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Math Help - Point of Intersection

  1. #1
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    Question Point of Intersection

    Hello everyone. I am new to this forum and have a simple question (at least I hope it is simple).

    I have a segment defined by two points (P0 and P1) and a convex polygon defined by a set of vertices n. I would like to know how to find the point of intersection (if it exists) for the segment and the convex polygon - can anyone help me?

    BTW, the points for both the segment and the convex polygon are defined in X, Y, and Z coordinate space and the segment could be parallel to the plane containing the convex polygon.

    Thank you.
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  2. #2
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    Smile

    Just to be sure, attached is a simple JPEG of what I would like to accomplish. I would like to calculate the actual point between P0 and P1 that intersects the polygon.


    Thank you.
    Attached Thumbnails Attached Thumbnails Point of Intersection-lineintersect.jpg  
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  3. #3
    MHF Contributor

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    This is complicated but it is the simplest way I can think of. Each of the sides of the polygon can be written as a linear equation. You can check to determine if one of the points is "inside" the polygon and the other "outside
    (if an edge is ax+ by+ c= 0, then (x_0,y_0) and (x_1,y_1) are on the same side if ax_0+ by_0+ c has the same sign as ax_1+ by_1+ c.) Once you have determined that the two points are outside and inside the polygon you can determine where the line between them intersect a side.
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