Subject: Re: Point inside a triangle
Date: Thu, 20 Nov 1997 13:09:39 -0500
From: Alex Bogomolny

Dear Irina:

I said "stupid" on an impulse that stemmed from a combination of quick thoughts:

  1. You never so much as hinted that your problem is 3d. To me it was natural to assume it's 2d. Why?
  2. Probability that a point is inside a flat shape in 3d is 0. Although I do not know your exact problem but, based on the above, I would assume there is no reason to worry whether the point is on the plane not to mention its being inside a triangle. Just say "No". You'll be right most of the time. Mathematically speaking, a 2d shape has no internal points in 3d (being a nowhere dense set.) Why to talk of insides of an object that has no inside to start with.

However, in 3d, you still may depend on your 2d experience. If your triangle is given by its vertices, you can easily consider their projections on coordinate planes. No transformations are involved. If projections of a point belong to the three respective projections of a triangle, then the point is "inside".

Alexander Bogomolny

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