Triangle and parametric coordinates

Question

I'm studying on a book where it says: "A triangle is the set of points

where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates here) of the triangle"

I don't understand this statement. How come that each point in a triangle surface can be expressed as the expression above?

Answer 1

Figured out: p0 is a point inside the triangle, u and v are the barycentric coordinates that are "weights" to use dp/du and dp/dv that represent how much does the surface vary in both directions (they're vectors since p is the barycentric equation for the triangle). u and v are b1 and b2 since b0 = 1 - b1 - b2 (barycentric coords sum to 1)