Parametric Form of Circle EquationDate: 08/04/2003 at 04:47:30 From: Francis Chong Subject: Parametric form of circle equation in 3D Space Dear Dr. Math, If I know the center and radius of a circle, and three points on the circle, can I find the parametric form of the circle equation in 3D space? Date: 08/04/2003 at 12:51:03 From: Doctor George Subject: Re: Parametric form of circle equation in 3D Space Hi Francis, To get a parametric equation follow this procedure. 1. Let N be a unit normal vector for the plane. 2. Let C be the circle center, and let R be the radius. 3. Let U be a unit vector from C toward a point on the circle. 4. Let V = N x U. 5. Let A be the paramter. 6. A point P is on the circle if... P = C + R cos(A) U + R sin(A) V You can verify this result be checking the distance from P to the plane, and the distance from P to C. Does that make sense? Write again if you need more help. - Doctor George, The Math Forum http://mathforum.org/dr.math/ |
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