ARAP plus plus : an extension of the local/global approach to mesh parameterization

作者：Wang, Zhao; Luo, Zhong-xuan^*; Zhang, Jie-lin; Saucan, Emil

来源：Frontiers of Information Technology and Electronic Engineering, 2016, 17(6): 501-515.

DOI：10.1631/FITEE.1500184

• Mesh parameterization
• Convex combination weights
• Stretch operator
• Jacobian matrix

Mesh parameterization is one of the fundamental operations in computer graphics (CG) and computeraided design (CAD). In this paper, we propose a novel local/global parameterization approach, ARAP++, for single-and multi-boundary triangular meshes. It is an extension of the as-rigid-as-possible (ARAP) approach, which stitches together 1-ring patches instead of individual triangles. To optimize the spring energy, we introduce a linear iterative scheme which employs convex combination weights and a fitting Jacobian matrix corresponding to a prescribed family of transformations. Our algorithm is simple, efficient, and robust. The geometric properties (angle and area) of the original model can also be preserved by appropriately prescribing the singular values of the fitting matrix. To reduce the area and stretch distortions for high-curvature models, a stretch operator is introduced. Numerical results demonstrate that ARAP++ outperforms several state-of-the-art methods in terms of controlling the distortions of angle, area, and stretch. Furthermore, it achieves a better visualization performance for several applications, such as texture mapping and surface remeshing.

• 出版日期2016-6
• 单位大连理工大学