490 Pages
    by A K Peters/CRC Press

    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