Journal
ACM TRANSACTIONS ON GRAPHICS
Volume 39, Issue 4, Pages -Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3386569.3392435
Keywords
bijective parameterizations; coarse shell meshes; triangle inequality-based barriers
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Funding
- National Natural Science Foundation of China [61802359, 61672482, 11626253]
- USTC Research Funds of the Double First-Class Initiative [YD0010002003]
- Anhui Provincial Natural Science Foundation [1808085QF208]
- Zhejiang Lab [2019NB0AB03]
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We propose a novel method to efficiently compute bijective parameterizations with low distortion on disk topology meshes. Our method relies on a second-order solver. To design an efficient solver, we develop two key techniques. First, we propose a coarse shell to substantially reduce the number of collision constraints that are used to guarantee overlap-free boundaries. During the optimization process, the shell ensures the Hessian matrix with a fixed nonzero structure and a low density, thereby significantly accelerating the optimization. The second is a triangle inequality-based barrier function that effectively ensures non-intersecting boundaries. Our barrier function is C-infinity inside the locally supported region and its convex second-order approximation is able to be analytically obtained. Compared to state-of-the-art methods for optimizing bijective parameterizations, our method exhibits better scalability and is about six times faster. The performance of our bijective parameterization algorithm is comparable to state-of-the-art methods of locally flip-free parameterizations. A large number of experimental results have shown the capability and feasibility of our method.
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