Add technical definition for manifoldness

[tetrapod00]

Part of #10417. Also documents changes for godotengine/godot#94321.

[tetrapod00]

We need to check that this layman's definition is still correct

[fire]

The triangle vertices must appear clockwise when viewed from outside the Godot Engine manifold mesh.

It can be split into two layperson explanations.

1. The Godot Engine triangle mesh winding order should be clockwise.
2. All the windings should be clockwise. There is no mixing between clockwise and counterclockwise.

[fire]

@elalish Do you know if we need to explain something about normals? I didn't see that in your explanation.

[elalish]

Technically the three of these except for self-intersection are more precisely defined by the manifold definition below. Self-intersection should be avoided, but Manifold is robust to it at least, and it's difficult to test in practice.

As for winding direction - the manifoldness definition below already restricts us to an oriented 2-manifold, so there can't be any mixing of CW and CCW. Like self-intersection, CCW can be hard to test reliably. And manifold will handle inverted meshes just fine - it's simply that CW triangles will lead to negative volume. I would trust a positive volume check over checking CCW. Likewise, normals are not very trustworthy.

[elalish]

I guess I would say the triangles are CCW - this is what defines the sign of the volume and inside vs outside. There's nothing you can do to make them CW.

[fire]

Clarification for others:

Godot Engine has a different handedness than elalish/manifold. So, the winding order is swapped.

[fire]

REQUIRED

• it must be closed,
• every edge must connect to only two other faces.
• volume must exist

NOT RECOMMENDED

• negative volume
• self-intersection
• interior faces

[elalish]

Hmm, Manifold is in the lower-right - Z-up and right-handed, so it looks like Godot has the same handedness? Or does Godot just use CW triangle winding as positive?

[fire]

https://docs.godotengine.org/en/latest/classes/class_arraymesh.html#arraymesh

Note: Godot uses clockwise winding order for front faces of triangle primitive modes.

[fire]

What do we need to do to get this completed?

[tetrapod00]

If it's all correct to you now, this is mergable, but I'd like to leave it up for a day or so before merging to give others a chance to review, since I did write it myself.

[elalish]

LGTM

[tetrapod00]

Pushed a minor wording correction.

[tetrapod00]

Merged. Thanks fire and especially elalish for taking the time to review!