Solution to problem overlapping maps

h.cpp

using namespace std;
#include <algorithm>
#include <iostream>
#include <iterator>
#include <sstream>
#include <fstream>
#include <cassert>
#include <cstdlib>
#include <cstring>
#include <string>
#include <cstdio>
#include <vector>
#include <cmath>
#include <queue>
#include <stack>
#include <map>
#include <set>

#define D(x) cout << #x " = " << (x) << endl

const double EPS = 1e-8;

int cmp(double x, double y = 0, double tol = EPS){
    return (x <= y + tol) ? (x + tol < y) ? -1 : 0 : 1;
}

const double pi = 2 * acos(0);

int main(){
    double w, h, x0, y0, s, r;
    while (cin >> w >> h >> x0 >> y0 >> s >> r){
        if (w == 0) break;
        r = r * pi / 180.0;
        s = s / 100.0;
        
        // Los puntos del mapa pequeño se pueden expresar así
        // rotar (r), escalar (s) y trarladar (x0, y0) el punto original
        // [nx] = [s * cos r  -s * sin r] [x] + [x0]
        // [ny] = [s * sin r   s * cos r] [y] + [y0]
        
        // Un punto igual en los dos mapas cumple que nx = x and ny = y
        // [x] = [s * cos r  -s * sin r] [x] + [x0]
        // [y] = [s * sin r   s * cos r] [y] + [y0]
        
        // Despejando
        // [x] - [s * cos r  -s * sin r] [x] = [x0]
        // [y] - [s * sin r   s * cos r] [y] = [y0]
        
        // Reescribiendo
        // [1 0] [x] - [s * cos r  -s * sin r] [x] = [x0]
        // [0 1] [y] - [s * sin r   s * cos r] [y] = [y0]
        
        // Factor común
        // { [1 0] - [s * cos r  -s * sin r] } [x] = [x0]
        // { [0 1] - [s * sin r   s * cos r] } [y] = [y0] 
        
        // Sumando
        // [ 1 - s * cos r    s * sin r  ] [x] = [x0]
        // [  -s * sin r    1 - s * cos r] [y] = [y0]
        
        // Se tiene un sistema de la forma Ax = b
        // Hallar la inversa de A
        // A = [a b]   Inv(A) =  __1__ [d  -b]
        //     [c d]            det(A) [-c  a]
        
        double a = 1 - s * cos(r);
        double b = s * sin(r);
        double c = -s * sin(r);
        double d = 1 - s * cos(r);
        
        double det = a * d - c * b;
        assert(cmp(det) != 0);
        
        // x = Inv(A) * b
        // [x] = (d * x0 - b * y0) / det(A)
        // [y] = (-c * x0 + a * y0) / det(A)
        
        double x = (d * x0 - b * y0) / det;
        double y = (-c * x0 + a * y0) / det;
        
        printf("%.2lf %.2lf\n", x, y);
    }
    return 0;
}