Re: [Algorithms] 3d Lines Intersection

[Eric H. <er...@ac...>]

Albert_J wrote:

> Is there a good algo for finding a point of intersection between two *3D lines*?
> The lines is specified by their point (x,y,z) and their direction (dx,dy,dz)
>
> I've searched the web, but all of them seems to explain about 2D lines intersection only.

An answer (but not online, unfortunately): Goldman, Intersection of Two Lines in Three-Space,
Graphics Gems, p. 304.

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