Curves and Surfaces

Pierre-Jean Laurent, Alain Le Mehaute, Larry Schumaker

• Preface, Contributors, Properties of Interpolating Means with Exponential-Type Weights, Approximating Reachable Sets by Extrapolation Methods, Unimodality Property of Quartic B-splines, Object Oriented Spline Software, On Polynomial Functions Defining the Geometric Continuity Between Two (SBR) Surfaces, A 3D Generalized Voronoi Diagram for a Set of Polyhedra, Variational Design of Rational Bézier Curves and Surfaces, An Introduction to Padé Approximations, Discrete Curves and Curvature Constraints, A Necessary and Sufficient Condition for the C[sup(K)] Continuity of Triangular Rational Surfaces, Monotonicity Preserving Representations, Splines Focales, A Surface-Surface Intersection Algorithm with a Fast Clipping Technique, Zonoidal Surfaces, Spline Conversion: Existing Solutions and Open Problems, A Stepwise Algorithm for Converting B-Splines, Best Constrained Approximations of Planar Curves by Bezier Curves, Projective Blossoms and Derivatives, Characterizations of the Set of Rational Parametric Curves with Rational Offsets, A Necessary and Sufficient Condition for Joining B-Rational Curves with Geometric Continuity G[sup(3)], Generalizations of Bézier Curves and Surfaces, Corner Cutting Algorithms and Totally Positive Matrices, Piecewise Polynomial Approximation of Spheres, Non-polynomial Polar Forms, Curvature of Rational Quadratic Splines, B-Spline Knot-Line Elimination and Bezier Continuity Conditions, Applications of Constrained Polynomials to Curve and Surface Approximation, Semi-regular B-spline Surfaces: Generalized Lofting by B-splines, On Best Convex Interpolation of Curves, Approximate Conversion arid Data Compression of Integral and Rational B-spline Surfaces, A Geometrical Approach to Interpolation on Quadric Surfaces, Finding Shortest Paths on Surfaces, Polygonalization of Algebraic Surfaces, A Knot Removal Strategy for Spline Curves, Computation of Curvatures Related to Surface-Surface Blending, Least-Squares Optimization of Thread Surfaces, A Multivariate Generalization of the de Boor-Fix Formula, A Metric for Parametric Approximation, Mathematical Modelling of Free-Form Curves and Surfaces from Discrete Points with NURBS, Evaluating Surface Intersections in Lower Dimensions, The Iterative Solution of a Nonlinear Inverse Problem from Industry: Design of Reflectors, Splines with Prescribed Modified Moments, G[sup(2)]-Continuous Cubic Algebraic Splines and Their Efficient Display, Splines in a Topological Setting, A Characterization of Connecting Maps as Nonlinear Roots of the Identity, Applications of the Dual Bézier Representation of Rational Curves and Surfaces, Interpolation with an Arc Length Constraint, Curve Reconstruction, The Ubiquitous Ellipse, Axial Convexity: A Well-shaped Shape Property, Variation Diminution and Blossoming for Curves and Surfaces, Approximation with Helix Splines, Simplex Splines Support Surprisingly Strong Symmetric Structures and Subdivision, An Object-Oriented Framework for Curves and Surfaces with Applications, Designing a Progressive Lens, Multiplication as a General Operation for Splines, Symmetric TB-spline Schemes,