P4724 【模板】三维凸包(简洁)

题目描述

给出空间中n个点，求凸包表面积。

输入格式

第一行一个整数n，表示点数。

接下来n行，每行三个实数x，y，z描述坐标。

输出格式

输出凸包表面积，保留3位小数。

输入输出样例

输入 #1

4 

0 0 0

1 0 0

0 1 0

0 0 1

输出 #1

2.366

说明/提示

n≤2000

#include<bits/stdc++.h>//三维凸包

using namespace std;
const int N = 2010;
const double eps = 1e-9;
int n, cnt, vis[N][N];
double ans;

double Rand() { return rand() / (double) RAND_MAX; }

double reps() { return (Rand() - 0.5) * eps; }

struct Node {
    double x, y, z;

    void shake() {
        x += reps();
        y += reps();
        z += reps();
    }

    double len() { return sqrt(x * x + y * y + z * z); }

    Node operator-(Node A) { return (Node) {x - A.x, y - A.y, z - A.z}; }

    Node operator*(Node A) { return (Node) {y * A.z - z * A.y, z * A.x - x * A.z, x * A.y - y * A.x}; }

    double operator&(Node A) { return x * A.x + y * A.y + z * A.z; }
} A[N];

struct Face {
    int v[3];

    Node Normal() { return (A[v[1]] - A[v[0]]) * (A[v[2]] - A[v[0]]); }

    double area() { return Normal().len() / 2.0; }
} f[N], C[N];

int see(Face a, Node b) { return ((b - A[a.v[0]]) & a.Normal()) > 0; }

void Convex_3D() {
    f[++cnt] = (Face) {1, 2, 3};
    f[++cnt] = (Face) {3, 2, 1};
    for (int i = 4, cc = 0; i <= n; i++) {
        for (int j = 1, v; j <= cnt; j++) {
            if (!(v = see(f[j], A[i]))) C[++cc] = f[j];
            for (int k = 0; k < 3; k++) vis[f[j].v[k]][f[j].v[(k + 1) % 3]] = v;
        }
        for (int j = 1; j <= cnt; j++)
            for (int k = 0; k < 3; k++) {
                int x = f[j].v[k], y = f[j].v[(k + 1) % 3];
                if (vis[x][y] && !vis[y][x]) C[++cc] = (Face) {x, y, i};
            }
        for (int j = 1; j <= cc; j++) f[j] = C[j];
        cnt = cc;
        cc = 0;
    }
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    for (int i = 1; i <= n; i++) cin >> A[i].x >> A[i].y >> A[i].z, A[i].shake();
    Convex_3D();
    for (int i = 1; i <= cnt; i++) ans += f[i].area();
    cout << fixed << setprecision(3) << ans << endl;
    return 0;
}