Mend gaps in meshes caused by trigonometric funcs.

[Lielay9]

Fixes: #93865
Supersedes: #94199

Simple, ugly solution: Ensure last iteration uses the same values as the first. Here's a cheat-sheet to help reviewing:

sin(τ) = 0
cos(τ) = 1
sin(π) = 0
cos(π) = -1
sin(π/2) = 1
cos(π/2) = 0
sin(0) = 0
cos(0) = 1

[Lielay9]

Avoid unnecessary addition and subtraction.

sin((x+1)π/2) == cos(xπ/2)
cos((x+1)π/2) == -sin(xπ/2)

[Lielay9]

Cosine and sine already calculated above: reuse.

[Lielay9]

Hi, I also work on CSG, would it be ok to also test CSGMesh3D too?

Originally posted by @fire in #94199 (comment)

Tested CSG-meshes! Since only the sphere had gaps, I stuffed it to this pr~

[fire]

I suspect the capsule also has the same gap.

[Lielay9]

I suspect the capsule also has the same gap.

I don't think we have CSGCapsules...

[fire]

Any of these meshes can be put into CSGMesh3D https://docs.godotengine.org/en/stable/classes/class_primitivemesh.html

From earlier testing RibbonTrailMesh, SphereMesh and PlaneMesh mathematically cannot work.

[Lielay9]

Ah! I see! All the primitive meshes that had gaps are already included CapsuleMesh, CylinderMesh, SphereMesh, TorusMesh and TubeTrailMesh ^^/ This means there shouldn't be gaps in CSGMesh3D either! Or at least those that are caused by the trig functions... but I haven't found other causes and my naive test passes for all the shapes.

[fire]

I have tested all primitive mesh shapes except those that aren't mathematically usable with CSG.

The manifold definition requires the meshes to be watertight.

Note that the pull request is insufficient; will also need the Godot Engine master as of eb51030 or newer

csg-mend-gaps-game-project.zip

Edited:

Did not do a style review.

[Repiteo]

Thanks!