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Discrete multiscale vector field decomposition
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DOI：10.1145/882262.882290.png)
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While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-difference methods. In this paper. we propose a set of simple and accurate tools for the analysis of 3D discrete vector fields on arbitrary tetrahedral,rids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergence-free part, a curl-free part. and a harmonic part. We show how our discrete approach matches its well-known smooth analog, called the Helmotz-Hodge decomposition, and that the resulting computational tools have very intuitive geometric interpretation. We demonstrate the versatility of these tools in a series of applications, ranging from data visualization to fluid and deformable object simulation.
Keyword:
vector fields
variational approaches
Hodge decomposition
scale-space description
animation
visualization
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