Subdivision Methods for Geometric Design: A Constructive Approach
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
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Chapter 2 An Integral Approach to Uniform Subdivision
Chapter 3 Convergence Analysis for Uniform Subdivision Schemes
Chapter 4 A Differential Approach to Uniform Subdivision
Chapter 5 Local Approximation of Global Differential Schemes
Chapter 6 Variational Schemes for Bounded Domains
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affine transformations algorithm applied approximation B-spline basis function B´ezier curves bilinear subdivision bivariate box splines box-spline scaling function Chapter characteristic map cm[x 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 Figure finite difference flow function n[x geometric Given Green’s function grid 12kZ harmonic splines initial initial vector inner product matrix integer translates integral interpolation iteration Laurent series limit functions limit surfaces linear combination method natural cubic splines nm[x ofthe piecewise linear piecewise polynomial pk[x plot polyharmonic splines quad averaging quad meshes 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 topological triangle meshes uniform uniform convergence univariate valence values vectors pk vertices yields zero