توضیحاتی در مورد کتاب :
در حال حاضر علاقه زیادی به روش های ریاضی برای نمایش و دستکاری منحنی ها و سطوح پیچیده در یک محیط کامپیوتر دیجیتال وجود دارد. این اثر ویرایش شده مجموعه ای از مقالات نظرسنجی کوتاه و مقالات تحقیقاتی طولانی است که به تعدادی از موضوعات مهم برای توسعه در این زمینه می پردازد. از جمله آنها می توان به بازسازی سه بعدی، خطوط صفحه نازک، پیوستگی هندسی، فشرده سازی تصویر و توابع شعاعی اشاره کرد. مقالات نظرسنجی بر روی چندین زیرحوزه به ویژه فعال نظریه تقریب، از جمله توموگرافی، موجک ها، تقریب محدود، خطوط چند متغیره، تقریب تصاویر، و فشرده سازی سطح تمرکز می کنند.
فهرست مطالب :
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
توضیحاتی در مورد کتاب به زبان اصلی :
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