It is the simplest surface. It requires three non-coincident points to define an infinite plane.

Consider a plane defined by three non collinear points $P_{0}, P_{1}, P_{2} .$ We start with two vectors $\left(P_{2}-P_{1}\right)$ and $\left(P_{3}-R\right) .$ They can serve as local co ordinate axes on the plane with point $P_{1}$ as the local origin. u and v are the parameters.

The resulting plane equation is,

$\begin{aligned} P(u, v) &=P_{1}+u\left(P_{2}-P_{1}\right)+v\left(P_{2}-R\right) \\ &=P_{1}(1-u-v)+P_{2} u+P_{3} v \end{aligned}$

To limit the area covered to just the triangle whose corners are $P_{1}, P_{2}, P_{3}$ .

$P_{1},$ when $u=0$ and $v=0$

$P_{2},$ when $u=1$ and $v=0$

$P_{3},$ when $u=0$ and $v=1$

The entire triangle can be obtained by varying u and v under the conditions,

$u \geq 0, v \geq 0$ and $u+v \leq 1$