Find intersection point between a ray and a face?

[silver_angel]

I have a 3D polygon and a ray! Please tell me how can I know if they intersect together and how to find intersection point between them?

 

[HallsofIvy]

HOW are you given them?? If you are given their equations, then the equation of the plane should be something like: Ax+ By+ Cz= d while the ray would be given by parametric equations- x= at+ b, y= ct+ d, z= et+ f with t>= 0, say.
Put those equations for x, y, z, in terms of t, into the equation of the plane and solve the equation for t. If t>= 0, put it into the equations for the ray to find (x,y,z). If t<0 then the ray does not go through the plane- it goes the "away from" the plane.

(It is possible that the coefficient of t in the final equation will be 0. In that case the ray is parallel to the plane.)

 

[silver_angel]

Incase I have 3 points define a triangle (x1,y1,z1),(x2,y2,z2),(x3,y3,z3). And 2 points define a ray (xr1,yr1,zr1),(xr2,yr2,zr2). Could you tell me how can I check if that ray go through that triangle and the intersection point if they have? And more, if you could, please show me the best formula for that!

Thank you so much!