solutions, which produces a major speed-up. The authors verified that the algorithm is efficient in practice in low and moderately low (up to 10,000) dimensions and claim it does not exhibit numerical stability problems in its floating-point operations. A C++ implementation of the algorithm is available as an open-source project. Extremal points optimal sphere proposed the "extremal points optimal sphere" method with controllable speed to accuracy approximation to solve the bounding sphere problem. This method works by taking a set of direction vectors and projecting all points onto each vector in ; serves as a speed-accuracy trade-off variable. An exact solver is applied to the extremal points of these projections. The algorithm then iterates over the remaining points, if any, growing the sphere if necessary. For large this method is orders of magnitude faster than exact methods, while giving comparable results. It has a worst case time of . See also Bounding volume Circumscribed sphere, circumscribed circle References External links Smallest Enclosing Circle Problem – describes several algorithms for enclosing a point set, including Megiddo's linear-time algorithm Geometric algorithms Spheres