The Mathematics of Surfaces IX: Proceedings of the Ninth Ima Conference on the Mathematics of Surfaces

ISBN-13: 9781447111535 / Angielski / Miękka / 2012 / 500 str.

Roberto Cipolla; Ralph Martin

Opis

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.

Spis treści

Meshless Paramterization 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 Fir 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.- Least-Squares Fitting of Algenbraic 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.- Symmetry - A 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 Bernstein-Form 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.