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Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.
Boundary representations, Geometric algorithms, languages, and systems
Charlie Wang, "Computing Length-Preserved Free Boundary for Quasi-Developable Mesh Segmentation", IEEE Transactions on Visualization & Computer Graphics, vol. 14, no. , pp. 25-36, January/February 2008, doi:10.1109/TVCG.2007.1067
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