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Last time, we looked at quarter-tiles. This was an auto-tiling technique for square grids. Each cell in the grid is associated with a terrain (i.e. either solid or empty). Then the squares were split in four, and each quarter was assigned an appropriate quarter-tile.

Otho-tiles extends this procedure to work with irregular grids, even non-square grids. We just have to alter the procedure a little, and be ready to deform the quarter tiles fit in place.

Ortho is a Conway Operator. It can be thought of as the extension of dividing a square into 4. It divides each n-gon into n “kites” or “ortho-cells”. Each kite is a four sided shape containing the cell center, one corner, and the midpoint of the two edges adjacent to that corner.

The appeal of the ortho operation is it can take any polygonal grid, no matter how irregular, and convert it into a grid of 4 sided shapes. And it’s much easier to work with something that has a consistent number of sides.

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