bzoj1964: hull 三维凸包

传送门

二维平面四个点求凸包面积->任选三个点面积之和/2

三维平面五个点求凸包体积->任选四个点体积之和/2

二维平面三个点面积->二个二维向量行列式值的绝对值/2

三维平面四个点体积->三个三维向量行列式值的绝对值/6

 //Achen
 #include<algorithm>
 #include<iostream>
 #include<cstring>
 #include<cstdlib>
 #include<vector>
 #include<cstdio>
 #include<queue>
 #include<cmath>
 #include<set>
 #include<map>
 #define Formylove return 0
 #define For(i,a,b) for(int i=(a);i<=(b);i++)
 #define Rep(i,a,b) for(int i=(a);i>=(b);i--)
 typedef long long LL;
 typedef double db;
 using namespace std;

 template<typename T>void read(T &x)  {
     char ch=getchar(); x=; T f=;
     while(ch!='-'&&(ch<''||ch>'')) ch=getchar();
     if(ch=='-') f=-,ch=getchar();
     for(;ch>=''&&ch<='';ch=getchar()) x=x*+ch-''; x*=f;
 }

 struct pt {
     db x,y,z;
     pt(db x=0.0,db y=0.0,db z=0.0):x(x),y(y),z(z){}
 }p[];
 pt operator -(const pt&A,const pt&B) { return pt(A.x-B.x,A.y-B.y,A.z-B.z); }

 db calc(pt p1,pt p2,pt p3,pt p4) {
     p1=p1-p4; p2=p2-p4; p3=p3-p4;
     db rs=(p1.x*p2.y*p3.z-p3.x*p2.y*p1.z+p1.y*p2.z*p3.x-p1.x*p2.z*p3.y+p1.z*p2.x*p3.y-p1.y*p2.x*p3.z);
     return fabs(rs)/6.0;
 }

 int main() {
 #ifdef ANS
     freopen(".in","r",stdin);
     freopen(".out","w",stdout);
 #endif
     while(scanf("%lf%lf%lf",&p[].x,&p[].y,&p[].z)!=EOF) {
         db ans=;
         For(i,,) scanf("%lf%lf%lf",&p[i].x,&p[i].y,&p[i].z);
         For(i,,) For(j,i+,) For(k,j+,) For(l,k+,)
             ans+=calc(p[i],p[j],p[k],p[l]);
         ans/=2.0;
         printf("%.2lf\n",ans);
     }
     Formylove;
 }