bzoj1964: hull 三维凸包

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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;

 }