# ray/triangle intersection + uv calculation

Hello,

What is the most direct way to intersect a ray with a triangle and compute the associated uv coordinates at this point ?

(something less consuming than matrix operations if possible)

Google a little about barycentric coordinate and I think that you can find all you want about this.

Or more simple (but not really more speed) if you have already your proper algorithm for to find the point of intersection (say P) of a triangle ABC and a line from P0 to P1 …

First, you compute distances from P to A, B and C:

dA = distance from A to P
dB = distance from B to P
dC = distance from C to B

sum = dA + dB + dC
coefA = dA / sum
coefB = dB / sum
coefC = dC / sum

So, the texture coordinate at point P is :

uP = uA * coefA + uB * coefB + uC * coefC
vP = vA * coefA + vB * coefB + vC * coefC

Note too that you can apply this to alls points P into the triangle ABC and to be applied to another style of coordinates such as color componants for example …

Thanks !
I first calculated my own barycentric formulas, however it requires far more operations than yours. But yours involve square roots operation, so… Well I have to give it a try 