Jerome E. Lengyel

Compression of time-dependent geometry

Methods for coding a time-dependent geometry stream (164, 165) include geometric transform coder, a basis decomposition coder, a column/row prediction coder, and space-time level of detail coder. The basis decomposition coder uses principal component analysis to decompose a time dependent geometry matrix into basis vectors and weights. The weights and basis vectors are coded separately. Optionally, the residual between a mesh constructed from the weight and basis vectors and the original mesh can be encoded as well. The column/row predictor exploits coherence in a matrix of time dependent geometry by encoding differences among neighboring rows and columns (166). Row and column sorting (163) optimizes this form of coding by re-arranging rows and columns to improve similarity among neighboring rows/columns. The space-time level of detail coder converts a time-dependent geometry stream into a hierarchical structure, including levels of detail in the space and time dimensions, and expansion records. The expansion records specify how to reconstruct (172) a mesh from deltas representing differences between levels of detail.

Real-time fur over arbitrary surfaces

We introduce a method for real-time rendering of fur on surfaces of arbitrary topology. As a pre-process, we simulate virtual hair with a particle system, and sample it into a volume texture. Next, we parameterize the texture over a surface of arbitrary topology using “lapped textures” — an approach for applying a sample texture to a surface by repeatedly pasting patches of the texture until the surface is covered. The use of lapped textures permits specifying a global direction field for the fur over the surface. At runtime, the patches of volume textures are rendered as a series of concentric shells of semi-transparent medium. To improve the visual quality of the fur near silhouettes, we place “fins” normal to the surface and render these using conventional 2D texture maps sampled from the volume texture in the direction of hair growth. The method generates convincing imagery of fur at interactive rates for models of moderate complexity. Furthermore, the scheme allows real-time modification of viewing and lighting conditions, as well as local control over hair color, length, and direction. Additional

Real-Time Fur

Hair adds compelling richness to computer graphics scenes. This paper describes techniques for lighting and rendering short hair in real-time on current PC graphics hardware. Level-of-detail representations for drawing fur span the viewing distance from close-ups using procedurally generated alpha-blended lines, to mid and far views using volumetric textures, and on to distant views using anisotropic texture map rendering. Real-time lighting with soft-edged shadows is consistent across the level-of-detail representations.

Parameterized environment maps

Static environment maps fail to capture local reflections including effects like selfreflections and parallax in the reflected imagery. We instead propose parameterized environment maps (PEMs), a set of per-view environment maps which accurately reproduce local reflections at each viewpoint as computed by an offline ray tracer. Even with a small set of viewpoint samples, PEMs support plausible movement away from and between the pre-rendered viewpoint samples while maintaining local reflections. They also make use of environment maps supported in graphics hardware to provide real-time exploration of the pre-rendered space. In addition to parameterization by viewpoint, our notion of PEM extends to general, multidimensional parameterizations of the scene, including relative motions of objects and lighting changes. Our contributions include a technique for inferring environment maps providing a close match to ray-traced imagery. We also explicitly infer and encode all MIPMAP levels of the PEMs to achieve higher accuracy. We propose layered environment maps that separate local and distant reflected geometry. We explore several types of environment maps including finite spheres, ellipsoids, and boxes that better approximate the environmental geometry. We demonstrate results showing faithful local reflections in an interactive viewer. Additional

Parameterized Animation Compression

We generalize image-based rendering by exploiting texture-mapping graphics hardware to decompress ray-traced “animations”. Rather than ID time, our animations are parameterized by two or more arbitrary variables representing view/lighting changes and rigid object motions. To best match the graphics hardware rendering to the input ray-traced imagery, we describe a novel method to infer parameterized texture maps for each object by modeling the hardware as a linear system and then performing least-squares optimization. The parameterized textures are compressed as a multidimensional Laplacian pyramid on fixed size blocks of parameter space. This scheme captures the coherence in parameterized animations and, unlike previous work, decodes directly into texture maps that load into hardware with a few, simple image operations. We introduce adaptive dimension splitting in the Laplacian pyramid and separate diffuse and specular lighting layers to further improve compression. High-quality results are demonstrated at compression ratios up to 800:1 with interactive playback on current consumer graphics cards.