Barycentric Coordinates of a Point on a Line Given a point and a line segment, how do you calculate the barycentric coordinates of the point to the line?

bool BarycentricCoordinates(const Vector3&amp; point, const Vector3&amp; a, const Vector3&amp; b, float&amp; u, float&amp; v, float epsilon)
If you have a point $C$ on a line defined by a point $A$ and a point $B$, here is how you calculate the barycentric coordinates $(t_0,t_1)$:

$t_0 = \frac{sqrt((C_x-A_x)^2+(C_y-A_y)^2)}{sqrt((B_x-A_x)^2+(B_y-A_y)^2)}$

$t_1 = 1.0 - t_0$

In other words, you calculate the length of the vector from $A$ to $C$, and divide that by the length of the vector from $A$ to $B$.  This gives you $t_0$, and you can subtract that from 1.0 to get $t_1$ since barycentric coordinates always add up to 1.0.

A more mathish style version of the above is this:

$t_0 = \frac{\left\| C-A\right\|}{\left\| B-A\right\|}$

$t_1 = 1.0 - t_0$

But it's important to note that $C$ must be on the line defined by $A$ and $B$.  If that isn't the case, let us know and let us know what it is you are trying to do specifically.  For instance, maybe you want to project some other point $D$ onto the line $\overline{AB}$ and then find the barycentric coordinates of that projected point?