Journal
ACM TRANSACTIONS ON GRAPHICS
Volume 36, Issue 4, Pages -Publisher
ASSOC COMPUTING MACHINERY
DOI: 10.1145/3072959.3073646
Keywords
mesh parametrization; global parametrization; injective maps; discrete harmonic
Categories
Funding
- Israel Science Foundation [1869/15, 2102/15]
Ask authors/readers for more resources
We present a method for locally injective seamless parametrization of triangular mesh surfaces of arbitrary genus, with or without boundaries, given desired cone points and rational holonomy angles (multiples of 2 pi/q for some positive integer q). The basis of the method is an elegant generalization of Tutte's spring embedding theorem to this setting. The surface is cut to a disk and a harmonic system with appropriate rotation constraints is solved, resulting in a harmonic global parametrization (HGP) method. We show a remarkable result: that if the triangles adjacent to the cones and boundary are positively oriented, and the correct cone and turning angles are induced, then the resulting map is guaranteed to be locally injective. Guided by this result, we solve the linear system by convex optimization, imposing convexification frames on only the boundary and cone triangles, and minimizing a Laplacian energy to achieve harmonicity. We compare HGP to state-of-the-art methods and see that it is the most robust, and is significantly faster than methods with comparable robustness.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available