Subdivision Methods for Geometric Design: A Constructive ApproachSubdivision 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 techniquesCovers practical topics including uniform Bezier and B-Spline curves, polyhedral meshes, Catmull-Clark subdivision for quad meshes and objects with sharp creases and pointed verticesA companion website provides example code and concept implementations of subdivision concepts in an interactive Mathematica environment |
Contents
1 | |
Chapter 2 An Integral Approach to Uniform Subdivision | 27 |
Chapter 3 Convergence Analysis for Uniform Subdivision Schemes | 62 |
Chapter 4 A Differential Approach to Uniform Subdivision | 91 |
Chapter 5 Local Approximation of Global Differential Schemes | 120 |
Chapter 6 Variational Schemes for Bounded Domains | 157 |
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Common terms and phrases
affine transformations algorithm analysis applied approach approximation B-spline basis function Bézier curves bilinear subdivision bivariate box splines box-spline scaling function Chapter characteristic map coefficients compute cone spline construct corresponding cubic splines defined derivative difference mask differential equation direction vectors discrete dk[x eigenvalues eigenvectors entries example expressed extraordinary vertex finite difference flow function p[x Given harmonic splines initial initial vector inner product matrix integer grid integer translates integral interpolation iteration Laurent series limit functions limit surfaces linear combination method natural cubic splines pê[x piecewise linear piecewise polynomial pk[x plot po[x polyharmonic splines quad averaging quad meshes quadratic recurrence refinement relation resulting rounds of subdivision rows sequence smooth solutions subdivision mask subdivision mask s[x subdivision matrix subdivision rules subdivision scheme subdivision surfaces surfaces of revolution Theorem three rounds tion triangle meshes uniform uniform convergence univariate valence values vectors pk vertices yields zero