Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computational Geometry: Theory and Applications
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Discrete exterior calculus
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
| Hi-index | 0.01 |
We introduce a novel method for the construction of discrete conformal mappings from (regions of) embedded meshes to the plane. Our approach is based on circle patterns, i.e., arrangements of circles---one for each face---with prescribed intersection angles. Given these angles the circle radii follow as the unique minimizer of a convex energy. The method has two principal advantages over earlier approaches based on discrete harmonic mappings: (1) it supports very flexible boundary conditions ranging from natural boundaries to control of the boundary shape via prescribed curvatures; (2) the solution is based on a convex energy as a function of logarithmic radius variables with simple explicit expressions for gradients and Hessians, greatly facilitating robust and efficient numerical treatment. We demonstrate the versatility and performance of our algorithm with a variety of examples.