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. |
Contents
Functions as Fractals | 1 |
An Integral Approach to Uniform Subdivision | 27 |
Convergence Analysis for Uniform Subdivision Schemes | 62 |
Local Approximation of Global Differential Schemes | 120 |
Variational Schemes for Bounded Domains | 157 |
Averaging Schemes for Polyhedral Meshes | 198 |
Spectral Analysis at an Extraordinary Vertex | 239 |
| 276 | |
Other editions - View all
Subdivision Methods for Geometric Design: A Constructive Approach Joe Warren,Henrik Weimer Limited preview - 2001 |
Common terms and phrases
affine transformations algorithm analysis applied approximation associated B-spline basis function basis function n[x Bézier curves bilinear subdivision bivariate box splines Chapter characteristic map coefficients compute cone spline construct corresponding cubic splines defined derivative difference mask differential equation direction vectors discrete eigenvalues eigenvectors entries example expressed extraordinary vertex finite difference flow function p[x Given Green's function 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 p₁ p₁[x piecewise linear piecewise polynomial pk[x plot po[x polyharmonic splines quad averaging quad meshes recurrence refinement relation resulting rounds of subdivision rows sequence smooth solutions 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 vector pk vertices yields zero
Popular passages
Page 278 - Banded matrices with banded inverses II: Locally finite decomposition of spline spaces, Constructive Approximation 9 (1993), 263-282.
Page 281 - Multiresolution Analysis for Surfaces of Arbitrary Topological Type," ACM Transactions on Graphics 16(1), pp.
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 [1] Alfeld, P.: Scattered data interpolation in three or more variables.
References to this book
Physically Based Rendering: From Theory to Implementation Matt Pharr,Greg Humphreys Limited preview - 2004 |
Digital Modeling of Material Appearance Julie Dorsey,Holly E. Rushmeier,François X. Sillion No preview available - 2008 |