三维凸包模板
poj3528
#include <cstring> #include <cstdio> #include <cmath> #include <algorithm> using namespace std; #define inf 0x7fffffff #define max(a,b) (a>b?a:b) #define min(a,b) (a<b?a:b) #define eps 1e-7 #define MAXV 505 //三维点 struct pt { double x, y, z; pt() {} pt(double _x, double _y, double _z): x(_x), y(_y), z(_z) {} pt operator - (const pt p1) { return pt(x - p1.x, y - p1.y, z - p1.z); } pt operator * (pt p) { return pt(y*p.z-z*p.y, z*p.x-x*p.z, x*p.y-y*p.x); //叉乘 } double operator ^ (pt p) { return x*p.x+y*p.y+z*p.z; //点乘 } }; struct _3DCH { struct fac { int a, b, c; //表示凸包一个面上三个点的编号 bool ok; //表示该面是否属于最终凸包中的面 }; int n; //初始点数 pt P[MAXV]; //初始点 int cnt; //凸包表面的三角形数 fac F[MAXV*8]; //凸包表面的三角形 int to[MAXV][MAXV]; double vlen(pt a) { return sqrt(a.x*a.x+a.y*a.y+a.z*a.z); //向量长度 } double area(pt a, pt b, pt c) { return vlen((b-a)*(c-a)); //三角形面积*2 } double volume(pt a, pt b, pt c, pt d) { return (b-a)*(c-a)^(d-a); //四面体有向体积*6 } //正：点在面同向 double ptof(pt &p, fac &f) { pt m = P[f.b]-P[f.a], n = P[f.c]-P[f.a], t = p-P[f.a]; return (m * n) ^ t; } void deal(int p, int a, int b) { int f = to[a][b]; fac add; if (F[f].ok) { if (ptof(P[p], F[f]) > eps) dfs(p, f); else { add.a = b, add.b = a, add.c = p, add.ok = 1; to[p][b] = to[a][p] = to[b][a] = cnt; F[cnt++] = add; } } } void dfs(int p, int cur) { F[cur].ok = 0; deal(p, F[cur].b, F[cur].a); deal(p, F[cur].c, F[cur].b); deal(p, F[cur].a, F[cur].c); } bool same(int s, int t) { pt &a = P[F[s].a], &b = P[F[s].b], &c = P[F[s].c]; return fabs(volume(a, b, c, P[F[t].a])) < eps && fabs(volume(a, b, c, P[F[t].b])) < eps && fabs(volume(a, b, c, P[F[t].c])) < eps; } //构建三维凸包 void construct() { cnt = 0; if (n < 4) return; bool sb = 1; //使前两点不公点 for (int i = 1; i < n; i++) { if (vlen(P[0] - P[i]) > eps) { swap(P[1], P[i]); sb = 0; break; } } if (sb)return; sb = 1; //使前三点不公线 for (int i = 2; i < n; i++) { if (vlen((P[0] - P[1]) * (P[1] - P[i])) > eps) { swap(P[2], P[i]); sb = 0; break; } } if (sb)return; sb = 1; //使前四点不共面 for (int i = 3; i < n; i++) { if (fabs((P[0] - P[1]) * (P[1] - P[2]) ^ (P[0] - P[i])) > eps) { swap(P[3], P[i]); sb = 0; break; } } if (sb)return; fac add; for (int i = 0; i < 4; i++) { add.a = (i+1)%4, add.b = (i+2)%4, add.c = (i+3)%4, add.ok = 1; if (ptof(P[i], add) > 0) swap(add.b, add.c); to[add.a][add.b] = to[add.b][add.c] = to[add.c][add.a] = cnt; F[cnt++] = add; } for (int i = 4; i < n; i++) { for (int j = 0; j < cnt; j++) { if (F[j].ok && ptof(P[i], F[j]) > eps) { dfs(i, j); break; } } } int tmp = cnt; cnt = 0; for (int i = 0; i < tmp; i++) { if (F[i].ok) { F[cnt++] = F[i]; } } } //表面积 double area() { double ret = 0.0; for (int i = 0; i < cnt; i++) { ret += area(P[F[i].a], P[F[i].b], P[F[i].c]); } return ret / 2.0; } //体积 double volume() { pt O(0, 0, 0); double ret = 0.0; for (int i = 0; i < cnt; i++) { ret += volume(O, P[F[i].a], P[F[i].b], P[F[i].c]); } return fabs(ret / 6.0); } //表面三角形数 int facetCnt_tri() { return cnt; } //表面多边形数 int facetCnt() { int ans = 0; for (int i = 0; i < cnt; i++) { bool nb = 1; for (int j = 0; j < i; j++) { if (same(i, j)) { nb = 0; break; } } ans += nb; } return ans; } }hull; int main() { int i,n; while(scanf("%d",&hull.n)!=EOF) { for(i = 0 ; i < hull.n ;i++) scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z); hull.construct(); printf("%.3f\n",hull.area()); } return 0; }