Do 2 parallel line segments overlap, and where?

Boris Karloff · 2003-11-24T13:23:38

I''m trying to figure out some basic line-collision stuff, and most of it works pretty well, using the good old y=mx + b equation, where m is the slope and b is the point where the line intersects the y-axis. Anyhoo, all this works out pretty well, except on parallel lines. Now, most texts I''ve found argue that parallel line segments do not intersect. In other words, if the slope of both segments is equal, then the lines are parallel and will never intersect. True, but if the line segments are both part of the -same- infinite line, they might overlap each other. What I want to know is if, and where, that happens. Now, figuring out if two line segments are parallel is easy, as in that case m1 is equal to m2. (or the x-values must all be the same, in which case the line segments are exactly vertical) Figuring out if they''re both part of the same infinite line is also easy: if they are parallel AND both intercepts are equal (they intersect the y-axis at the same point), they are part of the same line, and this is the -only- case where they might overlap, right? Now, I''m stuck. I can''t figure out how to calculate if they overlap each other, and if so, where. The line segments both have a start and an end point, and I''d like to know when segment one encounters segment 2 for the first time, and where it encounters it for the last time. (Later on, I''d like to know when two objects traveling along the segments collide if they both travel at a given speed, but I figured that''s another topic.) Surely, there must be a relatively easy way to figure this out, and searching on various subjects has yielded no results, so far... Can anyone give me a hand on this subject?

Math and Physics Programming

Started by Boris Karloff November 16, 2003 04:56 PM

10 comments, last by Boris Karloff 20 years, 4 months ago

Platinum314

206

November 24, 2003 10:31 AM

Depends on what geometric axioms you want to use.

The sentence below is true.The sentence above is false.And by the way, this sentence only exists when you are reading it.

Boris Karloff

484

Author

November 24, 2003 01:23 PM

quote:Original post by MrScout
furthermore, if the slopes of the lines are the same, unless they got a point in common, they don''t intersect. (In 2-space!!!!!!)

I know, but if they have a point in common, they''ll overlap, in which case there''s still chance of collision.

quote:Original post by MrScout
But using y=mx+b you still can''t represent a vertical line - you''ll divide by zero!

Now I''m not gonna lecture you over the evils of y=mx+b, but I''ll just tell ya to watch for division by zero. :-/

I know. It''s easily fixed by testing if the start and end x or y are the same. If that''s the case, just set the slope to a really high number. As long as the world dimensions don''t get exorbitantly high, that''ll work fine.

It''s a bit of a hack, but it works well in this particular case, and is far more comprehensible, and thus less error-prone.

In this specific case, mind you.

Nein heer du smign. ah open up the nine im heer du shmine

Do 2 parallel line segments overlap, and where?

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Do 2 parallel line segments overlap, and where?

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