Re: Sphere formula
- To: mathgroup at smc.vnet.net
- Subject: [mg109460] Re: Sphere formula
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Wed, 28 Apr 2010 01:59:01 -0400 (EDT)
If you meant 3 points in 2 space (you don't), I think the circle's equation can be found as follows: zero = Det@({ {x^2 + y^2, x, y, 1}, {x1^2 + y1^2, x1, y1, 1}, {x2^2 + y2^2, x2, y2, 1}, {x3^2 + y3^2, x3, y3, 1} }) eqns = Thread[ DeleteCases[ Flatten@CoefficientList[(x - a)^2 + (y - b)^2 - rsq - c zero, {x, y}], 0] == 0]; Solve[eqns, {a, b, c, rsq}] // Together (output omitted) The center is {a, b}, and the radius is Sqrt@rsq. If you mean 3 points in 3 space (I think you do), you'll need some more work... but the above might give you ideas. Bobby On Tue, 27 Apr 2010 03:05:16 -0500, S. B. Gray <stevebg at roadrunner.com> wrote: > 1. The center of a sphere through 4 points has a very nice determinant > form. (http://mathworld.wolfram.com/Sphere.html) What I want is a nice > formula for the center of a sphere through 3 points, where the center is > in the plane of the three points. I have a formula but it's a horrible > mess of hundreds of lines, even after FullSimplify. > > 2. (Unlikely) Is there a way to get Mathematica to put a long formula > into a > matrix/determinant form if there is a nice one? > > Any tips will be appreciated. > > Steve Gray > -- DrMajorBob at yahoo.com