牛客练习赛41 E 球的体积并

 两个球的体积相加减去交就是并

#include <bits/stdc++.h>

using namespace std;

typedef long long LL;
const int maxn=1e5+5;
const int maxm=5e5+5;
const int inf=0x3f3f3f3f;

#define PI acos(-1.0)
 
typedef struct point {
    double x,y,z;
    point() {
 
    }
    point(double a, double b,double c) {
        x = a;
        y = b;
        z = c;
    }
    point operator -(const point &b)const {     //返回减去后的新点
        return point(x - b.x, y - b.y,z-b.z);
    }
    point operator +(const point &b)const {     //返回加上后的新点
        return point(x + b.x, y + b.y,z+b.z);
    }
    //数乘计算
    point operator *(const double &k)const {    //返回相乘后的新点
        return point(x * k, y * k,z*k);
    }
    point operator /(const double &k)const {    //返回相除后的新点
        return point(x / k, y / k,z/k);
    }
    double operator *(const point &b)const {    //点乘
        return x*b.x + y*b.y+z*b.z;
    }
}point;
double dist(point p1, point p2) {       //返回平面上两点距离
    return sqrt((p1 - p2)*(p1 - p2));
}
typedef struct sphere {//球
    point centre;
    double r;
}sphere;
 
double Sphere_s(sphere a) {
    return 4 * PI * a.r * a.r * a.r / 3.0;
}
 
double SphereInterVS(sphere a, sphere b) {
    double d = dist(a.centre, b.centre);//球心距
   // cout << d << " " << (a.r + b.r) << endl;
    if(d >= (a.r + b.r)) return 0;
    if(a.r > b.r) swap(a, b);
    if(d + a.r <= b.r) return Sphere_s(a);
    double t = (d*d + a.r*a.r - b.r*b.r) / (2.0 * d);//
    double h = sqrt((a.r*a.r) - (t*t)) * 2;//h1=h2，球冠的高
    double angle_a = 2 * acos((a.r*a.r + d*d - b.r*b.r) / (2.0 * a.r*d));  //余弦公式计算r1对应圆心角，弧度
    double angle_b = 2 * acos((b.r*b.r + d*d - a.r*a.r) / (2.0 * b.r*d));  //余弦公式计算r2对应圆心角，弧度
    double l1 = ((a.r*a.r - b.r*b.r) / d + d) / 2;
    double l2 = d - l1;
    double x1 = a.r - l1, x2 = b.r - l2;//分别为两个球缺的高度
    double v1 = PI*x1*x1*(a.r - x1 / 3);//相交部分r1圆所对应的球缺部分体积
    double v2 = PI*x2*x2*(b.r - x2 / 3);//相交部分r2圆所对应的球缺部分体积
    return v1 + v2;//相交部分体积
}
 
 
 
int main()
{
    point p1, p2;
    double r1, r2;
    scanf("%lf %lf %lf %lf", &p1.x, &p1.y, &p1.z, &r1);
    scanf("%lf %lf %lf %lf", &p2.x, &p2.y, &p2.z, &r2);
    sphere s1 = {p1, r1}, s2 = {p2, r2};
    printf("%.10f\n", Sphere_s(s1) + Sphere_s(s2) - SphereInterVS(s1, s2));
    return 0;
}