Barycentric Coordinates

This is when Bary loses his way home after a drink and can’t seem to find his way back.

Typical use¶

Barycentric Coordinates, as typically used in the industry, is a 2 components coordinate system that defines a position within a triangle. They are often returned as results of intersection operation on mesh or triangles, or for interpolation purposes.

The boring stuff¶

Let T be a triangle defined by it’s points P0, P1 and P2
The barycentric coordinates U and V defines a unique position X within that triangle with:

X = P0*W + P1*U + P2*V
where W = 1-U-V

or

X = P0 + (P1-P0)*U + (P2-P0)*V