Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces (Hardcover)

Prevalent in animation movies and interactive games, subdivision methods allow users to design and implement simple but efficient schemes for rendering curves and surfaces. Adding to the current subdivision toolbox, Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces introduces geometry editing and manipulation schemes (GEMS) and covers both subdivision and wavelet analysis for generating and editing parametric curves and surfaces of desirable geometric shapes. The authors develop a complete constructive theory and effective algorithms to derive synthesis wavelets with minimum support and any desirable order of vanishing moments, along with decomposition filters.

Through numerous examples, the book shows how to represent curves and construct convergent subdivision schemes. It comprehensively details subdivision schemes for parametric curve rendering, offering complete algorithms for implementation and theoretical development as well as detailed examples of the most commonly used schemes for rendering both open and closed curves. It also develops an existence and regularity theory for the interpolatory scaling function and extends cardinal B-splines to box splines for surface subdivision.

Keeping mathematical derivations at an elementary level without sacrificing mathematical rigor, this book shows how to apply bottom-up wavelet algorithms to curve and surface editing. It offers an accessible approach to subdivision methods that integrates the techniques and algorithms of bottom-up wavelets.

在動畫電影和互動遊戲中普遍存在的細分方法，允許使用者設計和實現簡單但高效的曲線和曲面渲染方案。《Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces》作為當前細分工具箱的一部分，引入了幾何編輯和操作方案（GEMS），並涵蓋了用於生成和編輯具有理想幾何形狀的參數化曲線和曲面的細分和小波分析。作者們發展了一個完整的建構性理論和有效的算法，以獲得具有最小支持和任意理想消失矩的合成小波，以及分解濾波器。

通過眾多示例，本書展示了如何表示曲線並構建收斂的細分方案。它全面介紹了用於參數化曲線渲染的細分方案，提供了完整的實施算法和理論發展，以及對於渲染開放和封閉曲線最常用方案的詳細示例。它還為插值縮放函數開發了存在性和正則性理論，並將基礎B樣条擴展為曲面細分的盒狀樣条。

本書將數學推導保持在基礎水平，同時不牺牲數學嚴謹性，展示了如何將自底向上的小波算法應用於曲線和曲面編輯。它提供了一種易於理解的細分方法，將自底向上小波的技術和算法整合在一起。