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

The position and size of the circular holes is limited.

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

See

https://www2.mathematik.tu-darmstadt.de/~ehartmann/cdgen0104.pdf

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

(*Further developed February 2020 see* Inner Geometry (Triangulation) )

*also with a hole defined by points*

How to add a circular hole:

**Update: October 7th**

Another variant of the sphere with holes was created. A parameter object is used .The rough side length of the triangles is to be indicated. Thus the forms sphere and cylinder (later torus) can be connected exactly with each other.

```
const g = new THREE.BufferGeometry( );
const parameters = {
d: 0.08, // rough side length of the triangles
div4: 30, // division of the quarter of the great circle (orthodrome)
holes: [
// circular hole, 3 elements: [ theta, phi, div4Hole ], div4Hole <= div4
[ 1.82, 0.41, 12 ],
[ 0.72, 2.55, 13 ],
// points hole,: array of points theta, phi, ... (last point is connected to first)
[ 0,0, 0.5,-0.8, 0.25,-0.27, 0.4,0.3, 0.3,0.72 ]
]
}
sphereWithHoles( g, parameters );
```

Try it out: TriangulationSphereWithHolesP

**Update: October 18th**

The algorithm for the sphere with holes previously contained no check whether the current front overlaps.

In very many cases with few holes this is not a problem.

But it can lead to errors in more complicated cases!

**The overlap check has been completed.**

*By the way: It is always necessary for the cylinder!*

See also Addon for triangulation of implicit surfaces/ forms with holes