A method is described for texturing surfaces using decals, images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O(N log N ) discrete approximation to the exponential map which requires only a single additional step in Dijkstra's graph-distance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/feature-matching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.

We describe an extension of B-splines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of B-splines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral control mesh instead of a rectangular one; the resulting surface approximates the polyhedral mesh much as a B-spline approximates its rectangular control mesh. Like a Bspline, the surface is a single, continuous object. This is achieved by modeling the domain of the surface with a manifold whose topology matches that of the polyhedral mesh, then embedding this domain into 3-space using a basis-function/control-point formulation. We provide a constructive approach to building a manifold.

This paper takes a systematic look at methods for estimating the curvature of surfaces represented by triangular meshes. We have developed a suite of test cases for assessing the sensitivity of curvature calculations to noise, mesh resolution, and mesh regularity. These tests are applied to existing discrete curvature approximation techniques and common surface fitting methods. We also look at alternatives to the standard parameterization techniques. The results illustrate the impact of noise and mesh related issues on the accuracy of these methods and provide guidance in choosing an appropriate method for applications requiring curvature estimates.

We have created a system for capturing both the three-dimensional geometry and color and shading information for human facial expressions. We use this data to reconstruct photorealistic, 3D animations of the captured expressions. The system uses a large set of sampling points on the face to accurately track the three dimensional deformations of the face. Simultaneously with the tracking of the geometric data, we capture multiple high resolution, registered video images of the face. These images are used to create a texture map sequence for a three dimensional polygonal face model which can then be rendered on standard 3D graphics hardware. The resulting facial animation is surprisingly life-like and looks very much like the original live performance. Separating the capture of the geometry from the texture images eliminates much of the variance in the image data due to motion, which increases compression ratios. Although the primary emphasis of our work is not compression we have investigated the use of a novel method to compress the geometric data based on principal components analysis. The texture sequence is compressed using an MPEG4 video codec. Animations reconstructed from 512x512 pixel textures look good at data rates as low as 240 Kbits per second.

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