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 (F²→Bool) × (F²→Bool) → (F²→Bool).

For_each q ∈ F² and M_a, M_b ∈ F² → Bool:

(M_a*M_b)q := ⋁_{p ∈ F²} : M_a(p) ∧ M_b(q−p)

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

See also: Boost Polygon’s minkowski tutorial