studies within the SCIRun problem solving environment. The modular, component-based nature of SCIRun enables a natural integration of the SimX runtime modules with the simula- tion codes that constitute the experiments underlying the study, and provides a rich steering and visualization environment for study interactions. Experience with a computational study involving a SCIRun deﬁbrillator device simulation code (DeﬁbSim) highlights these advantages, and identiﬁes several avenues for future work.to the scientist or domain application developers.
@InProceedings{CG_0149,
author = {Siu-Man Yau and  Eitan Grinspun and  Vijay Karamcheti and  Denis Zorin},
title = {{S}im{X} meets {S}{C}{I}{R}un: {A} {C}omponent-based {I}mplementation of a {C}omputational {S}tudy {S}ystem},
booktitle = {IEEE International Parallel & Distributed Processing Symposium},
pages = {322},
month = {Mar},
year = {2007}
}


#### Cubic Shells,

Akash Garg, Eitan Grinspun, Max Wardetzky, Denis Zorin,
Symposium on Computer Animation, Aug, 2007.
Hinge-based bending models are widely used in the physically-based animation of cloth, thin plates and shells. We propose a hinge-based model that is simpler to implement, more efficient to compute, and offers a greater number of effective material parameters than existing models. Our formulation builds on two mathematical observations: (a) the bending energy of curved flexible surfaces can be expressed as a cubic polynomial if the surface does not stretch; (b) a general class of anisotropic materials—those that are orthotropic—is captured by appropriate choice of a single stiffness per hinge. Our contribution impacts a general range of surface animation applications, from isotropic cloth and thin plates to orthotropic fracturing thin shells.
@InProceedings{CG_0140,
author = {Akash Garg and  Eitan Grinspun and  Max Wardetzky and  Denis Zorin},
title = {{C}ubic {S}hells},
booktitle = {Symposium on Computer Animation},
pages = {91--98},
month = {Aug},
year = {2007}
}


#### Discrete Laplace operators: No free lunch,

Max Wardetzky, Saurabh Mathur, Felix Kälberer and Eitan Grinspun,
Symposium on Geometry Processing, Jul, 2007.
Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set of natural properties for discrete Laplace operators for triangular surface meshes. We prove an important theoretical limitation: discrete Laplacians cannot satisfy all natural properties; retroactively, this explains the diversity of existing discrete Laplace operators. Finally, we present a family of operators that includes and extends well-known and widely-used operators.
@InProceedings{CG_0139,
author = {Max Wardetzky and  Saurabh Mathur and  Felix Kälberer and Eitan Grinspun},
title = {{D}iscrete {L}aplace operators: {N}o free lunch},
booktitle = {Symposium on Geometry Processing},
pages = {33--37},
month = {Jul},
year = {2007}
}


#### Final-Placement BRDF Editing,

Aner Ben-Artzi,
PhD Thesis, Department of Computer Science, Columbia University, May, 2007.
The scene descriptions of computer-generated worlds include the geometry and location of objects, the lighting configuration, and the material properties of object surfaces. Material properties can often be described with the Bi-directional Reflectance Distribution Function (BRDF). The BRDF is a function that encodes the way light interacts with a surface, giving rise to different material perceptions, such as wood, metal, or plastic. Using traditional rendering techniques it is not possible to modify the BRDF of a complex scene while rendering it at interactive rates. Therefore, BRDFs are often chosen in simplified scenarios, and only later rendered in their final placement within a scene with complex geometry and lighting. This can lead to unexpected results since the appearance of objects depends on the interaction of lighting, geometry, and materials. In this thesis, I discuss how to use precomputation-based rendering techniques to allow for interactive rendering of changing BRDFs in scenes with complex lighting and geometry, including cast shadows and global illumination. This new capability allows artists and designers to choose the material properties of objects based on accurate feedback so they can have confidence that their decisions are well-informed. Final-placement decision making has been shown for lighting design, and this work is inspired by such precomputed radiance transfer (PRT) for interactive relighting. Linear rendering via a dot-product is introduced for BRDF editing in direct, complex lighting with cast shadows. This requires a new linear BRDF representation that is useful for both editing and rendering. For BRDF editing with global illumination, the image is no longer linear in the BRDFs of the scene. Therefore a new bilinear reflection operator is introduced to enable precomputing a polynomial representation that captures the higher-order interactions of editable BRDFs. Optimizations for both the precomputation and rendering phases are presented. The final render-time operation is a per-pixel dot-product whose complexity is independent of geometric and lighting complexity, as these aspects of the scene are fixed. Runtime improvements including curve-switching, object freezing, and incremental rendering are used to improve rendering performance without loss of quality.
@InCollection{CG_0137,
author = {Aner Ben-Artzi},
title = {{F}inal-{P}lacement {B}{R}{D}{F} {E}diting},
school = {PhD Thesis, Department of Computer Science, Columbia University},
year = {2007}
}


#### A note on the triangle-centered quadratic interpolation discretization of the shape operator ,

Jason Reisman, Eitan Grinspun, Denis Zorin,
Technical Report, Department of Computer Science, Columbia University and New York University, May, 2007.
In this note we consider a simple shape operator discretization for general meshes, based on computing an interpolating quadratic function passing through vertices of a triangle and its edge-adjacent neighbors. This approximation is computationally simple and consistent for a broad class of meshes. However, its convergence properties in the context of mesh optimization problems are not as good as some of the previously proposed techniques and it suffers from instabilities for certain point configurations.
@TechReport{CG_0141,
author = {Jason Reisman and  Eitan Grinspun and  Denis Zorin},
title = {{A} note on the triangle-centered quadratic interpolation discretization of the shape operator },
booktitle = {Technical Report, Department of Computer Science, Columbia University and New York University},
month = {May},
year = {2007}
}


### 2006

#### Modeling Illumination Variation with Spherical Harmonics,

Ravi Ramamoorthi,
Face Processing: Advanced Modeling Methods, 2006.
The appearance of objects including human faces can vary dramatically with the lighting. We present results that use spherical harmonic illumination basis functions to understand this variation for face modeling and recognition, as well as a number of other applications in graphics and vision.
@InCollection{CG_0042,
author = {Ravi Ramamoorthi},
title = {{M}odeling {I}llumination {V}ariation with {S}pherical {H}armonics},
booktitle = {Face Processing: Advanced Modeling Methods},
pages = {385--424},
year = {2006}
}


#### Computing discrete shape operators on general meshes [Eurographics 2006 Best Paper, 3rd Place] ,

Eitan Grinspun, Yotam Gingold, Jason Reisman, Denis Zorin,
Eurographics (Computer Graphics Forum), Vol.25, No.3, 2006.
Discrete curvature and shape operators, which capture complete information about directional curvatures at a point, are essential in a variety of applications: simulation of deformable two-dimensional objects, variational modeling and geometric data processing. In many of these applications, objects are represented by meshes. Currently, a spectrum of approaches for formulating curvature operators for meshes exists, ranging from highly accurate but computationally expensive methods used in engineering applications to efficient but less accurate techniques popular in simulation for computer graphics. We propose a simple and efficient formulation for the shape operator for variational problems on general meshes, using degrees of freedom associated with normals. On the one hand, it is similar in its simplicity to some of the discrete curvature operators commonly used in graphics; on the other hand, it passes a number of important convergence tests and produces consistent results for different types of meshes and mesh refinement.
@Article{CG_0030,
author = {Eitan Grinspun and  Yotam Gingold and  Jason Reisman and  Denis Zorin},
title = {{C}omputing discrete shape operators on general meshes [{E}urographics 2006 {B}est {P}aper, 3rd {P}lace] },
journal = {Eurographics (Computer Graphics Forum)},
volume = {25},
number = {3},
pages = {547--556},
year = {2006}
}


#### Reflectance Sharing: Predicting Appearance from a Sparse Set of Images of a Known Shape,

Todd Zickler, Ravi Ramamoorthi, Sebastian Enrique and Peter Belhumeur,
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.28, No.8, Aug, 2006.
We develop the theoretical framework and practical results for image-based rendering of spatially-varying reflectance from a very small number of images. In doing so, we trade off some spatial variation of the reflectance for an increased number of angular samples. The upcoming PAMI paper also includes a novel Fourier analysis of spatial and angular coherence.
@Article{CG_0039,
author = {Todd Zickler and  Ravi Ramamoorthi and  Sebastian Enrique and Peter Belhumeur},
title = {{R}eflectance {S}haring: {P}redicting {A}ppearance from a {S}parse {S}et of {I}mages of a {K}nown {S}hape},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {28},
number = {8},
pages = {1287--1302},
month = {Aug},
year = {2006}
}


#### Efficient Shadows from Sampled Environment Maps,

Aner Ben-Artzi, Ravi Ramamoorthi and Maneesh Agrawala,
Journal of Graphics Tools, Vol.11, No.1, 2006.
There are a number of recent methods to importance sample environment maps. However, these techniques do not exploit the coherence in visibility between nearby rays. We investigate a number of alternatives and develop a simple technique that can speed up the rendering of scenes lit by natural illumination by an order of magnitude with essentially no loss in accuracy.
@Article{CG_0041,
author = {Aner Ben-Artzi and  Ravi Ramamoorthi and Maneesh Agrawala},
title = {{E}fficient {S}hadows from {S}ampled {E}nvironment {M}aps},
journal = {Journal of Graphics Tools},
volume = {11},
number = {1},
pages = {13--36},
year = {2006}
}


#### A Compact Factored Representation of Heterogeneous Subsurface Scattering,

Pieter Peers, Karl vom Berge, Wojciech Matusik, Ravi Ramamoorthi, Jason Lawrence, Szymon Rusinkiewicz, and Philip Dutre,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
Heterogeneous subsurface scattering in translucent materials is one of the most beautiful but complex effects. We acquire spatial BSSRDF datasets using a projector, and develop a novel nonlinear factorization that separates a homogeneous kernel, and heterogeneous discontinuities. This enables rendering of complex spatially-varying translucent materials.
@Article{CG_0036,
author = {Pieter Peers and  Karl vom Berge and  Wojciech Matusik and  Ravi Ramamoorthi and  Jason Lawrence and  Szymon Rusinkiewicz and Philip Dutre},
title = {{A} {C}ompact {F}actored {R}epresentation of {H}eterogeneous {S}ubsurface {S}cattering},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
pages = {746--753},
year = {2006}
}


#### Acquiring Scattering Properties of Participating Media by Dilution,

Srinivasa Narasimhan, Mohit Gupta, Craig Donner, Ravi Ramamoorthi, Shree Nayar and Henrik Jensen,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
We present a simple device and technique for robustly estimating the properties of a broad class of participating media that can be either (a) diluted in water such as juices or beverages, (b) dissolved in water such as powders and sugar/salt crystals, or (c) suspended in water, such as impurities. By diluting in water, we can measure robustly in the single scattering regime.
@Article{CG_0037,
author = {Srinivasa Narasimhan and  Mohit Gupta and  Craig Donner and  Ravi Ramamoorthi and  Shree Nayar and Henrik Jensen},
title = {{A}cquiring {S}cattering {P}roperties of {P}articipating {M}edia by {D}ilution},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
pages = {1003--1012},
year = {2006}
}


#### Fast Separation of Direct and Global Components of a Scene using High-Frequency Illumination,

Shree Nayar, Gurunandan Krishnan, Michael Grossberg and Ramesh Raskar,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
@Article{CG_0110,
author = {Shree Nayar and  Gurunandan Krishnan and  Michael Grossberg and Ramesh Raskar},
title = {{F}ast {S}eparation of {D}irect and {G}lobal {C}omponents of a {S}cene using {H}igh-{F}requency {I}llumination},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
year = {2006}
}


#### Inverse Shade Trees for Non-Parametric Material Representation and Editing,

Jason Lawrence, Aner Ben-Artzi, Christopher DeCoro, Wojciech Matusik, Hanspeter Pfister, Ravi Ramamoorthi, Szymon Rusinkiewicz,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
We develop an inverse shade tree framework of hierarchical matrix factorizations to provide intuitive, editable representations of high-dimensional measured reflectance datasets of spatially-varying appearance. We introduce a new alternating constrained least squares framework for these decompositions, that preserves the key features of linearity, positivity, sparsity and domain-specific constraints. The SVBRDF is decomposed onto 1D curves and 2D maps, that are easily edited.
@Article{CG_0033,
author = {Jason Lawrence and  Aner Ben-Artzi and  Christopher DeCoro and  Wojciech Matusik and  Hanspeter Pfister and  Ravi Ramamoorthi and  Szymon Rusinkiewicz},
title = {{I}nverse {S}hade {T}rees for {N}on-{P}arametric {M}aterial {R}epresentation and {E}diting},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
pages = {735--745},
year = {2006}
}


#### Multiview Radial Catadioptric Imaging for Scene Capture,

Sujit Kuthirummal and Shree Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
@Article{CG_0108,
author = {Sujit Kuthirummal and Shree Nayar},
title = {{M}ultiview {R}adial {C}atadioptric {I}maging for {S}cene {C}apture},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
year = {2006}
}


#### Photorealistic Rendering of Rain Streaks,

Kshitiz Garg and Shree Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
@Article{CG_0109,
author = {Kshitiz Garg and Shree Nayar},
title = {{P}hotorealistic {R}endering of {R}ain {S}treaks},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
year = {2006}
}


#### Projection Defocus Analysis for Scene Capture and Image Display,

Li Zhang and Shree Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
@Article{CG_0111,
author = {Li Zhang and Shree Nayar},
title = {{P}rojection {D}efocus {A}nalysis for {S}cene {C}apture and {I}mage {D}isplay},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
year = {2006}
}


#### Real-Time BRDF Editing in Complex Lighting,

Aner Ben-Artzi, Ryan Overbeck and Ravi Ramamoorthi,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
In this project, we develop the theory and algorithms to for the first time allow users to edit measured and analytic BRDFs in real time to design materials in their final placement in a scene with complex natural illumination and cast shadows. The system can take as input a variety of analytic and data-driven reflectance models, including the curve-based BRDFs obtained from the inverse shade tree factorization.
@Article{CG_0034,
author = {Aner Ben-Artzi and  Ryan Overbeck and Ravi Ramamoorthi},
title = {{R}eal-{T}ime {B}{R}{D}{F} {E}diting in {C}omplex {L}ighting},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
pages = {945--954},
year = {2006}
}


#### Real-Time Soft Shadows in Dynamic Scenes using Spherical Harmonic Exponentiation,

Zhong Ren, Rui Wang, John Snyder, Kun Zhou, Xinguo Liu, Bo Sun, Peter-Pike Sloan, Hujun Bao, Qunsheng Peng, and Baining Guo,
SIGGRAPH (ACM Transactions on Graphics), Aug, 2006.
Previous methods for soft shadows numerically integrate over many light directions at each receiver point, testing blocker visibility in each direction. We introduce a method for real-time soft shadows in dynamic scenes illuminated by large, low-frequency light sources where such integration is impractical. Our method operates on vectors representing low-frequency visibility of blockers in the spherical harmonic basis. Blocking geometry is modeled as a set of spheres; relatively few spheres capture the low-frequency blocking effect of complicated geometry. At each receiver point, we compute the product of visibility vectors for these blocker spheres as seen from the point. Instead of computing an expensive SH product per blocker as in previous work, we perform inexpensive vector sums to accumulate the log of blocker visibility. SH exponentiation then yields the product visibility vector over all blockers. We show how the SH exponentiation required can be approximated accurately and efficiently for low-order SH, accelerating previous CPUbased methods by a factor of 10 or more, depending on blocker complexity, and allowing real-time GPU implementation.
@Article{CG_0121,
author = {Zhong Ren and  Rui Wang and  John Snyder and  Kun Zhou and  Xinguo Liu and  Bo Sun and  Peter-Pike Sloan and  Hujun Bao and  Qunsheng Peng and Baining Guo},
title = {{R}eal-{T}ime {S}oft {S}hadows in {D}ynamic {S}cenes using {S}pherical {H}armonic {E}xponentiation},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
month = {Aug},
year = {2006}
}


#### Time-Varying Surface Appearance: Acquisition, Modeling and Rendering,

Jinwei Gu, Chien-I Tu, Ravi Ramamoorthi, Peter Belhumeur, Wojciech Matusik and Shree Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.25, No.3, 2006.
We conduct the first comprehensive study of time-varying surface appearance, including acquisition of the first database of time-varying processes like burning, drying and decay. We then develop a nonlinear space-time appearance factorization (STAF) that allows easy editing or manipulation such as control, transfer and texture synthesis. We demonstrate a variety of novel time-varying rendering applications using the STAF model.
@Article{CG_0035,
author = {Jinwei Gu and  Chien-I Tu and  Ravi Ramamoorthi and  Peter Belhumeur and  Wojciech Matusik and Shree Nayar},
title = {{T}ime-{V}arying {S}urface {A}ppearance: {A}cquisition, {M}odeling and {R}endering},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {25},
number = {3},
pages = {762--771},
year = {2006}
}


#### Exploiting Temporal Coherence for Incremental All-Frequency Relighting,

Ryan Overbeck, Aner Ben-Artzi, Ravi Ramamoorthi and Eitan Grinspun,
Eurographics Symposium on Rendering, 2006.
Current PRT methods exploit spatial coherence of the lighting (such as with wavelets) and of light transport (such as with CPCA). We consider a significant, yet unexplored form of coherence, temporal coherence of the lighting from frame to frame. We achieve speedups of 3x-4x over conventional PRT with minimal implementation effort, and can trivially be added to almost any existing PRT algorithm.
@InProceedings{CG_0040,
author = {Ryan Overbeck and  Aner Ben-Artzi and  Ravi Ramamoorthi and Eitan Grinspun},
title = {{E}xploiting {T}emporal {C}oherence for {I}ncremental {A}ll-{F}requency {R}elighting},
booktitle = {Eurographics Symposium on Rendering},
year = {2006}
}


#### Time-Varying BRDFs,

Bo Sun, Kalyan Sunkavalli, Ravi Ramamoorthi, Peter Belhumeur, and Shree Nayar,
Eurographics Workshop on Natural Phenomena, Sep, 2006.
The properties of virtually all real-world materials change with time, causing their BRDFs to be time-varying. However, none of the existing BRDF models and databases take time variation into consideration; they represent the appearance of a material at a single time instance. In this work, we address the acquisition, analysis, modeling and rendering of a wide range of time-varying BRDFs. We have developed an acquisition system that is capable of sampling a material¡¯s BRDF at multiple time instances, with each time sample acquired within 36 seconds. We have used this acquisition system to measure the BRDFs of a wide range of time-varying phenomena which include the drying of various types of paints (watercolor, spray, and oil), the drying of wet rough surfaces (cement, plaster, and fabrics), the accumulation of dusts (household and joint compound) on surfaces, and the melting of materials (chocolate). Analytic BRDF functions are fit to these measurements and the model parameters¡¯ variations with time are analyzed. Each category exhibits interesting and sometimes non-intuitive parameter trends. These parameter trends are then used to develop analytic time-varying BRDF (TVBRDF) models. The analytic TVBRDF models enable us to apply effects such as paint drying and dust accumulation to arbitrary surfaces and novel materials.
@InProceedings{CG_0120,
author = {Bo Sun and  Kalyan Sunkavalli and  Ravi Ramamoorthi and  Peter Belhumeur and Shree Nayar},
title = {{T}ime-{V}arying {B}{R}{D}{F}s},
booktitle = {Eurographics Workshop on Natural Phenomena},
month = {Sep},
year = {2006}
}


#### A Theory of Spherical Harmonic Identities for BRDF/Lighting Transfer and Image Consistency,

Dhruv Mahajan, Ravi Ramamoorthi and Brian Curless,
European Conference on Computer Vision, 2006.
We develop new mathematical results based on the spherical harmonic convolution framework for reflection. We derive novel identities, which are the angular frequency domain analogs to common spatial domain invariants such as reflectance ratios. These lead to more general transfer algorithms for inverse rendering, and a novel framework for checking the consistency of images, to detect tampering.
@InProceedings{CG_0038,
author = {Dhruv Mahajan and  Ravi Ramamoorthi and Brian Curless},
title = { {A} {T}heory of {S}pherical {H}armonic {I}dentities for {B}{R}{D}{F}/{L}ighting {T}ransfer and {I}mage {C}onsistency},
booktitle = {European Conference on Computer Vision},
pages = {41--55 (vol IV)},
year = {2006}
}


#### A Quadratic Bending Model for Inextensible Surfaces,

Miklós Bergou, Max Wardetzky, David Harmon, Denis Zorin, and Eitan Grinspun,
Fourth Eurographics Symposium on Geometry Processing, Jun, 2006.
Efficient computation of curvature-based energies is important for practical implementations of geometric modeling and physical simulation applications. Building on a simple geometric observation, we provide a version of a curvature-based energy expressed in terms of the Laplace operator acting on the embedding of the surface. The corresponding energy, being quadratic in positions, gives rise to a constant Hessian in the context of isometric deformations. The resulting isometric bending model is shown to significantly speed up common cloth solvers, and when applied to geometric modeling situations built on Willmore flow to provide runtimes which are close to interactive rates.
@InProceedings{CG_0009,
author = {Mikl{\'{o}}s Bergou and  Max Wardetzky and  David Harmon and  Denis Zorin and Eitan Grinspun},
title = {{A} {Q}uadratic {B}ending {M}odel for {I}nextensible {S}urfaces},
booktitle = {Fourth Eurographics Symposium on Geometry Processing},
pages = {227--230},
month = {Jun},
year = {2006}
}


#### Sim-X: Parallel System Software for Interactive Multi-Experiment Computational Studies,

Siu-Man Yau, Eitan Grinspun, Vijay Karamcheti, and Denis Zorin,
International Parallel & Distributed Processing Symposium, Vol.20, No.25-2, Apr, 2006.
Advances in high-performance computing have led to the broad use of computational studies in everyday engineering and scientific applications. A single study may require thousands of computational experiments, each corresponding to individual runs of simulation software with different parameter settings; in complex studies, the pattern of parameter changes is complex and may have to be adjusted by the user based on partial simulation results. Unfortunately, existing tools have limited high-level support for managing large ensembles of simultaneous computational experiments. In this paper, we present a system architecture for interactive computational studies targeting two goals. The first is to provide a framework for high-level user interaction with computational studies, rather than individual experiments; the second is to maximize the size of the studies that can be performed at close to interactive rates. We describe a prototype implementation of the system and demonstrate performance improvements obtained using our approach for a simple model problem.
@InProceedings{CG_0029,
author = {Siu-Man Yau and  Eitan Grinspun and  Vijay Karamcheti and Denis Zorin},
title = {{S}im-{X}: {P}arallel {S}ystem {S}oftware for {I}nteractive {M}ulti-{E}xperiment {C}omputational {S}tudies},
booktitle = {International Parallel & Distributed Processing Symposium},
volume = {20},
number = {25-2},
month = {Apr},
year = {2006}
}


#### Discrete Shells Origami,

Robert Burgoon, Eitan Grinspun, Zoë Wood,
Proceedings of Computers And Their Applications, Mar, 2006.
We introduce a way of simulating the creation of simple Origami (paper folding). The Origami is created in a thin shell simulation that realistically models the behavior and physical properties of paper. We demonstrate how to fold and crease the simulated paper wherever the user desires.
@InProceedings{CG_0115,
author = {Robert Burgoon and  Eitan Grinspun and  Zo{\"{e}} Wood},
title = {{D}iscrete {S}hells {O}rigami},
booktitle = {Proceedings of Computers And Their Applications},
pages = {180--187},
month = {Mar},
year = {2006}
}


#### Exploiting Temporal Coherence for Pre-computation Based Rendering,

Ryan Overbeck,
Masters Thesis, Department of Computer Science, Columbia University, No.cucs, May, 2006.
Precomputed radiance transfer (PRT) generates impressive images with complex illumi- nation, materials and shadows with real-time interactivity. These methods separate the scene’s static and dynamic components allowing the static portion to be computed as a preprocess. In this work, we hold geometry static and allow either the lighting or BRDF to be dynamic. To achieve real-time performance, both static and dynamic components are compressed by exploiting spatial and angular coherence. Temporal coherence of the dynamic component from frame to frame is an important, but unexplored additional form of coherence. In this thesis, we explore temporal coherence of two forms of all-frequency PRT: BRDF material editing and lighting design. We develop incremental methods for approximating the differences in the dynamic component between consecutive frames. For BRDF editing, we find that a pure incremental approach allows quick convergence to an exact solution with smooth real-time response. For relighting, we observe vastly differing degrees of temporal coherence accross levels of the lighting’s wavelet hierarchy. To address this, we develop an algorithm that treats each level separately, adapting to available coherence. The proposed methods are othogonal to other forms of coherence, and can be added to almost any PRT algorithm with minimal implementation, computation, or memory overhead. We demonstrate our technique within existing codes for nonlinear wavelet approximation, changing view with BRDF factorization, and clustered PCA. Exploiting temporal coherence of dynamic lighting yields a 3×–4× per- formance improvement, e.g., all-frequency effects are achieved with 30 wavelet coefficients, about the same as low-frequency spherical harmonic methods. Distinctly, our algorithm smoothly converges to the exact result within a few frames of the lighting becoming static.
@MastersThesis{CG_0116,
author = {Ryan Overbeck},
title = {{E}xploiting {T}emporal {C}oherence for {P}re-computation {B}ased {R}endering},
school = {Master's Thesis, Department of Computer Science, Columbia University},
year = {2006}
}


### 2005

#### A Fourier Theory for Cast Shadows,

Ravi Ramamoorthi, Melissa Koudelka and Peter Belhumeur,
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.27, No.2, 2005.
@Article{CG_0112,
author = {Ravi Ramamoorthi and  Melissa Koudelka and Peter Belhumeur},
title = {{A} {F}ourier {T}heory for {C}ast {S}hadows},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {27},
number = {2},
pages = {288--295},
year = {2005}
}


#### Spacetime Stereo: A Unifying Framework for Depth from Triangulation ,

James Davis, Diego Nehab, Ravi Ramamoorthi and Szymon Rusinkiewicz,
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.27, No.2, 2005.
@Article{CG_0113,
author = {James Davis and  Diego Nehab and  Ravi Ramamoorthi and Szymon Rusinkiewicz},
title = {{S}pacetime {S}tereo: {A} {U}nifying {F}ramework for {D}epth from {T}riangulation },
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {27},
number = {2},
pages = {296--302},
year = {2005}
}


#### A Practical Analytic Single Scattering Model for Real Time Rendering,

Bo Sun, Ravi Ramamoorthi, Srinivasa Narasimhan and Shree Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.24, No.3, 2005.
We present a physically-based model that allows for real-time rendering of a variety of scattering effects like glows around light sources, the effects of scattering on surface shading, and the appearance with complex lighting and BRDFs. The model is based on an analytic integration of the single scattering equations, and can be implemented with simple fragment programs on modern graphics hardware.
@Article{CG_0043,
author = {Bo Sun and  Ravi Ramamoorthi and  Srinivasa Narasimhan and Shree Nayar},
title = {{A} {P}ractical {A}nalytic {S}ingle {S}cattering {M}odel for {R}eal {T}ime {R}endering},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {24},
number = {3},
pages = {1040--1049},
year = {2005}
}


#### Efficiently Combining Positions and Normals for Precise 3D Geometry,

Diego Nehab, Szymon Rusinkiewicz, James Davis and Ravi Ramamoorthi,
SIGGRAPH (ACM Transactions on Graphics), Vol.24, No.3, 2005.
We show how depth and normal information, such as from a depth scanner and from photometric stereo, can be efficiently combined to remove the distortions and noise in both, producing very high quality meshes for computer graphics.
@Article{CG_0044,
author = {Diego Nehab and  Szymon Rusinkiewicz and  James Davis and Ravi Ramamoorthi},
title = {{E}fficiently {C}ombining {P}ositions and {N}ormals for {P}recise 3{D} {G}eometry},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {24},
number = {3},
pages = {536--543},
year = {2005}
}


#### Removing Photography Artifacts using Gradient Projection and Flash-Exposure Sampling,

Amit Agarwal, Ramesh Raskar, Shree Nayar and Yuanzhen Li,
SIGGRAPH (ACM Transactions on Graphics), Vol.24, No.3, 2005.
@Article{CG_0114,
author = {Amit Agarwal and  Ramesh Raskar and  Shree Nayar and Yuanzhen Li},
title = {{R}emoving {P}hotography {A}rtifacts using {G}radient {P}rojection and {F}lash-{E}xposure {S}ampling},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {24},
number = {3},
pages = {828--835},
year = {2005}
}


#### Adaptive Numerical Cumulative Distribution Functions for Efficient Importance Sampling,

Jason Lawrence, Szymon Rusinkiewicz and Ravi Ramamoorthi,
EuroGraphics Symposium on Rendering, 2005.
Importance sampling high-dimensional functions like lighting and BRDFs is increasingly important, but a direct tabular representation has storage cost exponential in the number of dimensions. By placing samples non-uniformly, we show that we can develop compact CDFs that enable new applications like sampling from oriented environment maps and multiple importance sampling.
@InProceedings{CG_0045,
author = {Jason Lawrence and  Szymon Rusinkiewicz and Ravi Ramamoorthi},
title = {{A}daptive {N}umerical {C}umulative {D}istribution {F}unctions for {E}fficient {I}mportance {S}ampling},
booktitle = {EuroGraphics Symposium on Rendering},
pages = {11--20},
year = {2005}
}


#### Reflectance Sharing: Image-Based Rendering from a Sparse Set of Images,

Todd Zickler, Sebastian Enrique, Ravi Ramamoorthi and Peter Belhumeur,
EuroGraphics Symposium on Rendering, 2005.
@InProceedings{CG_0005,
author = {Todd Zickler and   Sebastian Enrique and  Ravi Ramamoorthi and Peter Belhumeur},
title = {{R}eflectance {S}haring: {I}mage-{B}ased {R}endering from a {S}parse {S}et of {I}mages},
booktitle = {EuroGraphics Symposium on Rendering},
year = {2005}
}


### 2004

#### A Signal-Processing Framework for Reflection,

Ravi Ramamoorthi and Pat Hanrahan,
ACM Transactions on Graphics, Vol.23, No.4, Oct, 2004.
We present a signal-processing framework for analyzing the reflected light field from a homogeneous convex curved surface under distant illumination. This generalizes many of our previous results, showing a unified framework for 2D, 3D lambertian, 3D isotropic and 3D anisotropic cases.
@Article{CG_0046,
author = {Ravi Ramamoorthi and Pat Hanrahan},
title = {{A} {S}ignal-{P}rocessing {F}ramework for {R}eflection},
journal = {ACM Transactions on Graphics},
volume = {23},
number = {4},
pages = {1004--1042},
month = {Oct},
year = {2004}
}


#### Lighting sensitive display,

Shree Nayar, Peter Belhumeur and Terry Boult ,
ACM Transactions on Graphics, Vol.23, No.4, Oct, 2004.
@Article{CG_0016,
author = {Shree Nayar and   Peter Belhumeur  and Terry Boult },
title = {{L}ighting sensitive display},
journal = {ACM Transactions on Graphics},
volume = {23},
number = {4},
pages = {963--979},
month = {Oct},
year = {2004}
}


#### Efficient BRDF Importance Sampling Using a Factored Representation,

Jason Lawrence, Szymon Rusinkiewicz and Ravi Ramamoorthi,
SIGGRAPH (ACM Transactions on Graphics), Vol.23, No.3, 2004.
We introduce a Monte Carlo Importance sampling technique for general analytic and measured BRDFs based on a new BRDF factorization.
@Article{CG_0048,
author = {Jason Lawrence and  Szymon Rusinkiewicz and Ravi Ramamoorthi},
title = {{E}fficient {B}{R}{D}{F} {I}mportance {S}ampling {U}sing a {F}actored {R}epresentation},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {23},
number = {3},
pages = {494--503},
year = {2004}
}


#### Eyes for Relighting,

Ko Nishino and Shree Nayar,
SIGGRAPH (ACM Transactions on Graphics), Vol.23, No.3, 2004.
@Article{CG_0019,
author = { Ko Nishino and Shree Nayar},
title = {{E}yes for {R}elighting},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {23},
number = {3},
pages = {704--711},
year = {2004}
}


#### Triple Product Wavelet Integrals for All-Frequency Relighting,

Ren Ng, Ravi Ramamoorthi and Pat Hanrahan,
SIGGRAPH (ACM Transactions on Graphics), Vol.23, No.3, 2004.
We propose a new mathematical and computational analysis of pre-computed light transport. We use factored forms, separately pre-computing the effects of visibility and material properties. Rendering then requires computing triple product integrals at each vertex, involving the lighting, visibility and BRDF. Our main contribution is a general analysis of these triple products likely to have broad applicability in computer graphics and numerical analysis.
@Article{CG_0047,
author = {Ren Ng and  Ravi Ramamoorthi and Pat Hanrahan},
title = {{T}riple {P}roduct {W}avelet {I}ntegrals for {A}ll-{F}requency {R}elighting},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {23},
number = {3},
pages = {475--485},
year = {2004}
}


#### Practical Rendering of Multiple Scattering Effects in Participating Media,

Simon Premoze, Michael Ashikhmin, Jerry Tessendorf, Ravi Ramamoorthi and Shree Nayar,
EuroGraphics Symposium on Rendering, No.2004, 2004.
Volumetric light transport effects are significant for many materials like skin, smoke, clouds, snow or water. In particular, one must consider the multiple scattering of light within the volume. We develop a general framework for incorporating analytic point spread functions based on beam spreading, while considering multiple scattering in inhomogeneous media.
@InProceedings{CG_0050,
author = {Simon Premoze and  Michael Ashikhmin and  Jerry Tessendorf and  Ravi Ramamoorthi and Shree Nayar},
title = {{P}ractical {R}endering of {M}ultiple {S}cattering {E}ffects in {P}articipating {M}edia},
booktitle = {EuroGraphics Symposium on Rendering},
number = {2004},
year = {2004}
}


#### A Fourier Theory for Cast Shadows,

Ravi Ramamoorthi, Melissa Koudelka and Peter Belhumeur,
European Conference on Computer Vision (ECCV), 2004.
@InProceedings{CG_0017,
author = {Ravi Ramamoorthi and  Melissa Koudelka and Peter Belhumeur},
title = {{A} {F}ourier {T}heory for {C}ast {S}hadows},
booktitle = {European Conference on Computer Vision (ECCV)},
pages = {146--162 (vol 1)},
year = {2004}
}


#### A Discrete Model for Inelastic Deformation of Thin Shells,

Yotam Gingold, Adrian Secord, Jefferson Y. Han, Eitan Grinspun, Denis Zorin,
Technical Report, Courant Institute of Mathematical Sciences, New York University, Aug, 2004.
We introduce a method for simulating the inelastic deformation of thin shells: we model plasticity and fracture of curved, deformable objects such as light bulbs, egg-shells and bowls. Our novel approach uses triangle meshes yet evolves fracture lines unrestricted to mesh edges. We present a novel measure of bending strain expressed in terms of surface invariants such as lengths and angles. We also demonstrate simple techniques to improve the robustness of standard timestepping as well as collision response algorithms.
@TechReport{CG_0118,
author = {Yotam Gingold and  Adrian Secord and  Jefferson Y. Han and  Eitan Grinspun and  Denis Zorin},
title = {{A} {D}iscrete {M}odel for {I}nelastic {D}eformation of {T}hin {S}hells},
booktitle = {Technical Report, Courant Institute of Mathematical Sciences, New York University},
month = {Aug},
year = {2004}
}


### 2003

#### Natural Hierarchical Refinement for Finite Element Methods,

Petr Krysl, Eitan Grinspun, and Peter Schröder,
International Journal for Numerical Methods in Engineering, Vol.56, No.8, 2003.
Current formulations of adaptive finite element mesh refinement seem simple enough, but their implementations prove to be a formidable task. We offer an alternative approach called CHARMS: Conforming Hierarchical Adaptive Refinement Methods. Our method yields equivalent adapted approximation spaces wherever the traditional mesh refinement is applicable, but proves to be significantly simpler to implement. At the same time it is much more powerful in that it is general (no special tricks are required for different types of finite elements), and applicable for some newer approximations where traditional mesh refinement concepts are not of much help, for instance on subdivision surfaces.
@Article{CG_0012,
author = {Petr Krysl and  Eitan Grinspun and Peter Schr{\"{o}}der},
title = {{N}atural {H}ierarchical {R}efinement for {F}inite {E}lement {M}ethods},
journal = {International Journal for Numerical Methods in Engineering},
volume = {56},
number = {8},
pages = {1109–1124},
year = {2003}
}


#### All-Frequency Shadows Using Non-Linear Wavelet Lighting Approximation,

Ren Ng, Ravi Ramamoorthi and Pat Hanrahan,
SIGGRAPH (ACM Transactions on Graphics), Vol.22, No.3, 2003.
We present a method, based on pre-computed light transport, for real-time rendering of objects under all-frequency, time-varying illumination represented as a high-resolution environment map. For accurate rendering, using non-linear wavelets is an order of magnitude faster than using linear spherical harmonics, the current best technique.
@Article{CG_0053,
author = {Ren Ng and  Ravi Ramamoorthi and Pat Hanrahan},
title = {{A}ll-{F}requency {S}hadows {U}sing {N}on-{L}inear {W}avelet {L}ighting {A}pproximation},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {22},
number = {3},
pages = {376--381},
year = {2003}
}


#### Sparse Matrix Solvers on the GPU: Conjugate Gradients and Multigrid,

Jeff Bolz, Ian Farmer, Eitan Grinspun, and Peter Schröder,
SIGGRAPH (ACM Transactions on Graphics), Vol.22, No.3, Jul, 2003.
Many computer graphics applications require high-intensity numerical simulation. We show that such computations can be performed efficiently on the GPU, which we regard as a full function streaming processor with high floating-point performance. We implemented two basic, broadly useful, computational kernels: a sparse matrix conjugate gradient solver and a regular-grid multigrid solver. Realtime applications ranging from mesh smoothing and parameterization to fluid solvers and solid mechanics can greatly benefit from these, evidence our example applications of geometric flow and fluid simulation running on NVIDIA\\\'s GeForce FX using geometric flow (cube smoothing movie, 3D photography scan denoising movie) and fluid simulation (particle advection movie) as application examples.
@Article{CG_0028,
author = {Jeff Bolz and  Ian Farmer and  Eitan Grinspun and Peter Schr{\"{o}}der},
title = {{S}parse {M}atrix {S}olvers on the {G}{P}{U}: {C}onjugate {G}radients and {M}ultigrid},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {22},
number = {3},
pages = {917--924},
month = {Jul},
year = {2003}
}


#### Structured Importance Sampling of Environment Maps,

Sameer Agarwal, Ravi Ramamoorthi, Serge Belongie and Henrik Jensen,
SIGGRAPH (ACM Transactions on Graphics), Vol.22, No.3, 2003.
We introduce structured importance sampling, a new technique for efficiently rendering scenes illuminated by distant natural illumination given in an environment map.
@Article{CG_0054,
author = {Sameer Agarwal and  Ravi Ramamoorthi and  Serge Belongie and Henrik Jensen},
title = {{S}tructured {I}mportance {S}ampling of {E}nvironment {M}aps},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {22},
number = {3},
pages = {605--612},
year = {2003}
}


#### Discrete Shells,

Eitan Grinspun, Anil Hirani, Mathieu Desbrun and Peter Schröder,
ACM SIGGRAPH / Eurographics Symposium on Computer Animation, Aug, 2003.
In this paper we introduce a discrete shell model describing the behavior of thin flexible structures, such as hats, leaves, and aluminum cans, which are characterized by a curved undeformed configuration. Previously such models required complex continuum mechanics formulations and correspondingly complex algorithms. We show that a simple shell model can be derived geometrically for triangle meshes and implemented quickly by modifying a standard cloth simulator. Our technique convincingly simulates a variety of curved objects with materials ranging from paper to metal, as we demonstrate with several examples including a comparison of a real and simulated falling hat
@InProceedings{CG_0010,
author = {Eitan Grinspun and  Anil Hirani and  Mathieu Desbrun and Peter Schr{\"{o}}der},
title = {{D}iscrete {S}hells},
booktitle = {ACM SIGGRAPH / Eurographics Symposium on Computer Animation},
pages = {62--67},
month = {Aug},
year = {2003}
}


#### Spacetime Stereo: A Unifying Framework for Depth from Triangulation,

James Davis, Ravi Ramamoorthi and Szymon Rusinkiewicz,
IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2003.
We propose a common framework, spacetime stereo, which unifies many previous depth from triangulation methods like stereo, laser scanning, and coded structured light. As a practical example, we discuss a new temporal stereo technique for improved shape estimation in static scenes under variable illumination.
@InProceedings{CG_0052,
author = {James Davis and  Ravi Ramamoorthi and Szymon Rusinkiewicz},
title = {{S}pacetime {S}tereo: {A} {U}nifying {F}ramework for {D}epth from {T}riangulation},
booktitle = {IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
pages = {359--366 (vol 2)},
year = {2003}
}


#### Using Specularities for Recognition,

Margarita Osadchy, David Jacobs and Ravi Ramamoorthi,
International Conference on Computer Vision, 2003.
We present the first method for using specularities as a positive feature for lighting-insensitive recognition. The method is applied to very difficult objects like shiny crockery and wine glasses.
@InProceedings{CG_0051,
author = {Margarita Osadchy and  David Jacobs and Ravi Ramamoorthi},
title = {{U}sing {S}pecularities for {R}ecognition},
booktitle = {International Conference on Computer Vision},
pages = {1512--1519},
year = {2003}
}


#### The Basis Refinement Method,

Eitan Grinspun,
PhD Thesis, Caltech, 2003.
Finite element solvers are critical in computer graphics, engineering, medical and biological application areas. For large problems, the use of adaptive refinement methods can tame otherwise intractable computational costs. Current formulations of adaptive finite element mesh refinement seem straightforward, but their implementations prove to be a formidable task. We offer an alternative point of departure which yields equivalent adapted approximation spaces wherever the traditional mesh refinement is applicable, but proves to be significantly simpler to implement. At the same time it is much more powerful in that it is general (no special tricks are required for different types of finite elements), and applicable to novel discretizations where traditional mesh refinement concepts are not of much help, for instance on subdivision surfaces.
@InCollection{CG_0117,
author = {Eitan Grinspun},
title = {{T}he {B}asis {R}efinement {M}ethod},
school = {PhD Thesis, Department of Computer Science, Columbia University},
year = {2003}
}


### 2002

#### Analytic PCA Construction for Theoretical Analysis of Lighting Variability in Images of a Lambertian Object,

Ravi Ramamoorthi,
IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.24, No.10, Oct, 2002.
We explain for the first time some classic empirical results on lighting variability, and take a first step toward analyzing many classic vision problems under complex lighting.
@Article{CG_0055,
author = {Ravi Ramamoorthi},
title = {{A}nalytic {P}{C}{A} {C}onstruction for {T}heoretical {A}nalysis of {L}ighting {V}ariability in {I}mages of a {L}ambertian {O}bject},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {24},
number = {10},
pages = {1322--1333},
month = {Oct},
year = {2002}
}


#### CHARMS: A Simple Framework for Adaptive Simulation,

Eitan Grinspun, Petr Krysl and Peter Schröder,
SIGGRAPH (ACM Transactions on Graphics), Vol.21, No.3, Jul, 2002.
Finite element solvers are a basic component of simulation applications; they are common in computer graphics, engineering, and medical simulations. Although adaptive solvers can be of great value in reducing the often high computational cost of simulations they are not employed broadly. Indeed, building adaptive solvers can be a daunting task especially for 3D finite elements. In this paper we are introducing a new approach to produce conforming, hierarchical, adaptive refinement methods (CHARMS). The basic principle of our approach is to refine basis functions, not elements. This removes a number of implementation headaches associated with other approaches and is a general technique independent of domain dimension (here 2D and 3D), element type (eg, triangle, quad, tetrahedron, hexahedron), and basis function order (piecewise linear, higher order B-splines, Loop subdivision, etc.). The (un-)refinement algorithms are simple and require little in terms of data structure support. We demonstrate the versatility of our new approach through 2D and 3D examples, including medical applications and thin-shell animations.
@Article{CG_0013,
author = {Eitan Grinspun and  Petr Krysl and Peter Schr{\"{o}}der},
title = {{C}{H}{A}{R}{M}{S}: {A} {S}imple {F}ramework for {A}daptive {S}imulation},
journal = {SIGGRAPH (ACM Transactions on Graphics)},
volume = {21},
number = {3},
pages = {281--290},
month = {Jul},
year = {2002}
}


#### Frequency Space Environment Map Rendering,

Ravi Ramamoorthi and Pat Hanrahan,
SIGGRAPH, ACM Transactions on Graphics, Vol.21, No.3, 2002.
We present a new method for real-time rendering of objects with complex isotropic BRDFs under distant natural illumination, as specified by an environment map. Our approach is based on spherical frequency space analysis.
@Article{CG_0056,
author = {Ravi Ramamoorthi and Pat Hanrahan},
title = {{F}requency {S}pace {E}nvironment {M}ap {R}endering},
journal = {SIGGRAPH, ACM Transactions on Graphics},
volume = {21},
number = {3},
pages = {517--526},
year = {2002}
}


### 2001

#### Normal Bounds for Subdivision-Surface Interference Detection ,

Eitan Grinspun and Peter Schröder,
IEEE VIS \'01: Proceedings of the conference on Visualization \'01, Oct, 2001.
Interference detection is vital for simulation and animation. Our interest was born of a larger project: using the Subdivision Element Method and the thin-shell equations we produce realistic animations of crushing, crumpling, and wrinkling. In this paper we derive normal bounds for subdivision surfaces and use these to develop an efficient algorithm for collision detection with specific optimizations for self-interference. The normal bounds are also useful for CAD and rendering
@Article{CG_0014,
author = {Eitan Grinspun and Peter Schröder},
title = {{N}ormal {B}ounds for {S}ubdivision-{S}urface {I}nterference {D}etection },
journal = {IEEE VIS \'01: Proceedings of the conference on Visualization \'01},
pages = {333--340},
month = {Oct},
year = {2001}
}


#### On the relationship between Radiance and Irradiance: Determining the illumination from images of a convex Lambertian object,

Ravi Ramamoorthi and Pat Hanrahan,
Journal of the Optical Society of America, Vol.18, No.10, Oct, 2001.
This paper considers the 3D Lambertian case using spherical harmonics and derives an analytic formula for the irradiance in terms of the radiance, including the 9 parameter Lambertian BRDF approximation. One practical application is interactive rendering with An Efficient Representation for Irradiance Environment Maps.
@Article{CG_0058,
author = {Ravi Ramamoorthi and Pat Hanrahan},
title = {{O}n the relationship between {R}adiance and {I}rradiance: {D}etermining the illumination from images of a convex {L}ambertian object},
journal = {Journal of the Optical Society of America},
volume = {18},
number = {10},
pages = {2448--2459},
month = {Oct},
year = {2001}
}


#### A Signal-Processing Framework for Inverse Rendering,

Ravi Ramamoorthi and Pat Hanrahan,
SIGGRAPH, 2001.
This paper is the most mathematical so far and derives the theory for the general 3D case with arbitrary isotropic BRDFs. It also applies the results to the practical problem of inverse rendering under complex illumination.
@Article{CG_0059,
author = {Ravi Ramamoorthi and Pat Hanrahan},
title = {{A} {S}ignal-{P}rocessing {F}ramework for {I}nverse {R}endering},
journal = {SIGGRAPH},
pages = {117--128},
year = {2001}
}


#### An Efficient Representation for Irradiance Environment Maps,

Ravi Ramamoorthi and Pat Hanrahan,
SIGGRAPH, 2001.
We consider the rendering of diffuse objects under distant illumination, as specified by an environment map. Using an analytic expression for the irradiance in terms of spherical harmonic coefficients of the lighting, we show that one needs to compute and use only 9 coefficients, corresponding to the lowest-frequency modes of the illumination, in order to achieve average errors of only 1%.
@Article{CG_0060,
author = {Ravi Ramamoorthi and Pat Hanrahan},
title = {{A}n {E}fficient {R}epresentation for {I}rradiance {E}nvironment {M}aps},
journal = {SIGGRAPH},
pages = {497--500},
year = {2001}
}


#### Analysis of Planar Light Fields From Homogeneous Convex Curved Surfaces Under Distant Illumination,

Ravi Ramamoorthi and Pat Hanrahan,
SPIE Proceedings of Human Vision and Electronic Imaging VI (part of Photonics West, 2001), 2001.
This relatively simple to read paper is the first on the reflection is convolution idea underlying my PhD thesis, and considers the 2D case using only Fourier transforms.
@InProceedings{CG_0057,
author = {Ravi Ramamoorthi and Pat Hanrahan},
title = {{A}nalysis of {P}lanar {L}ight {F}ields {F}rom {H}omogeneous {C}onvex {C}urved {S}urfaces {U}nder {D}istant {I}llumination},
booktitle = {SPIE Proceedings of Human Vision and Electronic Imaging VI (part of Photonics West, 2001)},
pages = {185--198},
year = {2001}
}


### 2000

#### Efficient Image-Based Methods for Rendering Soft Shadows,

Maneesh Agrawala, Ravi Ramamoorthi, Alan Heirich and Laurent Moll,
SIGGRAPH, 2000.
We present two efficient image-based approaches for computation and display of high-quality soft shadows from area light sources. Our methods are related to shadow maps and provide the associated benefits.
@Article{CG_0061,
author = {Maneesh Agrawala and  Ravi Ramamoorthi and  Alan Heirich and Laurent Moll},
title = {{E}fficient {I}mage-{B}ased {M}ethods for {R}endering {S}oft {S}hadows},
journal = {SIGGRAPH},
pages = {375--384},
year = {2000}
}


### 1999

#### Creating Generative Models from Range Images,

Ravi Ramamoorthi and James Arvo,
SIGGRAPH, 1999.
We have explored the creation of high-level parametric models from low-level range data. Our model-based approach is relatively insensitive to noise and missing data and is fairly robust.
@Article{CG_0062,
author = {Ravi Ramamoorthi and James Arvo},
title = {{C}reating {G}enerative {M}odels from {R}ange {I}mages},
journal = {SIGGRAPH},
pages = {195--204},
year = {1999}
}


#### Non-Linear Mechanics and Collisions for Subdivision Surfaces,

Eitan Grinspun, Fehmi Cirak, Peter Schröder, and Michael Ortiz,
Technical Report, 1999.
Numerically accurate simulation of the mechanical behavior of thin flexible structures is important in application areas ranging from engineering design to animation special effects. Subdivision surfaces provide a unique opportunity to integrate geometric modeling with concurrent finite element analysis of thin flexible structures. Their mechanics are governed by the so-called thin-shell equations. We present a concise treatment of thin-shell equations including dynamic behavior, scalable material models, and the treatment of collisions (detection as well as response). The resulting energy minimization problem is non-linear and in turn able to capture effects of far more realism than linear models. We demonstrate these claims with a number of simulations which exhibit characteristic effects of real world experiments
@TechReport{CG_0015,
author = {Eitan Grinspun and  Fehmi Cirak and  Peter Schr{\"{o}}der and Michael Ortiz},
title = {{N}on-{L}inear {M}echanics and {C}ollisions for {S}ubdivision {S}urfaces},
booktitle = {Technical Report},
year = {1999}
}


### 1997

#### Fast Construction of Accurate Quaternion Splines,

Ravi Ramamoorthi and Alan H. Barr,
SIGGRAPH, 1997.
We have explored the use of improved numerical approaches for optimization to automatically create animation from keyframes. The numerical tools developed include adaptive refinement based on the Euler-Lagrange error functional. We have applied this approach to quaternion splines, greatly speeding up a numerical method to construct the optimal rotational curve.
@Article{CG_0063,
author = {Ravi Ramamoorthi and Alan H. Barr},
title = {{F}ast {C}onstruction of {A}ccurate {Q}uaternion {S}plines},
journal = {SIGGRAPH},
pages = {287--292},
year = {1997}
}


#### Dynamic Splines with Constraints for Animation,

Ravi Ramamoorthi,
Caltech CS-TR-97-03, Mar, 1997.
We have explored the use of improved numerical approaches for optimization to automatically create animation from keyframes. The numerical tools developed include adaptive refinement based on the Euler-Lagrange error functional. We have applied this approach to quaternion splines, greatly speeding up a numerical method to construct the optimal rotational curve.
@TechReport{CG_0064,
author = {Ravi Ramamoorthi},
title = {{D}ynamic {S}plines with {C}onstraints for {A}nimation},
booktitle = {Caltech CS-TR-97-03},
month = {Mar},
year = {1997}
}