The Mathematics of Surfaces IX

These proceedings collect the papers accepted for presentation at the bien nial IMA Conference on the Mathematics of Surfaces, held in the University of Cambridge, 4-7 September 2000. While there are many international con ferences in this fruitful borderland of mathematics, computer graphics and engineering, this is the oldest, the most frequent and the only one to concen trate on surfaces. Contributors to this volume come from twelve different countries in Eu rope, North America and Asia. Their contributions reflect the wide diversity of present-day applications which include modelling parts of the human body for medical purposes as well as the production of cars, aircraft and engineer ing components. Some applications involve design or construction of surfaces by interpolating or approximating data given at points or on curves. Others consider the problem of 'reverse engineering'-giving a mathematical descrip tion of an already constructed object. We are particularly grateful to Pamela Bye (at the Institue of Mathemat ics and its Applications) for help in making arrangements; Stephanie Harding and Karen Barker (at Springer Verlag, London) for publishing this volume and to Kwan-Yee Kenneth Wong (Cambridge) for his heroic help with com piling the proceedings and for dealing with numerous technicalities arising from large and numerous computer files. Following this Preface is a listing of the programme committee who with the help of their colleagues did much work in refereeing the papers for these proceedings.

Includes the latest research into the applications of the mathematics of surfaces International contributor base, from both academia and industry

Klappentext

This book contains the Proceedings of the Ninth Mathematics of Surfaces Conference organised by the Institute of Mathematics and its Applications, and held in Cambridge, UK, on 4th - 6th September 2000. The papers describe the mathematical construction, representation, approximation, recognition, and manipulation of surfaces, with an emphasis on computational methods. Highlights include invited papers from M. Floater (SNTEF, Norway), O. Faugeras (INRIA, France), P. Giblin (Liverpool University, UK), M.-S. Kim (Seoul National University, Korea), J. Koenderink (University of Utrecht, Netherlands), N. Patrikalakis (MIT, USA), H. Pottmann (Technical University of Vienna, Austria) and R. Schaback (University of Göttingen, Germany).

Inhalt
Meshless Parameterization and B-Spline Surface Approximation.- Computation of Local Differential Parameters on Irregular Meshes.- Remarks on Meshless Local Construction of Surfaces.- Gaussian and Mean Curvature of Subdivision Surfaces.- Best Fit Translational and Rotational Surfaces for Reverse Engineering Shapes.- Problem Reduction to Parameter Space.- Higher Order Singularities in Piecewise Linear Vector Fields.- Landmarks of a Surface.- Time-Optimal Paths Covering a Surface.- Surface Evolution and Representation using Geometric Algebra.- Interactive Design of Complex Mechanical Parts using a Parametric Representation.- Surfaces in the Mind's Eye.- Shape-from-Texture from Eigenvectors of Spectral Distortion.- Camera Calibration from Symmetry.- Dynamic Shapes of Arbitrary Dimension: The Vector Distance Functions.- LeastSquares Fitting of Algebraic Spline Curves via Normal Vector Estimation.- Use of Reverse Automatic Differentiation in Ship Hull Optimisation.- Symmetry Sets and Medial Axes in Two and Three Dimensions.- SymmetryA Research Direction in Curve and Surface Modelling; Some Results and Applications.- Functions and Methods to Analyze and Construct Developable Hull Surfaces.- Bipolar and Multipolar Coordinates.- Polar Curves and Surfaces.- Boundary Representation Models: Validity and Rectification.- Interval and Affine Arithmetic for Surface Location of Power and BernsteinForm Polynomials.- A Class of Bernstein Polynomials that Satisfy Descartes' Rule of Signs Exactly.- On Approximation in Spaces of Geometric Objects.- Representing the Time-Dependent Geometry of the Heart for Fluid Dynamical Analysis.- Application of Point-Based Smoothing to the Design of Flying Surfaces.- Modelling of Material Property Variation for Layered Manufacturing.