CCPC-Wannafly Winter Camp Day2 (Div2, onsite) H Cosmic Cleaner 球交体积

H-Cosmic Cleaner
题解：求球交体积的题目，取横截面积进行微积分，然后一堆公式运算，巴拉巴拉模板题😜

#include<stdio.h>
#include<bits/stdc++.h>

using namespace std;
const double PI = acos(-1.0);
typedef long long ll;
const int maxn=120;
struct point {
    double x,y,z;
    point() {}
    void Init(double a, double b,double c){
        x = a;
        y = b;
        z = c;
    }
    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;
    }
};
double dist(point p1, point p2) {       //返回平面上两点距离
    return sqrt((p1 - p2)*(p1 - p2));
}
struct sphere {//球
    double r;
    point centre;
};
void SphereInterVS(sphere a, sphere b,double &v) {
    double d = dist(a.centre, b.centre);//球心距
    if(d>=a.r+b.r)return;
    if(a.r-d>=b.r){
        v+=PI*4.0/3.0*b.r*b.r*b.r;
        return;
    }
    if(a.r<=b.r-d){
        v+=PI*4.0/3.0*a.r*a.r*a.r;
        return;
    }
    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
     v += v1 + v2;//相交部分体积
}
struct Node{
    double x,y,z,r;
}a[maxn];
double x,y,z,r;
int n;
double Solve(){
    double v=0;
    sphere A,B;
    A.r=r;
    A.centre.Init(x,y,z);
    for(int i=0;i<n;i++){
        B.r=a[i].r;
        B.centre.Init(a[i].x,a[i].y,a[i].z);
        SphereInterVS(A,B,v);
    }
    return v;
}
int main(){
    int t,tt=1;
    /*sphere A,B; A.r=1; A.centre.Init(0,0,0); B.r=1; B.centre.Init(0,0,0); double v=0; SphereInterVS(A,B,v); printf("%lf",v);*/
    scanf("%d",&t);
    while(tt<=t){
        scanf("%d",&n);
        for(int i=0;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",&x,&y,&z,&r);
        printf("Case #%d: %.10lf\n",tt++,Solve());
    }
    return 0;
}