1st Edition
Curves and Surfaces
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
Preface
Contributors
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
Biography
Pierre-Jean Laurent, Alain Le Mehaute, Larry Schumaker