Curves and Surfaces  book cover
1st Edition

Curves and Surfaces

ISBN 9781568810393
Published July 15, 1994 by A K Peters/CRC Press
490 Pages

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Book Description

This volume documents the results and presentations, related to aspects of geometric design, of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application. From the table of contents: - Object Oriented Spline Software - An Introduction to Pade Approximations - Zonoidal Surfaces - Projective Blossoms and Derivatives - Piecewise Polynomial Approximation of Spheres - A Geometrical Approach to Interpolation on Quadric Surfaces

Table of Contents



Properties of Interpolating Means with Exponential-Type Weights

G. Allasia and R. Besenghi

Approximating Reachable Sets by Extrapolation Methods

R. Baier and F. Lempio

Unimodality of Quartic B-splines

P. J. Barry

Object Oriented Spline Software

R. Bartels

On Polynomial Functions Defining the Geometric Continuity between Two (SBR) Surfaces

J. L. Bauchat

A 3D Generalized Voronoi Diagram for a Set of Polyhedra

E. Bertin and J.-M. Chassery

Variational Design of Rational Bézier Curves and Surfaces

G. P. Bonneau and H. Hagen

An Introduction to Padé Approximations

C. Brezinski

Discrete Curves and Curvature Constraints

H. G. Burchard

A Necessary and Sufficient Condition for the Ck Continuity of Triangular Rational Surfaces

J. C. Canonne

Monotonicity Preserving Representations

J. M. Carnicer and J. M. Peña

Splines Focales

P. de Faget de Casteljau

A Surface-Surface Intersection Algorithm with a Fast Clipping Technique

M. Daniel and A. Nicolas

Zonoidal Surfaces

O. Daoudi, B. Lacolle, N. Szafran, and P. Valentin

Spline Conversion: Existing Solutions and Open Problems

T. Dokken and T. Lyche

A Stepwise Algorithm for Converting B-Splines

M. Eck and J. Hadenfeld

Best Constrained Approximations of Planar Curves by Bézier Curves

E. F. Eisele

Projective Blossoms and Derivatives

G. Farin

Characterizations of the Set of Rational Parametric Curves with Rational Offsets

J. C. Fiorot and Th. Gensane

A Necessary and Sufficient Condition for Joining B-Rational Curves with Geometric Continuity G3

J. C. Fiorot and P. Jeannin

Generalizations of Bézier Curves and Surfaces

I. Gânscă, Gh. Coman, and L. Ţâmbulea

Corner Cutting Algorithms and Totally Positive Matrices

M. Gasca and J. M. Peña

Pricewise Polynomial Approximation of Spheres

S. Glærum

Non-polynomial Polar Forms

D. Gonsor and M. Neamtu

Curvature of Rational Quadratics Splines

T. N. T. Goodman

B-Spline Knot-Line Elimination and Bézier Continuity Conditions

R. Gormaz

Applications of Constrained Polynomials to Curve and Surface Approximation

R. J. Goult

Semi-regular B-spline Surfaces: Generalized Lofting by B-splines

J. Gravesen

On Best Convex Interpolation of Curves

C. Henninger and K. Scherer

Approximate Conversion and Data Compression of Integral and Rational B-spline Surfaces

J. Hoschek and F.-J. Schneider

A Geometrical Approach to Interpolation on Quadric Surfaces

B. Jüttler and R. Dietz

Finding Shortest Paths on Surfaces

R. Kimmel, A. Amir and A. M. Bruekstein

Polygonalization of Algebraic Surfaces

R. Klein

A Knot Removal Strategy for Spline Curves

J. C. Koua Brou

Computation of Curvatures Related to Surface-Surface Blending

I. Lef

Least Squares Optimization of Thread Surfaces

M. Léger, J.-M. Morvan, and M. Thibaut

A Multivariate Generalization of the de Boor-Fix Formula

S. Lodha and R. Goldman

A Metric for Parametric Approximation

T. Lyche and K. Mørken

Mathematical Modelling of Free-Form Curves and Surfaces from Discrete Points with NURBS

W. Ma and J.-P. Kruth

Evaluating Surface Intersections in Lower Dimensions

D. Manocha, A. Varshney, and H. Weber

The Iterative Solution of a Nonlinear Inverse Problem from Industry: Design of Reflectors

A. Neubauer

Splines with Prescribed Modified Moments

H. J. Oberle and G. Opfer

G2-Continuous Cubic Algebraic Splines and Their Efficient Display

M. Paluszny and R. R. Patterson

Splines in a Topological Setting

S. Pesco and G. Tavares

A Characterization of Connecting Maps as Nonlinear Roots of the Identity

J. Peters

Applications of the Dual Bézier Representation of Rational Curves and Surfaces

H. Pottmann

Bifurcation Phenomenon in a Tool Path Computation

J. F. Rameau

Interpolation with an Arc Length Constraint

J. A. Roulier and B. Piper

Curves Reconstruction

J.-C. Roux

The Ubiquitous Ellipse
G. Sapiro and A. M. Bruckstein

Axial Convexity: a Well-shaped Shape Property

T. Sauer

Variation Diminution and Blossoming for Curves and Surfaces

G. Schmeltz

Approximation with Helix Splines

G. Seemann

Simplex Splines Support Surprisingly Strong Symmetric Structures and Subdivision

H.-P. Seidel and A. H. Vermeulen

An Object-Oriented Framework for Curves and Surfaces with Applications

Ph. Slusallek, R. Klein, A. Kolb, and G. Greiner

Designing of a Progressive Lens

M. Tazeroualti

Multiplication as a General Operation for Splines

K. Ueda

Symmetric TB-spline Schemes

M. G. Wagner and H. Pottmann

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