Triangulation sphere with holes

There are two different simple versions of spheres with holes.
Sphere with up to 6 coordinate planes parallel holes

In order to arrange the holes freely, a different procedure is required.
A version uses a division of the hemispheres.
http://threejs.hofk.de/sphere/SphereCutAsWanted.html
20190522-1525-36123
The position and size of the circular holes is limited.


The triangulation according to an algorithm by E. Hartmann is much more flexible.

See


Chapter 7
TRIANGULATION OF IMPLICIT SURFACES

I adapted / simplified the algorithm for the simple case of the sphere and also used an alternative angle calculation.
http://threejs.hofk.de/Triangulation/TriangulationSphereWithHoles.html


The structure of the procedure:

20190621-1502-07694
20190621-1501-23232

How to add a hole:20190621-0902-39694

Hole defined by points:20190621-1810-32432

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Severe maths! :+1: All that we like! :beers:

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With the sphere, it’s still elementary math.

When I have integrated the hole sphere into my addon THREEg I will try to implement the complete algorithm of Professor Hartmann. I contacted him about this.

There is a program by him, but it is written in Pascal and I can’t take it over immediately. The languages offer quite different possibilities. Besides, everyone has his own programming style. For threejs you should store the points and indices according to the requirements of BufferGeometry.

de / en
https://www2.mathematik.tu-darmstadt.de/~ehartmann/ see B) 2) 2’)

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