PolygonArea.java

/**
 * Implementation of the net.sf.geographiclib.PolygonArea class
 *
 * Copyright (c) Charles Karney (2013-2019) <charles@karney.com> and licensed
 * under the MIT/X11 License.  For more information, see
 * https://geographiclib.sourceforge.io/
 **********************************************************************/
package net.sf.geographiclib;

/**
 * Polygon areas.
 * <p>
 * This computes the area of a geodesic polygon using the method given
 * Section 6 of
 * <ul>
 * <li>
 *   C. F. F. Karney,
 *   <a href="https://doi.org/10.1007/s00190-012-0578-z">
 *   Algorithms for geodesics</a>,
 *   J. Geodesy <b>87</b>, 43&ndash;55 (2013)
 *   (<a href="https://geographiclib.sourceforge.io/geod-addenda.html">
 *   addenda</a>).
 * </ul>
 * <p>
 * Arbitrarily complex polygons are allowed.  In the case self-intersecting of
 * polygons the area is accumulated "algebraically", e.g., the areas of the 2
 * loops in a figure-8 polygon will partially cancel.
 * <p>
 * This class lets you add vertices one at a time to the polygon.  The area
 * and perimeter are accumulated at two times the standard floating point
 * precision to guard against the loss of accuracy with many-sided polygons.
 * At any point you can ask for the perimeter and area so far.  There's an
 * option to treat the points as defining a polyline instead of a polygon; in
 * that case, only the perimeter is computed.
 * <p>
 * Example of use:
 * <pre>
 * {@code
 * // Compute the area of a geodesic polygon.
 *
 * // This program reads lines with lat, lon for each vertex of a polygon.
 * // At the end of input, the program prints the number of vertices,
 * // the perimeter of the polygon and its area (for the WGS84 ellipsoid).
 *
 * import java.util.*;
 * import net.sf.geographiclib.*;
 *
 * public class Planimeter {
 *   public static void main(String[] args) {
 *     PolygonArea p = new PolygonArea(Geodesic.WGS84, false);
 *     try {
 *       Scanner in = new Scanner(System.in);
 *       while (true) {
 *         double lat = in.nextDouble(), lon = in.nextDouble();
 *         p.AddPoint(lat, lon);
 *       }
 *     }
 *     catch (Exception e) {}
 *     PolygonResult r = p.Compute();
 *     System.out.println(r.num + " " + r.perimeter + " " + r.area);
 *   }
 * }}</pre>
 **********************************************************************/
public class PolygonArea {

  private Geodesic _earth;
  private double _area0;        // Full ellipsoid area
  private boolean _polyline;    // Assume polyline (don't close and skip area)
  private int _mask;
  private int _num;
  private int _crossings;
  private Accumulator _areasum, _perimetersum;
  private double _lat0, _lon0, _lat1, _lon1;
  private static int transit(double lon1, double lon2) {
    // Return 1 or -1 if crossing prime meridian in east or west direction.
    // Otherwise return zero.
    // Compute lon12 the same way as Geodesic.Inverse.
    lon1 = GeoMath.AngNormalize(lon1);
    lon2 = GeoMath.AngNormalize(lon2);
    double lon12 = GeoMath.AngDiff(lon1, lon2).first;
    int cross =
      lon1 <= 0 && lon2 > 0 && lon12 > 0 ? 1 :
      (lon2 <= 0 && lon1 > 0 && lon12 < 0 ? -1 : 0);
    return cross;
  }
  // an alternate version of transit to deal with longitudes in the direct
  // problem.
  private static int transitdirect(double lon1, double lon2) {
    // We want to compute exactly
    //   int(ceil(lon2 / 360)) - int(ceil(lon1 / 360))
    // Since we only need the parity of the result we can use std::remquo but
    // this is buggy with g++ 4.8.3 and requires C++11.  So instead we do
    lon1 = lon1 % 720.0; lon2 = lon2 % 720.0;
    return ( ((lon2 <= 0 && lon2 > -360) || lon2 > 360 ? 1 : 0) -
             ((lon1 <= 0 && lon1 > -360) || lon1 > 360 ? 1 : 0) );
  }
  // reduce Accumulator area to allowed range
  private static double AreaReduceA(Accumulator area, double area0,
                                    int crossings,
                                    boolean reverse, boolean sign) {
    area.Remainder(area0);
    if ((crossings & 1) != 0)
      area.Add((area.Sum() < 0 ? 1 : -1) * area0/2);
    // area is with the clockwise sense.  If !reverse convert to
    // counter-clockwise convention.
    if (!reverse)
      area.Negate();
    // If sign put area in (-area0/2, area0/2], else put area in [0, area0)
    if (sign) {
      if (area.Sum() > area0/2)
        area.Add(-area0);
      else if (area.Sum() <= -area0/2)
        area.Add(+area0);
    } else {
      if (area.Sum() >= area0)
        area.Add(-area0);
      else if (area.Sum() < 0)
        area.Add(+area0);
    }
    return 0 + area.Sum();
  }
  // reduce double area to allowed range
  private static double AreaReduceB(double area, double area0,
                                    int crossings,
                                    boolean reverse, boolean sign) {
    area = GeoMath.remainder(area, area0);
    if ((crossings & 1) != 0)
      area += (area < 0 ? 1 : -1) * area0/2;
    // area is with the clockwise sense.  If !reverse convert to
    // counter-clockwise convention.
    if (!reverse)
      area *= -1;
    // If sign put area in (-area0/2, area0/2], else put area in [0, area0)
    if (sign) {
      if (area > area0/2)
        area -= area0;
      else if (area <= -area0/2)
        area += area0;
    } else {
      if (area >= area0)
        area -= area0;
      else if (area < 0)
        area += area0;
    }
    return 0 + area;
  }

  /**
   * Constructor for PolygonArea.
   * <p>
   * @param earth the Geodesic object to use for geodesic calculations.
   * @param polyline if true that treat the points as defining a polyline
   *   instead of a polygon.
   **********************************************************************/
  public PolygonArea(Geodesic earth, boolean polyline) {
    _earth = earth;
    _area0 = _earth.EllipsoidArea();
    _polyline = polyline;
     _mask = GeodesicMask.LATITUDE | GeodesicMask.LONGITUDE |
       GeodesicMask.DISTANCE |
       (_polyline ? GeodesicMask.NONE :
        GeodesicMask.AREA | GeodesicMask.LONG_UNROLL);
     _perimetersum = new Accumulator(0);
     if (!_polyline)
       _areasum = new Accumulator(0);
     Clear();
  }

  /**
   * Clear PolygonArea, allowing a new polygon to be started.
   **********************************************************************/
  public void Clear() {
    _num = 0;
    _crossings = 0;
    _perimetersum.Set(0);
    if (!_polyline) _areasum.Set(0);
    _lat0 = _lon0 = _lat1 = _lon1 = Double.NaN;
  }

  /**
   * Add a point to the polygon or polyline.
   * <p>
   * @param lat the latitude of the point (degrees).
   * @param lon the latitude of the point (degrees).
   * <p>
   * <i>lat</i> should be in the range [&minus;90&deg;, 90&deg;].
   **********************************************************************/
  public void AddPoint(double lat, double lon) {
    lon = GeoMath.AngNormalize(lon);
    if (_num == 0) {
      _lat0 = _lat1 = lat;
      _lon0 = _lon1 = lon;
    } else {
      GeodesicData g = _earth.Inverse(_lat1, _lon1, lat, lon, _mask);
      _perimetersum.Add(g.s12);
      if (!_polyline) {
        _areasum.Add(g.S12);
        _crossings += transit(_lon1, lon);
      }
      _lat1 = lat; _lon1 = lon;
    }
    ++_num;
  }

  /**
   * Add an edge to the polygon or polyline.
   * <p>
   * @param azi azimuth at current point (degrees).
   * @param s distance from current point to next point (meters).
   * <p>
   * This does nothing if no points have been added yet.  Use
   * PolygonArea.CurrentPoint to determine the position of the new vertex.
   **********************************************************************/
  public void AddEdge(double azi, double s) {
    if (_num > 0) {             // Do nothing if _num is zero
      GeodesicData g = _earth.Direct(_lat1, _lon1, azi, s, _mask);
      _perimetersum.Add(g.s12);
      if (!_polyline) {
        _areasum.Add(g.S12);
        _crossings += transitdirect(_lon1, g.lon2);
      }
      _lat1 = g.lat2; _lon1 = g.lon2;
      ++_num;
    }
  }

  /**
   * Return the results so far.
   * <p>
   * @return PolygonResult(<i>num</i>, <i>perimeter</i>, <i>area</i>) where
   *   <i>num</i> is the number of vertices, <i>perimeter</i> is the perimeter
   *   of the polygon or the length of the polyline (meters), and <i>area</i>
   *   is the area of the polygon (meters<sup>2</sup>) or Double.NaN of
   *   <i>polyline</i> is true in the constructor.
   * <p>
   * Counter-clockwise traversal counts as a positive area.
   **********************************************************************/
  public PolygonResult Compute() { return Compute(false, true); }
  /**
   * Return the results so far.
   * <p>
   * @param reverse if true then clockwise (instead of counter-clockwise)
   *   traversal counts as a positive area.
   * @param sign if true then return a signed result for the area if
   *   the polygon is traversed in the "wrong" direction instead of returning
   *   the area for the rest of the earth.
   * @return PolygonResult(<i>num</i>, <i>perimeter</i>, <i>area</i>) where
   *   <i>num</i> is the number of vertices, <i>perimeter</i> is the perimeter
   *   of the polygon or the length of the polyline (meters), and <i>area</i>
   *   is the area of the polygon (meters<sup>2</sup>) or Double.NaN of
   *   <i>polyline</i> is true in the constructor.
   * <p>
   * More points can be added to the polygon after this call.
   **********************************************************************/
  public PolygonResult Compute(boolean reverse, boolean sign) {
    if (_num < 2)
      return new PolygonResult(_num, 0, _polyline ? Double.NaN : 0);
    if (_polyline)
      return new PolygonResult(_num, _perimetersum.Sum(), Double.NaN);

    GeodesicData g = _earth.Inverse(_lat1, _lon1, _lat0, _lon0, _mask);
    Accumulator tempsum = new Accumulator(_areasum);
    tempsum.Add(g.S12);

    return
      new PolygonResult(_num, _perimetersum.Sum(g.s12),
                        AreaReduceA(tempsum, _area0,
                                    _crossings + transit(_lon1, _lon0),
                                    reverse, sign));
  }

  /**
   * Return the results assuming a tentative final test point is added;
   * however, the data for the test point is not saved.  This lets you report
   * a running result for the perimeter and area as the user moves the mouse
   * cursor.  Ordinary floating point arithmetic is used to accumulate the
   * data for the test point; thus the area and perimeter returned are less
   * accurate than if AddPoint and Compute are used.
   * <p>
   * @param lat the latitude of the test point (degrees).
   * @param lon the longitude of the test point (degrees).
   * @param reverse if true then clockwise (instead of counter-clockwise)
   *   traversal counts as a positive area.
   * @param sign if true then return a signed result for the area if
   *   the polygon is traversed in the "wrong" direction instead of returning
   *   the area for the rest of the earth.
   * @return PolygonResult(<i>num</i>, <i>perimeter</i>, <i>area</i>) where
   *   <i>num</i> is the number of vertices, <i>perimeter</i> is the perimeter
   *   of the polygon or the length of the polyline (meters), and <i>area</i>
   *   is the area of the polygon (meters<sup>2</sup>) or Double.NaN of
   *   <i>polyline</i> is true in the constructor.
   * <p>
   * <i>lat</i> should be in the range [&minus;90&deg;, 90&deg;].
   **********************************************************************/
  public PolygonResult TestPoint(double lat, double lon,
                                 boolean reverse, boolean sign) {
    if (_num == 0)
      return new PolygonResult(1, 0, _polyline ? Double.NaN : 0);

    double perimeter = _perimetersum.Sum();
    double tempsum = _polyline ? 0 : _areasum.Sum();
    int crossings = _crossings;
    int num = _num + 1;
    for (int i = 0; i < (_polyline ? 1 : 2); ++i) {
      GeodesicData g =
        _earth.Inverse(i == 0 ? _lat1 : lat, i == 0 ? _lon1 : lon,
                       i != 0 ? _lat0 : lat, i != 0 ? _lon0 : lon,
                       _mask);
      perimeter += g.s12;
      if (!_polyline) {
        tempsum += g.S12;
        crossings += transit(i == 0 ? _lon1 : lon,
                             i != 0 ? _lon0 : lon);
      }
    }

    if (_polyline)
      return new PolygonResult(num, perimeter, Double.NaN);

    return new PolygonResult(num, perimeter,
                             AreaReduceB(tempsum, _area0, crossings,
                                         reverse, sign));
  }

  /**
   * Return the results assuming a tentative final test point is added via an
   * azimuth and distance; however, the data for the test point is not saved.
   * This lets you report a running result for the perimeter and area as the
   * user moves the mouse cursor.  Ordinary floating point arithmetic is used
   * to accumulate the data for the test point; thus the area and perimeter
   * returned are less accurate than if AddPoint and Compute are used.
   * <p>
   * @param azi azimuth at current point (degrees).
   * @param s distance from current point to final test point (meters).
   * @param reverse if true then clockwise (instead of counter-clockwise)
   *   traversal counts as a positive area.
   * @param sign if true then return a signed result for the area if
   *   the polygon is traversed in the "wrong" direction instead of returning
   *   the area for the rest of the earth.
   * @return PolygonResult(<i>num</i>, <i>perimeter</i>, <i>area</i>) where
   *   <i>num</i> is the number of vertices, <i>perimeter</i> is the perimeter
   *   of the polygon or the length of the polyline (meters), and <i>area</i>
   *   is the area of the polygon (meters<sup>2</sup>) or Double.NaN of
   *   <i>polyline</i> is true in the constructor.
   **********************************************************************/
  public PolygonResult TestEdge(double azi, double s,
                                boolean reverse, boolean sign) {
    if (_num == 0)              // we don't have a starting point!
      return new PolygonResult(0, Double.NaN, Double.NaN);

    int num = _num + 1;
    double perimeter = _perimetersum.Sum() + s;
    if (_polyline)
      return new PolygonResult(num, perimeter, Double.NaN);

    double tempsum =  _areasum.Sum();
    int crossings = _crossings;
    {
      double lat, lon, s12, S12, t;
      GeodesicData g =
        _earth.Direct(_lat1, _lon1, azi, false, s, _mask);
      tempsum += g.S12;
      crossings += transitdirect(_lon1, g.lon2);
      crossings += transit(g.lon2, _lon0);
      g = _earth.Inverse(g.lat2, g.lon2, _lat0, _lon0, _mask);
      perimeter += g.s12;
      tempsum += g.S12;
    }

    return new PolygonResult(num, perimeter,
                             AreaReduceB(tempsum, _area0, crossings,
                                         reverse, sign));
  }

  /**
   * @return <i>a</i> the equatorial radius of the ellipsoid (meters).  This is
   *   the value inherited from the Geodesic object used in the constructor.
   **********************************************************************/
  public double EquatorialRadius() { return _earth.EquatorialRadius(); }

  /**
   * @return <i>f</i> the flattening of the ellipsoid.  This is the value
   *   inherited from the Geodesic object used in the constructor.
   **********************************************************************/
  public double Flattening() { return _earth.Flattening(); }

  /**
   * Report the previous vertex added to the polygon or polyline.
   * <p>
   * @return Pair(<i>lat</i>, <i>lon</i>), the current latitude and longitude.
   * <p>
   * If no points have been added, then Double.NaN is returned.  Otherwise,
   * <i>lon</i> will be in the range [&minus;180&deg;, 180&deg;].
   **********************************************************************/
  public Pair CurrentPoint() { return new Pair(_lat1, _lon1); }

  /**
   * @deprecated An old name for {@link #EquatorialRadius()}.
   * @return <i>a</i> the equatorial radius of the ellipsoid (meters).
   **********************************************************************/
  // @Deprecated
  public double MajorRadius() { return EquatorialRadius(); }
}