There are three address spaces for a grid: cells, edges and vertices. The cell address space is the natural address space by the row and column of the cell. For example, if a grid is m x n cells, the top-left cell is at address (0, 0), the top-right cell is at address (0, n - 1), the bottom right cell is at address (m - 1, n - 1), and so on.
The vertex address space corresponds to the cell address to the south east of the vertex. So, for example, in a grid with m x n cells, the vertex at the top left is at address (0, 0) because the cell to the south east of it is cell (0, 0). The special case is for vertices at the right or bottom of the grid because these vertices do not have cells to their south easts. In these cases the vertices have the address that a cell would have if there was one to their south east. For example, in an m x n grid, the top right vertex has address (0, n), the bottom right vertex has address (m, n) and so on.
The edge address space is made up of horizontal and vertical edges. For a horizontal edge, it will have the address of the vertex at its left tip. For a vertical edge, it will have the address of the vertex at its top tip.cs
v(0,0) ----- e(0,0,h) ----- v(0,1) ----- ... ----- e(0,n-1,h) ----- v(0,n)
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e(0,0,v) c(0,0) e(0,1,v) ... c(0,n-s) e(0,n,v)
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v(1,0) ----- e(1,0,h) ----- v(1,1) ----- ... ----- e(1,n-1,h) ------ v(1,n)
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. . . . .
. . . . .
. . . . .
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v(m-1,0) -- e(m-1,0,h) -- v(m-2,1) ----- ... ---- e(m-1,n-1,h) ----- v(m-1,n)
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e(m-1,0,v) c(m-1,1) e(m-1,1,v) ... c(m-1,n-2) e(m-1,n,v)
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v(m,0) ----- e(m,0,h) ----- v(m,1) ----- ... ----- e(m,n-1,h) ------ v(m,n)