Mathematical Methods in Computer Aided Geometric Design II

✍ Scribed by Tom Lyche, Larry L. Schumaker

• Publisher: Elsevier Inc, Academic Press
• Year: 1992
• Tongue: English
• Leaves: 633
• Series: v. 2
• Category: Library

✦ Synopsis

This volume is based on an international conference held in June 1991, and contains tutorial and original research-level papers on mathematical methods in CAGD and image processing. Leading researchers (Barnsley, Chui, Seidell, de Casteljau) have authored invited survey papers on spline and Bezier methods for curve and surface modeling, visualization, and data fitting as well as connections with wavelets and fractals, and their applications in image processing. This is a very successful area with the dual computer graphics/applied mathematics market

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
PREFACE, Page viii
PARTICIPANTS, Pages ix-xvii
Symmetrizing Multiaffine Polynomials, Pages 1-7, Phillip J. Barry
Norm Estimates for Inverses of Distance Matrices, Pages 9-18, B.J.C. Baxter
Numerical Treatment of Surface–Surface Intersection and Contouring, Pages 19-28, Karl–Heinz Brakhage
Modeling Closed Surfaces: A Comparison of Existing Methods, Pages 29-42, P. Brunet, A. Vinacua
A New Characterization of Plane Elastica, Pages 43-56, Guido Brunnett
POLynomials, POLar Forms, and InterPOLation, Pages 57-68, Paul de Faget de Casteljau
Pyramid Patches Provide Potential Polynomial Paradigms, Pages 69-100, A.S. Cavaretta, C.A. Micchelli
Implicitizing Rational Surfaces with Base Points by Applying Perturbations and the Factors of Zero Theorem, Pages 101-110, Eng-Wee Chionh, Ronald N. Goldman
Wavelets and Multiscale Interpolation, Pages 111-133, Charles K. Chui, Xianliang Shi
Decomposition of Splines, Pages 135-160, M. Dæhlen, T. Lyche
A Curve Intersection Algorithm with Processing of Singular Cases: Introduction of a Clipping Technique, Pages 161-170, Marc Daniel
Best Approximations of Parametric Curves by Splines, Pages 171-184, W.L.F. Degen
An Approximately G1 Cubic Surface Interpolant, Pages 185-196, Tony DeRose, Stephen Mann
On the G2 Continuity of Piecewise Parametric Surfaces, Pages 197-207, Wenhui Du, Francis J.M. Schmitt
Stationary and Non-Stationary Binary Subdivision Schemes, Pages 209-216, Nira Dyn, David Levin
MQ–Curves are Curves in Tension, Pages 217-228, Matthias Eck
Offset Approximation Improvement by Control Point Perturbation, Pages 229-237, G. Elber, E. Cohen
Curves and Surfaces in Geometrical Optics, Pages 239-260, Rida T. Farouki, Jean–Claude A. Chastang
Evaluation and Properties of the Derivative of a NURBS Curve, Pages 261-274, Michael S. Floater
Hybrid Cubic Bézier Triangle Patches, Pages 275-286, Thomas A. Foley, Karsten Opitz
Modelling Geological Structures Using Splines, Pages 287-296, Lars A. Frøyland, Jan Pajchel, Arne Lakså
Wonderful Triangle: A Simple, Unified, Algorithmic Approach to Change of Basis Procedures in Computer Aided Geometric Design, Pages 297-320, Ronald N. Goldman, Phillip J. Barry
An Arbitrary Mesh Network Scheme Using Rational Splines, Pages 321-329, John A. Gregory, P.K. Yuen
Bézier Curves and Surface Patches on Quadrics, Pages 331-342, Josef Hoschek
Monotonicity Preserving Interpolation Using C2 Rational Cubic Bézier Curves, Pages 343-350, M.K. Ismail
Minimization of Interpolating Spline Curves with Bounded Derivatives, Pages 351-358,CP1-CP4, Per Erik Koch
On Piecewise Quadratic G2 Approximation and Interpolation, Pages 359-366, J. Kozak, M. Lokar
Non-affine Blossoms and Subdivision for Q-Splines, Pages 367-380, Rekha Kulkarni, Pierre-Jean Laurent, Marie-Laurence Mazure
On a Class of Data Parametrizations: Variations on a Theme of Epstein, II, Pages 381-390, E.T.Y. Lee
Wavelets and Image Compression, Pages 391-400, Bradley J. Lucier
Lower Bounds on the Dimension of Bivariate Spline Spaces and Generic Triangulations, Pages 401-412, Carla Manni
Geometric Contact of Order p Between Two Surfaces, Pages 413-418, Marie-Laurence Mazure
On Non-Parametric Constrained Interpolation, Pages 419-430, B.H. Ong, K. Unsworth
Tensor Product Slices, Pages 431-440, R. Pfeifle, R. Bartels, R. Goldman
Construction of Smooth Surfaces by Piecewise Tensor Product Polynomials, Pages 441-455, A.R.M. Piah
The Virtues of Cyclides in CAGD, Pages 457-473, Mike Pratt
Simple Surfaces Have No Simple C1 Parametrization, Pages 475-480, Hartmut Prautzsch, Wilfried Trump
Some Tools for Quasi-Interpolation on Cardinal Grids, Pages 481-496, Christophe Rabut
Discrete Bézier Curves and Surfaces, Pages 497-515, Paul Sablonnière
Rational Geometric Curve Interpolation, Pages 517-535, R. Schaback
Curvature Properties of Parametric Triangular Bézier Patches, Pages 537-548, G. Schmeltz
Offsets of Polynomial Bézier Curves: Hermite Approximation with Error Bounds, Pages 549-558, Thomas W. Sederberg, David B. Buehler
Representing Piecewise Polynomials as Linear Combinations of Multivariate B-Splines, Pages 559-566, H.-P. Seidel
An Explicit Derivation of Discretely Shaped Beta-spline Basis Functions of Arbitrary Order, Pages 567-584, Gadiel Seroussi, Brian A. Barsky
Discrete Convolution Schemes, Pages 585-596, Yohanes Stefanus, Ronald Goldman
A Method for Removing the Singularities from Gregory Surfaces, Pages 597-606, Kenji Ueda
Bivariate Spline Approximation by Penalized Least Squares, Pages 607-614, N. Weyrich
Interpolation with g-splines, Pages 615-626, Rainer Zeifang