Distance from Circle to Line in 3-DDate: 8/9/96 at 19:56:2 From: Ryan Bay Subject: Distance from Circle to Line in 3-D Dear Dr. Math, What is the analytic formula for the nearest distance from a circle to a line or line segment in 3-space? Also, what are the coordinates for the nearest points on the circle and line? Thank you very much for your time. Yours, Ryan Bay Physics grad student Date: 8/11/96 at 12:8:54 From: Doctor Anthony Subject: Re: Distance from Circle to Line in 3-D A circle in 3D will be defined as the surface of intersection of some conicoid (e.g. sphere or cone) with a plane. If you then have the coordinates of the centre of the circle, you can next determine the equation of the plane containing the given line and the centre of the circle. Where this plane cuts the circle is the point on the circle of nearest approach, and its distance from the given line is the shortest distance between the line and the circle. There is no simple formula to give this information, since the circle in 3D cannot be expressed by some simple formula. -Doctor Anthony, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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