New ConvexGeometry based on QuickHull

[Mugen87]

This PR introduces a QuickHull implementation for generating convex hulls. Features:

• Average-case time complexity of O(nlogn) instead of O(n^2)
• More robust (solves ConvexHull example is broken #10624)
• New ConvexGeometry and ConvexBufferGeometry
• Documentation of all new entities

I've prepared two simple examples (with a 50k vertices model) so you can better compare the execution times (see console):

Old Implementation O(n^2)
New Implementation O(nlogn)

As you can see in the code the QuickHull implementation is not part of ConvexGeometry but a standalone entity. So you can do e.g. new THREE.QuickHull().setFromObject( mesh ) to create the bounding volume for a 3D object as with Box3. ConvexGeometry uses the result of THREE.QuickHull to compute the geometry data. But you can also use it for other purposes like collision detection.

The implementation is mainly based on /~https://github.com/maurizzzio/quickhull3d so credit goes to @Maurizzzio for his great work!

[mrdoob]

Great stuff as always!

However, just like with DecalGeometry, I think it would be better to keep it in examples/js/geometries/.

[WestLangley]

I think this is really great! :)

The only thing that bothers me is the creation of the class you call Vertex. It is really an element of a linked list.

In three.js, the term 'vertex' has special meaning: as vertex of a triangle, or as a point on the surface of a mesh.

I would call it QPoint or something.

[Mugen87]

@WestLangley Ok, i'll try to figure out a different name 👍 . QPoint sounds already good. Maybe i will also change VertexList to QPointList.

However, just like with DecalGeometry, I think it would be better to keep it in examples/js/geometries/.

@mrdoob The problem is that the implementation of QuickHull3 is more complex and the module system is a great help here. And unlike DecalGeometry, the code should work uniformly with all geometries you can create with the library. (I know we want to keep the core of the library as small as possible. Just wanted to highlight these facts. I accept of course both solutions.)

[Mugen87]

Okay, i moved to code to examples. I renamed Vertex to VertexNode because it's more consistent to the rest of the naming conventions in QuickHull. Hope, that's okay 👍

[mrdoob]

Sweet!

[mrdoob]

Thanks!

[Mugen87]

Yay! 🎉

I think we can close now the following issues: #10624 and #8416

[WestLangley]

Thanks @Mugen87 !