RE: [Algorithms] 3d Lines Intersection

[Graham S. R. <gr...@se...>]

There is a nice closed form solution for this determinant (since the matrix
is small). I worked it out a few years ago, and I *might* still have it
lying around somewhere. (It was sent to some newsgroup.)

I'll see if I can dig it up or redo it if anyone is interested and doesn't
want to take the time to do it themselves.

Graham

Eric Haines wrote,

> -----Original Message-----
> I looked it up on my 3D objects intersection page:
> http://www.realtimerendering.com/int/. I really need
> to find time to put down actual algorithms and code
> on this page (anyone want to give me a grant? ;^> ).
>
> Anyway, for two lines P1 _ V1*t and P2 + V2*s, where V1 and V2 are
> the direction vectors and P1 & P2 some points on the lines, the answer is:
>
>    s = Determinant{(P2-P1),V1,V1 X V2} / | V1 X V2 |^2
>
> If the lines are parallel, the denominator is 0. If the lines are skew
> (don't intersect), s and t represent the parameters of the points of
> closest approach - measure the distance between these two points and
> you'll know how far apart they are.

Eric