# Ellipsoid Collision

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a) How can i Compute the Bounding Ellipsoid from the list of Vertices b) How can i test this bounding ellipsoid to the scene? Loop all the triangles in the scene? then how can i test a triangle to the Bounding ellipse

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i ony have an answer to your last question: transform your triangles with the inverse of your elipse matrix, so that you can test them against a unit sphere.

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the quick method that I can think of is that you can calculate the bounding AABB of the object (that one is easy), so the ellipsoid center will be box center, and the bigger radius is box height, smaller radius is box width.

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 the quick method that I can think of is that you can calculate the bounding AABB of the object (that one is easy), so the ellipsoid center will be box center, and the bigger radius is box height, smaller radius is box width.
What about a point near a corner of the AABB? It is unlikely to be contained in the ellipsoid you describe. Building an AABB can be used as a first step in building an axis-aligned bounding ellipsoid, but some further math is required. Depending on the object, though, your method may provide a 'good enough' fit.

You can do ellipsoid-triangle collision using the method eelco described. Using this approach, ellipsoids can be a good choice for object-world interaction, especially when the objects are axis-aligned and radially symmetrical about the axis of rotation (such as with a humanoid character). IMO it may not be worth trying to construct the ellipsoid from a point set; rather, just choose the radii empirically so that they roughly enclose the object.

I'll also say that depending on what sort of collision detection you're doing, there are other options besides ellipsoids that may be easier to work with.

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