求解集合点的最小包围球

// Copyright 2001, softSurfer (www.softsurfer.com) // This code may be freely used and modified for any purpose // providing that this copyright notice is included with it. // SoftSurfer makes no warranty for this code, and cannot be held // liable for any real or imagined damage resulting from its use. // Users of this code must verify correctness for their application. // Assume that classes are already given for the objects: // Point and Vector with // coordinates {float x, y;} // operators for: // Point = Point ± Vector // Vector = Point - Point // Vector = Vector ± Vector // Vector = Scalar * Vector (scalar product) // Vector = Vector / Scalar (scalar division) // Ball with a center and radius {Point center; float radius;} //=================================================================== // dot product which allows vector operations in arguments #define dot(u,v) ((u).x * (v).x + (u).y * (v).y) #define norm2(v) dot(v,v) // norm2 = squared length of vector #define norm(v) sqrt(norm2(v)) // norm = length of vector #define d(u,v) norm(u-v) // distance = norm of difference // fastBall(): a fast approximation of the bounding ball for a point set // based on the algorithm given by [Jack Ritter, 1990] // Input: an array V[] of n points // Output: a bounding ball = {Point center; float radius;} void fastBall( Point V[], int n, Ball* B) { Point C; // Center of ball float rad, rad2; // radius and radius squared float xmin, xmax, ymin, ymax; // bounding box extremes int Pxmin, Pxmax, Pymin, Pymax; // index of V[] at box extreme // find a large diameter to start with // first get the bounding box and V[] extreme points for it xmin = xmax = V[0].x; ymin = ymax = V[0].y; Pxmin = Pxmax = Pymin = Pymax = 0; for (int i=1; i xmax) { xmax = V[i].x; Pxmax = i; } if (V[i].y < ymin) { ymin = V[i].y; Pymin = i; } else if (V[i].y > ymax) { ymax = V[i].y; Pymax = i; } } // select the largest extent as an initial diameter for the ball Vector dVx = V[Pxmax] - V[Pxmin]; // diff of Vx max and min Vector dVy = V[Pymax] - V[Pymin]; // diff of Vy max and min float dx2 = norm2(dVx); // Vx diff squared float dy2 = norm2(dVy); // Vy diff squared if (dx2 >= dy2) { // x direction is largest extent C = V[Pxmin] + (dVx / 2.0); // Center = midpoint of extremes rad2 = norm2(V[Pxmax] - C); // radius squared } else { // y direction is largest extent C = V[Pymin] + (dVy / 2.0); // Center = midpoint of extremes rad2 = norm2(V[Pymax] - C); // radius squared } rad = sqrt(rad2); // now check that all points V[i] are in the ball // and if not, expand the ball just enough to include them Vector dV; float dist, dist2; for (int i=0; iCenter = C; B->radius = rad; return; }