Cross-ratios and angles determine a polygon
Proceedings of the fourteenth annual symposium on Computational geometry
Optimal Möbius Transformations for Information Visualization and Meshing
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
Algorithm 843: Improvements to the Schwarz-Christoffel toolbox for MATLAB
ACM Transactions on Mathematical Software (TOMS)
Asymptotic Gauss--Jacobi quadrature error estimation for Schwarz--Christoffel integrals
Journal of Approximation Theory
Finite volume numerical simulation of viscoelastic flows in general orthogonal coordinates
Mathematics and Computers in Simulation
Delaunay triangulation by a technical insertion point applied for complexes geometries
Journal of Computational Methods in Sciences and Engineering - Intelligent Systems and Knowledge Management (Part II)
Conjugate function method for numerical conformal mappings
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz--Christoffel transformation. The new algorithm, CRDT (for cross-ratios of the Delaunay triangulation), is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. We believe that CRDT solves all difficulties with crowding and global convergence, although these facts depend on conjectures that we have so far not been able to prove. We demonstrate convergence with computational experiments. The Riemann mapping has applications in two-dimensional potential theory and mesh generation. We demonstrate CRDT on problems in long, thin regions in which no other known algorithm can perform comparably.