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Derivation of ru = SQRT {3( i2 + ij + j2)}


Figure: Example of a reuse pattern i, j.

Note that the axes of coordinates i and j have a relative angle of 60 degrees. The distance between the cell centers can be expressed by invoking Pythagoras for a triangle with one angle of 60 degrees.

Moreover, we use that the distance between the centers of two neighboring cells is SQRT(3) times the size of an edge R of the hexagonal cell. This gives

ru = SQRT {( i2 + 2ijcos(pi/3) + j2)} SQRT{3} R.

Surface Areas

A single cell of edge R has size 
         3 SQRT{3}
SR   = ----------  R2
            2
The surface area of a cluster of C cells is
         3 SQRT{3}   ru2
Sc   = ----------   ----
            2          3
Combining this gives ru = SQRT(3 C) R

back to discussion of reuse patterns



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