Curves and Surfaces with Applications in CAGD

A. Le Méhauté, C. Rabut, and L. L. Schumaker (eds.)

Vanderbilt University Press, 1997, 481 pp.

ISBN 0-8265-1293-3

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . x Parallelization Strategies for the B-Spline Curve Interpolation Problem

M. D’Apuzzo and L. Maddalena . . . . . . . . . . . . . . . . . 1 Connection-Matrix Splines by Divided Differences

R. H. Bartels and J. C. Beatty . . . . . . . . . . . . . . . . . . 9 Massic-Vector-Based Conics Modelling

J. P. Bécar and J. C. Fiorot . . . . . . . . . . . . . . . . . . 17 Globally G^{1} Free Form Surfaces Using Kirchhoff-Love Plate Energy Methods

M. Bercovier, O. Volpin and T. Matskewich . . . . . . . . . . . 25 A New Approach to Tchebycheffian B-Splines

D. Bister and H. Prautzsch . . . . . . . . . . . . . . . . . . . 35 Flaw Removal on Surfaces

J. Bousquet and M. Daniel . . . . . . . . . . . . . . . . . . . 43 On Some Polynomial Curves Derived from Trigonometric Kernels

J. Cao, H. H. Gonska and D. P. Kacsó . . . . . . . . . . . . . . 53 Spline Curves in Polar and Cartesian Coordinates

G. Casciola and S. Morigi . . . . . . . . . . . . . . . . . . . 61 La Tolérance d’usinage chez Citroën dans les années (19)60

P. de Faget de Casteljau . . . . . . . . . . . . . . . . . . . . 69 Avoiding Local Minima for Deformable Curves in Image Analysis

L. D. Cohen . . . . . . . . . . . . . . . . . . . . . . . . . 77 Variable Degree Polynomial Splines

P. Costantini . . . . . . . . . . . . . . . . . . . . . . . . . 85 Approximation of Monotone Functions: A Counter Example

R. A. DeVore, D. Leviatan and I. A. Shevchuk . . . . . . . . . . 95 Uniform Point Distribution on a Circle

J-C. Fiorot and I. Cattiaux-Huillard . . . . . . . . . . . . . . . 103 BR-form of an Entire Rational Curve with a Preassigned Point

J-C. Fiorot and P. Jeannin . . . . . . . . . . . . . . . . . . . 111

Optimal Convexity Preserving Bases M. García-Esnaola and J. M. Peña . . . . . . . . . . . . . . . 119

Rational Interpolation on the Unit Circle Th. Gensane . . . . . . . . . . . . . . . . . . . . . . . . . 127

Designing Nonlinear Models for Flexible Curves S. Girard, B. Chalmond and J. M. Dinten . . . . . . . . . . . . 135

SK–spline Interpolation on the Torus using Number Theoretic Knots S. Gomes, A. K. Kushpel, J. Levelsey and D. L. Ragozin . . . . . . 143

Shape Preserving Interpolation by G^{2} Curves in Three Dimensions T. N. T. Goodman and B. H. Ong . . . . . . . . . . . . . . . 151

Fairing Bicubic B-Spline Surfaces using Simulated Annealing S. Hahmann and S. Konz . . . . . . . . . . . . . . . . . . . 159

Positivity and Convexity Criteria for Bernstein-Bézier Polynomials Over Simplices

T. X. He . . . . . . . . . . . . . . . . . . . . . . . . . . 169

Fitting Uncertain Data with NURBS W. Heidrich, R. Bartels and G. Labahn . . . . . . . . . . . . . 177

Interpolation and Approximation with Developable Surfaces J. Hoschek and M. Schneider . . . . . . . . . . . . . . . . . . 185

Sectional Curvature–Preserving Interpolation of Contour Lines B. Jüttler . . . . . . . . . . . . . . . . . . . . . . . . . . 203

Analysis of Curvature Related Surface Shape Properties J. Kaasa and G. Westgaard . . . . . . . . . . . . . . . . . . 211

On an Almost–convex–hull Property D. Kacsó and H.–J. Wenz . . . . . . . . . . . . . . . . . . . 217

Developable Surfaces with Creases Y. L. Kergosien . . . . . . . . . . . . . . . . . . . . . . . . 223

Universal Parameterizations of Some Rational Surfaces R. Krasauskas . . . . . . . . . . . . . . . . . . . . . . . . 231

Curves on Surfaces for Computer Graphics: Theoretical Results Y. Kuzmin and M. Daniel . . . . . . . . . . . . . . . . . . . 239

Generalized Tension B-splines B. I. Kvasov and P. Sattayatham . . . . . . . . . . . . . . . . 247

Shape Effects with Polynomial Chebyshev Splines P. J. Laurent, M. L. Mazure and G. Morin . . . . . . . . . . . . 255 Interpolation with Triangulations and Curvature Minimization

M. Léger . . . . . . . . . . . . . . . . . . . . . . . . . . . 263

On Convexity and Subharmonicity of some Functions on Triangles J. Lorente-Pardo, P. Sablonnière and M. C. Serrano-Pérez . . . . . 271

Marching Methods in Surface-Surface Intersection E. Malgras . . . . . . . . . . . . . . . . . . . . . . . . . . 279

Algorithms from Blossoms S. Mann . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Generalized Parameter Representations of Tori, Dupin Cyclides and Supercyclides

C. Mäurer . . . . . . . . . . . . . . . . . . . . . . . . . 295

Korovkin Type Results for Shape Preserving Operators F.-J. Muñoz-Delgado and D. Cárdenas-Morales . . . . . . . . . . 303

Stable Progressive Smoothing A. Nigro . . . . . . . . . . . . . . . . . . . . . . . . . . . 311

Riemannian Quadratics L. Noakes . . . . . . . . . . . . . . . . . . . . . . . . . . 319

Approximation of Offset Curves and Surfaces by Discrete Smoothing D^{m}-splines

M. Pasadas, J. J. Torrens and M. C. López de Silanes . . . . . . 329

Algorithm for Computing the Product of two B-splines L. Piegl and W. Tiller . . . . . . . . . . . . . . . . . . . . . 337

Smoothing Spatial Cubic B-splines under Shape Constraints K. G. Pigounakis and P. D. Kaklis . . . . . . . . . . . . . . . 345

Some Error Estimates for Periodic Interpolation on Full and Sparse Grids

G. Pöplau and F. Sprengel . . . . . . . . . . . . . . . . . . 355

Curved Surfaces Reconstruction Based on Parallels W. Puech, J.-M. Chassery and I. Pitas . . . . . . . . . . . . . . 363

Zonal Kernels, Approximations and Positive Definiteness on Spheres and Compact Homogeneous Spaces

D. L. Ragozin and J. Levesley . . . . . . . . . . . . . . . . . 371

Interpolation by Pieces of Euler’s Elastica K.-D. Reinsch . . . . . . . . . . . . . . . . . . . . . . . . 379

A Knot Insertion Algorithm for Weighted Cubic Splines Mladen Rogina . . . . . . . . . . . . . . . . . . . . . . . . 387

Rational Speed Pseudo-Quadratic B-Splines M. A. Sabin . . . . . . . . . . . . . . . . . . . . . . . . . 395 A Parameterization Technique for the Control Point Form Method

A. Sestini and R. Morandi . . . . . . . . . . . . . . . . . . . 403

Planar Shape Enhancement and Exaggeration A. Steiner, R. Kimmel and A. M. Bruckstein . . . . . . . . . . . 411

On Geometric Continuity of Isophotes H. Theisel . . . . . . . . . . . . . . . . . . . . . . . . . . 419

A Sequence of Bézier Curves Generated by Successive Pedal-Point Constructions

K. Ueda . . . . . . . . . . . . . . . . . . . . . . . . . . 427

From Degenerate Patches to Triangular and Trimmed Patches M. Vigo, N. Pla and P. Brunet . . . . . . . . . . . . . . . . . 435

Spline Orbifolds J. Wallner and H. Pottmann . . . . . . . . . . . . . . . . . . 445

Numerically Stable Conversion Between The Bézier and B-Spline Forms of a Curve

J. R. Winkler . . . . . . . . . . . . . . . . . . . . . . . . 465

G^{2} Continuous G-Splines: An Interpolation Property R. Zeifang . . . . . . . . . . . . . . . . . . . . . . . . . . 473