[Harbin Online Contest 2010][Cubic Rotation][三维坐标旋转]

/*
题目：Cubic Rotation
题目来源：Harbin Online Contest 2010
    http://acm.hrbeu.edu.cn/index.php?act=problem&id=1006&cid=16
题目难度：中等
题目内容或思路：
    三维空间坐标旋转
    没有什么特别的技巧就是把旋转矩阵算出来
    参考自http://dumbear.com/blog/?p=143
    题目Sample有问题,Sample Input 中第二个Sample的“275”改成“270”
做题日期：2011.2.26
*/
#include <cstdio>
#include <cstdlib>
#include <climits>
#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <queue>
#include <map>
#include <vector>
#include <bitset>
#include <cmath>
#include <set>
using namespace std;

const double eps = 1e-8;
const double pi = acos(-1.0);

struct cpoint {
    double x, y;
    cpoint(double xx = 0, double yy = 0): x(xx), y(yy) {}
};

int dcmp(double x) {
    if (x < -eps) return -1; else return x > eps;
}

double cross(cpoint p0, cpoint p1, cpoint p2) {
    return (p1.x - p0.x) * (p2.y - p0.y) - (p2.x - p0.x) * (p1.y - p0.y);
}

int PointEqual(cpoint a, cpoint b) {
    return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
}

double sqr(double x) { return x * x; }

double dissqr(cpoint a, cpoint b) {
    return sqr(a.x - b.x) + sqr(a.y - b.y);
}

cpoint bp;

int PolarCmp(const cpoint &p1, const cpoint &p2) {
    int u = dcmp(cross(bp, p1, p2));
    return u > 0 || (u == 0 && dcmp(dissqr(bp, p1) - dissqr(bp, p2)) < 0);
}

void graham(cpoint pin[], int n, cpoint ch[], int &m) {
    int i, j, k, u, v;
    memcpy(ch, pin, n * sizeof(cpoint));
    for (i = k = 0; i < n; ++i) {
        u = dcmp(ch[i].x - ch[k].x);
        v = dcmp(ch[i].y - ch[k].y);
        if (v < 0 || (v == 0 && u < 0)) k = i;
    }
    bp = ch[k];
    sort(ch, ch + n, PolarCmp);
    n = unique(ch, ch + n, PointEqual) - ch;
    if (n <= 1) { m = n; return ;}
    if (dcmp(cross(ch[0], ch[1], ch[n - 1])) == 0) {
        m = 2; ch[1] = ch[n - 1]; return;
    }
    ch[n++] = ch[0];
    for (i = 1, j = 2; j < n; ++j) {
        while (i > 0 && dcmp(cross(ch[i - 1], ch[i], ch[j])) <= 0) i--;
        ch[++i] = ch[j];
    }
    m = i;
}

double PolygonArea(cpoint p[], int n) {
    if (n < 3) return 0;
    double s = p[0].y * (p[n - 1].x - p[1].x);
    for (int i = 1; i < n; ++i)
        s += p[i].y * (p[i - 1].x - p[(i + 1) % n].x);
    return fabs(s / 2);
}


struct vpoint {
    double x, y, z;
    vpoint(double xx = 0, double yy = 0, double zz = 0)
        : x(xx), y(yy), z(zz) {}
};

double dis(vpoint a, vpoint b) {
    return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y) + sqr(a.z - b.z));
}

// 三维点a绕向量p0p1旋转后坐标(旋转按照右手定则)
vpoint rotate(vpoint a, vpoint p0, vpoint p1, double angle) {
    double d, s, c, x, y, z, x1, y1, z1;
    d = dis(p0, p1);   s = sin(angle);   c = cos(angle);
    x = (p1.x - p0.x) / d;    x1 = a.x - p0.x;
    y = (p1.y - p0.y) / d;    y1 = a.y - p0.y;
    z = (p1.z - p0.z) / d;    z1 = a.z - p0.z;
    p0.x += x1*(c+x*x*(1-c)) + y1*(x*y*(1-c)-z*s) + z1*(x*z*(1-c)+y*s);
    p0.y += y1*(c+y*y*(1-c)) + z1*(y*z*(1-c)-x*s) + x1*(y*x*(1-c)+z*s);
    p0.z += z1*(c+z*z*(1-c)) + x1*(z*x*(1-c)-y*s) + y1*(z*y*(1-c)+x*s);
    return p0;
}

int dir[8][3] = {
    {0, 0, 0}, {1, 0, 0}, {0, 1, 0}, {0, 0, 1},
    {0, 1, 1}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}
};

void solve() {
    vpoint v[8], s, e;
    cpoint cp[8];    
    double len, x, y, z, angle;
    scanf("%lf%lf%lf%lf", &len, &x, &y, &z);
    scanf("%lf%lf%lf", &s.x, &s.y, &s.z);
    scanf("%lf%lf%lf", &e.x, &e.y, &e.z);
    scanf("%lf", &angle);
    angle *= pi / 180;
    for (int i = 0; i < 8; ++i) {
        v[i].x = x + dir[i][0] * len;
        v[i].y = y + dir[i][1] * len;
        v[i].z = z + dir[i][2] * len;
        v[i] = rotate(v[i], s, e, angle);
        cp[i] = cpoint(v[i].x, v[i].y);
    }
    cpoint ch[10];
    int m;
    graham(cp, 8, ch, m);
    printf("%.2lf\n", PolygonArea(ch, m));
}

int main() {
#ifndef ONLINE_JUDGE
    freopen("D:\\in.txt", "r", stdin);
#endif
    int cas;
    scanf("%d", &cas);
    while (cas--) {
        solve();
    }
    return 0;
}