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An Intro to Diagonal and Orthogonal Movement on Exotic Grids Part 2

May 20, 2012

Part 1: Squares Hexagons and Triangles
Part 2: Pentagons and Octogons
Part 3: Septagins, Nonogons, and Decagons

This is Pentagon Tessellation, pentagonal grid, pent grid, etc

There are a wide variety of pentagon grids, of multiple shapes, orientations, and patterns. This Pent Grid is composed of two different pentagons, and each different pentagon varies between two different orientations.

A Rook on a Pent Grid

Like the triangle grid in the previous post, strict orthogonal movement encounters corners with regularity. So to create a single trajectory, the rook must oscillate between two directions. Rank 1 Orthogonal Alt 2.

For 4 of the cardinal directions this creates clean movement, the rook alternates color and shape in a single path. The fifth direction proves to be slightly different, the straight down path. On this path, the rook passes from a white pentagon of one orientation to a white pentagon of the second orientation. It then makes two moves to return to the pentagon that matches the first.

This could be considered a Rank 3 movement; however, moving from white pentagon to white pentagon occurs in the original movement and does not deviate. The combined vectors of the other two movements equal the vector from the white to white movement. While this is a Rank 3 movement, I would include it as a standard move on a pentagrid, as it acts closer to a fifth cardinal direction than a Rank 1 or 2 movement would be in this circumstance.

The Pent Grid is the first grid where different ranks of movement make sense along different cardinal directions. With many odd numbered grids, there is one side of a shape that creates an altered movement pattern. There are multiple choices to resolve these possibilities, I certainly don’t have any objective answers, but when making these decisions gameplay is my primary concern.

A Bishop on a Pent Grid

Like Orthogonal movement, diagonal movement on a Pent Grid occurs with 2 different ranks of movement. Lateral movement occurs corner to corner, Rank 0 movement, while vertical movement travels along 1 edge, Rank 1 Movement.

For 3 of the pentagon’s vertices, Rank 0 movement is impossible without crossing an edge, but perfectly reasonable for the last two corners. Rank 1 movement is also possible from every corner, and would certainly be a possible choice for movement options. However, including rank 0 diagonal movement instead of rank 1 where possible in this instance differentiates diagonal and orthogonal moves to a greater extent and maintains 5 very clean cardinal directions. Bishops’ movement remains only on one color tile, but there is some overlap of orthogonal and diagonal movement from the same square. The pent grid is a messy place, but solid rules up front would make it a very interesting place to play.

There have been some rules floating around about movement on grids of this type, but certainly nothing standardized.

This is a Octagon Tessellation, square and octagon grid, 8&4 Grid, or Octo Grid

The Octo Grid is a tessellation comprised of two shapes in a repeating pattern. Where the pent grid was a messy ordeal, the octo grid is fairly straightforward. Though the addition of a shape with a different number of sides creates two different movement templates depending on the originating square.

A Rook on a Octo Grid

Easy to visualize, an octagon has 8 sides that it shares completely with a single separate space. Because the shapes maintain the same orientation, alternating movement trajectories are not necessary. With 8 cardinal directions, the rook has many, many movement options. Interesting, from a square, its movement options are similar but reduced to 4 movement options.

A Bishop on an Octo Grid

Alternately, the bishop has comparatively few movement options. There are no rank 0 movement’s available, and each pair of corners connects to a single octagon, halving the bishops movement options. At first glance, the bishop looks to have only a subset of the rooks movements; however, the bishop “jumps” the squares, moving only along octagon of one color. Not always optimal, but this does prove to be an interesting movement mechanic depending on the type of game you would use it for. From octagon, there is some overlap between orthogonal and diagonal movements, but interestingly, it still takes two spaces of orthogonal movement to account for a single diagonal move.

Furthermore, Bishop on a Square,

Interestingly, though the rook loses half of its movement options while on a square, the bishop maintains its four cardinal directions with Rank 1 movements, but can only move along the square spaces.

That’s it for this section, stay tuned for the next post where we tackle some of the more exotic and confusing grid.


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