Mathematical Methods for Curves and Surfaces

M. Daehlen, T. Lyche, and L. L. Schumaker (eds.)

Vanderbilt University Press 1995

ISBN 8265-1268-2

NOTE: The links in this document are to postscript files. Their average size is about 150K. However, a number of the papers include postscript figures, and their sizes range up to 7MB. Files larger than 1MB are marked with a #

Preface

Participants

Contents

* Rachid Ait Haddou and Luc Biard:

G2 Approximation of an Offset Curve by Tschirnhausen Quartics

* Peter Alfeld, Marian Neamtu, and Larry L. Schumaker:

Circular Bernstein-Bezier Polynomials

* M. Atteia and H. Jaouni:

The Construction of a Basis of Periodic Wavelets

# Cristin Barghiel, Richard Bartels and David Forsey:

Pasting Spline Surfaces

* M. Bozzini and L. Lenarduzzi:

Recovering a Function with Discontinuities in Dimension Two

* G. Brunnett, P.~E. Crouch and F. Silva Leite

Spline Elements on Spheres

* M. D. Buhmann, F. Derrien and A. Le Mehaute

Spectral Properties and Knot Removal for Interpolation by Pure Radial Sums

* J. M. Carnicer, M. Garcia and J. M. Pena

Convex Curves from Convex Control Polygons

* Paul de Faget de Casteljau

Courbes et Profils Esthetiques contre Fonctions Orthogonales

* W. L. F. Degen

High Accuracy Approximation of Parametric Curves

# George C. Donovan, Jeffrey S. Geronimo and Douglas P. Hardin

A Class of Orthogonal Multiresolution Analyses in 2D

* N. Dyn, J.~A. Gregory and D. Levin

Piecewise Uniform Subdivision Schemes

* M. Ellens and E. Cohen

An Approach to C^(-1) and C^(0) Feature Lines

* G. Farin

The Geometry of C^1 Projective Curves and Surfaces

# Gregory E. Fasshauer

Adaptive Least Squares Fitting with Radial Basis Functions on the Sphere

* M. S. Floater

Rational Cubic Implicitization

* Tim N. T. Goodman

Bernstein-Schoenberg Operators

# Baining Guo

Avoiding Topological Anomalies in Quadric Surface Patches

* A. W. Habib and R. N. Goldman

Notions of Geometric Continuity Based on Geometric Invariants

# Jan Hadenfeld

Local Energy Fairing of B--Spline Surfaces

* Mark A. Halstead, Brian A. Barsky, Stanley A. Klein and Robert B. Mandell

Geometric Modeling of the Cornea Using Videokeratography

* T. Hermann, G. Lukacs and T. Varady

Techniques for Variable Radius Rolling Ball Blends

* Christoph M. Hoffmann and Jorg Peters

Geometric Constraints for CAGD

* Josef Hoschek and Helmut Pottmann

Interpolation and Approximation with Developable B--Spline Surfaces

* Armin Iske

Characterization of Function Spaces Associated with Conditionally Positive Definite Functions

* B. Juttler

Spatial Rational Motions and their Application in Computer Aided Geometric Design

* Leif Kobbelt

Interpolatory Refinement as a Low Pass Filter

* Leif Kobbelt and Hartmut Prautzsch

Approximating the Length of a Spline by its Control Polygon

* Andreas Kolb, Helmut Pottmann, and Hans-Peter Seidel

Surface Reconstruction Based Upon Minimal Norm Networks

* Suresh Lodha and Ron Goldman

Duality between Degree Elevation and Differentiation for B-bases and L-bases

* Weiyin Ma and Jean-Pierre Kruth

NURBS Curve and Surface Fitting and Interpolation

* Stephen Mann

Using Local Optimization in Surface Fitting

* C. Manni and P. Sablonniere

C^1 Comonotone Hermite Interpolation via Parametric Surfaces

* A. Markus, G. Renner and J. Vancza

Genetic Algorithms in Free Form Curve Design

* Marie-Laurence Mazure

Blossoming of Chebyshev Splines

* Even Mehlum

Appell and the Apple (Nonlinear Splines in Space)

* Knut Morken

Parametric Interpolation by Quadratic Polynomials in the Plane

* M. Pasadas, M. C. Lopez de Silanes and J. J. Torrens

Approximation of Parametric Surfaces by Discrete Smoothing D^m-splines with Tangent Conditions

* Helmut Pottmann

Studying NURBS Curves and Surfaces with Classical Geometry

* M. J. D. Powell

An Algorithm that Straightens and Smooths Piecewise Linear Curves in Two Dimensions

* Dirk-Jan Ripmeester

Upper Bounds on the Dimension of Bivariate Spline Spaces and Duality in the Plane

* Paul Sablonniere and Driss Sbibih

Some Families of B-splines with Hexagonal Support on a Three-direction Mesh

* R. Schaback

Creating Surfaces from Scattered Data Using Radial Basis Functions

* Thomas W. Sederberg and Eugene Greenwood

Shape Blending of 2--D Piecewise Curves

* Kenji Ueda

Normalized Cyclide Bezier Patches

* R. van Damme and L. Alboul

Tight Triangulations

* T. Varady and A. P. Rockwood

Vertex Blending Based on the Setback Split

* J. Warren

Binary Subdivision Schemes for Functions over Irregular Knot Sequences

* Frank Weller and Hans Hagen

Tensor-Product Spline Spaces with Knot Segments

* Zongmin Wu

Characterization of Positive Definite Radial Functions