2球相交 求体积和 很多人的板子应该都是从

https://blog.csdn.net/enterprise_/article/details/81624174

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int maxn = 6000+5;
const int INF = 0x3f3f3f3f;
const int cx[]= {0,0,1,-1};
const int cy[]= {1,-1,0,0};
const double eps= 1>>10;
const int maxv = 100+5;
const double PI=acos(-1.0);

int n,m,k,t;

struct node {
	double x,y,z,r;
} a[maxn];

double dx,dy,dr,dz;

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
	double r;
	point centre;
} sphere;

double res(sphere a, sphere b) {
	double v=0;
	double d = dist(a.centre, b.centre);//球心距
	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 v = v1 + v2;//相交部分体积
}

int main() {
	cin>>t;
	int cas=1;
	while(t--) {
		scanf("%d",&n);
		for(int i=1; i<=n; i++) {
			scanf("%lf %lf %lf %lf",&a[i].x,&a[i].y,&a[i].z,&a[i].r);
		}
		scanf("%lf %lf %lf %lf",&dx,&dy,&dz,&dr);
		sphere tp,b;
		b.centre.x=dx;
		b.centre.y=dy;
		b.centre.z=dz;
		b.r=dr;
		double V=0;
		for(int i=1; i<=n; i++) {
			double len=abs(sqrt((a[i].x-dx)*(a[i].x-dx)+(a[i].y-dy)*(a[i].y-dy)+(a[i].z-dz)*(a[i].z-dz)));
			if(len>dr+a[i].r) continue;
			else if(len<=dr-a[i].r) {
				V+=4*PI*a[i].r*a[i].r*a[i].r/3;
				continue;
			} else {
				tp.centre.x=a[i].x;
				tp.centre.y=a[i].y;
				tp.centre.z=a[i].z;
				tp.r=a[i].r;
				V+=res(tp,b);
			}
		}
		// cout<<V<<endl;
		printf("Case #%d: %.9lf\n",cas++,V);
	}
	return 0;
}