Mathematical Methods in Computer Aided Geometric Design
Published on 10. May 2014
628 pages
978-1-4832-5780-8 (ISBN)
Description
Mathematical Methods in Computer Aided Geometric Design covers the proceedings of the 1988 International Conference by the same title, held at the University of Oslo, Norway. This text contains papers based on the survey lectures, along with 33 full-length research papers. This book is composed of 39 chapters and begins with surveys of scattered data interpolation, spline elastic manifolds, geometry processing, the properties of Bézier curves, and Gröbner basis methods for multivariate splines. The next chapters deal with the principles of box splines, smooth piecewise quadric surfaces, some applications of hierarchical segmentations of algebraic curves, nonlinear parameters of splines, and algebraic aspects of geometric continuity. These topics are followed by discussions of shape preserving representations, box-spline surfaces, subdivision algorithm parallelization, interpolation systems, and the finite element method. Other chapters explore the concept and applications of uniform bivariate hermite interpolation, an algorithm for smooth interpolation, and the three B-spline constructions. The concluding chapters consider the three B-spline constructions, design tools for shaping spline models, approximation of surfaces constrained by a differential equation, and a general subdivision theorem for Bézier triangles. This book will prove useful to mathematicians and advance mathematics students.
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Tom Lyche | Larry L. Schumaker
Mathematical Methods in Computer Aided Geometric Design: v. 1
Book
01/1989
Academic Press
€66.85
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Content
PrefaceParticipantsScattered Data Interpolation in Three or More VariablesSome Applications of Discrete Dm SplinesSpline Elastic ManifoldsGeometry Processing: Curvature Analysis and Surface-Surface IntersectionThree Examples of Dual Properties of Bézier CurvesWhat is the Natural Generalization of a Bézier Curve?Convexity and a Multidimensional Version of the Variation Diminishing Property of Bernstein PolynomialsGröbner Basis Methods for Multivariate SplinesOn Finite Element Interpolation ProblemsThe Design of Curves and Surfaces by Subdivision AlgorithmsA Data Dependent Parametrization for Spline ApproximationOn the Evaluation of Box SplinesSmooth Piecewise Quadric SurfacesInserting New Knots Into Beta-Spline CurvesRecursive Subdivision and Iteration in Intersections and Related ProblemsRational Curves and SurfacesHierarchical Segmentations of Algebraic Curves and Some ApplicationsAn Algorithm for Shape Preserving Parametric Interpolating Curves with G2 ContinuityKnot Selection for Parametric Spline InterpolationSplines and Estimation of Nonlinear ParametersOn Beta-Continuous Functions and Their Application to the Construction of Geometrically Continuous Curves and SurfacesAlgebraic Aspects of Geometric ContinuityShape Preserving RepresentationsGeometric ContinuityCurvature Continuous Triangular InterpolantsBox-Spline SurfacesParallelization of the Subdivision Algorithm for Intersection of Bézier Curves on the FPS T20Composite Quadrilateral Finite Elements of Class CrA Knot Removal Strategy for Scattered Data in R2Interpolation Systems and the Finite Element MethodUniform Bivariate Hermite InterpolationA Survey of Applications of an Affine Invariant NormAn Algorithm for Smooth Interpolation to Scattered Data in R2Some Remarks on Three B-Spline ConstructionsModified B-Spline Approximation for Quasi-Interpolation or FilteringDesign Tools for Shaping Spline ModelsA Process Oriented Design Method for Three-Dimensional CAD SystemsOpen Questions in the Application of Multivariate B-SplinesOn Global GC2 Convexity Preserving Interpolation of Planar Curves by Piecewise Bézier PolynomialsBest Interpolation with Free Nodes by Closed CurvesSegmentation Operators on Coons' PatchesA General Subdivision Theorem for Bézier TrianglesCardinal Interpolation with Translates of Shifted Bivariate Box-SplinesApproximation of Surfaces Constrained by a Differential Equation Using Simplex SplinesA Construction for VC1 Continuity of Rational Bézier Patches
