Ray Triangle Intersection question

[markraz]

Hi below is a formula for finding a Ray Triangle Intersection. My question is with the bottom equation e + (t * d) = a + beta(b - a) + alpha ( c - a)
if I solve this, what is Beta and alpha going to tell me?

Thanks in adavnce

Ray

 

[Cubist]

That's gamma, not alpha. The real numbers beta and gamma will tell you where the ray intersects the plane of the triangle. If beta≥0 and gamma≥0 and beta+gamma≤1 then the ray will intersect within the triangle. If the ray intersects exactly at vector "a" then beta and gamma will both be zero. If the ray intersects at "b", then beta will be 1 and gamma 0. If the ray intersects half way between a and b then beta will be 1/2 and gamma 0.

You could think of beta and gamma in a similar way to an (x,y) coordinate, but in this scenario the axes aren't (usually) orthogonal to each other because they are two of the sides of the triangle.

 

[markraz]

That's gamma, not alpha. The real numbers beta and gamma will tell you where the ray intersects the plane of the triangle. If beta≥0 and gamma≥0 and beta+gamma≤1 then the ray will intersect within the triangle. If the ray intersects exactly at vector "a" then beta and gamma will both be zero. If the ray intersects at "b", then beta will be 1 and gamma 0. If the ray intersects half way between a and b then beta will be 1/2 and gamma 0.

You could think of beta and gamma in a similar way to an (x,y) coordinate, but in this scenario the axes aren't (usually) orthogonal to each other because they are two of the sides of the triangle.

great thanks so much