converting to Barycentric coordinate system

I hav开发者_如何学运维e a set of planes which I have calculated the points of intersection in the standard XYZ cartesian coordinate system. I have used actionscript.

I would like to project the intersection points (shown circled in blue in the pictures below) down to the triangular base and then calculate the Barycentric coordinates.

Any help would be greatly appreciated

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This is a good link showing and explaining how to convert from Cartesian to Barycentric coordinates