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How to get the coordinates inside

  1. Mar 21, 2009 #1
    What's the formula on how to get the coordinates inside of:
    a) Square
    b) Triangle
    c) Circle
    d) Oval

    I tried the formula here, for triangle, (http://2000clicks.com/mathhelp/GeometryPointAndTriangle3.htm [Broken]) but sometimes even though the point is inside it says it is not.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 21, 2009 #2
    A half-plane is given by an equation of the form [tex]xn_x+yn_y-d\ge 0[/tex] where [tex](n_x,n_y)[/tex] is the inward pointing normal vector of the boundary line, and [tex]d=p_xn_x+p_yn_y[/tex], where [tex](p_x,p_y)[/tex] is a point on the boundary.

    To test if a point is inside the half-plane, you only need to check the above inequality.

    Since a triangle (resp. a square) is the intersection of 3 (resp. 4) half-planes, you just need to figure out their equations and do the test for each one.

    For an ellipse of the form [tex]ax^2+by^2-c=0[/tex], the corresponding inequality for the points inside it is [tex]ax^2+by^2-c\le 0[/tex].
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