# Interpolating point on a quad [closed]

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.

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.

-

## closed as off topic by Qiaochu YuanDec 12 '11 at 14:52

Questions on Mathematics Stack Exchange are expected to relate to math within the scope defined by the community. Consider editing the question or leaving comments for improvement if you believe the question can be reworded to fit within the scope. Read more about reopening questions here.If this question can be reworded to fit the rules in the help center, please edit the question.

The line containing $P$ isn't parallel to anything? – J. M. Sep 13 '11 at 12:28
– lhf Sep 13 '11 at 12:30
@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.