4.0. Overlap between shapes

It is critical to determine rapidly, the degree of overlap between adjacent polygons on a two-dimensional plane^[3] when the optimisation process drives parts to intermediate locations.

^[3] Warped planes in 3-d can be formed from 2-d shapes laid in3d forms.

Consider a case where three parts comprise of polygons of 1, m and n sides respectively. If overlap detection for all sides of all polygons was made. (Im+nm+ln) calculations are required to test whether every line comprising each of the three polygons intersects another. Most practical part enveloping polygons can have m excess of 50 sides, In order to reduce this complexity of calculation for every iteration of an optimisation process, the authors enveloped every part with a dynamic rectangular bounding rectangle.