Quote:
Originally Posted by jacksoncapper  It's just the z co-ordinate was not in any way included in the gaussian matrix, therefore I can't see any way that the z co-ordinates played a part in determining whether the 3D lines intersect. I can extract the z value at the end just fine, but the [0,1] lambda value (and the other one) was only determined from the x and y co-ordinates. Do you know what I mean? Sorry if I am not explaining this well. I trust you know better than I do, please correct me if I'm wrong. |
The point of intersection of two lines is a problem with two free parameters
that have to be determined. Thus we only need two equations to find these
parameters (usually). But we have three equations, and there are three
posibilities for what that third equation does for us:
1. It can be inconsitent with the first two
2. It can be consistent and give the same result when used in place of one of the other equations
3. It can add no information about the parameters at all (which is the case here)
Hence you only need two of the three equations (as long as they are independent) to find the parameters, then the third needs to check to see that it is not inconsistent with the values found.
RonL