Curve and Surface Design

Pierre-Jean Laurent, Paul Sablonnieère, and Larry L. Schumaker

Vanderbilt University Press, Nashville, 2000

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . ix Factorizations of Normalized Totally Positive Systems

J. M. Carnicer and E. Mainar . . . . . . . . . . . . . . . . . . 1 Intersections et Convergence

Paul de Faget de Casteljau . . . . . . . . . . . . . . . . . . . . 9 Implicitization Matrices in the Style of Sylvester with the Order of Bézout

Eng-Wee Chionh, Ming Zhang, and Ronald Goldman . . . . . . 17 Better Pasting via Quasi-Interpolation

Blair Conrad and Stephen Mann . . . . . . . . . . . . . . . . 27 Conjugate Silhouette Nets

W. L. F. Degen . . . . . . . . . . . . . . . . . . . . . . . . 37 From PS–splines to NURPS

Paul Dierckx and Joris Windmolders . . . . . . . . . . . . . . 45 Distance Calculation between a Point and a NURBS Surface

Eva Dyllong and Wolfram Luther . . . . . . . . . . . . . . . . 55 Curves from Motion, Motion from Curves

Rida T. Farouki . . . . . . . . . . . . . . . . . . . . . . . 63 Curvature and Tangency Handles for Control of Convex Cubic Shapes

G. Figueroa, M. Paluszny, and F. Tovar . . . . . . . . . . . . . 91 Monotonicity Conditions of Curvature for Bézier-de Casteljau Curves

Jean-Charles Fiorot and Laurent Schiavon . . . . . . . . . . . . 99 From Local Approximation to a G^{1} Global Representation

Cédric Gérot, Dominique Attali, and Annick Montanvert . . . . . . 109 A Class of Totally Positive Blending B-Bases

Laura Gori, Laura Pezza, and Francesca Pitolli . . . . . . . . . . 119 Rational Ruled Surfaces Passing through Two Fixed Lines

Gueorgui H. Gueorguiev . . . . . . . . . . . . . . . . . . . . 127 Deformation Criteria for the Direct Manipulation of Free Form Surfaces

Stéphane Guillet and Jean-Claude Léon . . . . . . . . . . . . . 135 Generation of Surfaces with Smooth Highlight Lines

Masatake Higashi, Hiroto Harada, and Mitsuru Kuroda . . . . . . 145

MIPS: An Efficient Global Parametrization Method Kai Hormann and Günther Greiner . . . . . . . . . . . . . . . 153

Comparison of Different Multisided Patches Using Algebraic Geometry

Kȩstutis Karčiauskas and Rimvydas Krasauskas . . . . . . . . . 163

N-sided Surface Generation from Arbitrary Boundary Edges Kiyotaka Kato . . . . . . . . . . . . . . . . . . . . . . . . 173

Advantages of Topological Tools in Localization Methods Mohammed Khachan and Patrick Chenin . . . . . . . . . . . . 183

Fast Voronoi Diagrams and Offsets on Triangulated Surfaces Ron Kimmel and James A. Sethian . . . . . . . . . . . . . . . 193

On the Geometry of Texture Ron Kimmel, Nir A. Sochen, and Ravi Malladi . . . . . . . . . . 203

Optimization of a Curve Approximation Based on NURBS Interpolation Jérôme Lépine, François Guibault, Marie-Gabrielle Vallet

and Jean-Yves Trépanier . . . . . . . . . . . . . . . . . . 213

Filling N-sided Holes Using Combined Subdivision Schemes Adi Levin . . . . . . . . . . . . . . . . . . . . . . . . . . 221

Dealing with Topological Singularities in Volumetric Reconstruction H. Lopes, L. G. Nonato, S. Pesco, and G. Tavares . . . . . . . . . 229

Linear Envelopes for Uniform B–spline Curves David Lutterkort and Jörg Peters . . . . . . . . . . . . . . . . 239

N-sided Surfaces: a Survey Pierre Malraison . . . . . . . . . . . . . . . . . . . . . . . 247

Approximated Planes in Parallel Coordinates Tanya Matskewich, Alfred Inselberg and Michel Bercovier . . . . . 257

Applications of Sphere Geometry in Canal Surface Design Christoph Mäurer . . . . . . . . . . . . . . . . . . . . . . . 267

Geometric Computing with CGAL and LEDA Kurt Mehlhorn and Stefan Schirra . . . . . . . . . . . . . . . 277

A Geometric Approach for Knot Selection in Convexity-Preserving Spline Approximation

R. Morandi, D. Scaramelli, and A. Sestini . . . . . . . . . . . 287

Convergence of Approximations for Arrangements of Curves Manuela Neagu and Bernard Lacolle . . . . . . . . . . . . . . 297 The (2-5-2) Spline Function

Jae H. Park and Leonard A. Ferrari . . . . . . . . . . . . . . . 307

Error Analysis of Algorithms for Evaluating Bernstein-Bézier-Type Multivariate Polynomials

J. M. Peña . . . . . . . . . . . . . . . . . . . . . . . . . 315

A Basis for Homogeneous Polynomial Solutions to Homogeneous Constant Coefficient PDE’s: An Algorithmic Approach Through Apolarity

Michel Pocchiola and Gert Vegter . . . . . . . . . . . . . . . 325

Triangular G^{2}-Splines Hartmut Prautzsch and Georg Umlauf . . . . . . . . . . . . . . 335

On Calculating with Lower Order Chebyshev Splines Mladen Rogina and Tina Bosner . . . . . . . . . . . . . . . . 343

A Declarative Modeler for B-Spline Curves Vincent Rossignol and Marc Daniel . . . . . . . . . . . . . . . 353

Diffuse Curvature Computation for Surface Recognition J. M. Savignat, O. Stab, A. Rassineux, and P. Villon . . . . . . . 363

Discrete Fairing of Curves and Surfaces Based on Linear Curvature Distribution

R. Schneider and L. Kobbelt . . . . . . . . . . . . . . . . . 371

Triangulating Trimmed NURBS Surfaces Chang Shu and Pierre Boulanger . . . . . . . . . . . . . . . . 381

Surface Interpolation of Non-four-sided and Concave Area by NURBS Boundary Gregory Patches

Junji Sone, Kouichi Konno, and Hiroaki Chiyokura . . . . . . . 389

Central Conics on Parabolic Dupin Cyclides Kenji Ueda . . . . . . . . . . . . . . . . . . . . . . . . . . 399

Adaptive Parameterization and Approximation for CAD Data Reduction G. Wahu, J. M. Brun, and A. Bouras . . . . . . . . . . . . . . 407

On the Geometry of Sculptured Surface Machining Johannes Wallner and Helmut Pottmann . . . . . . . . . . . . . 417

Extensions: Extrapolation Methods for CAD Hans J. Wolters . . . . . . . . . . . . . . . . . . . . . . . . 433