Elsevier S & T

Subdivision Methods for Geometric Design: A Constructive Approach

Warren, Joe; Weimer, Henrik

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Table of contents
  • Cover
  • Copyright Pageiv
  • Contentsvii
  • Forewordv
  • Prefacexi
  • Table of Symbolsxiii
  • Chapter 1. Subdivision: Functions as Fractals1
  • 1.1 Functions1
  • 1.2 Fractals9
  • 1.3 Subdivision18
  • 1.4 Overview25
  • Chapter 2. An Integral Approach to Uniform Subdivision27
  • 2.1 A Subdivision Scheme for B-splines28
  • 2.2 A Subdivision Scheme for Box Splines40
  • 2.3 B-splines and Box Splines as Piecewise Polynomials52
  • Chapter 3. Convergence Analysis for Uniform Subdivision Schemes62
  • 3.1 Convergence of a Sequence of Functions63
  • 3.2 Analysis of Univariate Schemes69
  • 3.3 Analysis of Bivariate Schemes81
  • Chapter 4. A Differential Approach to Uniform Subdivision91
  • 4.1 Subdivision for B-splines92
  • 4.2 Subdivision for Box Splines99
  • 4.3 Subdivision for Exponential B-splines103
  • 4.4 A Smooth Subdivision Scheme with Circular Precision110
  • Chapter 5. Local Approximation of Global Differential Schemes120
  • 5.1 Subdivision for Polyharmonic Splines120
  • 5.2 Local Approximations to Polyharmonic Splines129
  • 5.3 Subdivision for Linear Flows141
  • Chapter 6. Variational Schemes for Bounded Domains157
  • 6.1 Inner Products for Stationary Subdivision Schemes157
  • 6.2 Subdivision for Natural Cubic Splines167
  • 6.3 Minimization of the Variational Scheme180
  • 6.4 Subdivision for Bounded Harmonic Splines188
  • Chapter 7. Averaging Schemes for Polyhedral Meshes198
  • 7.1 Linear Subdivision for Polyhedral Meshes198
  • 7.2 Smooth Subdivision for Quad Meshes204
  • 7.3 Smooth Subdivision for Triangle Meshes226
  • 7.4 Other Types of Polyhedral Schemes232
  • Chapter 8. Spectral Analysis at an Extraordinary Vertex239
  • 8.1 Convergence Analysis at an Extraordinary Vertex239
  • 8.2 Smoothness Analysis at an Extraordinary Vertex249
  • 8.3 Verifying the Smoothness Conditions for a Given Scheme259
  • 8.4 Future Trends in Subdivision272
  • References276
  • Index287
Book details
  • Vendor Elsevier S & T
  • SKU 9781558604469
  • ISBN-13 9780080498324
  • Author Warren, Joe; Weimer, Henrik
  • Category Computers
  • Subject Computer Graphics

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Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.

The only book devoted exclusively to subdivision techniques
Covers practical topics including uniform Bezier and B-Spline curves, polyhedral meshes, Catmull-Clark subdivision for quad meshes and objects with sharp creases and pointed vertices
A companion website provides example code and concept implementations of subdivision concepts in an interactive Mathematica environment