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Triangle Intersection and Barycentric Coordintes

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Hi all,

So the attached image below is about using barycentric coordinates to solve ray-triangle intersection. I was hoping someone could clear up some of the things that were mentioned in the post.

For the most part, I do understand what P', X, and Y are.

He goes on to say that we should construct a matrix A made up of only the vectors X and Y. After this, multiplying the he says to multiple the inverse of A by P'. But A has no inverse since it's not a square matrix, correct?

[img]http://i.imgur.com/2JxNA.png[/img]

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With a triangle in 2D the matrix is square and the inverse exists in general. You basically do a coordinate transform to a non-orthogonal coordinate system.

With a triangle in 3D he projects the point P' on the plane spanned by X and Y and then expresses the point in the local coordinate system. This is what the generalized inverse does.

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