Computing barycentric coordinate

I find a good website that teach me how to compute a barycentric coordinate of point P in the triangle T(v0,v1,v2). The formula can also be used to find is whether the P is inside T, which is the problem i want to solve.

Here is the link to the full explanation.

In short, the formula is like this:

u = V₁-V_0;
v = V₂-V_0;
w = P-V_0;

The parametric coordinates (s,t) of P is the solution of the equation: w = su + tv, and the barycentric coordinates of P = b₀V₀ + b₁V₁ + b₂V₂ are equal to: b₀ = (1-s-t), b₁ = s, and b₂ = t which satisfy: b₀ + b₁ + b₂ = 1.

We can compute the solutions for s and t using only dot products as:

Thanks very much to Dan Sunday at http://softsurfer.com/index.html for providing the solution.