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[ZMT+04]  Vector Field Design on Surfaces

Zhang:2004:VFD (Technical report)
Author(s)Zhang E., Mischaikow K. and Turk G.
Title« Vector Field Design on Surfaces »
NumberGIT-GVU-04-16
InstitutionGeorgia Institute of Technology, GVU Center
Year2004
URLhttp://www.cc.gatech.edu/gvu/reports/2004/abstracts/04-16.html

Abstract
Vector field design on surfaces is necessary for many graphics applications: example-based texture synthesis, non-photorealistic rendering, and fluid simulation. A vector field design system should allow a user to create a large variety of complex vector fields with relatively little effort. In this paper, we present a vector field design system for surfaces that allows the user to control the number of singularities in the vector field and their placement. Our system combines basis vector fields to make an initial vector field that meets the user's specifications. The initial vector field often contains unwanted singularities. Such singularities cannot always be eliminated, due to the Poincare-Hopf index theorem. To reduce the effect caused by these singularities, our system allows a user to move a singularity to a more favorable location or to cancel a pair of singularities. These operations provide topological guarantees for the vector field in that they only affect the user-specified singularities. Other editing operations are also provided so that the user may change the topological and geometric characteristics of the vector field. We demonstrate our vector field design system for several applications: example-based texture synthesis, painterly rendering of images, and pencil sketch illustrations of smooth surfaces.

BibTeX code
@techreport{Zhang:2004:VFD,
  optpostscript = {},
  www = {http://web.engr.oregonstate.edu/~zhange/vecfld_design.html},
  number = {GIT-GVU-04-16},
  optaddress = {},
  author = {Eugene Zhang and Konstantin Mischaikow and Greg Turk},
  optkey = {},
  optannote = {},
  opttype = {},
  url = {http://www.cc.gatech.edu/gvu/reports/2004/abstracts/04-16.html},
  localfile = {papers/Zhang.2004.VFD.pdf},
  optkeywords = {},
  optmonth = {},
  optciteseer = {},
  optdoi = {},
  abstract = {Vector field design on surfaces is necessary for many graphics
              applications: example-based texture synthesis, non-photorealistic
              rendering, and fluid simulation. A vector field design system
              should allow a user to create a large variety of complex vector
              fields with relatively little effort. In this paper, we present a
              vector field design system for surfaces that allows the user to
              control the number of singularities in the vector field and their
              placement. Our system combines basis vector fields to make an
              initial vector field that meets the user's specifications. The
              initial vector field often contains unwanted singularities. Such
              singularities cannot always be eliminated, due to the
              Poincare-Hopf index theorem. To reduce the effect caused by these
              singularities, our system allows a user to move a singularity to a
              more favorable location or to cancel a pair of singularities.
              These operations provide topological guarantees for the vector
              field in that they only affect the user-specified singularities.
              Other editing operations are also provided so that the user may
              change the topological and geometric characteristics of the vector
              field. We demonstrate our vector field design system for several
              applications: example-based texture synthesis, painterly rendering
              of images, and pencil sketch illustrations of smooth surfaces.},
  title = {{V}ector {F}ield {D}esign on {S}urfaces},
  year = {2004},
  institution = {Georgia Institute of Technology, GVU Center},
}

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