Generic 3D bounds

[kvark]

Closes #117
Fixes #125

Infrastructure to do frustum culling based on Sphere or Aabb bounds. More can be implemented for the Bound trait. Example code:

let projection = PerspectiveFov {
        fovy: rad(1f32),
        aspect: 1f32,
        near: 1f32,
        far: 10f32,
};
let frustum = projection.to_frustum();
let bound = Sphere {
    center: Point3::new(0f32, 3f32, -5f32),
    radius: 1f32,
};
match frustum.contains(&bound) {
    Relation::In => show(),
    Relation::Cross => show_anyway(),
    Relation::Out => cull(),
}

[brendanzab]

oopsie

[kvark]

nice find ;) fixed now!

[ghost]

Thanks for cleaning this up.

[ghost]

I think there is a bug here, if r is Relation::Cross and cur is In the state will be Relation::In instead of Relation::Cross

This might be nicer as a match too:

match (cur, r) {
    (Relation::Out, _) | (_,  Relation::Out) => Relation::Out,
    (Relation::Cross, _) | (_,  Relation::Cross) => Relation::Cross,
    _ => Relation::In
}

[kvark]

The condition cur == Cross || r == In will be false, so the outcome will take the other arm, which is just r, which is exactly Cross. So I think condition is still correct?

[ghost]

You are right. What about about the case where cur == Cross && r == Out?

[kvark]

cur == Cross would let it go the first arm, which results in cur, which is Cross. I believe this is still correct?

[ghost]

I think there are two cases missing here. If cur == Out and r == In The result should still be Out where it will be marked as In. The other case if cur == Cross && r == Out the result should be once again Out where it would be marked as Cross.

[kvark]

cur == Out && r == In would result in Out, since it's the first arm of the condition. You are correct about the second case though, Cross shouldn't overwrite Out, and I need to fix the condition.

[kvark]

I fixed the condition now. Thank you for spotting the logical error. Your attention to detail is highly professional!

[ghost]

Should we handle the NaN case?

[kvark]

It would just return Cross for the matter of Relation. Not sure what would be a better way to handle it.

[ghost]

This needs to be rebased.

[kvark]

Rebased now.

[kvark]

We'd want to implement relate_clip_space for Aabb3 in an efficient way, described here:
https://fgiesen.wordpress.com/2010/10/17/view-frustum-culling/

But that could be done later on without breaking the interface.

[ghost]

I'm not sure why Travis is not building this...

[kvark]

It was a bad merge on my part. The upcoming build should be fine though.

[kvark]

Another thing to do would be adding a benchmark for frustum culling. This would be handy for the optimized relate_clip_space, so will probably be implemented with it.

[ghost]

Thanks~