re sphere from points bolson carson u washington edu edward bolson writes boy this will be embarassing if it is trivial or an faq given points non coplanar how does one find the sphere that is center and radius exactly fitting those points i know how to do it for a circle from points but do not immediately see a straightforward way to do it in d i have checked some geometry books graphics gems and farin but am still at a loss please have mercy on me and provide the solution it s not a bad question i don t have any refs that list this algorithm either but thinking about it a bit it shouldn t be too hard take three of the points and find the plane they define as well as the circle that they lie on you say you have this algorithm already find the center of this circle the line passing through this center perpendicular to the plane of the three points passes through the center of the sphere repeat with the unused point and two of the original points this gives you two different lines that both pass through the sphere s origin their interection is the center of the sphere the radius is easy to compute it s just the distance from the center to any of the original points i ll leave the math to you but this is a workable algorithm an alternate method would be to take pairs of points the plane formed by the perpendicular bisector of each line segment pair also contains the center of the sphere three pairs will form three planes intersecting at a point this might be easier to implement steve spworley netcom com
