Finding a point within a circle

This is a discussion on Finding a point within a circle within the C++ Programming forums, part of the General Programming Boards category; This is either a total newbie question or then it's a totally difficult question. Anyhow. I'm working on a gravity-simulation ...

  1. #1
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    Finding a point within a circle

    This is either a total newbie question or then it's a totally difficult question. Anyhow.
    I'm working on a gravity-simulation program and I'm right now working on a method to define all points within a circle and it seems that I've struck a dead end. I can't think of anything.
    I think that analytic geometry holds the key to this, but I haven't figured it out.
    So: I don't necessarily need code. I'll just need a method to discern between points inside and outside of a circle whose function and radius are known.

  2. #2
    Fingerstyle Guitarist taylorguitarman's Avatar
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    the equation of a circle is x^2 + y^2 = r^2

    all points within the circle
    x^2 + y^2 <= r^2

    all points outside of circle
    x^2 + y^2 > r^2

    I'm pretty sure that's right.
    Last edited by taylorguitarman; 09-23-2001 at 12:29 PM.

  3. #3
    Ethereal Raccoon Procyon's Avatar
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    That's only if the circle is located at (0, 0).

    More generally, a circle is specified by three variables:

    center x-coordinate (xo)
    center y-coordinate (yo)
    radius (r)

    The circle is then defined by the equation:

    (x - xo)^2 + (y - yo)^2 = r^2.

    If a point (x, y) is inside the circle, therefore, the follwing statement will be true:

    (x - xo)^2 + (y - yo)^2 < r^2.

  4. #4
    Fingerstyle Guitarist taylorguitarman's Avatar
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    good point.

    just a simple translation of the points gets it to (0,0).

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