When defining an Oriented Bounding Box by the 3 ortho-normal sides of the box, I wondered what would the consequences be of letting those three edges be at any arbitrary angle?
The first question is if any 3 arbitrary edges do not always perfectly define a rhombohedron (ie the combination of edge lengths and angles doesn't work out right). This is an assumption on my part that any 3 edges joined at a common point will form one of the opposite corners of the rhombohedron. If this is not the case then I will definitely stick with an ortho-box.
The second problem is the containment test which I think should be the same. I'm assuming 6 dot products; 1 for each edge of the opposing corners.
Oriented Bounding Box or Bounding Rhombohedron?
if the 3 edges you speak of end up coplanar, You could potentially lose the volume that you are guaranteed by having an obb using an orthonormal basis.
As long as the basis vectors are linearly independent (so cross product of any 2 pairs is not the zero vector, or the determinant of the matrix formed by the 3 basis vectors is non-zero) you would be ok.
EDIT: Not sure if cross product pairs is a good enough test for coplanarity (i.e. I think I'm wrong), I'm on the beer again. The determinant test should be fine though.
What gets me is that the feature is equivalent to attaching a object transform to all rigid bodies instanced. I'd therefore consider it redundant and not much of a wise choice in general considering you might be willing to write a custom collision solver for each different shape pair.
When defining an Oriented Bounding Box by the 3 ortho-normal sides of the box, I wondered what would the consequences be of letting those three edges be at any arbitrary angle?
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