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CaptainBlack · #2 January 18th, 2008, 07:56 AM

Quote:

Originally Posted by jacksoncapper

I have been trying so long to do this simple thing. I have two 3D line segments, each represented by two points. I need to know if and where these two lines intersect, but I need a method that I can implement programmatically in an algorithm. Please any help would be greatly appreciated.

Let the points be $\bf{x}$ and $\bf{y}$ and $\bf{u}$ and $\bf{v}$ . Then the line segments are:

$\bold{l_1}=\bold{x}+ \lambda (\bold{y}-\bold{x}),\ \lambda \in [0,1]$
$\bold{l_2}=\bold{u}+ \mu (\bold{v}-\bold{u}),\ \mu \in [0,1]$

The lines intersect if there are $\lambda,\ \mu \in [0,1]$ such that:

$\bold{x}+ \lambda (\bold{y}-\bold{x})=\bold{u}+ \mu (\bold{v}-\bold{u})$

Now write these out in terms of the components and you have three
simultaneous linear equations for $\lambda$ and $\mu$ . If there is a solution
with $\lambda$ and $\mu \in [0,1]$ then the line segments intersect.

RonL