Patterns on a surface

Chris J K Williams

OAI: oai:purehost.bath.ac.uk:openaire_cris_publications/5389fd5c-af06-4061-9453-b3ca775c2ceb • DOI: https://doi.org/10.1007/s00004-011-0068-2

The theory of heat flow on a surface shows that any curvilinear quadrilateral can be ‘tiled’ with curvilinear squares of varying size. This paper demonstrates a simple numerical technique for doing this that can also be applied to shapes other than quadrilaterals. In particular, any curvilinear triangle can be tiled with curvilinear equilateral triangles.

isothermal coordinates tension coefficient Dynamic relaxation tiling Differential geometry harmonic coordinates