Descript 
1 online resource (viii, 151 pages) : illustrations 

text rdacontent 

electronic isbdmedia 

online resource rdacarrier 
Series 
Synthesis lectures on computer graphics and animation, 19339003 ; # 18


Synthesis digital library of engineering and computer science


Synthesis lectures in computer graphics and animation ; # 18. 19339003

Note 
Part of: Synthesis digital library of engineering and computer science 

Includes bibliographical references (pages 145150) 

1. Introduction  1.1 Understanding the problem  1.1.1 Firstorder optimality is a linear complementarity problem  1.1.2 Nonsmooth root search reformulations  1.1.3 The boxed linear complementarity problem  1.1.4 Other reformulations  1.2 The problem in ndimensions  1.2.1 1D BLCP to 4D LCP  1.2.2 The boxed linear complementarity problem in higher dimensions  1.2.3 BLCP and the QP formulation  1.2.4 Converting BLCP to LCP  1.2.5 Nonsmooth reformulations of BLCP  1.3 Examples from physicsbased animation  1.3.1 Fluidsolid wall boundary conditions  1.3.2 Freeflowing granular matter  1.3.3 Density correction  1.3.4 Joint limits in inverse kinematics  1.3.5 Contact force examples  

2. Numerical methods  2.1 Pivoting methods  2.1.1 Direct methods for smallsized problems  2.1.2 Incremental pivoting "Baraff style"  2.2 Projection or sweeping methods  2.2.1 Splitting methods  2.2.2 Using a quadratic programming problem  2.2.3 The blocked GaussSeidel method  2.2.4 Staggering  2.2.5 The projected GaussSeidel subspace minimization method  2.2.6 The nonsmooth nonlinear conjugate gradient method  2.3 The interior point method  2.4 Newton methods  2.4.1 The minimum map Newton method  2.4.2 The FischerNewton method  2.4.3 Penalized FischerNewton method  2.4.4 Tips, tricks and implementation hacks  

3. Guide for software and selecting methods  3.1 Overview of numerical properties of methods covered  3.2 Existing practice on mapping models to methods  3.2.1 Existing software solutions  3.3 Future of LCPs in computer graphics  

A. Basic calculus  Order notation  What is a limit?  The smallo notation  The bigo notation  Lipschitz functions  Derivatives  B. Firstorder optimality conditions  C. Convergence, performance and robustness experiments  D. Num4LCP  Using Num4LCP  Bibliography  Authors' biographies 

Abstract freely available; fulltext restricted to subscribers or individual document purchasers 

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Linear complementarity problems (LCPs) have for many years been used in physicsbased 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 fluidwall 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/postdoc/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] 

Also available in print 

Mode of access: World Wide Web 

System requirements: Adobe Acrobat Reader 

Title from PDF title page (viewed on February 22, 2015) 
Link 
Print version: 9781627053716

Subject 
Computer animation  Mathematics


Linear complementarity problem  Mathematics


linear complementarity problems


Newton methods


splitting methods


interior point methods


convergence rates


performance study

Alt Author 
Erleben, Kenny, 1974, author

