Add Tetrahedron primitive to bevy_math::primitives

[Chubercik]

Objective

• Tracking Issue: Primitive Shapes #10572

There is no 3D primitive available for the common shape of a tetrahedron (3-simplex).

Solution

This PR introduces a new type to the existing math primitives:

• Tetrahedron: a polyhedron composed of four triangular faces, six straight edges, and four vertices

---

Changelog

Added

• Tetrahedron primitive to the bevy_math crate
• Tetrahedron tests (area, volume methods)
• impl_reflect! declaration for Tetrahedron in the bevy_reflect crate

[github-actions]

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[mweatherley]

FYI, I have also already done a substantial amount of work on this; I would recommend joining us in the math-dev channel on Discord to talk about some of the things that have come up!

[Chubercik]

Aw shucks, my bad 😅

I threw this PR draft out there after checking that there isn't anything that implements it in https://github.com/bevyengine/bevy/pulls, so that there is no doubling of efforts, but I guess I was too late anyway.

Should I close this PR?

[mweatherley]

This is fairly barebones, but I'd be happy to have this as a baseline!

[mweatherley]

Pretty happy with this! Thanks!

[Jondolf]

I think this looks good for an initial implementation :) We can build on this in follow-ups

[atlv24]

I'm really confused as to why this is the default tetrahedron. I would expect a regular tetrahedron, centered at the origin. Or at least one that contains the origin. This one satisfies none of those properties. Can we have it be this instead?

Suggested change

	Vec3::new(0.0, 0.5, 0.0),
	Vec3::new(-0.5, -0.5, 0.0),
	Vec3::new(0.5, -0.5, 0.0),
	Vec3::new(0.0, 0.0, 0.5),
	Vec3::new(0.5, 0.5, 0.5),
	Vec3::new(-0.5, -0.5, 0.5),
	Vec3::new(0.5, -0.5, -0.5),
	Vec3::new(-0.5, 0.5, -0.5),

[mweatherley]

I think this was chosen so that, in particular, its base is the Default Triangle3d. I guess it does contain the origin, but only on its boundary :)

[Chubercik]

What @mweatherley said, in practice it's just Triangle3d base + an extra vertex on the Z-axis.

I was thinking, if we go with your suggestion would it be possible to keep the tetrahedron upright? I think that's how people typically imagine this shape to look like.

[atlv24]

Suggested change

	/// `[0.0, 0.5, 0.0]`, `[-0.5, -0.5, 0.0]`, `[0.5, -0.5, 0.0]` and `[0.0, 0.0, 0.5]`.
	/// `[0.5, 0.5, 0.5]`, `[-0.5, -0.5, 0.5]`, `[0.5, -0.5, -0.5]` and `[-0.5, 0.5, -0.5]`.

[atlv24]

Suggested change

	/// Returns the default [`Tetrahedron`] with the vertices
	/// Returns a regular [`Tetrahedron`] centered at the origin with the vertices

[NthTensor]

I think the default tet should be centered on the origin. It's going to rotate strangely when people mesh it and apply transforms. I believe all other default primitives have their center of mass more or less at the origin.

[mweatherley]

I think the default tet should be centered on the origin. It's going to rotate strangely when people mesh it and apply transforms. I believe all other default primitives have their center of mass more or less at the origin.

I agree with this; there's obviously some tension in terms of making things match up, but that's less important than the ergonomics of actually using the shape. (Then again, I kind of think a lot of the default shapes are a little silly)

[Chubercik]

I think the default tet should be centered on the origin.

I guess that decision is being lifted off my shoulders, thanks for all the reviews!

For the record, I agree, though I still feel like having this primitive remain upright (three vertices on a plane that's parallel to the XY plane, one vertex above) would be desirable, but would cause icky vertex coordinates (especially if going for a regular tetrahedron), which is why I was hesitant.

[alice-i-cecile]

Thank you to everyone involved with the authoring or reviewing of this PR! This work is relatively important and needs release notes! Head over to bevyengine/bevy-website#1295 if you'd like to help out.