Polygon Convolution

Polygon convolution is the convolution of mappings of F2 → Bool, that are represented by polygons that indicate the boundary of the closed subset(s) of F2 that are mapped onto TRUE; were addition is replaced by the or operation. The convolution operator is here represented as * and has type (F2Bool) × (F2Bool) → (F2Bool).

For_each q ∈ F2 and Ma, Mb ∈ F2 → Bool:

(Ma*Mb)q := ⋁p ∈ F2 : Ma(p) ∧ Mb(qp)

Further let Pi := δM**i*, it seems that *δ*(*M**a***M**b*) = *δMa * Mb* ∧ *M**a* * *δM**b similar to the diffential of the product of two functions.

See also: Boost Polygon’s minkowski tutorial