Computational aspects of dynamic surfaces

  • Authors:

  • Ronald Fedkiw;Robert Edward Bridson

  • Affiliations:

  • -;-

  • Venue:
  • Computational aspects of dynamic surfaces
  • Year:
  • 2003

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Abstract

This thesis is concerned with various computational aspects of surface dynamics. By this I mean algorithms and data structures to support simulations of the physics taking place on or about two-dimensional manifolds. This includes internal dynamics (e.g. elastic forces) and external dynamics (e.g. collisions). The core of the thesis is simulating cloth motion, including the internal elastic dynamics, the external dynamics of contact and collision, and post-processing of the data for rendering. The contact and collision algorithm, based on the notion of a collision resolution pipeline where candidate trajectories are passed through several stages designed to resolve different classes of collisions, was subsequently adapted to rigid body simulation. Surface dynamics are also potentially the most important part of simulations of deformable objects, driving the deformation of the interior. Chapter 5 presents a tetrahedral mesh generation algorithm designed to support large surface deformations. Adaptivity is also discussed. Throughout the thesis implicit surfaces defined by level sets are used to represent geometry. Level sets are used in many other areas, especially computational fluid dynamics for simulations of the surface between distinct regions of flow (e.g. material boundaries). Their chief drawback is storage expense. Chapter 6 presents a data structure for efficiently storing level sets without needing to change algorithms designed for regular grids. An example application, an interactive sculpting tool, is presented to illustrate the structure.