Geometric modelling : Dagstuhl 2002 ; [this book contains selected papers that were presented at the 5th Dagstuhl seminar on Geometric Modelling in May 2002

In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications Front Matter....Pages i-viii An Algorithm for Parametric Quadric Patch Construction....Pages 1-12 Planar Development of Free-Form Surfaces: Quality Evaluation and Visual Inspection....Pages 13-27 Biorthogonal Loop-Subdivision Wavelets....Pages 29-39 Fairness Criteria for Algebraic Curves....Pages 41-51 Spline Curve Approximation and Design by Optimal Control Over the Knots....Pages 53-64 A Parametric Quartic Spline Interpolant to Position, Tangent and Curvature....Pages 65-78 Surface Compression Using a Space of C 1 Cubic Splines with a Hierarchical Basis....Pages 79-92 Evolutions of Polygons in the Study of Subdivision Surfaces....Pages 93-103 The Bézier Tangential Surface System: a Robust Dual Representation of Tangent Space....Pages 105-115 Bounding the Distance between 2D Parametric Bézier Curves and their Control Polygon....Pages 117-128 Wavelet-Based Multiresolution with $$ \sqrt[n]{2} $$ Subdivision....Pages 129-142 Quasi-Interpolants with Tension Properties from and in CAGD....Pages 143-160 Length Preserving Multiresolution Editing of Curves....Pages 161-170 The Convex Hull of Freeform Surfaces....Pages 171-183 Robust Spherical Parameterization of Triangular Meshes....Pages 185-193 Spine Based Shape Parameterisation for PDE Surfaces....Pages 195-206 Direct Segmentation of Algebraic Models for Reverse Engineering....Pages 207-220 Two Triangulation Methods Based on Edge Refinement....Pages 221-233 Efficient Collision Detection for Moving Ellipsoids Using Separating Planes....Pages 235-246 Back Matter....Pages 247-248 On the one hand, quadric surfaces, such as spheres, cylinders, cones as well as ellipsoids, paraboloids and hyperboloids, are very popular in applications such as mechanical engineering and architecture due to their appealing and practical shapes as well as their simple implicit and parametric representations.