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.
Author(s): Lionel Alberti, Bernard Mourrain (auth.), Ralph Martin, Malcolm Sabin, Joab Winkler (eds.)
Series: Lecture Notes in Computer Science 4647
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2007
Language: English
Pages: 514
Tags: Computer Graphics; Discrete Mathematics in Computer Science; Image Processing and Computer Vision; Symbolic and Algebraic Manipulation; Geometry; Computational Science and Engineering
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 -
