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r-adaptive parameterization of surfaces

Zayer, Rhaleb and Rössl, Christian and Seidel, Hans-Peter

MPI-I-2004-4-004. June 2004, 16 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
Surface mesh parameterization is a fundamental tool in
computer graphics, required for applications like e.g. texture mapping,
remeshing and morphing. Linear parameterization methods are of particular
interest. Their simplicity, efficiency and robustness, enables the
processing of detailed, large meshes. In practice, however,
the current linear schemes are limited to producing (quasi-)conformal
parameterizations and hence may suffer from considerable distortion e.g.
in length and area.
We present a novel approach to effectively reduce parametric
distortion. Our algorithm is simple, efficient and robust, as it
requires only the solution of a sparse linear system.
We smoothly adapt an existing quasi-conformal parameterization with
respect to different flow quantities such as areas, angles or edge
lengths. Our adaptive strategy offers a flexible means for
controlling distortion based on error equidistribution.
We show how this method can be extended from the planar setting to
spherical parameterizations, a problem which recently attracted a
lot of interest.
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  AUTHOR = {Zayer, Rhaleb and R{\"o}ssl, Christian and Seidel, Hans-Peter},
  TITLE = {r-adaptive parameterization of surfaces},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2004-4-004},
  MONTH = {June},
  YEAR = {2004},
  ISSN = {0946-011X},