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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Functions as Fractals
An Integral Approach to Uniform Subdivision
A Differential Approach to Uniform Subdivision
Local Approximation of Global Differential Schemes
Variational Schemes for Bounded Domains
Averaging Schemes for Polyhedral Meshes
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affine transformations algorithm analysis applying approximation associated B-spline basis function behavior Bézier curves bilinear subdivision bivariate box splines Catmull-Clark Chapter characteristic map circulant matrix coefficients compute cone spline construct corresponding cubic splines defined derivative difference mask differential equation direction vectors discrete eigenfunctions eigenvalues eigenvectors entries example expressed extraordinary vertex Figure finite difference function n(x functions pºſz Given Green's function harmonic splines initial initial vector inner product matrix integer translates integral interpolation knots limit functions limit surfaces linear combination mask six method multiresolution natural cubic splines observation p-ſh piecewise linear piecewise polynomial plot polyharmonic splines polyhedral meshes pºſh quad averaging quad meshes recurrence refinement relation resulting rounds of subdivision rows scaling relation sequence shows smooth solutions subdivision mask subdivision matrix subdivision rules subdivision scheme subdivision surfaces surface schemes surfaces of revolution Theorem three rounds tion uniform uniform convergence univariate valence values vertices 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.