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[PV+06]  Computing Contour Generators of Evolving Implicit Surfaces

Plantinga:2006:CCG (Article)
Author(s)Plantinga S. and Vegter G.
Title« Computing Contour Generators of Evolving Implicit Surfaces »
JournalACM Transactions on Graphics
Volume25
Number4
Page(s)1243--1280
Year2006

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 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 apparent contour for both generic views and generic time-dependent projections, for example, 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 by using a dynamic step size. An interval test guarantees the topological correctness. This initial contour generator can thus be maintained under a time-dependent projection by examining its singularities.

BibTeX code
@article{Plantinga:2006:CCG,
  optpostscript = {},
  number = {4},
  month = oct,
  author = {Simon Plantinga and Gert Vegter},
  optkey = {},
  optannote = {},
  localfile = {papers/Plantinga.2006.CCG.pdf},
  optkeywords = {},
  doi = {http://doi.acm.org/10.1145/1183287.1183288},
  optciteseer = {},
  journal = j-TOG,
  opturl = {},
  volume = {25},
  optwww = {},
  title = {{C}omputing {C}ontour {G}enerators of {E}volving {I}mplicit
           {S}urfaces},
  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 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 apparent contour
              for both generic views and generic time-dependent projections, for
              example, 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 by using a dynamic step size. An
              interval test guarantees the topological correctness. This initial
              contour generator can thus be maintained under a time-dependent
              projection by examining its singularities.},
  pages = {1243--1280},
  year = {2006},
}

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