Numerical Methods for Linear Complementarity Problems in Physics-Based Animation (Synthesis Lectures on Computer Graphics and Animation)

Sarah Niebe, Kenny Erleben

  • 出版商: Morgan & Claypool
  • 出版日期: 2015-01-01
  • 售價: $2,190
  • 貴賓價: 9.5$2,081
  • 語言: 英文
  • 頁數: 159
  • 裝訂: Paperback
  • ISBN: 1627053719
  • ISBN-13: 9781627053716
  • 相關分類: 物理學 PhysicsComputer Graphics
  • 海外代購書籍(需單獨結帳)

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商品描述

Linear complementarity problems (LCPs) have for many years been used in physics-based animation to model contact forces between rigid bodies in contact. More recently, LCPs have found their way into the realm of fluid dynamics. Here, LCPs are used to model boundary conditions with fluid-wall contacts. LCPs have also started to appear in deformable models and granular simulations. There is an increasing need for numerical methods to solve the resulting LCPs with all these new applications. This book provides a numerical foundation for such methods, especially suited for use in computer graphics. This book is mainly intended for a researcher/Ph.D. student/post-doc/professor who wants to study the algorithms and do more work/research in this area. Programmers might have to invest some time brushing up on math skills, for this we refer to Appendices A and B. The reader should be familiar with linear algebra and differential calculus. We provide pseudo code for all the numerical methods, which should be comprehensible by any computer scientist with rudimentary programming skills. The reader can find an online supplementary code repository, containing Matlab implementations of many of the core methods covered in these notes, as well as a few Python implementations [Erleben, 2011].

商品描述(中文翻譯)

線性互補問題(LCPs)多年來一直被用於基於物理的動畫中,以模擬接觸中剛體之間的接觸力。最近,LCPs 開始進入流體動力學的領域。在這裡,LCPs 被用來模擬流體與牆面接觸的邊界條件。LCPs 也開始出現在可變形模型和顆粒模擬中。隨著這些新應用的增加,對於解決所產生的 LCPs 的數值方法的需求也在上升。本書提供了這些方法的數值基礎,特別適合用於計算機圖形學。本書主要針對希望研究算法並在此領域進行更多工作/研究的研究人員/博士生/博士後/教授。程序員可能需要花一些時間來提升數學技能,為此我們參考附錄 A 和 B。讀者應該熟悉線性代數和微積分。我們為所有數值方法提供了偽代碼,任何具備基本編程技能的計算機科學家都應該能夠理解。讀者可以找到一個在線補充代碼庫,包含許多這些筆記中涵蓋的核心方法的 Matlab 實現,以及一些 Python 實現 [Erleben, 2011]。