Mathematical Methods for Curves and Surfaces: Oslo 2000

Tom Lyche and Larry Schumaker, eds.

Vanderbilt University Press, Nashville, 2001

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix

Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . x

Best-Fit of Implicit Surfaces and Plane Curves Sung Joon Ahn, Wolfgang Rauh, and Hans-Jürgen Warnecke . . . . . 1

Determination of Geometrical Invariants of Rationally Parametrized Conic Sections

Gudrun Albrecht . . . . . . . . . . . . . . . . . . . . . . 15

A Scattered Data Approximation Scheme for the Detection of Fault Lines G. Allasia, R. Besenghi and A. De Rossi . . . . . . . . . . . . . 25

Beta-Continuity Revisited: Determining Bézier Control Vertices to Construct Geometrically Continuous Curves and Surfaces

Brian A. Barsky and Ronald N. Goldman . . . . . . . . . . . . 35

Simplification of Closed Triangulated Surfaces Using Simulated Annealing Peer-Timo Bremer, Bernd Hamann, Oliver Kreylos

and Franz-Erich Wolter . . . . . . . . . . . . . . . . . . . 45

Planar Configurations with Simple Lagrange Interpolation Formulae J. M. Carnicer and M. Gasca . . . . . . . . . . . . . . . . . . 55

Approximating Semi-Structured Data with Different Errors Using Support Vector Machine Regression

A. Crampton, J. C. Mason, and D. A. Turner . . . . . . . . . . 63

Subdivision Surfaces in Feature Films Tony D. DeRose . . . . . . . . . . . . . . . . . . . . . . . 73

A 4-Point Hermite Subdivision Scheme Serge Dubuc and Jean-Louis Merrien . . . . . . . . . . . . . . 81

Optimizing 3D Triangulations Using Discrete Curvature Analysis Nira Dyn, Kai Hormann, Sun-Jeong Kim, and David Levin . . . . . 91

Refinable Spline Functions and Hermite Interpolation Tim N. T. Goodman . . . . . . . . . . . . . . . . . . . . . 103

Approximating Digital Shapes by Parametric Surfaces A. Ardeshir Goshtasby . . . . . . . . . . . . . . . . . . . . 119

Clifford Algebra and Flows Hans Hagen and Gerik Scheuermann . . . . . . . . . . . . . . 129 Error Estimates for the web-Spline Method

Klaus Höllig, Ulrich Reif, and Joachim Wipper . . . . . . . . . . 139

Hierarchical Scattered Data Filtering for Multilevel Interpolation Schemes

Armin Iske . . . . . . . . . . . . . . . . . . . . . . . . . 155

Bounding the Hausdorff Distance of Implicitly Defined and/or Parametric Curves

Bert Jüttler . . . . . . . . . . . . . . . . . . . . . . . . . 165

Biangle Surface Patches Kȩstutis Karčiauskas . . . . . . . . . . . . . . . . . . . . . 175

Single-Valued Tubular Surface Intersection Using Interval Arithmetic Hélio Lopes and Sinésio Pesco . . . . . . . . . . . . . . . . . 185

Surface Animation for Flower Growth Zhaoying Lu, Claire Willis, and Derek Paddon . . . . . . . . . . 195

Knot Insertion Algorithms and Local Linear Independence Esmeralda Mainar and Juan Manuel Peña . . . . . . . . . . . . 205

Local Tension Methods for Bivariate Scattered Data Interpolation Carla Manni . . . . . . . . . . . . . . . . . . . . . . . . . 215

Data Reduction in Surface Approximation Rossana Morandi and Alessandra Sestini . . . . . . . . . . . . . 237

The Analytic Blossom Géraldine Morin and Ron Goldman . . . . . . . . . . . . . . . 247

Bézier Curves: Topological Convergence of the Control Polygon Manuela Neagu, Emmanuelle Calcoen, and Bernard Lacolle …. 269

Local Lagrange Interpolation by Bivariate C^{1} Cubic Splines Günther Nürnberger, Larry L. Schumaker, and Frank Zeilfelder … 277

Stability of Collocation by Smooth Splines for Volterra Integral Equations

Peeter Oja . . . . . . . . . . . . . . . . . . . . . . . . . 289

G^{1}-Hermite Interpolation of Ruled Surfaces Martin Peternell . . . . . . . . . . . . . . . . . . . . . . . 297

Recovering Structural Information from Triangulated Surfaces Ch. Rössl, L. Kobbelt, and H.-P. Seidel . . . . . . . . . . . . . 307

Improved Bi-Laplacian Mesh Fairing Robert Schneider, Leif Kobbelt and Hans-Peter Seidel . . . . . . . 317

Approximate Envelope Reconstruction for Moving Solids U. Schwanecke and L. Kobbelt . . . . . . . . . . . . . . . . . 327 Towards the μ-Basis of a Rational Surface

Thomas W. Sederberg and Jianmin Zheng . . . . . . . . . . . . 337

A Strategy for the Construction of Piecewise Linear Prewavelets over Type-1 Triangulations in any Space Dimension

Erich Suter . . . . . . . . . . . . . . . . . . . . . . . . . 347

A Mixed Representation Approach to Offsets of Rational Curves Salim Taleb . . . . . . . . . . . . . . . . . . . . . . . . . 357

Pedal Curves and Surfaces Kenji Ueda . . . . . . . . . . . . . . . . . . . . . . . . . . 367

Generalizing the C^{4} Four-directional Box Spline to Surfaces of Arbitrary Topology

Luiz Velho . . . . . . . . . . . . . . . . . . . . . . . . . 377

Moving Least Squares Approximation on the Sphere Holger Wendland . . . . . . . . . . . . . . . . . . . . . . . 387

NURPS for Special Effects and Quadrics Joris Windmolders and Paul Dierckx . . . . . . . . . . . . . . 397

Computational Experiments with Resultants Joab R. Winkler . . . . . . . . . . . . . . . . . . . . . . . 405