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How is the Bounds.SqrDistance calculated behind the scene? What algorithm/formula does it use?
I am just looking to implement that SqrDistance method in a compute shader but not sure about the most efficient way of implementing it.
Answer by Bunny83 · Nov 05, 2021 at 09:11 AM
Well, the actual implementation is hidden in the native code of Unity. However since the Bounds is an AABB (axis aligned bounding box) that's actually quite simple. You just need to calculate the closest point on the surface of the bounds and then calculate the distance from that point. To get the closest point you just need to clamp the 3 components of the point you want to know the distance to against the min / max values of the bounds for each axis. Sounds complicated but it isn't.
So if you have min and max of your AABB as two vectors you get the projected point like this
float3 pointOnBounds = clamp(point, min, max);
In C# would would need to do 3 seperate clamp calls for each component. In a shader we can actually do this with a single line. So this line in HLSL is equivalent to this C# code:
Vector3 pointOnBounds;
pointOnBounds.x = Mathf.Clamp(point.x, min.x, max.x);
pointOnBounds.y = Mathf.Clamp(point.y, min.y, max.y);
pointOnBounds.z = Mathf.Clamp(point.z, min.z, max.z);
Once you have the point on the bounds you can simply calculate the distance by subtracting your point from it
float3 dir = pointOnBounds - point;
To get the squared distance that the direction vector represents, you just need to get the dot product with itself
float sqrDistance = dot(dir, dir);
or if you actually want to know the distance, you could directly use the distance method
float dist = distance(pointOnBounds, point);
Note: if your point is outside the AABB you get a distance / sqrDistance that is greater than 0. If the point is inside the AABB the distance would always be 0 since the projected point would always be itself.
Answer by andrew-lukasik · Nov 05, 2021 at 10:15 AM
SDF shaders use this equation:
// src* https://www.iquilezles.org/www/articles/distfunctions/distfunctions.htm
float sdBox( float3 p, float3 b )
{
float3 q = abs(p) - b;
return length(max(q,0.0)) + min(max(q.x,max(q.y,q.z)),0.0);
}
note:
returns signed distance
b(ox half size) is aabb.extents (i.e. aabb.size*0.5f )
p(oint) is relative to aabb.center