Constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. This book contains topics such as the applicability of various aspects of mathematics to engineering and computer science, especially in domains such as computer aided design, and computer vision.

Regularity Criteria for the Topology of Algebraic Curves and Surfaces.- Quadrangle Surface Tiling Through Contouring.- Surfaces with Piecewise Linear Support Functions over Spherical Triangulations.- A Developable Surface of Uniformly Negative Internal Angle Deficit.- Rational Maximal Parametrisations of Dupin Cyclides.- Discrete Harmonic Functions from Local Coordinates.- Computing the Topology of an Arrangement of Quartics.- Non-uniform B-Spline Subdivision Using Refine and Smooth.- Scattered Data Fitting on Surfaces Using Projected Powell-Sabin Splines.- Implicit Boundary Control of Vector Field Based Shape Deformations.- Tuning Subdivision Algorithms Using Constrained Energy Optimization.- Description of Surfaces in Parallel Coordinates by Linked Planar Regions.- Discrete Surface Ricci Flow: Theory and Applications.- Guided C 2 Spline Surfaces with V-Shaped Tessellation.- MOS Surfaces: Medial Surface Transforms with Rational Domain Boundaries.- Mean Value Bézier Surfaces.- Curvature Estimation over Smooth Polygonal Meshes Using the Half Tube Formula.- Segmenting Periodic Reliefs on Triangle Meshes.- Estimation of End Curvatures from Planar Point Data.- Inversion, Degree and Reparametrization for Rational Surfaces.- Discrete Surfaces in Isotropic Geometry.- An Appropriate Geometric Invariant for the C 2-Analysis of Subdivision Surfaces.- Curvature-Based Surface Regeneration.- Bounded Curvature Subdivision Without Eigenanalysis.- Facial Shape-from-Shading Using Principal Geodesic Analysis and Robust Statistics.- Statistical Methods for Surface Integration.- Skeleton Surface Generation from Volumetric Models of Thin Plate Structures for Industrial Applications.- Parallel Tangency in .- Condition Numbers and Least Squares Regression.- Propagation of GeometricTolerance Zones in 3D.

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