Research Overview

Physics-Based Sound Synthesis

We are exploring how to synthesize synchronized and realistic sounds automatically for a wide spectrum of physically based simulation models (rigid bodies [JP06], nonlinear thin-shells [CAJ09] and elastic rods [SJM17], splashing fluids [ZJ09,L+16], fracturing solids [ZJ10], self-collision chattering [BJ10], etc.). One major focus has been developing efficient reduced-order algorithms to synthesize vibrations and sound radiation to enable realistic, real-time sound models for future virtual environments. We are also exploring off-line methods for high-quality audio-visual rendering of general physics-based animations.

Pixar Research

My work at Pixar explores new ways of applying mathematics and physically based simulation to the Pixar creative process. Recently, I have been investigating analytical methods of mathematical physics to develop fast physics-based tools for artists, an example of which is our work on Kelvinlets for real-time deformable sculpting. After years of exploring numerical precomputation methods to solve equations ahead of time, it is interesting to revisit classical methods for “analytical precomputation.”

Deformation processing

By and large, many of our contributions address efficient deformation processing methods: fast precomputed Green’s function models [JP99, PvdDJ+01, JP03], hardware-accelerated skinning [JP02, JT05], data-driven animation using motion graphs [JF03, JTCW07], dimensional model reduction and nonlinear reduced-order dynamics [BJ05, AKJ08, KJ09], deformable collision processing [JP04, KSJP08, BJ10], vibration-based sound synthesis [JBP06, BDT+08, CAJ09], fast lattice shape matching [RJ07], and extra-warm yarn-level cloth [KJM08, KJM10].

Yarn-Level Cloth

Following the pioneering work of Terzopoulos and others more than three decades ago, computational models of cloth have been essentially “rubber sheets.” Starting with a sequence of works at Cornell with Steve Marschner and our students, we advanced fundamentally different computational cloth models based on direct simulation of constitutive yarns in pervasive contact. We devised a family of algorithms to efficiently simulate complex assemblies of inter-looping elastic rods and resolve millions of contacts [KJM08], along with space-time adaptive methods for exploiting temporal coherence in yarn-yarn contact computations [KJM10]. We invented Stitch Meshes to allow artists to interactively design realistic knitted garments with yarn-level details, while providing topological guarantees that the yarns will not unravel when simulated [YKJM12]. We continue to explore technology for faster and better simulation of yarn-level systems for the graphics and textile industries.

Numerical Methods for Reduced-order Models (ROMs)

Real-time and long-time simulation methods in computer graphics and sound have motivated the need for a variety of new reduced-order modeling techniques (dimension model reduction, low-dimensional subspace methods, etc.) that enable faster and cheaper simulations. We have long explored methods for reduced-order models (ROMs): precomputation-based schemes for data-driven ROM-based animation [JF03, JTCW07]; GPU-accelerated evaluation of deformable ROMs [JP02, JT05, BJ05]; dimensional model reduction methods for real-time subspace integration [BJ05]; cubature-based integration methods for subspace dynamics [AKJ08,CAJ09]; online model reduction (learning the basis and ROM “on the fly”) [KJ09]; ROM domain decomposition of nonlinear deformable models [KJ11] and efficient ROM-based simulation of fracture sound [ZJ10]; ROM-based multi-body contact solvers [KSJP08]; mode-adaptive, asynchronous integration of linear modal dynamics [ZJ11]; reduced-order collision processing via reduced-order bounding volume hierarchies [JP04], time-critical methods for hard real-time applications [KSJP08], and reduced-order self-collision processing [BJ10]; reduced-order water vibration and acoustic analysis [ZJ09,L+16]; and compression of ROM basis functions [L+14].

Physics-Based Sound Synthesis

We are exploring how to synthesize synchronized and realistic sounds automatically for a wide spectrum of physically based simulation models (rigid bodies [JP06], nonlinear thin-shells [CAJ09] and elastic rods [SJM17], splashing fluids [ZJ09,L+16], fracturing solids [ZJ10], self-collision chattering [BJ10], etc.). One major focus has been developing efficient reduced-order algorithms to synthesize vibrations and sound radiation to enable realistic, real-time sound models for future virtual environments. We are also exploring off-line methods for high-quality audio-visual rendering of general physics-based animations.

Pixar Research

My work at Pixar explores new ways of applying mathematics and physically based simulation to the Pixar creative process. Recently, I have been investigating analytical methods of mathematical physics to develop fast physics-based tools for artists, an example of which is our work on Kelvinlets for real-time deformable sculpting. After years of exploring numerical precomputation methods to solve equations ahead of time, it is interesting to revisit classical methods for “analytical precomputation.”

Deformation processing

By and large, many of our contributions address efficient deformation processing methods: fast precomputed Green’s function models [JP99, PvdDJ+01, JP03], hardware-accelerated skinning [JP02, JT05], data-driven animation using motion graphs [JF03, JTCW07], dimensional model reduction and nonlinear reduced-order dynamics [BJ05, AKJ08, KJ09], deformable collision processing [JP04, KSJP08, BJ10], vibration-based sound synthesis [JBP06, BDT+08, CAJ09], fast lattice shape matching [RJ07], and extra-warm yarn-level cloth [KJM08, KJM10].

Yarn-Level Cloth

Following the pioneering work of Terzopoulos and others more than three decades ago, computational models of cloth have been essentially “rubber sheets.” Starting with a sequence of works at Cornell with Steve Marschner and our students, we advanced fundamentally different computational cloth models based on direct simulation of constitutive yarns in pervasive contact. We devised a family of algorithms to efficiently simulate complex assemblies of inter-looping elastic rods and resolve millions of contacts [KJM08], along with space-time adaptive methods for exploiting temporal coherence in yarn-yarn contact computations [KJM10]. We invented Stitch Meshes to allow artists to interactively design realistic knitted garments with yarn-level details, while providing topological guarantees that the yarns will not unravel when simulated [YKJM12]. We continue to explore technology for faster and better simulation of yarn-level systems for the graphics and textile industries.

Numerical Methods for Reduced-order Models (ROMs)

Real-time and long-time simulation methods in computer graphics and sound have motivated the need for a variety of new reduced-order modeling techniques (dimension model reduction, low-dimensional subspace methods, etc.) that enable faster and cheaper simulations. We have long explored methods for reduced-order models (ROMs): precomputation-based schemes for data-driven ROM-based animation [JF03, JTCW07]; GPU-accelerated evaluation of deformable ROMs [JP02, JT05, BJ05]; dimensional model reduction methods for real-time subspace integration [BJ05]; cubature-based integration methods for subspace dynamics [AKJ08,CAJ09]; online model reduction (learning the basis and ROM “on the fly”) [KJ09]; ROM domain decomposition of nonlinear deformable models [KJ11] and efficient ROM-based simulation of fracture sound [ZJ10]; ROM-based multi-body contact solvers [KSJP08]; mode-adaptive, asynchronous integration of linear modal dynamics [ZJ11]; reduced-order collision processing via reduced-order bounding volume hierarchies [JP04], time-critical methods for hard real-time applications [KSJP08], and reduced-order self-collision processing [BJ10]; reduced-order water vibration and acoustic analysis [ZJ09,L+16]; and compression of ROM basis functions [L+14].

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