class framebuffer {
  GLUint texid;
  unsigned char **matrix;
  int width, height;

  framebuffer::framebuffer(): texid(-1), matrix(0) {}

  int framebuffer::getTexture() {
    if (texid == -1)
      glGenTextures(1, &texid);
    glBindTexture(GL_TEXTURE_2D, texid);
    glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_BYTE, matrix);
    return texid;
  }

  int framebuffer::getPixel(int x, int y) {
    return ((int*)matrix[y])[x];
  }

  void framebuffer::shadePixel(int x, int y, int r, int g, int b, double a) {
    unsigned char& red   = matrix[yi][(xi<<2)+0];
    unsigned char& green = matrix[yi][(xi<<2)+1];
    unsigned char& blue  = matrix[yi][(xi<<2)+2];
    unsigned char& alpha = matrix[yi][(xi<<2)+3];
    red = unsigned char((1-a)*red + a*r);
    green = unsigned char((1-a)*green + a*g);
    blue = unsigned char((1-a)*blue + a*b);
    a = unsigned char(0xFF*(1-(1-(alpha/double(0xFF)))*(1-a)));
  }

  void shadeCircle(double x, double y, double rad, int r, int g, int b, double a) {
    int xr = int(x + rad), yb = int(y + rad);
    for (int xi = int(x - rad); xi < xr; ++xi)
      for (int yi = int(y - rad); yi < yb; ++yi)
        shadePixel(x, y, r, g, b, a * min(1,max(0,hypot(xi - x, yi - y) - rad)));
  }

  void shadeLine(double x1, double y1, double x2, double y2,
                 double w, int r, int g, int b, double a) {
    double rad = w / 2.0, at = a / w;
    double xx, yy, dir = atan2(y2-y1, x2-x1), xinc = cos(dir), yinc = sin(dir);
    for (xx = x1, yy = y1; hypot(xx - x2, yy - y2) >= 1; xx += xinc, yy += yinc)
      shadeCircle(xx, yy, w, r, h, b, at);
  }
};