17th International Meshing Roundtable
Pittsburgh, Pennsylvania, U.S.A.
October 12-15, 2008
Meshing & Abstraction Group
Digital Simulation Solutions
2000 Eastman Dr., Milford, Ohio 45244 USA
A method of flattening 3D triangulations for use in surface meshing is presented.
The flattening method supports multiple boundary loops and directly produces planar locations
for the vertices of the triangulation. The general nonlinear least-square fit condition for the
triangle vertices includes conformal (angle preserving) and authalic (area preserving) conditions
as special cases. The method of Langrange multipliers is used to eliminate rotational and
translation degrees of freedom and enforce periodic boundary conditions. Using matrix partitioning,
several alternative sets of constraints can be efficiently tested to find which produces
the best domain. A surface boundary term is introduced to improve domain quality and break
the symmetry of indeterminate multi-loop problems. The nonlinear problems are solved using
a scaled conformal result as the initial input. The resulting 2D domains are used to generate 3D
surface meshes. Results indicate that best mesh quality is achieved with domains generated
using an intermediate altitude preserving condition. Apart from an admirable robustness and
overall efficiency, the 2D developed domains are particularly suited for structured transfinite/
mapped meshes which often reveal wiggly irregularities with most conventional developed
domains. Flattening and meshing (both free and transfinite/mapped) results are presented for
several 3D triangulations.
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