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I have a quad defined by four arbitrary points, A, B, C and D all on the same plane. I then have a known point on that quad, P.

The quad ABCD

I want to find the value of 's' as shown in the diagram above, where t and s are parametric values in the range (0, 1) that interpolate along the edges.

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closed as off topic by Qiaochu Yuan Dec 12 '11 at 14:52

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The line containing $P$ isn't parallel to anything? – J. M. Sep 13 '11 at 12:28
@J.M., it seems the OP is assuming bilinear interpolation on the quad. – lhf Sep 13 '11 at 12:32
Ah yes, inverse bilinear interpolation is what I'm talking about - guess that makes this a duplicate question – andygeers Sep 13 '11 at 12:39
Possibly interestingly related: "What is this technique, if not bilinear interpolation?" – Phrogz Jun 3 '14 at 16:14

Let $E$ be the point you show on $AB$ and $F$ be the point on $CD$. Then $E=A+t(B-A), F=C+t(D-C), P=E+s(F-E)$, where you can write these out componentwise.

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