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Partwise Cross-Parameterization via Nonregular Convex Hull Domains
October 2011 (vol. 17 no. 10)
pp. 1531-1544
Huai-Yu Wu, Peking University, Beijing and Chinese Academy of Sciences, Beijing
Chunhong Pan, Chinese Academy of Sciences, Beijing
Hongbin Zha, Peking University, Beijing
Qing Yang, Chinese Academy of Sciences, Beijing
Songde Ma, Chinese Academy of Sciences, Beijing
In this paper, we propose a novel partwise framework for cross-parameterization between 3D mesh models. Unlike most existing methods that use regular parameterization domains, our framework uses nonregular approximation domains to build the cross-parameterization. Once the nonregular approximation domains are constructed for 3D models, different (and complex) input shapes are transformed into similar (and simple) shapes, thus facilitating the cross-parameterization process. Specifically, a novel nonregular domain, the convex hull, is adopted to build shape correspondence. We first construct convex hulls for each part of the segmented model, and then adopt our convex-hull cross-parameterization method to generate compatible meshes. Our method exploits properties of the convex hull, e.g., good approximation ability and linear convex representation for interior vertices. After building an initial cross-parameterization via convex-hull domains, we use compatible remeshing algorithms to achieve an accurate approximation of the target geometry and to ensure a complete surface matching. Experimental results show that the compatible meshes constructed are well suited for shape blending and other geometric applications.

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Index Terms:
Cross-parameterization, nonregular approximation domains, convex hull, critical points, compatible remeshing, sketch-based segmentation.
Huai-Yu Wu, Chunhong Pan, Hongbin Zha, Qing Yang, Songde Ma, "Partwise Cross-Parameterization via Nonregular Convex Hull Domains," IEEE Transactions on Visualization and Computer Graphics, vol. 17, no. 10, pp. 1531-1544, Oct. 2011, doi:10.1109/TVCG.2010.231
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