Mesh parameterization methods and their applications by Alla Sheffer, Emil Praun, Kenneth Rose

By Alla Sheffer, Emil Praun, Kenneth Rose

Parameterizations among floor meshes and numerous domain names have quite a few functions in special effects and geometry processing. in recent times a variety of tools for parameterizing meshes were constructed, concentrating on diversified parameter domain names and targeting varied parameterization homes. Mesh Parameterization tools and their functions reports a number of the parameterization tools, summarizing the most principles of every method and targeting the sensible points of the tools. It additionally presents examples of the consequences generated through the various extra well known tools. while numerous tools tackle an analogous parameterization challenge, the survey strives to supply an target comparability among them according to standards similar to parameterization caliber, potency and robustness. Mesh Parameterization equipment and their functions presents tips to researchers and builders whilst assessing the suitability of alternative tools for numerous functions. The authors concentrate on the sensible elements of the tools to be had, resembling time complexity and robustness. in addition they offer a number of examples of parameterizations generated utilizing assorted equipment, permitting the reader to visually assessment and evaluate the implications.

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1) the input mesh is first segmented into nearly triangular patches. In this setting, the fixed-boundary methods introduce very little distortion when mapping the patches to the corresponding triangular base mesh faces. To reduce the distortion, the boundary of the 2D domain can be computed as part of the solution. Lee et al. 6(a)). The virtual boundary is fixed onto a given convex polygon and the mapping for the rest of the vertices is computed using Floater’s method [32]. 6). A similar idea was used by Kos and Varady [65].

To prevent flips, vertices are only permitted to move inside the kernel of neighboring vertices. When moving boundary vertices, the method also checks for boundary overlaps and prevents those. Thus, it guarantees that the resulting parameterization remains globally bijective throughout the procedure. The authors advocate the use of conformal mapping for remeshing [69] and surface fitting [53]. Instead of defining a planar parameterization in terms of vertex coordinates, the ABF method [113,114] defines it in terms of the angles of the planar triangles.

Hence existing methods aim at 28 Parameterization of Topological Disks minimizing linear distortion rather than completely eliminating it. Early parameterization techniques [7, 84, 78] introduced distance minimizing formulations which were numerically quite complex and thus hard to minimize. Sander et al. [107] introduce two metrics of parameterization stretch (L2 and L∞ ), described in Section 2. These two stretch metrics are now commonly used for comparing linear distortion between parameterizations [138, 118, 62].

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