Wavelet Subdivision Methods: Gems for Rendering Curves and Surfaces
暫譯: 小波細分方法:曲線與表面的渲染寶石
Chui, Charles, de Villiers, Johan
- 出版商: CRC
- 出版日期: 2019-11-25
- 售價: $3,070
- 貴賓價: 9.5 折 $2,917
- 語言: 英文
- 頁數: 479
- 裝訂: Quality Paper - also called trade paper
- ISBN: 0367452316
- ISBN-13: 9780367452315
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其他版本:
Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces (Hardcover)
相關主題
商品描述
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.
商品描述(中文翻譯)
在動畫電影和互動遊戲中廣泛應用的細分方法,允許用戶設計和實現簡單但高效的曲線和表面渲染方案。《Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces》在現有的細分工具箱中增加了幾何編輯和操作方案(GEMS),並涵蓋了細分和小波分析,以生成和編輯具有理想幾何形狀的參數曲線和表面。作者開發了一套完整的構造理論和有效的算法,以推導具有最小支撐和任何理想消失矩的合成小波,以及分解濾波器。
通過大量示例,本書展示了如何表示曲線並構建收斂的細分方案。它全面詳細地介紹了參數曲線渲染的細分方案,提供了完整的實現和理論發展算法,以及最常用的開放和封閉曲線渲染方案的詳細示例。它還為插值縮放函數發展了存在性和正則性理論,並將基數 B-splines 擴展到箱形樣條以進行表面細分。
本書在不犧牲數學嚴謹性的情況下,將數學推導保持在初級水平,展示了如何將自下而上的小波算法應用於曲線和表面編輯。它提供了一種可接近的細分方法,整合了自下而上的小波技術和算法。
作者簡介
Charles Chui is a Curators' Professor in the Department of Mathematics and Computer Science at the University of Missouri in St. Louis, and a consulting professor of statistics at Stanford University in California. Dr. Chui's research interests encompass applied and computational mathematics, with an emphasis on splines, wavelets, mathematics of imaging, and fast algorithms.
Johan de Villiers is a professor in the Department of Mathematical Sciences, Mathematics Division at Stellenbosch University in South Africa. Dr. de Villiers's research interests include computational mathematics, with an emphasis on wavelet and subdivision analysis.
作者簡介(中文翻譯)
查爾斯·崔 (Charles Chui) 是密蘇里州聖路易斯市密蘇里大學數學與計算機科學系的策展教授,同時也是加州史丹佛大學的統計學顧問教授。崔博士的研究興趣涵蓋應用數學和計算數學,特別強調樣條函數、波浪變換、影像數學以及快速演算法。
約翰·德·維利爾斯 (Johan de Villiers) 是南非史泰倫博斯大學數學科學系數學組的教授。德·維利爾斯博士的研究興趣包括計算數學,特別強調波浪變換和細分分析。