LEADER 00000nam  2200625 i 4500 
001    7033357 
003    IEEE 
005    20150222143346.0 
006    m    eo  d         
007    cr cn |||m|||a 
008    150222s2015    caua   foab   000 0 eng d 
020    9781627053723|qe-book 
020    |z9781627053716|qprint 
024 7  10.2200/S00621ED1V01Y201412CGR018|2doi 
035    (OCoLC)903883142 
040    CaBNVSL|beng|erda|cCaBNVSL|dCaBNVSL|dAS|dIIS 
050  4 TR897.7|b.N545 2015 
082 04 006.696|223 
100 1  Niebe, Sarah.,|eauthor 
245 10 Numerical methods for linear complementarity problems in 
       physics-based animation /|cSarah Niebe and Kenny Erleben 
264  1 San Rafael, California (1537 Fourth Street, San Rafael, CA
       94901 USA) :|bMorgan & Claypool,|c2015 
300    1 online resource (viii, 151 pages) :|billustrations 
336    text|2rdacontent 
337    electronic|2isbdmedia 
338    online resource|2rdacarrier 
490 1  Synthesis lectures on computer graphics and animation,
       |x1933-9003 ;|v# 18 
500    Part of: Synthesis digital library of engineering and 
       computer science 
504    Includes bibliographical references (pages 145-150) 
505 0  1. Introduction -- 1.1 Understanding the problem -- 1.1.1 
       First-order 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 n-dimensions -- 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 physics-based animation -- 1.3.1 Fluid-solid wall 
       boundary conditions -- 1.3.2 Free-flowing granular matter 
       -- 1.3.3 Density correction -- 1.3.4 Joint limits in 
       inverse kinematics -- 1.3.5 Contact force examples -- 
505 8  2. Numerical methods -- 2.1 Pivoting methods -- 2.1.1 
       Direct methods for small-sized 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 Gauss
       -Seidel method -- 2.2.4 Staggering -- 2.2.5 The projected 
       Gauss-Seidel 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 Fischer-Newton 
       method -- 2.4.3 Penalized Fischer-Newton method -- 2.4.4 
       Tips, tricks and implementation hacks -- 
505 8  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 -- 
505 8  A. Basic calculus -- Order notation -- What is a limit? --
       The small-o notation -- The big-o notation -- Lipschitz 
       functions -- Derivatives -- B. First-order optimality 
       conditions -- C. Convergence, performance and robustness 
       experiments -- D. Num4LCP -- Using Num4LCP -- Bibliography
       -- Authors' biographies 
506    Abstract freely available; full-text restricted to 
       subscribers or individual document purchasers 
510 0  Compendex 
510 0  INSPEC 
510 0  Google scholar 
510 0  Google book search 
520 3  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] 
530    Also available in print 
538    Mode of access: World Wide Web 
538    System requirements: Adobe Acrobat Reader 
588    Title from PDF title page (viewed on February 22, 2015) 
650  0 Computer animation|xMathematics 
650  0 Linear complementarity problem|xMathematics 
653    linear complementarity problems 
653    Newton methods 
653    splitting methods 
653    interior point methods 
653    convergence rates 
653    performance study 
700 1  Erleben, Kenny,|d1974-,|eauthor 
776 08 |iPrint version:|z9781627053716 
830  0 Synthesis digital library of engineering and computer 
       science 
830  0 Synthesis lectures in computer graphics and animation ;|v#
       18.|x1933-9003 
856 41 |zeBook(IEEE-MORGAN)|uhttp://ieeexplore.ieee.org/servlet/
       opac?bknumber=7033357