Use minor and major radii for Torus primitive shape

[Jondolf]

Objective

First, some terminology:

• Minor radius: The radius of the tube of a torus, i.e. the "half-thickness"
• Major radius: The distance from the center of the tube to the center of the torus
• Inner radius: The radius of the hole (if it exists), major_radius - minor_radius
• Outer radius: The radius of the overall shape, major_radius + minor_radius
• Ring torus: The familiar donut shape with a hole in the center, major_radius > minor_radius
• Horn torus: A torus that doesn't have a hole but also isn't self-intersecting, major_radius == minor_radius
• Spindle torus: A self-intersecting torus, major_radius < minor_radius

Different tori from Wikipedia, where R is the major radius and r is the minor radius:

Currently, Bevy's torus is represented by a radius and ring_radius. I believe these correspond to the outer radius and minor radius, but they are rather confusing and inconsistent names, and they make the assumption that the torus always has a ring.

I also couldn't find any other big engines using this representation; Godot and Unity ProBuilder use the inner and outer radii, while Unreal uses the minor and major radii. Blender supports both, but defaults to minor/major.

Bevy's Torus primitive should have an efficient, consistent, clear and flexible representation, and the current radius and ring_radius properties are not ideal for that.

Solution

Change Torus to be represented by a minor_radius and major_radius.

• Mathematically correct and consistent
• Flexible, not restricted to ring tori
• Computations and conversions are efficient
  • inner_radius = major_radius - minor_radius
  • outer_radius = major_radius + minor_radius
  • Mathematical formulae for things like area and volume rely on the minor and major radii, no conversion needed

Perhaps the primary issue with this representation is that "minor radius" and "major radius" are rather mathematical, and an inner/outer radius can be more intuitive in some cases. However, this can be mitigated with constructors and helpers.

[alice-i-cecile]

@NiseVoid, could I get your review?