newage_lightbulb
New member
- Joined
- Jun 3, 2015
- Messages
- 2
Hello, I was reading the line intersection algorithm posted on geomalgorithms.com (previously known as SoftSurfer) and I am stuck on something. Here is the quote:
"In any n-dimensional space, the two lines L1 and L2 are closest at unique points PC = P(sC) and QC = Q(tC) for which w(sC, tC) is the unique minimum for w(s,t). Further, if L1 and L2 are not parallel and do not intersect each other, then the segment PCQC joining these points is uniquely simultaneously perpendicular to both lines."
I don't get that last part. If two lines are not parallel and not intersecting, how can a segment between any two points on them be simultaneously perpendicular to both? I'm not the brightest math guy but can't a line only be simultaneously perpendicular to two others if those two others are parallel?
Thanks for any help.
"In any n-dimensional space, the two lines L1 and L2 are closest at unique points PC = P(sC) and QC = Q(tC) for which w(sC, tC) is the unique minimum for w(s,t). Further, if L1 and L2 are not parallel and do not intersect each other, then the segment PCQC joining these points is uniquely simultaneously perpendicular to both lines."
I don't get that last part. If two lines are not parallel and not intersecting, how can a segment between any two points on them be simultaneously perpendicular to both? I'm not the brightest math guy but can't a line only be simultaneously perpendicular to two others if those two others are parallel?
Thanks for any help.