Interpolating point on a quad

Question

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.

Answer 1

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.