#4947 fixing Overlapping Voronoi 3D sites

[satabol]

1. Fix some glitches of disappearing parts if spacing is growing.
2. Voronoi algorithm speed up. Has some glitches. qhull do not see some sites near each other.

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Sites 1 and 9 overlapped. QHull do not see them as overlapped.

for tests:
Voronoi on mesh.004.glitches.overlapped sites.blend.zip

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See also:

• https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Voronoi.html
• http://www.qhull.org/html/qh-quick.htm#options

[satabol]

Test:

Test.Voronoi.on.mesh.002.Good.edit.mp4

[satabol]

see also:

• https://en.wikipedia.org/wiki/Minimum_bounding_box_algorithms
• https://logicatcore.github.io/scratchpad/lidar/sensor-fusion/jupyter/2021/04/20/3D-Oriented-Bounding-Box.html

Description of optimization:

1. Optimization for except some bisects

1. if bbox_aligned is on the positive side of site then object will have no changes after bisect and all its vertices stay unchanged. One can skip that bisects.
   

2. if bbox_aligned is on the negative side of the site then object will be erased (clear) after bisect (if any bisects was before too). So one can skip all bisects and return empty object without of any bisects.
   

2. Optimization for bisect order
This program doesn't know anything about topology of mesh. So this algorithm observe this mesh as cloud of points with max concentration near the center_of_mass (not geometric center. geometric center do not point to the center of mass).

Radius has no specific value now but this is not need for this algorithm. It is very simple for now to select what plain to bisect first plain12 or plane23 when process site1? (Do you see this is not need to know the radius value?) Now obvious that bisect plane with center on negative side will remove more points from mesh geometry than plane with center on positive side. So plane12 is better plane13. So we simplify next bisects because they will be work with less geometry.
If there is two planes both with center on negative side then need first select a plane with bigger distance from center to plane:

here is the plane14 is better the plane12.
Positive side of planes has the same rule about distance. First plane has bigger distance from center to plane to remove maximum geometry on bisect.

3. test is spacing is more than all dists from planes to Site.
if all distance from planes to their site is less than a spacing/2 then the bisect will cutoff all vertices anyway:

so one can to skip all bisect and return nothing for this site.

Test File

Voronoi on mesh.005.tests with meshes and points.blend.zip

Content of file:

[satabol]

Result

[satabol]

All vectors math expressions aligned to direction to site_idx from site_pair_idx (all expressions with “plain_no” has “+” , no “-“ now).