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the composition was defined as follow:

(a,b) \in (R;S) <=> there is c | (a,c) \in R and (c,b) \in S .

If our two relations R and S are two convex polygon

Is there a geometric interpretation of the composition of two convex polygon ? for example :

the green polygon was the result of composition. How can i describe geometrically the result !!!

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1 Answer

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Will attempt an answer given the following considerations:

1. Elements (i.e $a$, $b$) are seen as points on axes (on some vector space)
2. A (binary) relation $R$ is seen as defining pairs on the vector space

In this sense each (binary) relation $R$ defines a region (or "area" or "surface") on this vector space, by defining which points of the space (i.e ordered pairs of $(a,b)$) belong to it.

So in this sense also, the composition of 2 (binary) relations $R \circ S$ defines a region of the space which is the intersection of the two regions defined by $R$ and $S$, plus all the points (of $R$ and $S$) which lead to or away from these intersection points

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