SIAM Journal on Computing
A fast algorithm to solve the Beltrami equation with applications to quasiconformal mappings
Journal of Computational Physics
Least squares conformal maps for automatic texture atlas generation
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
ABF++: fast and robust angle based flattening
ACM Transactions on Graphics (TOG)
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Conformal equivalence of triangle meshes
ACM SIGGRAPH 2008 papers
Globally Optimal Surface Mapping for Surfaces with Arbitrary Topology
IEEE Transactions on Visualization and Computer Graphics
IEEE Transactions on Visualization and Computer Graphics
Improving Chen and Han's algorithm on the discrete geodesic problem
ACM Transactions on Graphics (TOG)
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
A local/global approach to mesh parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Computing Extremal Quasiconformal Maps
Computer Graphics Forum
Computing quasiconformal maps using an auxiliary metric and discrete curvature flow
Numerische Mathematik
Interactive Applications for Sketch-Based Editable Polycube Map
IEEE Transactions on Visualization and Computer Graphics
An Intrinsic Algorithm for Parallel Poisson Disk Sampling on Arbitrary Surfaces
IEEE Transactions on Visualization and Computer Graphics
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Quasi-conformal maps have bounded conformal distortion, and are the natural extension of the conformal maps. The existing techniques to compute the quasi-conformal map require a global coordinate system; thus, they are limited to models of simple topological types, such as genus-0 or 1 surfaces, for which one can obtain the global coordinates by the global parameterization. This paper presents a simple yet effective technique for computing a quasi-conformal map on surfaces of non-trivial topology. Our method extends the quasi-conformal iteration method (Lui et al., 2012) [8] from the complex plane to the manifold setting. It requires neither numerical solver nor the global coordinate system, thus, is easy to implement. Moreover, thanks to its simple and parallel structure, our method is well suited for parallel computing. Experimental results on 3D models of various topological types demonstrate the efficacy of our technique.