Finite Element Method Simulation of 3D Deformable Solids (Synthesis Lectures on Visual Computing: Computer Graphics, Animation, Computational Photography, and Imaging)
暫譯: 三維可變形固體的有限元素法模擬(視覺計算綜合講座:計算機圖形學、動畫、計算攝影與影像)

Eftychios Sifakis, Jernej Barbič

商品描述

This book serves as a practical guide to simulation of 3D deformable solids using the Finite Element Method (FEM). It reviews a number of topics related to the theory and implementation of FEM approaches: measures of deformation, constitutive laws of nonlinear materials, tetrahedral discretizations, and model reduction techniques for real-time simulation. Simulations of deformable solids are important in many applications in computer graphics, including film special effects, computer games, and virtual surgery. The Finite Element Method has become a popular tool in many such applications. Variants of FEM catering to both offline and real-time simulation have had a mature presence in computer graphics literature. This book is designed for readers familiar with numerical simulation in computer graphics, who would like to obtain a cohesive picture of the various FEM simulation methods available, their strengths and weaknesses, and their applicability in various simulation scenarios. The book is also a practical implementation guide for the visual effects developer, offering a lean yet adequate synopsis of the underlying mathematical theory. Chapter 1 introduces the quantitative descriptions used to capture the deformation of elastic solids, the concept of strain energy, and discusses how force and stress result as a response to deformation. Chapter 2 reviews a number of constitutive models, i.e., analytical laws linking deformation to the resulting force that has successfully been used in various graphics-oriented simulation tasks. Chapter 3 summarizes how deformation and force can be computed discretely on a tetrahedral mesh, and how an implicit integrator can be structured around this discretization. Finally, chapter 4 presents the state of the art in model reduction techniques for real-time FEM solid simulation and discusses which techniques are suitable for which applications. Topics discussed in this chapter include linear modal analysis, modal warping, subspace simulation, and domain decomposition.

商品描述(中文翻譯)

本書作為使用有限元素法(Finite Element Method, FEM)進行三維可變形固體模擬的實用指南。它回顧了與FEM方法的理論和實現相關的多個主題:變形的度量、非線性材料的本構定律、四面體離散化,以及實時模擬的模型簡化技術。可變形固體的模擬在計算機圖形學的許多應用中都非常重要,包括電影特效、電腦遊戲和虛擬手術。有限元素法已成為許多此類應用中的流行工具。針對離線和實時模擬的FEM變體在計算機圖形學文獻中已經成熟存在。本書旨在為熟悉計算機圖形學中數值模擬的讀者提供一個整體的視角,了解各種可用的FEM模擬方法、它們的優缺點以及在各種模擬場景中的適用性。本書同時也是視覺特效開發者的實用實現指南,提供了對基礎數學理論的簡明而充分的概述。

第一章介紹了用於捕捉彈性固體變形的定量描述、應變能的概念,並討論了力和應力如何作為變形的反應而產生。第二章回顧了多個本構模型,即將變形與所產生的力聯繫起來的解析法則,這些法則已成功應用於各種面向圖形的模擬任務。第三章總結了如何在四面體網格上離散計算變形和力,以及如何圍繞這種離散化結構化隱式積分器。最後,第四章介紹了實時FEM固體模擬的模型簡化技術的最新進展,並討論了哪些技術適合哪些應用。本章討論的主題包括線性模態分析、模態變形、子空間模擬和領域分解。

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