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[PV+03b]  Contour Generators of Evolving Implicit Surfaces

Plantinga:2003:CGE (In proceedings)
Author(s)Plantinga S. and Vegter G.
Title« Contour Generators of Evolving Implicit Surfaces »
InProceedings of the Eighth ACM Symposium on Solid Modeling and Applications (SM 2003, Seattle, Washington, USA)
Page(s)23--32
Year2003
PublisherACM Press
AddressNew York

Abstract
The contour generator is an important visibility feature of a smooth object seen under parallel projection. It is the curve on the surface which separates front-facing regions from back facing regions. The apparent contour is the projection of the contour generator onto a plane perpendicular to the view direction. Both curves play an important role in computer graphics. Our goal is to obtain fast and robust algorithms that compute the contour generator with a guarantee of topological correctness. To this end, we first study the singularities of the contour generator and the apparent contour, for generic views, and for generic time-dependent projections, e.g. when the surface is rotated or deformed. The singularities indicate when components of the contour generator merge or split as time evolves.We present an algorithm to compute an initial contour generator, using a dynamic step size. An interval test guarantees the topological correctness. This initial contour generator can then be maintained under a time-dependent projection by examining its singularities.

BibTeX code
@inproceedings{Plantinga:2003:CGE,
  opteditor = {},
  optpostscript = {},
  optorganization = {},
  author = {Simon Plantinga and Gert Vegter},
  optkey = {},
  optannote = {},
  optseries = {},
  address = {New York},
  localfile = {papers/Plantinga.2003.CGE.pdf},
  optisbn = {},
  publisher = {ACM Press},
  optkeywords = {},
  doi = {http://doi.acm.org/10.1145/781606.781614},
  optmonth = {},
  optciteseer = {},
  opturl = {},
  optcrossref = {},
  optwww = {},
  booktitle = {Proceedings of the Eighth ACM Symposium on Solid Modeling and
               Applications (SM 2003, Seattle, Washington, USA)},
  optvolume = {},
  optnumber = {},
  abstract = {The contour generator is an important visibility feature of a
              smooth object seen under parallel projection. It is the curve on
              the surface which separates front-facing regions from back facing
              regions. The apparent contour is the projection of the contour
              generator onto a plane perpendicular to the view direction. Both
              curves play an important role in computer graphics. Our goal is to
              obtain fast and robust algorithms that compute the contour
              generator with a guarantee of topological correctness. To this
              end, we first study the singularities of the contour generator and
              the apparent contour, for generic views, and for generic
              time-dependent projections, e.g. when the surface is rotated or
              deformed. The singularities indicate when components of the
              contour generator merge or split as time evolves.We present an
              algorithm to compute an initial contour generator, using a dynamic
              step size. An interval test guarantees the topological
              correctness. This initial contour generator can then be maintained
              under a time-dependent projection by examining its
              singularities.},
  title = {{C}ontour {G}enerators of {E}volving {I}mplicit {S}urfaces},
  year = {2003},
  pages = {23--32},
}

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