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Convex boundary angle based flattening

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

April 2003, 16 pages.

Status: available - back from printing

Angle Based Flattening is a robust parameterization method that finds a quasi-conformal mapping by solving a non-linear optimization problem. We take advantage of a characterization of convex planar drawings of triconnected graphs to introduce new boundary constraints. This prevents boundary intersections and avoids post-processing of the parameterized mesh. We present a simple transformation to e ectively relax the constrained minimization problem, which improves the convergence of the optimization method. As a natural extension, we discuss the construction of Delaunay flat meshes. This may further enhance the quality of the resulting parameterization.

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  AUTHOR = {Zayer, Rhaleb and Roessl, Christian and Seidel, Hans-Peter},
  TITLE = {Convex boundary angle based flattening},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2003-4-003},
  MONTH = {April},
  YEAR = {2003},
  ISSN = {0946-011X},