Computation of Curves and Surfaces

1. Front Matter

   Pages i-ix

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2. Discrete Methods for Curves and Surface Representation

   1. Front Matter

      Pages 1-1

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   2. Stationary Subdivision, Fractals and Wavelets

      • Wolfgang Dahmen, Charles A. Micchelli

      Pages 3-26

   3. Recursive Triangles

      • R. N. Goldman

      Pages 27-72

   4. Exact and Approximate Conversion of Spline Curves and Spline Surfaces

      • Josef Hoschek

      Pages 73-116

   5. Discrete B-Splines and Conversion Problems

      • Tom Lyche

      Pages 117-134

3. Interpolation and Data Fitting

   1. Front Matter

      Pages 135-135

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   2. Vertex Splines and Their Applications to Interpolation of Discrete Data

      • Charles K. Chui

      Pages 137-181

   3. Shape Preserving Interpolation

      • F. Fontanella

      Pages 183-214

   4. Multivariate Polynomial Interpolation

      • M. Gasca

      Pages 215-236

   5. A Finite Element Approach to Surface Reconstruction

      • A. Le Méhauté

      Pages 237-274

   6. Reconstructing 3D Objects from Cross-Sections

      • Larry L. Schumaker

      Pages 275-309

4. Multivariate Splines and Applications

   1. Front Matter

      Pages 311-311

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   2. Quasiinterpolants and Approximation Power of Multivariate Splines

      • Carl de Boor

      Pages 313-345

   3. Polyhedral Splines

      • T. N. T. Goodman

      Pages 347-382

   4. Practice of Bivariate Quadratic Simplicial Splines

      • C. R. Traas

      Pages 383-422

5. Algebraic and Differential Geometric Techniques

   1. Front Matter

      Pages 423-423

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   2. Algebraic and Differential Geometric Methods in C.A.G.D.

      • Wolfgang Boehm

      Pages 425-455

   3. Smooth Parametric Surfaces and n-Sided Patches

      • John A. Gregory, Vincent K. H. Lau, Jianwei Zhou

      Pages 457-498

   4. Algebraic and Numerical Techniques for Offsets and Blends

      • Christoph M. Hoffmann

      Pages 499-528

Assembled here is a collection of articles presented at a NATO ADVANCED STU­ DY INSTITUTE held at Puerto de la Cruz, Tenerife, Spain during the period of July 10th to 21st, 1989. In addition to the editors of these proceedings Professor Larry L. Schumaker from Vanderbilt University, Nashville, Tennessee, served as a member of the international organizing committee. The contents of the contribu­ tions fall within the heading of COMPUTATION OF CURVES AND SURFACES and therefore address mathematical and computational issues pertaining to the dis­ play, modeling, interrogation and representation of complex geometrical objects in various scientific and technical environments. As is the intent of the NATO ASI program the meeting was two weeks in length and the body of the scientific activities was organized around prominent experts. Each of them presented lectures on his current research activity. We were fortunate to have sixteen distinguished invited speakers representing nine NATO countries: W. Bohm (Federal Republic of Germany), C. de Boor (USA), C.K. Chui (USA), W. Dahmen (Federal Republic of Germany), F. Fontanella (Italy), M. Gasca (Spain), R. Goldman (Canada), T.N.T. Goodman (UK), J.A. Gregory (UK), C. Hoffman (USA), J. Hoschek (Federal Republic of Germany), A. Le Mehaute (France), T. Lyche (Norway), C.A. Micchelli (USA), 1.1. Schumaker (USA), C. Traas (The Netherlands). The audience consisted of both young researchers as well as established scientists from twelve NATO countries and several non-NATO countries.

• 3D
• Approximation
• Interpolation
• finite element method
• fractal
• wavelet
• partial differential equations

• Institut für Mathematik I, Freie Universität, Berlin, Germany

  Wolfgang Dahmen

• Department of Applied Mathematics, University of Zaragoza, Zaragoza, Spain

  Mariano Gasca

• IBM T.J. Watson Research Center, Yorktown Heights, USA

  Charles A. Micchelli

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