Real-Time Global Illumination and Sound Propagation on Graphics Hardware and GPUs: analytic models for area lights, bidirectional texture functions, caustics, low-frequency distant environmental lighting/environment maps, motion blur and depth of field, precomputed radiance transfer (PRT), ray tracing, reflections and refractions, single scattering in inhomogeneous participating media, soft shadows and inter-reflections on dynamic geometry, sound propagation, spatially-varying BRDF (SVBRDF) rendering and acquisition.
Spherical Harmonics (SH) for Real-Time Rendering: spherical harmonic exponentiation, zonal harmonics (ZH) and rotation, spherical harmonic products and squares, spherical harmonic rotation, spherical harmonic basis functions, projection and reconstruction.
Stretch Metrics and Algorithms for Parameterizing Surface Signals and Building Compact Texture Maps.
Signal Processing and Sampling for Computer Graphics: filtering/antialiasing, compression, spectral analysis.
Numerical Techniques and Nonlinear Optimization: analytic and numerical integration, interval analysis, shape approximation, surface signal fitting/approximation, PDEs for vector graphics.
Layered, Incremental, and Hierarchical Rendering: animation compression using precomputed texture maps, sprites without depth, visibility sorting, image caching, precomputed volume hierarchies for rendering complex scenes, silhouette clipping/antialiasing, foveated rendering.
Geometric Modeling/Approximation: interactive placement and assembly, physically-based mesh deformation, procedural modeling and shape design with parametric surfaces, sphere set approximation, mechanism design.
Interval Methods for Collision Detection and other Applications in Computer Graphics.