Yep, there is…

For precise mathematical definition see wiki - http://en.wikipedia.org/wiki/Barycentric_coordinate_system_(mathematics)#Barycentric_coordinates_on_triangles - in short, barycentric coordinates for triangle are defined as 3 coordinates (U, V, W) where U + V + W = 1, and each represents unit-distance between our defined point and each point forming triangle (e.g. where U = 1 and V, W = 0, we’re sitting on point A; V = 1 and U, W = 0 we’re on point B, etc.).

Basically these coordinates are very important for interpolating values (this is important for pixel shading, of course I’ll give a word about these in article I’m working on), for example they’re needed for computing per-pixel normals or depth on pixel in triangle (+ only multiply and addition operations are needed when using these).

Also they’re wide used in ray-triangle tests - basically you test whether point projected on triangle’s plane along ray has coordinates between 0 and 1, and U + V + W = 1 (if any of the cases is wrong, then you haven’t hit the triangle, otherwise you hit) … plus you can actually use these right after for texture coordinate computation and such things.

If there a way to know how far a point is from the closest edge on a triangle? Perhaps in 0..1 range?