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// cheap-ruler-java is licensed under the BSD 3-Clause
// License, https://opensource.org/licenses/BSD-3-Clause
//
// Copyright (c) 2020, Ian Emmons. All rights reserved.
package mobi.emmons.cheap_ruler;
import java.util.ArrayList;
import java.util.List;
/**
* A collection of very fast approximations to common geodesic measurements.
* Useful for performance-sensitive code that measures things on a city scale.
* Can be an order of magnitude faster than corresponding
* Turf methods.
*
* The approximations are based on the
* WGS84
* ellipsoid model of the Earth, projecting coordinates to a flat surface
* that approximates the ellipsoid around a certain latitude. For distances
* under 500 kilometers and not on the poles, the results are very precise
* — within 0.1% margin of error compared to
* Vincenti
* formulas, and usually much less for shorter distances.
*
*
This library is a A Java port of the original
* JavaScript library.
*/
public final class CheapRuler {
// Values that define the WGS84 ellipsoid model of the Earth:
private static double RE = 6378.137; // equatorial radius
private static double FE = 1.0 / 298.257223563; // flattening
private static double E2 = FE * (2 - FE);
private static double RAD = Math.PI / 180.0;
private final double ky;
private final double kx;
/**
* Creates a CheapRuler instance valid for geodesic computations near the given
* latitude.
*
* @param latitude The latitude of interest, expressed in decimal degrees
* @param unit The distance unit to use in computations
* @return A CheapRuler instance
*/
public static CheapRuler fromLatitude(double latitude, Unit unit) {
return new CheapRuler(latitude, unit);
}
/**
* Creates a CheapRuler instance valid for the given tile coordinates.
*
* @param y Y parameter of the tile of interest
* @param z Z parameter of the tile of interest
* @param unit The distance unit to use in computations
* @return A CheapRuler instance
*/
public static CheapRuler fromTile(int y, int z, Unit unit) {
if (y < 0) {
throw new IllegalArgumentException("y must be non-negative");
}
if (z < 0 || z >= 32) {
throw new IllegalArgumentException(String.format(
"z is out of the range [0, 32)", z));
}
double n = Math.PI * (1.0 - 2.0 * (y + 0.5) / (1 << z));
double latitude = Math.atan(Math.sinh(n)) / RAD;
return new CheapRuler(latitude, unit);
}
private CheapRuler(double latitude, Unit unit) {
// Curvature formulas from https://en.wikipedia.org/wiki/Earth_radius#Meridional
double mul = RAD * RE * unit.getMultiplier();
double coslat = Math.cos(latitude * RAD);
double w2 = 1 / (1 - E2 * (1 - coslat * coslat));
double w = Math.sqrt(w2);
// multipliers for converting longitude and latitude degrees into distance
kx = mul * w * coslat; // based on normal radius of curvature
ky = mul * w * w2 * (1 - E2); // based on meridonal radius of curvature
}
/**
* Computes the square of the distance between two points.
*
* @param a The first point
* @param b The second point
* @return The square of the distance between the two points
*/
public double squareDistance(Point a, Point b) {
double dx = longDiff(a.getLat(), b.getLat()) * kx;
double dy = (a.getLon() - b.getLon()) * ky;
return dx * dx + dy * dy;
}
/**
* Computes the distance between two points.
*
* @param a The first point
* @param b The second point
* @return The distance between the two points
*/
public double distance(Point a, Point b) {
return Math.sqrt(squareDistance(a, b));
}
/**
* Computes the bearing between two points in angles.
*
* @param a The first point
* @param b The second point
* @return The bearing between the two points
*/
public double bearing(Point a, Point b) {
double dx = longDiff(b.getLat(), a.getLat()) * kx;
double dy = (b.getLon() - a.getLon()) * ky;
return Math.atan2(dx, dy) / RAD;
}
/**
* Computes a new point given distance and bearing from the starting point.
*
* @param origin The point from which to start
* @param dist The distance from the origin point
* @param bearing The bearing from the origin point
* @return A new point as indicated
*/
public Point destination(Point origin, double dist, double bearing) {
double a = bearing * RAD;
return offset(origin, Math.sin(a) * dist, Math.cos(a) * dist);
}
/**
* Computes a new point given easting and northing offsets from the starting
* point.
*
* @param origin The point from which to start
* @param dx The easting offset
* @param dy The northing offset
* @return A new point as indicated
*/
public Point offset(Point origin, double dx, double dy) {
return new Point(origin.getLat() + dx / kx, origin.getLon() + dy / ky);
}
/**
* Computes the distance along a line.
*
* @param points The line (an array of points)
* @return The distance
*/
public double lineDistance(LineString points) {
double total = 0;
for (int i = 1; i < points.size(); ++i) {
total += distance(points.get(i - 1), points.get(i));
}
return total;
}
/**
* Computes the area of a polygon.
*
* @param poly The polygon (an array of rings, each of which is an array of points)
* @return The area
*/
public double area(Polygon poly) {
double sum = 0;
for (int i = 0; i < poly.size(); ++i) {
LinearRing ring = poly.get(i);
int len = ring.size();
for (int j = 0, k = len - 1; j < len; k = j++) {
sum += longDiff(ring.get(j).getLat(), ring.get(k).getLat())
* (ring.get(j).getLon() + ring.get(k).getLon()) * (i != 0 ? -1.0 : 1.0);
}
}
return (Math.abs(sum) / 2.0) * kx * ky;
}
/**
* Computes a point at a specified distance along a line.
*
* @param line The line (an array of points)
* @param dist The distance along the line
* @return The indicated point
*/
public Point along(LineString line, double dist) {
double sum = 0;
if (line.isEmpty()) {
return new Point(0, 0);
}
if (dist <= 0) {
return line.get(0);
}
for (int i = 0; i < line.size() - 1; ++i) {
Point p0 = line.get(i);
Point p1 = line.get(i + 1);
double d = distance(p0, p1);
sum += d;
if (sum > dist) {
return interpolate(p0, p1, (dist - (sum - d)) / d);
}
}
return line.get(line.size() - 1);
}
/**
* Computes the distance from a point p to the line segment between points a and b.
*
* @param p The point in question
* @param a One end of the line segment
* @param b The other end of the line segment
* @return The indicated distance
*/
public double pointToSegmentDistance(Point p, Point a, Point b) {
double t = 0.0;
double x = a.getLat();
double y = a.getLon();
double dx = longDiff(b.getLat(), x) * kx;
double dy = (b.getLon() - y) * ky;
if (dx != 0.0 || dy != 0.0) {
t = (longDiff(p.getLat(), x) * kx * dx + (p.getLon() - y) * ky * dy)
/ (dx * dx + dy * dy);
if (t > 1.0) {
x = b.getLat();
y = b.getLon();
} else if (t > 0.0) {
x += (dx / kx) * t;
y += (dy / ky) * t;
}
}
return distance(p, new Point(x, y));
}
/**
* Computes a tuple of the form <point, index, t> where point is the
* closest point on the line from the given point, index is the start index of
* the segment with the closest point, and t is a parameter from 0 to 1 that
* indicates where the closest point is on that segment.
*
* @param line The line (an array of points)
* @param p The point in question
* @return The indicated tuple
*/
public PointIndexT pointOnLine(LineString line, Point p) {
double minDist = Double.POSITIVE_INFINITY;
double minX = 0;
double minY = 0;
double minT = 0;
int minI = 0;
if (line.isEmpty()) {
return new PointIndexT(new Point(0, 0), 0, 0);
}
for (int i = 0; i < line.size() - 1; ++i) {
double t = 0.;
double x = line.get(i).getLat();
double y = line.get(i).getLon();
double dx = longDiff(line.get(i + 1).getLat(), x) * kx;
double dy = (line.get(i + 1).getLon() - y) * ky;
if (dx != 0. || dy != 0.) {
t = (longDiff(p.getLat(), x) * kx * dx
+ (p.getLon() - y) * ky * dy) / (dx * dx + dy * dy);
if (t > 1) {
x = line.get(i + 1).getLat();
y = line.get(i + 1).getLon();
} else if (t > 0) {
x += (dx / kx) * t;
y += (dy / ky) * t;
}
}
double sqDist = squareDistance(p, new Point(x, y));
if (sqDist < minDist) {
minDist = sqDist;
minX = x;
minY = y;
minI = i;
minT = t;
}
}
return new PointIndexT(
new Point(minX, minY),
minI,
Math.max(0.0, Math.min(1.0, minT)));
}
/**
* Computes a part of the given line between the start and the stop points (or
* their closest points on the line).
*
* @param start The start point
* @param stop The stop point
* @param line The line (an array of points)
* @return The indicated portion of the line
*/
public LineString lineSlice(Point start, Point stop, LineString line) {
PointIndexT p1 = pointOnLine(line, start);
PointIndexT p2 = pointOnLine(line, stop);
if (p1.getIndex() > p2.getIndex()
|| (p1.getIndex() == p2.getIndex() && p1.getT() > p2.getT())) {
PointIndexT tmp = p1;
p1 = p2;
p2 = tmp;
}
List slice = new ArrayList<>();
slice.add(p1.getPoint());
int l = p1.getIndex() + 1;
int r = p2.getIndex();
if (line.get(l) != slice.get(0) && l <= r) {
slice.add(line.get(l));
}
for (int i = l + 1; i <= r; ++i) {
slice.add(line.get(i));
}
if (line.get(r) != p2.getPoint()) {
slice.add(p2.getPoint());
}
return new LineString(slice);
}
/**
* Computes the part of the given line between the start and the stop points as
* indicated by distances along the line.
*
* @param start The distance from the start of the line to the start point
* @param stop The distance from the start of the line to the stop point
* @param line The line (an array of points)
* @return The indicated portion of the line
*/
public LineString lineSliceAlong(double start, double stop, LineString line) {
double sum = 0;
List slice = new ArrayList<>();
for (int i = 1; i < line.size(); ++i) {
Point p0 = line.get(i - 1);
Point p1 = line.get(i);
double d = distance(p0, p1);
sum += d;
if (sum > start && slice.size() == 0) {
slice.add(interpolate(p0, p1, (start - (sum - d)) / d));
}
if (sum >= stop) {
slice.add(interpolate(p0, p1, (stop - (sum - d)) / d));
return new LineString(slice);
}
if (sum > start) {
slice.add(p1);
}
}
return new LineString(slice);
}
/**
* Computes a bounding box object [w, s, e, n] centered on the given point and
* buffered by the given distance.
*
* @param p The center point
* @param buffer The buffer distance
* @return The indicated bounding box
*/
public Box bufferPoint(Point p, double buffer) {
double v = buffer / ky;
double h = buffer / kx;
return new Box(
new Point(p.getLat() - h, p.getLon() - v),
new Point(p.getLat() + h, p.getLon() + v));
}
/**
* Computes a bounding box object [w, s, e, n] centered on the given box and
* buffered by the given distance.
*
* @param box The center box
* @param buffer The buffer distance
* @return The indicated bounding box
*/
public Box bufferBBox(Box box, double buffer) {
double v = buffer / ky;
double h = buffer / kx;
return new Box(
new Point(box.getMin().getLat() - h, box.getMin().getLon() - v),
new Point(box.getMax().getLat() + h, box.getMax().getLon() + v));
}
/**
* Tests whether the given point is inside in the given bounding box.
*
* @param p The given point
* @param bbox The bounding box
* @return True if the point is inside the box, false otherwise.
*/
public static boolean insideBBox(Point p, Box bbox) {
return p.getLon() >= bbox.getMin().getLon()
&& p.getLon() <= bbox.getMax().getLon()
&& longDiff(p.getLat(), bbox.getMin().getLat()) >= 0
&& longDiff(p.getLat(), bbox.getMax().getLat()) <= 0;
}
/**
* Computes the point along a line segment at a given distance from the first
* endpoint.
*
* @param a One end of the line segment
* @param b The other end of the line segment
* @param t The distance from a
* @return The indicated point
*/
public static Point interpolate(Point a, Point b, double t) {
double dx = longDiff(b.getLat(), a.getLat());
double dy = b.getLon() - a.getLon();
return new Point(a.getLat() + dx * t, a.getLon() + dy * t);
}
private static double longDiff(double a, double b) {
return Math.IEEEremainder(a - b, 360.0);
}
}