Mathematical Methods for Curves and Surfaces: Oslo 2000

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Contains a carefully edited selection of papers that were presented at the Symposium on Trends in Approximation Theory, held in May 2000, and at the Oslo Conference on Mathematical Methods for Curves and Surfaces, held in July 2000. Mathematical Methods for Curves and Surfaces covers topics such as B├ęzier curves, conic sections, offsets, and wavelets.

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Editorial Reviews

From The Critics
Based on a July 2000 conference, this collection presents recent research on the numerical analysis of curves and surfaces. Topics of the 47 papers include a best-fit algorithm for implicit surfaces and plane curves, approximate implicitization, surface animation for flower growth, knot insertion algorithms and local linear independence, local tension methods for bivariate scattered data interpolation, the numerical stability of collocation by smooth splines for volterra integral equations, and computational experiments with resultants for scaled Bernstein polynomials. No index. Annotation c. Book News, Inc., Portland, OR (
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Product Details

  • ISBN-13: 9780826513786
  • Publisher: Vanderbilt University Press
  • Publication date: 7/1/2001
  • Series: Innovations in Applied Mathematics
  • Edition description: 1 ED
  • Pages: 400
  • Product dimensions: 6.30 (w) x 9.10 (h) x 1.30 (d)

Table of Contents

Best-Fit of Implicit Surfaces and Plane Curves 1
Determination of Geometrical Invariants of Rationally Parametrized Conic Sections 15
A Scattered Data Approximation Scheme for the Detection of Fault Lines 25
Beta-Continuity Revisited: Determining Bezier Control Vertices to Construct Geometrically Continuous Curves and Surfaces 35
Simplification of Closed Triangulated Surfaces Using Simulated Annealing 45
Planar Configurations with Simple Lagrange Interpolation Formulae 55
Approximating Semi-Structured Data with Different Errors Using Support Vector Machine Regression 63
Subdivision Surfaces in Feature Films 73
Approximate Implicitization 81
An Approach to Weak Approximate Implicitization 103
A 4-Point Hermite Subdivision Scheme 113
Univariate Adaptive Thinning 123
Optimizing 3D Triangulations Using Discrete Curvature Analysis 135
Refinable Spline Functions and Hermite Interpolation 147
Approximating Digital Shapes by Parametric Surfaces 163
Clifford Algebra and Flows 173
Surface Self-Intersection 183
Error Estimates for the web-Spline Method 195
Hierarchical Scattered Data Filtering for Multilevel Interpolation Schemes 211
Bounding the Hausdorff Distance Between Implicitly Defined and/or Parametric Curves 223
Biangle Surface Patches 233
Some Examples of Quasi-interpolants Constructed from Local Spline Projectors 243
Single-Valued Tubular Surface Intersection Using Interval Arithmetic 253
Surface Animation for Flower Growth 263
Multiresolution Editing of Pasted Surfaces 273
Knot Insertion Algorithms and Local Linear Independence 283
Local Tension Methods for Bivariate Scattered Data Interpolation 293
Data Reduction in Surface Approximation 315
The Analytic Blossom 325
Bezier Curves: Topological Convergence of the Control Polygon 347
What is the Natural Generalization of Univariate Splines to Higher Dimensions? 355
Local Lagrange Interpolation by Bivariate C[superscript 1] Cubic Splines 393
Stability of Collocation by Smooth Splines for Volterra Integral Equations 405
G[superscript 1]-Hermite Interpolation of Ruled Surfaces 413
Recovering Structural Information from Triangulated Surfaces 423
Lower Bounds for Bernstein-Bezier Condition Number 433
Improved Bi-Laplacian Mesh Fairing 445
Approximate Envelope Reconstruction for Moving Solids 455
Towards the [mu]-Basis of a Rational Surface 467
A Strategy for the Construction of Piecewise Linear Prewavelets over Type-1 Triangulations in any Space Dimension 477
A Mixed Representation Approach to Offsets of Rational Curves 487
Pedal Curves and Surfaces 497
Generalizing the C[superscript 4] Four-directional Box Spline to Surfaces of Arbitrary Topology 507
Moving Least Squares Approximation on the Sphere 517
NURPS for Special Effects and Quadrics 527
Computational Experiments with Resultants for Scaled Bernstein Polynomials 535
Deformation With Hierarchical B-Splines 545
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