凸包入门,求多边形面积
多边形面积无非就是些三角形的面积之和,然后以起点叉乘积除以二即可。
#include <iostream> #include <math.h> #include <stdio.h> #define eps 1e-8 #define zero(x) (((x)>0?(x):-(x))<eps) #define _sign(x) ((x)>eps?1:((x)<-eps?2:0)) struct point{int x, y; }; //计算cross product (P1-P0)x(P2-P0) int xmult(point p1, point p2, point p0){ return (p1.x - p0.x)*(p2.y - p0.y) - (p2.x - p0.x)*(p1.y - p0.y); } //graham算法顺时针构造包含所有共线点的凸包,O(nlogn) point p1, p2; int graham_cp(const void* a, const void* b){ double ret = xmult(*((point*) a), *((point*) b), p1); return zero(ret) ? (xmult(*((point*) a), *((point*) b), p2) > 0 ? 1 : -1) : (ret > 0 ? 1 : -1); } void _graham(int n, point* p, int& s, point* ch){ int i, k = 0; for (p1 = p2 = p[0], i = 1; i<n; p2.x += p[i].x, p2.y += p[i].y, i++) if (p1.y - p[i].y>eps || (zero(p1.y - p[i].y) && p1.x > p[i].x)) p1 = p[k = i]; p2.x /= n, p2.y /= n; p[k] = p[0], p[0] = p1; qsort(p + 1, n - 1, sizeof(point), graham_cp); for (ch[0] = p[0], ch[1] = p[1], ch[2] = p[2], s = i = 3; i < n; ch[s++] = p[i++]) for (; s>2 && xmult(ch[s - 2], p[i], ch[s - 1]) < -eps; s--); } int wipesame_cp(const void *a, const void *b) { if ((*(point *) a).y < (*(point *) b).y - eps) return -1; else if ((*(point *) a).y > (*(point *) b).y + eps) return 1; else if ((*(point *) a).x < (*(point *) b).x - eps) return -1; else if ((*(point *) a).x > (*(point *) b).x + eps) return 1; else return 0; } int _wipesame(point * p, int n) { int i, k; qsort(p, n, sizeof(point), wipesame_cp); for (k = i = 1; i < n; i++) if (wipesame_cp(p + i, p + i - 1) != 0) p[k++] = p[i]; return k; } //构造凸包接口函数,传入原始点集大小n,点集p(p原有顺序被打乱!) //返回凸包大小,凸包的点在convex中 //参数maxsize为1包含共线点,为0不包含共线点,缺省为1 //参数clockwise为1顺时针构造,为0逆时针构造,缺省为1 //在输入仅有若干共线点时算法不稳定,可能有此类情况请另行处理! int graham(int n, point* p, point* convex, int maxsize = 1, int dir = 1){ point* temp = new point[n]; int s, i; n = _wipesame(p, n); _graham(n, p, s, temp); for (convex[0] = temp[0], n = 1, i = (dir ? 1 : (s - 1)); dir ? (i < s) : i; i += (dir ? 1 : -1)) if (maxsize || !zero(xmult(temp[i - 1], temp[i], temp[(i + 1)%s]))) convex[n++] = temp[i]; delete []temp; return n; } int is_convex(int n, point* p){ int i, s[3] = { 1, 1, 1 }; for (i = 0; i < n && s[1] | s[2]; i++) s[_sign(xmult(p[(i + 1)%n], p[(i + 2)%n], p[i]))] = 0; return s[1] | s[2]; } double area_polygon(int n, point* p) { double s1 = 0, s2 = 0; int i; for (i = 0; i < n; i++) s1 += p[(i + 1)%n].y*p[i].x, s2 += p[(i + 1)%n].y*p[(i + 2)%n].x; return fabs(s1 - s2) / 2; } int main() { int n; point p[10005], convex[10005]; std::cin >> n; for (int i = 0; i < n; i++) { std::cin >> p[i].x >> p[i].y; } int size = graham(n, p, convex); int area = area_polygon(size, convex); std::cout << area/50 << std::endl; }