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Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Read more... Abstract: Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory Content: Front Matter, Page iii Copyright, Page iv PREFACE, Page x CONTRIBUTORS, Pages xi-xviii Parametrization for Data Approximation, Pages 1-4, Laurent Alt A Vector Spline Approximation With Application to Meteorology, Pages 5-10, L. Amodei, M.N. Benbourhim Kernel Estimation in Change-Point Hazard Rate Models, Pages 11-16, A. Antoniadis, G. Grégoire Spline Manifolds, Pages 17-25, Marc Attéia Use of Simulated Annealing to Construct Triangular Facet Surfaces, Pages 27-32, G. Baszenski, Larry L. Schumaker G1 and G2 Continuity Between (SBR) Surfaces, Pages 33-36, J.L. Bauchat, J.C. Fiorot, P. Jeannin Ray Tracing Rational Parametric Surfaces, Pages 37-42, Luc Biard, Patrick Chenin Energy-Based Segmentation of Sparse Range Data, Pages 43-50, Terrance E. Boult, Mark Lerner Error Estimates for Multiquadric Interpolation, Pages 51-58, M.D. Buhmann, N. Dyn A Geometrical Analysis for a Data Compression of 3D Anatomical Structures, Pages 59-65, V. Burdin, F. Ghorbel, J.L. de Bougrenet de la Tocnaye, C. Roux Ck Continuity of (SBR) Surfaces, Pages 67-70, J.C. Canonne, J.C. Fiorot, P. Jeannin A Note on Piecewise Monotonic Bivariate Interpolation, Pages 71-74, R.E. Carlson, F.N. Fritsch Real-Time Signal Analysis with Quasi-Interpolatory Splines and Wavelets, Pages 75-82, A.K. Chan, C.K. Chui Polynomial Expansions for Cardinal Interpolants and Orthonormal Wavelets, Pages 83-90, C.K. Chui, J. Stöckler, J.D. Ward, Joachim Stöckler Realtime Pipelined Spline Data Fitting for Sketched Curves, Pages 91-102, Elaine Cohen Remarks on Digital Terrain Modelling Accuracy, Pages 103-106, Y. Correc, A. Le Méhauté, Yves Correc, Alain Le Méhauté Convexity and Bernstein-Bézier Polynomials, Pages 107-134, Wolfgang Dahmen How to Draw a Curve Using Geometrical Data, Pages 135-138, J.P. Dedieu, Ch. Favardin The Generation of an Aerodynamical Propeller Using Partial Differential Equations, Pages 139-142, C. Dekanski, M.I.G. Bloor, M.J. Wilson Fast Computation of Cross-Validated Robust Splines and Other Non-linear Smoothing Splines, Pages 143-148, L.N. Deshpande, D. Girard Szasz-Mirakyan Quasi-interpolants, Pages 149-156, A. Tidjane Diallo Statistical Check On The Smoothing Parameter of a Method for Inversion of Fourier Series, Pages 157-160, M. Di Natale, D. Roux, L. Gotusso, R. Pavani A General Method of Treating Degenerate Bézier Patches, Pages 161-164, Wen-Hui Du, Francis J.M. Schmitt G1 Smooth Connection Between Rectangular and Triangular Bézier Patches at a Common Corner, Pages 165-168, Wen-Hui Du, F.J.M. Schmitt Regularity Conditions for a Class of Geometrically Continuous Curves and Surfaces, Pages 169-176, N. Dyn, D. Levin, I. Yad-Shalom Splines and Digital Signal Processing, Pages 177-180, L.A. Ferrari, D. Pang, K.F. Ustuner B-Rational Curves and Surfaces N-Rational Splines, Pages 181-184, J.C. Fiorot, P. Jeannin Reparametrizations of Polynomial and Rational Curves, Pages 185-188, J.C. Fiorot, S. Taleb Numerical Stability of Geometric Algorithms, Pages 189-192, Steven Fortune Solving Implicit ODEs by Simplicial Methods, Pages 193-196, Sergio de Freitas, Geovan Tavares On the Power of a posteriori Error Estimation for Numerical Integration and Function Approximation, Pages 197-207, Feng Gao Using the Refinement Equations for the Construction of Pre-Wavelets II: Powers of Two, Pages 209-246, Rong-Qing Jia, Charles A. Micchelli Elastica and Minimal–Energy Splines, Pages 247-250, Emery Jou, Weimin Han A Distributed Algorithm for Surface/Plane Intersection, Pages 251-254, A. Kaufmann Construction of Exponential Tension B-splines of Arbitrary Order, Pages 255-258, Per Erik Koch, Tom Lyche On the Almost Sure Limit of Probabilistic Recovery, Pages 259-262,CP1,CP2,263-265, Mark A. Kon A New Curve Tracing Algorithm and Some Applications, Pages 267-270, David J. Kriegman, Jean Ponce Pseudo-Cubic Weighted Splines Can Be C2 or G2, Pages 271-274, Rekha Kulkarni, Pierre-Jean Laurent Composite Cr-Triangular Finite Elements of PS Type on a Three Direction Mesh, Pages 275-278, Mohammed Laghchim Lahlou Dynamic Segmentation: Finding the Edge With Snake Splines, Pages 279-284, F. Leitner, I. Marque, S. Lavallée, P. Cinquin Recent Developments in the Strang-Fix Theory for Approximation Orders, Pages 285-292, William A. Light Aligning Frames with the Tangent Curve of a B-spline Curve, Pages 293-296, C.F. Louwe Kooijmans Error Estimates for Interpolation by Generalized Splines, Pages 297-306, W.R. Madych Varying the Shape Parameters of Rational Continuity, Pages 307-313, Dinesh Manocha, Brian A. Barsky Detecting Cusps and Inflection Points in Curves, Pages 315-319, Dinesh Manocha, John F. Canny Image-like Surfaces: Parallel Least Squares Approximation Methods, Pages 321-324, L. Bacchelli Montefusco, C. Guerrini, L. Puccio Local Kriging Interpolation: Application to Scattered Data on the Sphere, Pages 325-329, Pierre Montès Best Approximation of Circle Segments by Quadratic Bézier Curves, Pages 331-336, Knut Mørken A Procedure for Determining Starting Points for a Surface/Surface Intersection Algorithm, Pages 337-340, G. Müllenheim Norms of Inverses for Matrices Associated with Scattered Data, Pages 341-348, F.J. Narcowich, J.D. Ward 2D Sampling in Tomography, Pages 349-357, F. Natterer Subdividing Multivariate Polynomials Over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm, Pages 359-362, M. Neamtu Geometrically Smooth Interpolation by Triangular Bernstein–Bézier Patches With Coalescent Control Points, Pages 363-366, P.R. Pfluger, M. Neamtu Curve Fitting Using NURBS, Pages 367-370, Christine Potier, Mustapha Bel Guermah, Christine Vercken Univariate Multiquadric Interpolation: Some Recent Results, Pages 371-382, M.J.D. Powell Periodic Spline Interpolation of Functions of Bounded Variation, Pages 383-386, J. Prestin Least Squares Fitting by Linear Splines on Data Dependent Triangulations, Pages 387-390, Ewald Quak, L.L. Schumaker How to Build Quasi-Interpolants: Application to Polyharmonic B-Splines, Pages 391-402, Christophe Rabut Algorithms for Local Convexity of Bézier Curves and Surfaces, Pages 403-406, Thomas Rando, John Roulier Polynomial N-sided Patches, Pages 407-410, G. Renner Cubic Recursive Division With Bounded Curvature, Pages 411-414, M.A. Sabin ω-Convergence, A Criterion for Linear Approximation, Pages 415-420, M.A. Sabin Bernstein-Type Quasi-Interpolants, Pages 421-426, Paul Sablonnière Extension of the Problem of Best Interpolating Parametric Curves to L-Splines, Pages 427-432, K. Scherer Adaptive G1 Approximation of Range Data Using Triangular Patches, Pages 433-436, Francis Schmitt, Xin Chen, Wen-Hui Du, Farouk Sair Universal Splines and Geometric Continuity, Pages 437-444, H.-P. Seidel Procedural Construction of Patch-Boundary Curves, Pages 445-448, Leon A. Shirman, Carlo H. Séquin Efficient Computation of Multiple Knots Nonuniform Spline Functions, Pages 449-452, M.J. Silbermann, S.Y. Wang, L.A. Ferrari, Martine Silbermann Chebyshev Approximation in Rn by Curves and Linear Manifolds, Pages 453-456, Martin Streng, Wolfgang Wetterling A Building Method for Hierarchical Covering Spheres of a Given Set of Points, Pages 457-460, Leonardo Traversoni, Oscar Palacios The Variational Approach to Shape Preservation, Pages 461-476, Florencio I. Utreras Spline Fitting Numerous Noisy Data With Discontinuities, Pages 477-480, Christine Vercken, Christine Potier B-Spline Surfaces for Real-time Shape Design, Pages 481-484, J.S.M. Vergeest, C.G.C. van Dijk Conversion of a Composite Trimmed Bézier Surface Into Composite Bézier Surfaces, Pages 485-489, A.E. Vries-Baayens Multivariate Model Building With Additive Interaction and Tensor Product Thin Plate Splines, Pages 491-504, Grace Wahba Recursion Relations for 4 × 4 Determinants Related to Rational Cubic Bézier Curves, Pages 505-510, F. Yamaguchi, M. Niizeki, H. Fukunaga Lagrange Interpolation by Quadratic Splines On a Quadrilateral Domain of R2, Pages 511-514, Fatma Zedek Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation.

Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain.

This book is a valuable resource for mathematicians. Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain. This book is a valuable resource for mathematicians. There is a great deal of current interest in mathematical methods for representing and manipulating complicated curves and surfaces in a digital computer environment. This edited work is a collection of both short survey papers and long research papers, addressing a number of topics important to development in the field. Among these are 3-D reconstruction, thin plate splines, geometric continuity, image compression, and radial functions. The survey papers focus on several particularly active subareas of approximation theory, including tomography, wavelets, constrained approximation, multivariate splines, approximation of images, and surface compression Edited By Pierre-jean Laurent, Alain Le Méhauté, Larry L. Schumaker. Papers From The International Conference On Curves And Surfaces, Held June 21-27, 1990 In Chamonix-mont-blanc, And Organized By The Association Française D'approximation. Includes Bibliographical References.