   Point height from triangle
  I have a point in 3D space which I know is directly above a right triangle, and I am wondering how I could find the point at which point I currently have touches the triangle.  For example, assume I have 3 points representing a triangle at points (0, 5, 0), (0, 1, 4) and (4, 7, 0) and a point directly above the triangle at (2, 30, 2).  How would I go about finding the height at which the point touches the triangle?  I do not think raytracing is entirely necessary considering I already know that the point with a downward ray touches the triangle, I just need the y component of collision.  Thanks for any help with this.-Chris   
  I assume "directly above the triangle" means that the point's projection along the direction of interest lies inside the triangles contour, correct?If so, it will save some costs to check even that, but I don't think that you can avoid to shoot a ray at the triangle. However, due to its special track, the math effort will be relatively small.E.g. define a ray w/ origin at the "point above the tri" R0, and the direction straight downwardR(t) := R0 + t * [0,-1,0]you could see that all but the y component is independent from t:Ry(t) = R0y - tNow get a plane equation from the triangle( P - V ) dot n = 0where V is any of the tris vertex positions, and n = [nx,ny,nz] its normal.Setting in R(t) yields int' = ( ( R0 - V ) dot n ) / nyso thatR(t') is the point of hit on the plane. Since the projection is known to be inside the tris, the hit point on the plane is also inside the tris.If you only want to know Ry(t') you could avoid computing the other both co-orinates, of course.I don't think that there is a definitely easier way to do this, but maybe ...   