Patterns on a surface: the reconciliation of the circle and the square

Chris J K Williams

doi:10.1007/s00004-011-0068-2

Patterns on a surface: the reconciliation of the circle and the square

Chris J K Williams

Department of Architecture & Civil Engineering

Research output: Contribution to journal › Article › peer-review

4 Citations (SciVal)

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Abstract

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.

Original language	English
Pages (from-to)	281-295
Number of pages	15
Journal	Nexus Network Journal
Volume	13
Issue number	2
Early online date	7 Jun 2011
DOIs	https://doi.org/10.1007/s00004-011-0068-2
Publication status	Published - 1 Jul 2011

Keywords

isothermal coordinates
tension coefficient
dynamic relaxation
tiling
differential geometry
harmonic coordinates

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10.1007/s00004-011-0068-2

Williams_Nexus-Network-Journal_2011_13_2_281.pdf
The original publication is available at www.springerlink.com
Accepted author manuscript, 7.44 MB

Cite this

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AB - 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.

KW - isothermal coordinates

KW - tension coefficient

KW - dynamic relaxation

KW - tiling

KW - differential geometry

KW - harmonic coordinates

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Patterns on a surface: the reconciliation of the circle and the square

Abstract

Keywords

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