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Circle Equation in 3D Space

  1. Jul 4, 2008 #1
    Hey everyone,
    I would like to find out equation of circle in 3D space.
    My problem's details are:

    I have a sphere, and I need to calculate circle equation which its center is on sphere's center.
    To be clear, think about a sphere in x,y,z coordinate system where it's origin is at 0,0,0. And select a dot on the sphere surface. Now draw a circle which it's origin is at 0,0,0 (same as sphere) and also selected dot proves the circle (circle's at selected dot)...
    Well how can I calculate this circle's x,y,z values. :confused:

    It would be better if think this sphere at spherical system which is represented by radius r, teta angle, and phi angle. After finding these values I can calculate x,y,z values.

    I hope it was clear.. Thank you everybody, if you cannot understand let me explain a lil bit more.. :smile:
  2. jcsd
  3. Jul 4, 2008 #2


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  4. Jul 4, 2008 #3
    Yeap I saw that message before but it's kinda confusing... I am looking for a lil bit more clear answer...
  5. Jul 4, 2008 #4


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    A curve in 3 dimensions is not given by a single equation. A single equation in 3 dimensions always gives a 3- 1= 2 dimensional surface. For a curve you need either two equations (thinking of the curve as the intersection of two surfaces) or parametric equations: x, y, and z as functions of the parameter t, say.

    However, a single point on the surface of a sphere does NOT define a unique circle, even requiring the circle to have the same center as the sphere. You also need to specify a direction for the circle.

    Suppose you are given two points on the sphere. Then you have a unique "great circle" through those two points.
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