Mappings between Disks and Polygons

25 Feb 2019

Mappings between squares and disks have applications in computer graphics, and are interesting mathematically. Mappings between triangles and disks are less well-studied, but also interesting. Both can also be used as map projections in combination with a map projection from a hemisphere to a disk. In this Jupyter notebook, I implemented a bunch of mappings from disks to triangles and squares and calculated their area and conformal distortion.

Plots of the conformal mapping from the disk to a square or triangle.

2023-11-04: Spherical area coordinates, and a derived triangle center
2023-07-29: Homogeneous coordinates on the sphere with vectors
2022-08-30: Scaling the Schwarz triangle function
2022-08-27: Edges in the image of the Schwarz triangle function
2022-07-20: Area-preserving swirling of the disk
2022-03-03: Some dubious ways to calculate conformal polyhedral projections
2021-10-02: A variation on the Chamberlin trimetric map projection
2021-08-31: Snyder's equal-area projection
2021-06-12: Perspective projections with vectors
2021-05-29: A (sort of) Euclidean triangle on a non-Euclidean surface

Mappings between Disks and Polygons

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