POJ 2208 Pyramids 欧拉四面体

给出边长，直接就可以求出体积咯

关于欧拉四面体公式的推导及证明过程

2010-08-16 14:18

摘自：http://www.cnblogs.com/kuangbin/archive/2012/04/13/2446378.html

代码：

//#pragma comment(linker, "/STACK:16777216") //for c++ Compiler
#include <stdio.h>
#include <iostream>
#include <cstring>
#include <cmath>
#include <stack>
#include <queue>
#include <vector>
#include <algorithm>
#define ll long long
#define Max(a,b) (((a) > (b)) ? (a) : (b))
#define Min(a,b) (((a) < (b)) ? (a) : (b))
#define Abs(x) (((x) > 0) ? (x) : (-(x)))

using namespace std;

double P( double a,double b,double c,double d,double e ){
    return a*(b*c-d*e);
}

double EulerTetrahedron(double OA, double OB, double OC, double AB, double BC, double CA){
    OA *= OA;    OB *= OB;   OC *= OC;
    AB *= AB;    CA *= CA;   BC *= BC;
    double ans = 0;
    ans += P( OA,OB,OC,(OB+OC-BC)/2.,(OB+OC-BC)/2. );
    ans -= P( (OA+OB-AB)/2.,(OA+OB-AB)/2.,OC,(OA+OC-CA)/2.,(OB+OC-BC)/2. );
    ans += P( (OA+OC-CA)/2.,(OA+OB-AB)/2.,(OB+OC-BC)/2.,OB,(OA+OC-CA)/2.);
    return sqrt(ans/36);
}
int main(){
    double OA,OB,OC,AB,BC,CA;
    while( scanf("%lf%lf%lf%lf%lf%lf",&OA,&OB,&OC,&AB,&CA,&BC)!=EOF ){
        printf("%.4f\n",euler(OA, OB, OC, AB, BC, CA));
    }
    return 0;
}

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