The regions are the faces that result from partitioning the park with paths. Actually paths are extruded, but regions are considered separately. The regions are non-walkable, but can represent park partitions like flowerbeds or patches of grass, or a place where the tree is planted.
This is enchancement of the centered partitioning described in the previous post.
The new procedures were created
All vertices are moved towards a centroid by a relative distance to it (distance to centroid/centre is 1, move range clamped to [0 . .0.9].
- Edge Partitioning
Every edge is split with level n, for n = 0 no splitting occurs, for n = 1 we add one vertex in the middle, for n = 2 we evenly place two new vertices on the edge, splitting it into three edges.
Every vertex is reposition into the sum of two adjacent vertex and itself (v_curr + v_prev + v_next)*1/3; alternatively weight_middle, by default 1/3 can be used to adjust the neighbour weight (e.g. 0.5 means neighbours get 0.25 of weight each).
The image below shows on the example of a simple flowerbed partitioning with the application of Contraction, Edge Partitioning and then multiple Smoothing for the first inner loop, and additional Contraction for the most inner polygon.