Download e-book for iPad: Mesh parameterization methods and their applications by Alla Sheffer, Emil Praun, Kenneth Rose

By Alla Sheffer, Emil Praun, Kenneth Rose

ISBN-10: 1933019433

ISBN-13: 9781933019437

ISBN-10: 1933019891

ISBN-13: 9781933019895

Parameterizations among floor meshes and numerous domain names have a number of functions in special effects and geometry processing. in recent times various tools for parameterizing meshes were constructed, focusing on different parameter domain names and targeting assorted parameterization homes. Mesh Parameterization equipment and their purposes experiences a few of the parameterization tools, summarizing the most principles of every method and targeting the sensible elements of the equipment. It additionally offers examples of the consequences generated by means of a number of the extra well known equipment. whilst a number of equipment tackle a similar parameterization challenge, the survey strives to supply an target comparability among them in line with standards corresponding to parameterization caliber, potency and robustness. Mesh Parameterization tools and their purposes presents information to researchers and builders whilst assessing the suitability of alternative equipment for varied functions. The authors specialise in the sensible facets of the equipment to be had, resembling time complexity and robustness. in addition they supply a number of examples of parameterizations generated utilizing diverse equipment, permitting the reader to visually review and evaluate the implications.

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Fig. 5 Mappings to base, visualizing derivative magnitudes of the tangent field (gray: small; red: large). The figures come from Khodakovsky et al. [63]. 1. Simplicial and Quadrilateral Complexes 45 A transition function expresses the barycentric coordinates of a vertex with respect to a base domain face as barycentric coordinates for a neighboring base domain face. For this procedure, only the images of the base domain vertices needs to be fixed, rather than the edges as well as in the previous methods.

4. While methods that segment meshes into multiple charts implicitly generate charts with disk topology, seam cutting methods, such as those of Sheffer and Hart [117] and Gu et al. [41] require an explicit pre-processing stage to convert surfaces with high genus into topological disks. The generation of minimal length cuts that convert a high genus surface into a topological disk is NP-hard [30]. Lazarus et al. [70] introduce a method for extraction of canonical schema, converting a high genus surface into a topological disk which in practice produces relatively short cuts.

All of these techniques are very efficient and simple to implement as they only require solving a single linear system. 2. 3), or boundaries that differ significantly from the specified boundary of the planar domain. Thus, these techniques work best when the inputs have well-shaped nearly convex boundaries. 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.

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

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