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Oriented Bounding Box or Bounding Rhombohedron?

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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.

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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.

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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.

Edited by Paradigm Shifter

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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?
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.

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