re sphere from points from bolson carson u washington edu edward bolson given points non coplanar how does one find the sphere that is cnter and radius exactly fitting those points the equation of the sphere through the points x y z x y z is x y z x y z x y z x x x y y y z z z when this by determininant is expanded on its first column you get the equation in the form a x y z bx cy dz e if you need the center and radius jyst divide through by a it cannot be zero if the given points form a non degenerate tetrahedron and complete the square on x y and z to obtain x xc y yc z zc r rcb slacvm slac stanford edu bob beach
