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    Using Procedural RenderMan Shaders for Global Illurnination
    (Blackwell Science Ltd and the Eurographics Association, 1995) Slusallek, Philipp; Pflaum, Thomas; Seidel, Hans-Peter
    Global illumination techniques like radiosity or Monte-Carlo ray-tracing are becoming standard features of rendering systems. However, there is currently no accepted interface format which supports an appropriate physically-based scene description. In this paper we present extensions to the well-known RenderMan interface, which allow for a physically based scene description and support advanced global illumination techniques. Special emphasis has been laid on the support for procedural descriptions of reflection and emission by RenderMan surface shaders. So far, they could not be used with most global illumination algorithms. The extensions have been implemented in a physically-based rendering system and are illustrated with examples.
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    Fair Surface Reconstruction Using Quadratic Functionals
    (Blackwell Science Ltd and the Eurographics Association, 1995) Kolb, Andreas; Pottmann, Helmut; Seidel, Hans-Peter
    An algorithm for surface reconstruction from a polyhedron with arbitrary topology consisting of triangular faces is presented. The first variant of the algorithm constructs a curve network consisting of cubic Bezier curves meeting with tangent plane continuity at the vertices. This curve network is extended to a smooth surface by replacing each of the networks facets with a split patch consisting of three triangular Bezier patches. The remaining degrees of freedom of the curve network and the split patches are determined by minimizing a quadratic functional. This optimization process works either for the curve network and the split patches separately or in one simultaneous step. The second variant of our algorithm is based on the construction of an optimized curve network with higher continuity. Examples demonstrate the quality of the different methods.
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    Spherical Triangular B-splines with Application to Data Fitting
    (Blackwell Science Ltd and the Eurographics Association, 1995) Pfeifle, Ron; Seidel, Hans-Peter
    Triangular B-splines surfaces are a tool for representing arbitrary piecewise polynomial surfaces over planar triangulations, while automatically maintaining continuity properties across patch boundaries. Recently, Alfeld et al. [1] introduced the concept of spherical barycentric coordinates which allowed them to formulate Bernstein-Bezier polynomials over the sphere.In this paper we use the concept of spherical barycentric coordinates to develop a similar formulation for triangular B-splines, which we call spherical triangular B-splines. These splines defined over spherical triangulations share the same continuity properties and similar evaluation algorithms with their planar counterparts, but possess none of the annoying degeneracies found when trying to represent closed surfaces using planar parametric surfaces. We also present an example showing the use of these splines for approximating spherical scattered data.