Mathematics of Surfaces XII: 12th IMA International Conference, Sheffield, UK, September 4-6, 2007, Proceedings (Lecture Notes in Computer Science, 4647)

This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The 22 revised full papers presented together with 8 invited papers were carefully reviewed and selected from numerous submissions. Among the topics addressed is the applicability of various aspects of mathematics to engineering and computer science, especially in domains such as computer aided design, computer vision, and computer graphics. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces. Research is reported on theoretical aspects of surfaces including topology, parameterization, differential geometry, and conformal geometry, and also more practical topics such as geometric tolerances, computing shape from shading, and medial axes for industrial applications. Other specific areas of interest include subdivision schemes, solutions of differential equations on surfaces, knot insertion, surface segmentation, surface deformation, and surface fitting. Front Matter....Pages - Regularity Criteria for the Topology of Algebraic Curves and Surfaces....Pages 1-28 Quadrangle Surface Tiling Through Contouring....Pages 29-41 Surfaces with Piecewise Linear Support Functions over Spherical Triangulations....Pages 42-63 A Developable Surface of Uniformly Negative Internal Angle Deficit....Pages 64-77 Rational Maximal Parametrisations of Dupin Cyclides....Pages 78-92 Discrete Harmonic Functions from Local Coordinates....Pages 93-103 Computing the Topology of an Arrangement of Quartics....Pages 104-120 Non-uniform B-Spline Subdivision Using Refine and Smooth....Pages 121-137 Scattered Data Fitting on Surfaces Using Projected Powell-Sabin Splines....Pages 138-153 Implicit Boundary Control of Vector Field Based Shape Deformations....Pages 154-165 Tuning Subdivision Algorithms Using Constrained Energy Optimization....Pages 166-176 Description of Surfaces in Parallel Coordinates by Linked Planar Regions....Pages 177-208 Discrete Surface Ricci Flow: Theory and Applications....Pages 209-232 Guided C 2 Spline Surfaces with V-Shaped Tessellation....Pages 233-244 MOS Surfaces: Medial Surface Transforms with Rational Domain Boundaries....Pages 245-262 Mean Value Bézier Surfaces....Pages 263-274 Curvature Estimation over Smooth Polygonal Meshes Using the Half Tube Formula....Pages 275-289 Segmenting Periodic Reliefs on Triangle Meshes....Pages 290-306 Estimation of End Curvatures from Planar Point Data....Pages 307-319 Inversion, Degree and Reparametrization for Rational Surfaces....Pages 320-340 Discrete Surfaces in Isotropic Geometry....Pages 341-363 An Appropriate Geometric Invariant for the C 2 -Analysis of Subdivision Surfaces....Pages 364-377 Curvature-Based Surface Regeneration....Pages 378-390 Bounded Curvature Subdivision Without Eigenanalysis....Pages 391-411 Facial Shape-from-Shading Using Principal Geodesic Analysis and Robust Statistics....Pages 412-426 Statistical Methods for Surface Integration....Pages 427-441 Skeleton Surface Generation from Volumetric Models of Thin Plate Structures for Industrial Applications....Pages 442-464 Parallel Tangency in ${\mathbb R^3}$ ....Pages 465-479 Condition Numbers and Least Squares Regression....Pages 480-493 Propagation of Geometric Tolerance Zones in 3D....Pages 494-507 Back Matter....Pages - This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces. Research is reported on theoretical aspects of surfaces as well as more practical topics. Ralph Martin, Malcolm Sabin, Joab Winkler (eds.). Includes Bibliographical References And Index.