# Triangular tiles

mhwombat edited this page Jun 27, 2013 · 1 revision

## Triangular tiles

UnboundedTriGrid is an infinite, unbounded, grid filled with triangular tiles. The indexing scheme is illustrated below. If the x-coordinate is even, the triangle points up; if it's odd, the triangle points down. A line of tiles on a diagonal like / will have the same value for x. The quations used are presented in Implementation: Triangular tiles.

triTriGrid s returns a triangular grid with sides of length s, using triangular tiles.

As the size increases, the centre of the grid cycles between being a triangle pointing up, a triangle pointing down, and three triangles arranged to form a trefoil. In the diagram below, the central tiles are shaded grey.

paraTriGrid r c returns a grid in the shape of a parallelogram with r rows and c columns, using triangular tiles. The indexing scheme is illustrated below. If the x-coordinate is even, the triangle points up; if it's odd, the triangle points down. A line of tiles on a diagonal like / will have the same value for x.

Depending on whether the number of rows and columns is even or odd, the centre of the grid may be two tiles forming a lozenge leaning to the left, two tiles forming a lozenge leaning to the right, two tiles forming an upright lozenge, or tiles arranged to one or three "bowties". In the diagram below, the central tiles are shaded grey.

rectTriGrid r c returns a rectangular grid with r rows and c columns, using triangular tiles. In the current implementation, the number of rows must be even. The indexing scheme is illustrated below. If the x-coordinate is even, the triangle points up; if it's odd, the triangle points down. A line of tiles on a diagonal like / will have the same value for x.

torTriGrid r c returns a toroidal grid with r rows and c columns, using triangular tiles. The indexing scheme is illustrated below. If the x-coordinate is even, the triangle points up; if it's odd, the triangle points down. A line of tiles on a diagonal like / will have the same value for x.

yCylTriGrid r c returns a cylindrical grid with r rows and c columns, using triangular tiles. The indexing scheme is illustrated below. If the x-coordinate is even, the triangle points up; if it's odd, the triangle points down. A line of tiles on a diagonal like / will have the same value for x.

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