@MISC{Hauth_numericaltechniques, author = {Michael Hauth}, title = {Numerical Techniques for Cloth Simulation}, year = {} }

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Abstract

The modelling of physical systems often leads to partial or directly to ordinary differential equations. The solution of these equations usually is a dominant part of the total computational costs for a simulation or animation, therefore being the main focus of this chapter. Before addressing the numerical solution of ODEs- the temporal discretization or (time)integration- we take a brief look at the numerical techniques used for spatial discretization. Three techniques, not entirely unrelated, dominate the field. They are normally classified as particle systems, finite difference and finite element methods. 1.1 Particle Systems When using the particle system paradigm, the discretisation is already a part of the physical modelling process, as the continuous object is immediately represented as a set of discrete points with finite masses. Physical properties are specified by directly defining forces between these mass points. Typical representatives of this approach, that is very popular in cloth simulations, are mass-spring-damper systems [21, 26] and particle systems with forces defined directly by measured curves[6] or low order polynomial fits of this data[2]. 1.2 Finite Differences Another physical modelling concept is to specify physical behavior by minimizing some energy functionals defined on a continuous solid. The arising