Mathematics of Surfaces

This book constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.

Inhalt

Skeleton-Based Seam Computation for Triangulated Surface Parameterization.- Parameterizing N-Holed Tori.- Generic Parameterization of Bifurcating Structures.- Direct Computation of a Control Vertex Position on any Subdivision Level.- Optimising Triangulated Polyhedral Surfaces with Self-intersections.- Combinatorial Properties of Subdivision Meshes.- Watermarking 3D Polygonal Meshes Using the Singular Spectrum Analysis.- Compression of Arbitrary Mesh Data Using Subdivision Surfaces.- Triangle Mesh Duality: Reconstruction and Smoothing.- Hand Tracking Using a Quadric Surface Model and Bayesian Filtering.- Vector Transport for Shape-from-Shading.- A Graph-Spectral Method for Surface Height Recovery.- A Robust Reconstruction Algorithm of Displaced Butterfly Subdivision Surfaces from Unorganized Points.- Filling Holes in Point Clouds.- Trimming Local and Global Self-intersections in Offset Curves Using Distance Maps.- Using Line Congruences for Parameterizing Special Algebraic Surfaces.- Boundary Conditions for the 3-Direction Box-Spline.- The Plateau-Bézier Problem.- A Functional Equation Approach to the Computation of the Parameter Symmetries of Spline Paths.- Efficient One-Sided Linearization of Spline Geometry.- Procedural Modelling, Generative Geometry, and the International Standard ISO 10303 (STEP).- Variable-Free Representation of Manifolds via Transfinite Blending with a Functional Language.- Modified Affine Arithmetic Is More Accurate than Centered Interval Arithmetic or Affine Arithmetic.- On the Spine of a PDE Surface.- Application of PDE Methods to Visualization of Heart Data.