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A Semi‐Lagrangian Closest Point Method for Deforming Surfaces
Author(s) -
Auer S.,
Westermann R.
Publication year - 2013
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12228
Subject(s) - polygon mesh , triangulation , eulerian path , lagrangian , surface (topology) , computer science , representation (politics) , point (geometry) , flow (mathematics) , augmented lagrangian method , material point method , mathematics , geometry , algorithm , computer graphics (images) , finite element method , physics , politics , political science , law , thermodynamics
We present an Eulerian method for the real‐time simulation of intrinsic fluid dynamics effects on deforming surfaces. Our method is based on a novel semi‐Lagrangian closest point method for the solution of partial differential equations on animated triangle meshes. We describe this method and demonstrate its use to compute and visualize flow and wave propagation along such meshes at high resolution and speed. Underlying our technique is the efficient conversion of an animated triangle mesh into a time‐dependent implicit representation based on closest surface points. The proposed technique is unconditionally stable with respect to the surface deformation and, in contrast to comparable Lagrangian techniques, its precision does not depend on the level of detail of the surface triangulation.