球的体积并

Posted 2021-02-11 andromeda-galaxy

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;

const double pi = acos(-1);

const int MAX = 100 + 10;
const int inf = 1e9 + 7;

typedef struct {
    double x, y, z, r;
}Point;

int n;
Point a[MAX];
Point s;

//两点之间距离
double dis(Point p, Point q) {
    double ans = sqrt((p.x - q.x)*(p.x - q.x) + (p.y - q.y)*(p.y - q.y) + (p.z - q.z)*(p.z - q.z));
    return ans;
}

int main()
{
        int n=1;
        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", &s.x, &s.y, &s.z, &s.r);
        double ans = 0;
        for (int i = 0; i < n; i++) {
            double d = dis(s, a[i]);
            if (d >= s.r + a[i].r ) {
                continue;
            }
            else if (d + a[i].r <= s.r ) {
                ans += (4.0 / 3)*pi*a[i].r*a[i].r*a[i].r;
            }
            else if(d+s.r<=a[i].r)
            {
                ans += (4.0 / 3)*pi*s.r*s.r*s.r;
            }
            else {
                double co = (s.r*s.r + d * d - a[i].r*a[i].r) / (2.0*d*s.r);
                double h = s.r*(1 - co);
                ans += (1.0 / 3)*pi*(3.0*s.r - h)*h*h;
                co = (a[i].r*a[i].r + d * d - s.r*s.r) / (2.0*d*a[i].r);
                h = a[i].r*(1 - co);
                ans += (1.0 / 3)*pi*(3.0*a[i].r - h)*h*h;
            }
        }
        double x=4.0/3.0*pi*(a[0].r*a[0].r*a[0].r+s.r*s.r*s.r);
        printf("%.8lf
", x-ans);
    return 0;
}