Two-dimensional bounded area defined parametrically

How do I go about defining this area without using a piecewise function?

I think it has something to do with Bilinear Surfaces but I'm not sure how to get started.

• What kind of properties are you after for that surface? – joojaa Sep 13 '15 at 12:35

Let $A, B, C, D$ be the vertices of a quadrilateral $Q$ in the plane, in this order.
Then $f(u,v)=(1-u)(1-v)A + u(1-v)B + uvC + (1-u)vD$ maps the square $[0,1] \times [0,1]$ to $Q$.