Area of icosphere mesh triangles is inconsistent

[EmiOnGit]

Bevy version

0.13

What you did

I've noticed that the mesh generated by Sphere is not containing equally sized triangles.
See below for the minimal required code.

Sphere::default().mesh() creates a SphereMeshBuilder with SphereMeshBuilder::kind == SphereKind::Ico.
As normally expected, the documentation for SphereKind::Ico states:

An icosphere, a spherical mesh that consists of equally sized triangles.

However, I couldn't validate this with following code:

use bevy::{prelude::*, render::mesh::PrimitiveTopology};

fn main() {
    let sphere_mesh_builder = Sphere::default().mesh();
    // Make sure we use a `Icosphere`
    match sphere_mesh_builder.kind {
        SphereKind::Ico { .. } => {}
        _ => panic!(),
    }

    let mesh = sphere_mesh_builder.build();

    // indices of vertices
    let indices: Vec<usize> = mesh.indices().unwrap().iter().collect();
    // Extract position of vertices
    let positions = mesh
        .attribute(Mesh::ATTRIBUTE_POSITION)
        .unwrap()
        .as_float3()
        .unwrap();
    // Vertices 0,1,2,3,4,5 create triangles 0,1,2 and 3,4,5 since we have a `TriangleList`.
    assert_eq!(mesh.primitive_topology(), PrimitiveTopology::TriangleList);
    let areas: Vec<f32> = indices
        .chunks_exact(3)
        // triangle is &[usize;3]
        .map(|triangle| {
            let a = Vec3::from_array(positions[triangle[0]]);
            let b = Vec3::from_array(positions[triangle[1]]);
            let c = Vec3::from_array(positions[triangle[2]]);
            // a,b,c are the three corner points of the triangle
            (a, b, c)
        })
        .map(|(a, b, c)| area_of_triangle(a, b, c))
        .collect();
    println!("max area {:?}", areas.clone().into_iter().reduce(f32::max));
    println!("min area {:?}", areas.clone().into_iter().reduce(f32::min));
    println!("first 10 {:?}", &areas[..10]);
}
fn area_of_triangle(a: Vec3, b: Vec3, c: Vec3) -> f32 {
    let ab = b - a;
    let ac = c - a;
    ab.cross(ac).length() / 2.
}

max area Some(0.0743312)
min area Some(0.06445146)
first 10 [0.06445148, 0.064451486, 0.064451486, 0.06595752, 0.06595752, 0.06595753, 0.06482972, 0.0724672, 0.06482972, 0.07246719]

The formula for calculating the area of the triangle can be found here for example: 1 2

[alice-i-cecile]

Can you attach a screenshot of the wireframe of one of these generated icospheres? That may give us a better sense of what's wrong.

[Adamkob12]

Vertices 0,1,2,3,4,5 create triangles 0,1,2 and 3,4,5

Couldn't there be defined indices?
So the triangles wouldn't necessarily be defined in order like that.

[EmiOnGit]

Couldn't there be defined indices?

Yeah you're right, I didn't know about that so my fault.
When using the right indices, the area does still fluctuate but only by around 10%.
Not sure but this might be in the expected deviation, right?
Wireframe also looks as expected. I've also updated the code above.

[EmiOnGit]

Update:
It seems the triangles of icospheres are not designed to be exactely the same size to begin with. Therefore a change of following documentation for the Icosphere would be helpful to prevent further mistakes

An icosphere, a spherical mesh that consists of equally sized triangles.