Wavelet subdivision methods. GEMS for rendering curves and surfaces

Description

Front cover; Contents; List of Figures; List of Tables; Foreword; Preface; Teaching and Reading Guides; Chapter 1: OVERVIEW; Chapter 2: BASIS FUNCTIONS FOR CURVE REPRESENTATION; Chapter 3: CURVE SUBDIVISION SCHEMES; Chapter 4: BASIS FUNCTIONS GENERATED BY SUBDIVISION MATRICES; Chapter 5: QUASI-INTERPOLATION; Chapter 6: CONVERGENCE AND REGULARITY ANALYSIS; Chapter 7: ALGEBRAIC POLYNOMIAL IDENTITIES; Chapter 8: INTERPOLATORY SUBDIVISION; Chapter 9: WAVELETS FOR SUBDIVISION; Chapter 10: SURFACE SUBDIVISION; Chapter 11: EPILOGUE; Supplementary Readings; Back cover. 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 ope.  Read more... Abstract: Focusing on subdivision curves and surfaces, this book details wavelet methods for geometric design, editing, and algorithm development. It presents a study of the theory, methods, and construction algorithms for the ideal wavelet families associated with the subdivision schemes. It provides the necessary background on wavelet mathematics.  Read more... Content: OVERVIEW. BASIS FUNCTIONS FOR CURVE REPRESENTATION. CURVE SUBDIVISION SCHEMES. BASIS FUNCTIONS GENERATED BY SUBDIVISION MATRICES. QUASI-INTERPOLATION. CONVERGENCE AND REGULARITY ANALYSIS. ALGEBRAIC POLYNOMIAL IDENTITIES. INTERPOLATORY SUBDIVISION. WAVELETS FOR SUBDIVISION. SURFACE SUBDIVISION. EPILOGUE. SUPPLEMENTARY READINGS. INDEX.