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
Convergence Analysis for Uniform Subdivision Schemes
A Differential Approach to Uniform Subdivision
Local Approximation of Global Differential Schemes
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affine transformations algorithm analysis applying approach approximation associated averaging B-splines basis function behavior bounded box splines Chapter characteristic map coefficients column combination compute condition consider consists constant construct continuous converge corresponding cubic splines curve defined definition derivative difference differential equation direction discrete edges eigenvalues eigenvectors entries equation exact example expressed extraordinary vertex Figure finite flow follows four function n[x geometric Given grid initial inner product integral interpolation interval limit limit functions limit surfaces linear mask s[x mesh method multiplying Note observation operator origin particular piecewise plot points polygon polynomial position powers problem proof quad recurrence refinement regular relation resulting rows satisfies scaling function sequence shape shows simple smooth solutions splines subdivision mask subdivision matrix subdivision rules subdivision scheme surface Theorem tion topological transformations translates triangle uniform valence values 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.