Wavelet subdivision methods : GEMS for rendering curves and surfaces /: GEMS for rendering curves and surfaces. (2010)

• Record Type: Book
• Further Information: Note: Charles Chui, Johan de Villiers.
• Other Names: Chui, C. K; De Villiers, Johan, 1946-
• Contents: OVERVIEW; Curve representation and drawing; Free-form parametric curves; From subdivision to basis functions; Wavelet subdivision and editing; Surface subdivision BASIS FUNCTIONS FOR CURVE REPRESENTATION; Refinability and scaling functions; Generation of smooth basis functions; Cardinal B -splines; Stable bases for integer-shift spaces; Splines and polynomial reproduction CURVE SUBDIVISION SCHEMES; Subdivision matrices and stencils; B -spline subdivision schemes; Closed curve rendering; Open curve rendering BASIS FUNCTIONS GENERATED BY SUBDIVISION MATRICES ; Subdivision operators; The up-sampling convolution operation; Scaling functions from subdivision matrices; Convergence of subdivision schemes; Uniqueness and symmetry QUASI-INTERPOLATION ; Sum-rule orders and discrete moments ; Representation of polynomials; Characterization of sum-rule orders; Quasi-interpolants CONVERGENCE AND REGULARITY ANALYSIS; Cascade operators; Sufficient conditions for convergence; Hölder regularity; Positive refinement sequences; Convergence and regularity governed by two-scale symbols; A one-parameter family; Stability of the one-parameter family ALGEBRAIC POLYNOMIAL IDENTITIES; Fundamental existence and uniqueness theorem; Normalized binomial symbols; Behavior on the unit circle in the complex plane INTERPOLATORY SUBDIVISION ; Scaling functions generated by interpolatory refinement sequences; Convergence, regularity, and symmetry; Rendering of closed and open interpolatory curves; A one-parameter family of interpolatory subdivision operators WAVELETS FOR SUBDIVISION ; From scaling functions to synthesis wavelets; Synthesis wavelets with prescribed vanishing moments; Robust stability of synthesis wavelets; Spline-wavelets; Interpolation wavelets; Wavelet subdivision and editing SURFACE SUBDIVISION; Control nets and net refinement; Box splines as basis functions; Surface subdivision masks and stencils; Wavelet surface subdivision EPILOGUE SUPPLEMENTARY READINGS INDEX Exercises appear at the end of each chapter.
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2010
• Extent: 1 online resource, illustrations
• Subjects: 515/.2433; Wavelets (Mathematics); Curves -- Computer simulation; Surfaces -- Computer simulation; Computer graphics -- Mathematics
• Languages: English
• ISBNs: 9781439812167; 1439812160
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.