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Vector field design on surfaces (2006)
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| Citations: | 70 - 19 self |
BibTeX
@MISC{Zhang06vectorfield,
author = {Eugene Zhang and Konstantin Mischaikow and Greg Turk},
title = {Vector field design on surfaces},
year = {2006}
}
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Abstract
Vector field design on surfaces is necessary for many graphics applications: example-based texture synthesis, nonphotorealistic rendering, and fluid simulation. For these applications, singularities contained in the input vector field often cause visual artifacts. In this article, we present a vector field design system that allows the user to create a wide variety of vector fields with control over vector field topology, such as the number and location of singularities. Our system combines basis vector fields to make an initial vector field that meets user specifications. The initial vector field often contains unwanted singularities. Such singularities cannot always be eliminated due to the Poincaré-Hopf index theorem. To reduce the visual artifacts caused by these singularities, our system allows the user to move a singularity to a more favorable location or to cancel a pair of singularities. These operations offer topological guarantees for the vector field in that they only affect user-specified singularities. We develop efficient implementations of these operations based on Conley index theory. Our system also provides other editing operations so that the user may change the topological and geometric characteristics of the vector field. To create continuous vector fields on curved surfaces represented as meshes, we make use of the ideas of geodesic polar maps and parallel transport to interpolate vector values defined at the vertices of the mesh. We also use geodesic polar maps and parallel transport to create basis vector fields on surfaces that meet the user specifications. These techniques enable our vector field design system to work for both planar domains and curved surfaces.
Keyphrases
vector field design vector field basis vector field vector field design system user specification geodesic polar map visual artifact parallel transport initial vector field efficient implementation poincar hopf index theorem curved surface topological guarantee vector field topology input vector field example-based texture synthesis vector value planar domain unwanted singularity fluid simulation continuous vector field nonphotorealistic rendering many graphic application conley index theory favorable location geometric characteristic wide variety user-specified singularity
