signOfDet2x2 static method

int signOfDet2x2(double x1, double y1, double x2, double y2,)

Implementation

static int signOfDet2x2(double x1, double y1, double x2, double y2) {
  // returns -1 if the determinant is negative,
  // returns 1 if the determinant is positive,
  // retunrs 0 if the determinant is null.
  int sign;
  double swap;
  double k;
  int count = 0;

  // callCount++; // debugging only

  sign = 1;

  /*
       * testing null entries
       */
  if ((x1 == 0.0) || (y2 == 0.0)) {
    if ((y1 == 0.0) || (x2 == 0.0)) {
      return 0;
    } else if (y1 > 0) {
      if (x2 > 0) {
        return -sign;
      } else {
        return sign;
      }
    } else {
      if (x2 > 0) {
        return sign;
      } else {
        return -sign;
      }
    }
  }
  if ((y1 == 0.0) || (x2 == 0.0)) {
    if (y2 > 0) {
      if (x1 > 0) {
        return sign;
      } else {
        return -sign;
      }
    } else {
      if (x1 > 0) {
        return -sign;
      } else {
        return sign;
      }
    }
  }

  /*
       * making y coordinates positive and permuting the entries
       */
  /*
       * so that y2 is the biggest one
       */
  if (0.0 < y1) {
    if (0.0 < y2) {
      if (y1 > y2) {
        sign = -sign;
        swap = x1;
        x1 = x2;
        x2 = swap;
        swap = y1;
        y1 = y2;
        y2 = swap;
      }
    } else {
      if (y1 <= -y2) {
        sign = -sign;
        x2 = -x2;
        y2 = -y2;
      } else {
        swap = x1;
        x1 = -x2;
        x2 = swap;
        swap = y1;
        y1 = -y2;
        y2 = swap;
      }
    }
  } else {
    if (0.0 < y2) {
      if (-y1 <= y2) {
        sign = -sign;
        x1 = -x1;
        y1 = -y1;
      } else {
        swap = -x1;
        x1 = x2;
        x2 = swap;
        swap = -y1;
        y1 = y2;
        y2 = swap;
      }
    } else {
      if (y1 >= y2) {
        x1 = -x1;
        y1 = -y1;
        x2 = -x2;
        y2 = -y2;
      } else {
        sign = -sign;
        swap = -x1;
        x1 = -x2;
        x2 = swap;
        swap = -y1;
        y1 = -y2;
        y2 = swap;
      }
    }
  }

  /*
       * making x coordinates positive
       */
  /*
       * if |x2| < |x1| one can conclude
       */
  if (0.0 < x1) {
    if (0.0 < x2) {
      if (x1 > x2) {
        return sign;
      }
    } else {
      return sign;
    }
  } else {
    if (0.0 < x2) {
      return -sign;
    } else {
      if (x1 >= x2) {
        sign = -sign;
        x1 = -x1;
        x2 = -x2;
      } else {
        return -sign;
      }
    }
  }

  /*
       * all entries strictly positive x1 <= x2 and y1 <= y2
       */
  while (true) {
    count = count + 1;
    k = (x2 / x1).floorToDouble();
    x2 = x2 - k * x1;
    y2 = y2 - k * y1;

    /*
           * testing if R (new U2) is in U1 rectangle
           */
    if (y2 < 0.0) {
      return -sign;
    }
    if (y2 > y1) {
      return sign;
    }

    /*
           * finding R'
           */
    if (x1 > x2 + x2) {
      if (y1 < y2 + y2) {
        return sign;
      }
    } else {
      if (y1 > y2 + y2) {
        return -sign;
      } else {
        x2 = x1 - x2;
        y2 = y1 - y2;
        sign = -sign;
      }
    }
    if (y2 == 0.0) {
      if (x2 == 0.0) {
        return 0;
      } else {
        return -sign;
      }
    }
    if (x2 == 0.0) {
      return sign;
    }

    /*
           * exchange 1 and 2 role.
           */
    k = (x1 / x2).floorToDouble();
    x1 = x1 - k * x2;
    y1 = y1 - k * y2;

    /*
           * testing if R (new U1) is in U2 rectangle
           */
    if (y1 < 0.0) {
      return sign;
    }
    if (y1 > y2) {
      return -sign;
    }

    /*
           * finding R'
           */
    if (x2 > x1 + x1) {
      if (y2 < y1 + y1) {
        return -sign;
      }
    } else {
      if (y2 > y1 + y1) {
        return sign;
      } else {
        x1 = x2 - x1;
        y1 = y2 - y1;
        sign = -sign;
      }
    }
    if (y1 == 0.0) {
      if (x1 == 0.0) {
        return 0;
      } else {
        return sign;
      }
    }
    if (x1 == 0.0) {
      return -sign;
    }
  }
}