// License: GPL. For details, see LICENSE file.
package org.openstreetmap.josm.tools;
import java.awt.Rectangle;
import java.awt.geom.Area;
import java.awt.geom.Line2D;
import java.awt.geom.Path2D;
import java.math.BigDecimal;
import java.math.MathContext;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.EnumSet;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Set;
import org.openstreetmap.josm.Main;
import org.openstreetmap.josm.command.AddCommand;
import org.openstreetmap.josm.command.ChangeCommand;
import org.openstreetmap.josm.command.Command;
import org.openstreetmap.josm.data.coor.EastNorth;
import org.openstreetmap.josm.data.coor.LatLon;
import org.openstreetmap.josm.data.osm.BBox;
import org.openstreetmap.josm.data.osm.MultipolygonCreate;
import org.openstreetmap.josm.data.osm.Node;
import org.openstreetmap.josm.data.osm.NodePositionComparator;
import org.openstreetmap.josm.data.osm.OsmPrimitiveType;
import org.openstreetmap.josm.data.osm.Relation;
import org.openstreetmap.josm.data.osm.RelationMember;
import org.openstreetmap.josm.data.osm.Way;
/**
* Some tools for geometry related tasks.
*
* @author viesturs
*/
public final class Geometry {
private Geometry() {
// Hide default constructor for utils classes
}
public enum PolygonIntersection {FIRST_INSIDE_SECOND, SECOND_INSIDE_FIRST, OUTSIDE, CROSSING}
/**
* Will find all intersection and add nodes there for list of given ways.
* Handles self-intersections too.
* And makes commands to add the intersection points to ways.
*
* Prerequisite: no two nodes have the same coordinates.
*
* @param ways a list of ways to test
* @param test if false, do not build list of Commands, just return nodes
* @param cmds list of commands, typically empty when handed to this method.
* Will be filled with commands that add intersection nodes to
* the ways.
* @return list of new nodes
*/
public static Set<Node> addIntersections(List<Way> ways, boolean test, List<Command> cmds) {
int n = ways.size();
@SuppressWarnings("unchecked")
List<Node>[] newNodes = new ArrayList[n];
BBox[] wayBounds = new BBox[n];
boolean[] changedWays = new boolean[n];
Set<Node> intersectionNodes = new LinkedHashSet<>();
//copy node arrays for local usage.
for (int pos = 0; pos < n; pos ++) {
newNodes[pos] = new ArrayList<>(ways.get(pos).getNodes());
wayBounds[pos] = getNodesBounds(newNodes[pos]);
changedWays[pos] = false;
}
//iterate over all way pairs and introduce the intersections
Comparator<Node> coordsComparator = new NodePositionComparator();
for (int seg1Way = 0; seg1Way < n; seg1Way ++) {
for (int seg2Way = seg1Way; seg2Way < n; seg2Way ++) {
//do not waste time on bounds that do not intersect
if (!wayBounds[seg1Way].intersects(wayBounds[seg2Way])) {
continue;
}
List<Node> way1Nodes = newNodes[seg1Way];
List<Node> way2Nodes = newNodes[seg2Way];
//iterate over primary segmemt
for (int seg1Pos = 0; seg1Pos + 1 < way1Nodes.size(); seg1Pos ++) {
//iterate over secondary segment
int seg2Start = seg1Way != seg2Way ? 0: seg1Pos + 2;//skip the adjacent segment
for (int seg2Pos = seg2Start; seg2Pos + 1< way2Nodes.size(); seg2Pos ++) {
//need to get them again every time, because other segments may be changed
Node seg1Node1 = way1Nodes.get(seg1Pos);
Node seg1Node2 = way1Nodes.get(seg1Pos + 1);
Node seg2Node1 = way2Nodes.get(seg2Pos);
Node seg2Node2 = way2Nodes.get(seg2Pos + 1);
int commonCount = 0;
//test if we have common nodes to add.
if (seg1Node1 == seg2Node1 || seg1Node1 == seg2Node2) {
commonCount ++;
if (seg1Way == seg2Way &&
seg1Pos == 0 &&
seg2Pos == way2Nodes.size() -2) {
//do not add - this is first and last segment of the same way.
} else {
intersectionNodes.add(seg1Node1);
}
}
if (seg1Node2 == seg2Node1 || seg1Node2 == seg2Node2) {
commonCount ++;
intersectionNodes.add(seg1Node2);
}
//no common nodes - find intersection
if (commonCount == 0) {
EastNorth intersection = getSegmentSegmentIntersection(
seg1Node1.getEastNorth(), seg1Node2.getEastNorth(),
seg2Node1.getEastNorth(), seg2Node2.getEastNorth());
if (intersection != null) {
if (test) {
intersectionNodes.add(seg2Node1);
return intersectionNodes;
}
Node newNode = new Node(Main.getProjection().eastNorth2latlon(intersection));
Node intNode = newNode;
boolean insertInSeg1 = false;
boolean insertInSeg2 = false;
//find if the intersection point is at end point of one of the segments, if so use that point
//segment 1
if (coordsComparator.compare(newNode, seg1Node1) == 0) {
intNode = seg1Node1;
} else if (coordsComparator.compare(newNode, seg1Node2) == 0) {
intNode = seg1Node2;
} else {
insertInSeg1 = true;
}
//segment 2
if (coordsComparator.compare(newNode, seg2Node1) == 0) {
intNode = seg2Node1;
} else if (coordsComparator.compare(newNode, seg2Node2) == 0) {
intNode = seg2Node2;
} else {
insertInSeg2 = true;
}
if (insertInSeg1) {
way1Nodes.add(seg1Pos +1, intNode);
changedWays[seg1Way] = true;
//fix seg2 position, as indexes have changed, seg2Pos is always bigger than seg1Pos on the same segment.
if (seg2Way == seg1Way) {
seg2Pos ++;
}
}
if (insertInSeg2) {
way2Nodes.add(seg2Pos +1, intNode);
changedWays[seg2Way] = true;
//Do not need to compare again to already split segment
seg2Pos ++;
}
intersectionNodes.add(intNode);
if (intNode == newNode) {
cmds.add(new AddCommand(intNode));
}
}
}
else if (test && !intersectionNodes.isEmpty())
return intersectionNodes;
}
}
}
}
for (int pos = 0; pos < ways.size(); pos ++) {
if (!changedWays[pos]) {
continue;
}
Way way = ways.get(pos);
Way newWay = new Way(way);
newWay.setNodes(newNodes[pos]);
cmds.add(new ChangeCommand(way, newWay));
}
return intersectionNodes;
}
private static BBox getNodesBounds(List<Node> nodes) {
BBox bounds = new BBox(nodes.get(0));
for (Node n: nodes) {
bounds.add(n.getCoor());
}
return bounds;
}
/**
* Tests if given point is to the right side of path consisting of 3 points.
*
* (Imagine the path is continued beyond the endpoints, so you get two rays
* starting from lineP2 and going through lineP1 and lineP3 respectively
* which divide the plane into two parts. The test returns true, if testPoint
* lies in the part that is to the right when traveling in the direction
* lineP1, lineP2, lineP3.)
*
* @param lineP1 first point in path
* @param lineP2 second point in path
* @param lineP3 third point in path
* @param testPoint
* @return true if to the right side, false otherwise
*/
public static boolean isToTheRightSideOfLine(Node lineP1, Node lineP2, Node lineP3, Node testPoint) {
boolean pathBendToRight = angleIsClockwise(lineP1, lineP2, lineP3);
boolean rightOfSeg1 = angleIsClockwise(lineP1, lineP2, testPoint);
boolean rightOfSeg2 = angleIsClockwise(lineP2, lineP3, testPoint);
if (pathBendToRight)
return rightOfSeg1 && rightOfSeg2;
else
return !(!rightOfSeg1 && !rightOfSeg2);
}
/**
* This method tests if secondNode is clockwise to first node.
* @param commonNode starting point for both vectors
* @param firstNode first vector end node
* @param secondNode second vector end node
* @return true if first vector is clockwise before second vector.
*/
public static boolean angleIsClockwise(Node commonNode, Node firstNode, Node secondNode) {
return angleIsClockwise(commonNode.getEastNorth(), firstNode.getEastNorth(), secondNode.getEastNorth());
}
/**
* Finds the intersection of two line segments
* @return EastNorth null if no intersection was found, the EastNorth coordinates of the intersection otherwise
*/
public static EastNorth getSegmentSegmentIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
CheckParameterUtil.ensureValidCoordinates(p1, "p1");
CheckParameterUtil.ensureValidCoordinates(p2, "p2");
CheckParameterUtil.ensureValidCoordinates(p3, "p3");
CheckParameterUtil.ensureValidCoordinates(p4, "p4");
double x1 = p1.getX();
double y1 = p1.getY();
double x2 = p2.getX();
double y2 = p2.getY();
double x3 = p3.getX();
double y3 = p3.getY();
double x4 = p4.getX();
double y4 = p4.getY();
//TODO: do this locally.
//TODO: remove this check after careful testing
if (!Line2D.linesIntersect(x1, y1, x2, y2, x3, y3, x4, y4)) return null;
// solve line-line intersection in parametric form:
// (x1,y1) + (x2-x1,y2-y1)* u = (x3,y3) + (x4-x3,y4-y3)* v
// (x2-x1,y2-y1)*u - (x4-x3,y4-y3)*v = (x3-x1,y3-y1)
// if 0<= u,v <=1, intersection exists at ( x1+ (x2-x1)*u, y1 + (y2-y1)*u )
double a1 = x2 - x1;
double b1 = x3 - x4;
double c1 = x3 - x1;
double a2 = y2 - y1;
double b2 = y3 - y4;
double c2 = y3 - y1;
// Solve the equations
double det = a1*b2 - a2*b1;
double uu = b2*c1 - b1*c2 ;
double vv = a1*c2 - a2*c1;
double mag = Math.abs(uu)+Math.abs(vv);
if (Math.abs(det) > 1e-12 * mag) {
double u = uu/det, v = vv/det;
if (u>-1e-8 && u < 1+1e-8 && v>-1e-8 && v < 1+1e-8 ) {
if (u<0) u=0;
if (u>1) u=1.0;
return new EastNorth(x1+a1*u, y1+a2*u);
} else {
return null;
}
} else {
// parallel lines
return null;
}
}
/**
* Finds the intersection of two lines of infinite length.
* @return EastNorth null if no intersection was found, the coordinates of the intersection otherwise
* @throws IllegalArgumentException if a parameter is null or without valid coordinates
*/
public static EastNorth getLineLineIntersection(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
CheckParameterUtil.ensureValidCoordinates(p1, "p1");
CheckParameterUtil.ensureValidCoordinates(p2, "p2");
CheckParameterUtil.ensureValidCoordinates(p3, "p3");
CheckParameterUtil.ensureValidCoordinates(p4, "p4");
if (!p1.isValid()) throw new IllegalArgumentException();
// Convert line from (point, point) form to ax+by=c
double a1 = p2.getY() - p1.getY();
double b1 = p1.getX() - p2.getX();
double c1 = p2.getX() * p1.getY() - p1.getX() * p2.getY();
double a2 = p4.getY() - p3.getY();
double b2 = p3.getX() - p4.getX();
double c2 = p4.getX() * p3.getY() - p3.getX() * p4.getY();
// Solve the equations
double det = a1 * b2 - a2 * b1;
if (det == 0)
return null; // Lines are parallel
return new EastNorth((b1 * c2 - b2 * c1) / det, (a2 * c1 - a1 * c2) / det);
}
public static boolean segmentsParallel(EastNorth p1, EastNorth p2, EastNorth p3, EastNorth p4) {
CheckParameterUtil.ensureValidCoordinates(p1, "p1");
CheckParameterUtil.ensureValidCoordinates(p2, "p2");
CheckParameterUtil.ensureValidCoordinates(p3, "p3");
CheckParameterUtil.ensureValidCoordinates(p4, "p4");
// Convert line from (point, point) form to ax+by=c
double a1 = p2.getY() - p1.getY();
double b1 = p1.getX() - p2.getX();
double a2 = p4.getY() - p3.getY();
double b2 = p3.getX() - p4.getX();
// Solve the equations
double det = a1 * b2 - a2 * b1;
// remove influence of of scaling factor
det /= Math.sqrt(a1*a1 + b1*b1) * Math.sqrt(a2*a2 + b2*b2);
return Math.abs(det) < 1e-3;
}
private static EastNorth closestPointTo(EastNorth p1, EastNorth p2, EastNorth point, boolean segmentOnly) {
CheckParameterUtil.ensureParameterNotNull(p1, "p1");
CheckParameterUtil.ensureParameterNotNull(p2, "p2");
CheckParameterUtil.ensureParameterNotNull(point, "point");
double ldx = p2.getX() - p1.getX();
double ldy = p2.getY() - p1.getY();
if (ldx == 0 && ldy == 0) //segment zero length
return p1;
double pdx = point.getX() - p1.getX();
double pdy = point.getY() - p1.getY();
double offset = (pdx * ldx + pdy * ldy) / (ldx * ldx + ldy * ldy);
if (segmentOnly && offset <= 0)
return p1;
else if (segmentOnly && offset >= 1)
return p2;
else
return new EastNorth(p1.getX() + ldx * offset, p1.getY() + ldy * offset);
}
/**
* Calculates closest point to a line segment.
* @param segmentP1 First point determining line segment
* @param segmentP2 Second point determining line segment
* @param point Point for which a closest point is searched on line segment [P1,P2]
* @return segmentP1 if it is the closest point, segmentP2 if it is the closest point,
* a new point if closest point is between segmentP1 and segmentP2.
* @since 3650
* @see #closestPointToLine
*/
public static EastNorth closestPointToSegment(EastNorth segmentP1, EastNorth segmentP2, EastNorth point) {
return closestPointTo(segmentP1, segmentP2, point, true);
}
/**
* Calculates closest point to a line.
* @param lineP1 First point determining line
* @param lineP2 Second point determining line
* @param point Point for which a closest point is searched on line (P1,P2)
* @return The closest point found on line. It may be outside the segment [P1,P2].
* @since 4134
* @see #closestPointToSegment
*/
public static EastNorth closestPointToLine(EastNorth lineP1, EastNorth lineP2, EastNorth point) {
return closestPointTo(lineP1, lineP2, point, false);
}
/**
* This method tests if secondNode is clockwise to first node.
*
* The line through the two points commonNode and firstNode divides the
* plane into two parts. The test returns true, if secondNode lies in
* the part that is to the right when traveling in the direction from
* commonNode to firstNode.
*
* @param commonNode starting point for both vectors
* @param firstNode first vector end node
* @param secondNode second vector end node
* @return true if first vector is clockwise before second vector.
*/
public static boolean angleIsClockwise(EastNorth commonNode, EastNorth firstNode, EastNorth secondNode) {
CheckParameterUtil.ensureValidCoordinates(commonNode, "commonNode");
CheckParameterUtil.ensureValidCoordinates(firstNode, "firstNode");
CheckParameterUtil.ensureValidCoordinates(secondNode, "secondNode");
double dy1 = (firstNode.getY() - commonNode.getY());
double dy2 = (secondNode.getY() - commonNode.getY());
double dx1 = (firstNode.getX() - commonNode.getX());
double dx2 = (secondNode.getX() - commonNode.getX());
return dy1 * dx2 - dx1 * dy2 > 0;
}
/**
* Returns the Area of a polygon, from its list of nodes.
* @param polygon List of nodes forming polygon (EastNorth coordinates)
* @return Area for the given list of nodes
* @since 6841
*/
public static Area getArea(List<Node> polygon) {
Path2D path = new Path2D.Double();
boolean begin = true;
for (Node n : polygon) {
EastNorth en = n.getEastNorth();
if (en != null) {
if (begin) {
path.moveTo(en.getX(), en.getY());
begin = false;
} else {
path.lineTo(en.getX(), en.getY());
}
}
}
if (!begin) {
path.closePath();
}
return new Area(path);
}
/**
* Returns the Area of a polygon, from its list of nodes.
* @param polygon List of nodes forming polygon (LatLon coordinates)
* @return Area for the given list of nodes
* @since 6841
*/
public static Area getAreaLatLon(List<Node> polygon) {
Path2D path = new Path2D.Double();
boolean begin = true;
for (Node n : polygon) {
if (begin) {
path.moveTo(n.getCoor().lon(), n.getCoor().lat());
begin = false;
} else {
path.lineTo(n.getCoor().lon(), n.getCoor().lat());
}
}
if (!begin) {
path.closePath();
}
return new Area(path);
}
/**
* Tests if two polygons intersect.
* @param first List of nodes forming first polygon
* @param second List of nodes forming second polygon
* @return intersection kind
*/
public static PolygonIntersection polygonIntersection(List<Node> first, List<Node> second) {
Area a1 = getArea(first);
Area a2 = getArea(second);
return polygonIntersection(a1, a2);
}
/**
* Tests if two polygons intersect.
* @param a1 Area of first polygon
* @param a2 Area of second polygon
* @return intersection kind
* @since 6841
*/
public static PolygonIntersection polygonIntersection(Area a1, Area a2) {
return polygonIntersection(a1, a2, 1.0);
}
/**
* Tests if two polygons intersect.
* @param a1 Area of first polygon
* @param a2 Area of second polygon
* @param eps an area threshold, everything below is considered an empty intersection
* @return intersection kind
*/
public static PolygonIntersection polygonIntersection(Area a1, Area a2, double eps) {
Area inter = new Area(a1);
inter.intersect(a2);
Rectangle bounds = inter.getBounds();
if (inter.isEmpty() || bounds.getHeight()*bounds.getWidth() <= eps) {
return PolygonIntersection.OUTSIDE;
} else if (inter.equals(a1)) {
return PolygonIntersection.FIRST_INSIDE_SECOND;
} else if (inter.equals(a2)) {
return PolygonIntersection.SECOND_INSIDE_FIRST;
} else {
return PolygonIntersection.CROSSING;
}
}
/**
* Tests if point is inside a polygon. The polygon can be self-intersecting. In such case the contains function works in xor-like manner.
* @param polygonNodes list of nodes from polygon path.
* @param point the point to test
* @return true if the point is inside polygon.
*/
public static boolean nodeInsidePolygon(Node point, List<Node> polygonNodes) {
if (polygonNodes.size() < 2)
return false;
boolean inside = false;
Node p1, p2;
//iterate each side of the polygon, start with the last segment
Node oldPoint = polygonNodes.get(polygonNodes.size() - 1);
for (Node newPoint : polygonNodes) {
//skip duplicate points
if (newPoint.equals(oldPoint)) {
continue;
}
//order points so p1.lat <= p2.lat
if (newPoint.getEastNorth().getY() > oldPoint.getEastNorth().getY()) {
p1 = oldPoint;
p2 = newPoint;
} else {
p1 = newPoint;
p2 = oldPoint;
}
//test if the line is crossed and if so invert the inside flag.
if ((newPoint.getEastNorth().getY() < point.getEastNorth().getY()) == (point.getEastNorth().getY() <= oldPoint.getEastNorth().getY())
&& (point.getEastNorth().getX() - p1.getEastNorth().getX()) * (p2.getEastNorth().getY() - p1.getEastNorth().getY())
< (p2.getEastNorth().getX() - p1.getEastNorth().getX()) * (point.getEastNorth().getY() - p1.getEastNorth().getY()))
{
inside = !inside;
}
oldPoint = newPoint;
}
return inside;
}
/**
* Returns area of a closed way in square meters.
* (approximate(?), but should be OK for small areas)
*
* Relies on the current projection: Works correctly, when
* one unit in projected coordinates corresponds to one meter.
* This is true for most projections, but not for WGS84 and
* Mercator (EPSG:3857).
*
* @param way Way to measure, should be closed (first node is the same as last node)
* @return area of the closed way.
*/
public static double closedWayArea(Way way) {
//http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/
double area = 0;
Node lastN = null;
for (Node n : way.getNodes()) {
if (lastN != null) {
n.getEastNorth().getX();
area += (calcX(n) * calcY(lastN)) - (calcY(n) * calcX(lastN));
}
lastN = n;
}
return Math.abs(area/2);
}
protected static double calcX(Node p1){
double lat1, lon1, lat2, lon2;
double dlon, dlat;
lat1 = p1.getCoor().lat() * Math.PI / 180.0;
lon1 = p1.getCoor().lon() * Math.PI / 180.0;
lat2 = lat1;
lon2 = 0;
dlon = lon2 - lon1;
dlat = lat2 - lat1;
double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
return 6367000 * c;
}
protected static double calcY(Node p1){
double lat1, lon1, lat2, lon2;
double dlon, dlat;
lat1 = p1.getCoor().lat() * Math.PI / 180.0;
lon1 = p1.getCoor().lon() * Math.PI / 180.0;
lat2 = 0;
lon2 = lon1;
dlon = lon2 - lon1;
dlat = lat2 - lat1;
double a = (Math.pow(Math.sin(dlat/2), 2) + Math.cos(lat1) * Math.cos(lat2) * Math.pow(Math.sin(dlon/2), 2));
double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a));
return 6367000 * c;
}
/**
* Determines whether a way is oriented clockwise.
*
* Internals: Assuming a closed non-looping way, compute twice the area
* of the polygon using the formula {@code 2 * area = sum (X[n] * Y[n+1] - X[n+1] * Y[n])}.
* If the area is negative the way is ordered in a clockwise direction.
*
* See http://paulbourke.net/geometry/polyarea/
*
* @param w the way to be checked.
* @return true if and only if way is oriented clockwise.
* @throws IllegalArgumentException if way is not closed (see {@link Way#isClosed}).
*/
public static boolean isClockwise(Way w) {
if (!w.isClosed()) {
throw new IllegalArgumentException("Way must be closed to check orientation.");
}
double area2 = 0.;
int nodesCount = w.getNodesCount();
for (int node = 1; node <= /*sic! consider last-first as well*/ nodesCount; node++) {
LatLon coorPrev = w.getNode(node - 1).getCoor();
LatLon coorCurr = w.getNode(node % nodesCount).getCoor();
area2 += coorPrev.lon() * coorCurr.lat();
area2 -= coorCurr.lon() * coorPrev.lat();
}
return area2 < 0;
}
/**
* Returns angle of a segment defined with 2 point coordinates.
*
* @param p1
* @param p2
* @return Angle in radians (-pi, pi]
*/
public static double getSegmentAngle(EastNorth p1, EastNorth p2) {
CheckParameterUtil.ensureValidCoordinates(p1, "p1");
CheckParameterUtil.ensureValidCoordinates(p2, "p2");
return Math.atan2(p2.north() - p1.north(), p2.east() - p1.east());
}
/**
* Returns angle of a corner defined with 3 point coordinates.
*
* @param p1
* @param p2 Common endpoint
* @param p3
* @return Angle in radians (-pi, pi]
*/
public static double getCornerAngle(EastNorth p1, EastNorth p2, EastNorth p3) {
CheckParameterUtil.ensureValidCoordinates(p1, "p1");
CheckParameterUtil.ensureValidCoordinates(p2, "p2");
CheckParameterUtil.ensureValidCoordinates(p3, "p3");
Double result = getSegmentAngle(p2, p1) - getSegmentAngle(p2, p3);
if (result <= -Math.PI) {
result += 2 * Math.PI;
}
if (result > Math.PI) {
result -= 2 * Math.PI;
}
return result;
}
/**
* Compute the centroid/barycenter of nodes
* @param nodes Nodes for which the centroid is wanted
* @return the centroid of nodes
* @see Geometry#getCenter
*/
public static EastNorth getCentroid(List<Node> nodes) {
BigDecimal area = BigDecimal.ZERO;
BigDecimal north = BigDecimal.ZERO;
BigDecimal east = BigDecimal.ZERO;
// See https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon for the equation used here
for (int i = 0; i < nodes.size(); i++) {
EastNorth n0 = nodes.get(i).getEastNorth();
EastNorth n1 = nodes.get((i+1) % nodes.size()).getEastNorth();
if (n0 != null && n1 != null && n0.isValid() && n1.isValid()) {
BigDecimal x0 = new BigDecimal(n0.east());
BigDecimal y0 = new BigDecimal(n0.north());
BigDecimal x1 = new BigDecimal(n1.east());
BigDecimal y1 = new BigDecimal(n1.north());
BigDecimal k = x0.multiply(y1, MathContext.DECIMAL128).subtract(y0.multiply(x1, MathContext.DECIMAL128));
area = area.add(k, MathContext.DECIMAL128);
east = east.add(k.multiply(x0.add(x1, MathContext.DECIMAL128), MathContext.DECIMAL128));
north = north.add(k.multiply(y0.add(y1, MathContext.DECIMAL128), MathContext.DECIMAL128));
}
}
BigDecimal d = new BigDecimal(3, MathContext.DECIMAL128); // 1/2 * 6 = 3
area = area.multiply(d, MathContext.DECIMAL128);
if (area.compareTo(BigDecimal.ZERO) != 0) {
north = north.divide(area, MathContext.DECIMAL128);
east = east.divide(area, MathContext.DECIMAL128);
}
return new EastNorth(east.doubleValue(), north.doubleValue());
}
/**
* Compute center of the circle closest to different nodes.
*
* Ensure exact center computation in case nodes are already aligned in circle.
* This is done by least square method.
* Let be a_i x + b_i y + c_i = 0 equations of bisectors of each edges.
* Center must be intersection of all bisectors.
* <pre>
* [ a1 b1 ] [ -c1 ]
* With A = [ ... ... ] and Y = [ ... ]
* [ an bn ] [ -cn ]
* </pre>
* An approximation of center of circle is (At.A)^-1.At.Y
* @param nodes Nodes parts of the circle (at least 3)
* @return An approximation of the center, of null if there is no solution.
* @see Geometry#getCentroid
* @since 6934
*/
public static EastNorth getCenter(List<Node> nodes) {
int nc = nodes.size();
if(nc < 3) return null;
/**
* Equation of each bisector ax + by + c = 0
*/
double[] a = new double[nc];
double[] b = new double[nc];
double[] c = new double[nc];
// Compute equation of bisector
for(int i = 0; i < nc; i++) {
EastNorth pt1 = nodes.get(i).getEastNorth();
EastNorth pt2 = nodes.get((i+1) % nc).getEastNorth();
a[i] = pt1.east() - pt2.east();
b[i] = pt1.north() - pt2.north();
double d = Math.sqrt(a[i]*a[i] + b[i]*b[i]);
if(d == 0) return null;
a[i] /= d;
b[i] /= d;
double xC = (pt1.east() + pt2.east()) / 2;
double yC = (pt1.north() + pt2.north()) / 2;
c[i] = -(a[i]*xC + b[i]*yC);
}
// At.A = [aij]
double a11 = 0, a12 = 0, a22 = 0;
// At.Y = [bi]
double b1 = 0, b2 = 0;
for(int i = 0; i < nc; i++) {
a11 += a[i]*a[i];
a12 += a[i]*b[i];
a22 += b[i]*b[i];
b1 -= a[i]*c[i];
b2 -= b[i]*c[i];
}
// (At.A)^-1 = [invij]
double det = a11*a22 - a12*a12;
if(Math.abs(det) < 1e-5) return null;
double inv11 = a22/det;
double inv12 = -a12/det;
double inv22 = a11/det;
// center (xC, yC) = (At.A)^-1.At.y
double xC = inv11*b1 + inv12*b2;
double yC = inv12*b1 + inv22*b2;
return new EastNorth(xC, yC);
}
/**
* Returns the coordinate of intersection of segment sp1-sp2 and an altitude
* to it starting at point ap. If the line defined with sp1-sp2 intersects
* its altitude out of sp1-sp2, null is returned.
*
* @param sp1
* @param sp2
* @param ap
* @return Intersection coordinate or null
*/
public static EastNorth getSegmentAltituteIntersection(EastNorth sp1, EastNorth sp2, EastNorth ap) {
CheckParameterUtil.ensureValidCoordinates(sp1, "sp1");
CheckParameterUtil.ensureValidCoordinates(sp2, "sp2");
CheckParameterUtil.ensureValidCoordinates(ap, "ap");
Double segmentLenght = sp1.distance(sp2);
Double altitudeAngle = getSegmentAngle(sp1, sp2) + Math.PI / 2;
// Taking a random point on the altitude line (angle is known).
EastNorth ap2 = new EastNorth(ap.east() + 1000
* Math.cos(altitudeAngle), ap.north() + 1000
* Math.sin(altitudeAngle));
// Finding the intersection of two lines
EastNorth resultCandidate = Geometry.getLineLineIntersection(sp1, sp2,
ap, ap2);
// Filtering result
if (resultCandidate != null
&& resultCandidate.distance(sp1) * .999 < segmentLenght
&& resultCandidate.distance(sp2) * .999 < segmentLenght) {
return resultCandidate;
} else {
return null;
}
}
public static class MultiPolygonMembers {
public final Set<Way> outers = new HashSet<>();
public final Set<Way> inners = new HashSet<>();
public MultiPolygonMembers(Relation multiPolygon) {
for (RelationMember m : multiPolygon.getMembers()) {
if (m.getType().equals(OsmPrimitiveType.WAY)) {
if ("outer".equals(m.getRole())) {
outers.add(m.getWay());
} else if ("inner".equals(m.getRole())) {
inners.add(m.getWay());
}
}
}
}
}
/**
* Tests if the {@code node} is inside the multipolygon {@code multiPolygon}. The nullable argument
* {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
*/
public static boolean isNodeInsideMultiPolygon(Node node, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
return isPolygonInsideMultiPolygon(Collections.singletonList(node), multiPolygon, isOuterWayAMatch);
}
/**
* Tests if the polygon formed by {@code nodes} is inside the multipolygon {@code multiPolygon}. The nullable argument
* {@code isOuterWayAMatch} allows to decide if the immediate {@code outer} way of the multipolygon is a match.
* <p>
* If {@code nodes} contains exactly one element, then it is checked whether that one node is inside the multipolygon.
*/
public static boolean isPolygonInsideMultiPolygon(List<Node> nodes, Relation multiPolygon, Predicate<Way> isOuterWayAMatch) {
// Extract outer/inner members from multipolygon
final MultiPolygonMembers mpm = new MultiPolygonMembers(multiPolygon);
// Construct complete rings for the inner/outer members
final List<MultipolygonCreate.JoinedPolygon> outerRings;
final List<MultipolygonCreate.JoinedPolygon> innerRings;
try {
outerRings = MultipolygonCreate.joinWays(mpm.outers);
innerRings = MultipolygonCreate.joinWays(mpm.inners);
} catch (MultipolygonCreate.JoinedPolygonCreationException ex) {
Main.debug("Invalid multipolygon " + multiPolygon);
return false;
}
// Test if object is inside an outer member
for (MultipolygonCreate.JoinedPolygon out : outerRings) {
if (nodes.size() == 1
? nodeInsidePolygon(nodes.get(0), out.getNodes())
: EnumSet.of(PolygonIntersection.FIRST_INSIDE_SECOND, PolygonIntersection.CROSSING).contains(polygonIntersection(nodes, out.getNodes()))) {
boolean insideInner = false;
// If inside an outer, check it is not inside an inner
for (MultipolygonCreate.JoinedPolygon in : innerRings) {
if (polygonIntersection(in.getNodes(), out.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND
&& (nodes.size() == 1
? nodeInsidePolygon(nodes.get(0), in.getNodes())
: polygonIntersection(nodes, in.getNodes()) == PolygonIntersection.FIRST_INSIDE_SECOND)) {
insideInner = true;
break;
}
}
// Inside outer but not inside inner -> the polygon appears to be inside a the multipolygon
if (!insideInner) {
// Final check using predicate
if (isOuterWayAMatch == null || isOuterWayAMatch.evaluate(out.ways.get(0) /* TODO give a better representation of the outer ring to the predicate */)) {
return true;
}
}
}
}
return false;
}
}