Curves and Surfaces
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Curves and Surfaces

  1. 532 pages
  2. English
  3. PDF
  4. Only available on web
eBook - PDF

Curves and Surfaces

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Table of contents
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About This Book

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.

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Yes, you can access Curves and Surfaces by Pierre-Jean Laurent,Alain Le Méhauté,Larry L. Schumaker in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
ISBN
9781483263878
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. Curves and Surfaces
  3. Copyright Page
  4. Table of Contents
  5. PREFACE
  6. CONTRIBUTORS
  7. Chapter 1. Parametrization for Data Approximation
  8. Chapter 2. A Vector Spline Approximation With Application to Meteorology
  9. Chapter 3. Kernel Estimation in Change-Point Hazard Rate Models
  10. Chapter 4. Spline Manifolds
  11. Chapter 5. Use of Simulated Annealing to Construct Triangular Facet Surfaces
  12. Chapter 6. G1 and G2 Continuity Between (SBR) Surfaces
  13. Chapter 7. Ray Tracing Rational Parametric Surfaces
  14. Chapter 8. Energy-Based Segmentation of Sparse Range Data
  15. Chapter 9. Error Estimates for Multiquadric Interpolation
  16. Chapter 10. A Geometrical Analysis for a Data Compression of 3D Anatomical Structures
  17. Chapter 11. Ck Continuity of (SBR) Surfaces
  18. Chapter 12. A Note on Piecewise Monotonie Bivariate Interpolation
  19. Chapter 13. Real-Time Signal Analysis with Quasi-Interpolatory Splines and Wavelets
  20. Chapter 14. Polynomial Expansions for Cardinal Interpolants and Orthonormal Wavelets
  21. Chapter 15. Realtime Pipelined Spline Data Fitting for Sketched Curves
  22. Chapter 16. Remarks on Digital Terrain Modelling Accuracy
  23. Chapter 17. Convexity and Bernstein-Bézier Polynomials
  24. Chapter 18. How to Draw a Curve Using Geometrical Data
  25. Chapter 19. The Generation of an Aerodynamical Propeller Using Partial Differential Equations
  26. Chapter 20. Fast Computation of Cross-Validated Robust Splines and Other Non-linear Smoothing Splines
  27. Chapter 21. Szasz-Mirakyan Quasi-interpolants
  28. Chapter 22. Statistical Check On The Smoothing Parameter of a Method for Inversion of Fourier Series
  29. Chapter 23. A General Method of Treating Degenerate Bézier Patches
  30. Chapter 24. G1 Smooth Connection Between Rectangular and Triangular Bézier Patches at a Common Corner
  31. Chapter 25. Regularity Conditions for a Class of Geometrically Continuous Curves and Surfaces
  32. Chapter 26. Splines and Digital Signal Processing
  33. Chapter 27. B-Rational Curves and Surfaces N-Rational Splines
  34. Chapter 28. Reparametrizations of Polynomial and Rational Curves
  35. Chapter 29. Numerical Stability of Geometric Algorithms
  36. Chapter 30. Solving Implicit ODEs by Simplicial Methods
  37. Chapter 31. On the Power of a posteriori Error Estimation for Numerical Integration and Function Approximation
  38. Chapter 32. Using the Refinement Equations for the Construction of Pre-Wavelets II: Powers of Two
  39. Chapter 33. Elastica and Minimal-Energy Splines
  40. Chapter 34. A Distributed Algorithm for Surface/Plane Intersection
  41. Chapter 35. Construction of Exponential Tension B-splines of Arbitrary Order
  42. Chapter 36. On the Almost Sure Limit of Probabilistic Recovery
  43. Chapter 37. A New Curve Tracing Algorithm and Some Applications
  44. Chapter 38. Pseudo-Cubic Weighted Splines Can Be C2 or G2
  45. Chapter 39. Composite Cr-Triangular Finite Elements of PS Type on a Three Direction Mesh
  46. Chapter 40. Dynamic Segmentation: Finding the Edge With Snake Splines
  47. Chapter 41. Recent Developments in the Strang-Fix Theory for Approximation Orders
  48. Chapter 42. Aligning Frames with the Tangent Curve of a B-spline Curve
  49. Chapter 43. Error Estimates for Interpolation by Generalized Splines
  50. Chapter 44. Varying the Shape Parameters of Rational Continuity
  51. Chapter 45. Detecting Cusps and Inflection Points in Curves
  52. Chapter 46. Image-like Surfaces: Parallel Least Squares Approximation Methods
  53. Chapter 47. Local Kriging Interpolation: Application to Scattered Data on the Sphere
  54. Chapter 48. Best Approximation of Circle Segments by Quadratic Bézier Curves
  55. Chapter 49. A Procedure for Determining Starting Points for a Surface/Surface Intersection Algorithm
  56. Chapter 50. Norms of Inverses for Matrices Associated with Scattered Data
  57. Chapter 51. 2D Sampling in Tomography
  58. Chapter 52. Subdividing Multivariate Polynomials Over Simplices in Bernstein-Bézier Form Without de Casteljau Algorithm
  59. Chapter 53. Geometrically Smooth Interpolation by Triangular Bernstein-Bézier Patches With Coalescent Control Points
  60. Chapter 54. Curve Fitting Using NURBS
  61. Chapter 55. Univariate Multiquadric Interpolation: Some Recent Results
  62. Chapter 56. Periodic Spline Interpolation of Functions of Bounded Variation
  63. Chapter 57. Least Squares Fitting by Linear Splines on Data Dependent Triangulations
  64. Chapter 58. How to Build Quasi-Interpolants: Application to Polyharmonic B-Splines
  65. Chapter 59. Algorithms for Local Convexity of Bézier Curves and Surfaces
  66. Chapter 60. Polynomial N-sided Patches
  67. Chapter 61. Cubic Recursive Division With Bounded Curvature
  68. Chapter 62. ω-Convergence, A Criterion for Linear Approximation
  69. Chapter 63. Bernstein-Type Quasi-Interpolants
  70. Chapter 64. Extension of the Problem of Best Interpolating Parametric Curves to L-Splines
  71. Chapter 65. Adaptive G1 Approximation of Range Data Using Triangular Patches
  72. Chapter 66. Universal Splines and Geometric Continuity
  73. Chapter 67. Procedural Construction of Patch-Boundary Curves
  74. Chapter 68. Efficient Computation of Multiple Knots Nonuniform Spline Functions
  75. Chapter 69. Chebyshev Approximation in IRn by Curves and Linear Manifolds
  76. Chapter 70. A Building Method for Hierarchical Covering Spheres of a Given Set of Points
  77. Chapter 71. The Variational Approach to Shape Preservation
  78. Chapter 72. Spline Fitting Numerous Noisy Data With Discontinuities
  79. Chapter 73. B-Spline Surfaces for Real-time Shape Design
  80. Chapter 74. Conversion of a Composite Trimmed Bézier Surface Into Composite Bézier Surfaces
  81. Chapter 75. Multivariate Model Building With Additive Interaction and Tensor Product Thin Plate Splines
  82. Chapter 76. Recursion Relations for 4 x 4 Determinants Related to Rational Cubic Bézier Curves
  83. Chapter 77. Lagrange Interpolation by Quadratic Splines On a Quadrilateral Domain of IR2