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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An Integral Approach to Uniform Subdivision
Convergence Analysis for Uniform Subdivision Schemes
Local Approximation of Global Differential Schemes
Variational Schemes for Bounded Domains
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affine affine transformations analysis applied approach approximation associated averaging B-splines basis function bounded box splines Chapter coefficients column combination compute condition cone consider consists constant construct continuous converge corresponding cubic splines curve defined definition derivative difference difference mask differential equation direction discrete edges eigenvalues eigenvectors entries equation exact exactly example expressed extraordinary vertex Figure finite flow follows four function p[x geometric Given grid harmonic initial inner product integral interpolation interval limit limit functions limit surfaces linear mask s[x mesh method Note observation operator origin particular piecewise plot points polygon polynomial position powers problem proof quad recurrence relation respect resulting rows satisfies scaling function sequence shape shows simple smooth solutions subdivision mask subdivision matrix subdivision rules subdivision scheme supported surface Theorem tion topological transformations translates triangle uniform values variational vector vertices weighted yields zero
Page 278 - Banded matrices with banded inverses II: Locally finite decomposition of spline spaces, Constructive Approximation 9 (1993), 263-282.
Page 276 - ... the new material. Then, however, this non-conventional method might be even better suited for solving the given problem of deformation than any real material may be. Nevertheless, a task of further work is to design and implement methods of deformation derived from physical laws. References  Alfeld, P.: Scattered data interpolation in three or more variables.