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July 4th, 2015, 08:16 PM   #1
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Math Focus: Ordinary differential calculus, Geometry, algebraic function, discrete mathematics, programming math
Arrow Inside Triangle

How to find out a point(x,y) in a triangle or not?
How to find out a triangle inside in a triangle or not?
How to find out a triangle intersects in a triangle or not?

Here triangle ->C(x1, y1), B(x2, y2), C(x3, y3)

Have any formula or general process.
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Abdus Salam is offline  
 
July 6th, 2015, 09:57 AM   #2
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First, how are you given the point? I will assume that there is a coordinate system such that the point is given by "(x0, y0)" (if not then you can define such a coordinate system and derive the coordinates of the given point from what ever information is used to define it). Each of the sides of the triangle would be given, in that coordinate system, by an equation of the form aix+ biy= ci for i= 1, 2, and 3. A point in the interior of the triangle must satisfy either aix+ biy< ci or aix+ biy> ci for each line. A point is in the interior if it satisfies the proper inequality for every line.
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July 6th, 2015, 12:18 PM   #3
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Hi Abdus,

use the cross product, for example if the z-component of the three products ABxAP, BCxBP, CAxCP, has the same sign, then P is inside triangle ABC. You can find similar criteria for the other problems.


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Avni
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