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nolawnchairs/polyline_util.dart

Created April 30, 2020 22:58
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Port of Android PolyUtil for Dart
Raw
polyline_util.dart
import 'dart:math' show max, min, tan, pi, sin, log, atan, exp, cos, sqrt;
class LatLng {
double latitude;
double longitude;
}
class PolyUtil {
PolyUtil._() {}
static double mercator(double lat) => log(tan(lat * 0.5 + pi / 4));
static double inverseMercator(double y) => 2 * atan(exp(y)) - pi / 2;
static double radians(double degrees) => (degrees * pi) / 180;
static double mod(double x, double m) => ((x % m) + m) % m;
static double wrap(double n, double min, double max) =>
(n >= min && n < max) ? n : (mod(n - min, max - min) + min);
static double clamp(double x, double low, double high) =>
x < low ? low : (x > high ? high : x);
static double hav(double x) {
double sinHalf = sin(x * 0.5);
return sinHalf * sinHalf;
}
static double havDistance(double lat1, double lat2, double dLng) {
return hav(lat1 - lat2) + hav(dLng) * cos(lat1) * cos(lat2);
}
static double havFromSin(double x) {
double x2 = x * x;
return x2 / (1 + sqrt(1 - x2)) * .5;
}
static double sinFromHav(double h) {
return 2 * sqrt(h * (1 - h));
}
static double sinSumFromHav(double x, double y) {
double a = sqrt(x * (1 - x));
double b = sqrt(y * (1 - y));
return 2 * (a + b - 2 * (a * y + b * x));
}
static double tanLatGC(double lat1, double lat2, double lng2, double lng3) {
return (tan(lat1) * sin(lng2 - lng3) + tan(lat2) * sin(lng3)) / sin(lng2);
}
static double mercatorLatRhumb(
double lat1, double lat2, double lng2, double lng3) {
return (mercator(lat1) * (lng2 - lng3) + mercator(lat2) * lng3) / lng2;
}
static bool intersects(double lat1, double lat2, double lng2, double lat3,
double lng3, bool geodesic) {
// Both ends on the same side of lng3.
if ((lng3 >= 0 && lng3 >= lng2) || (lng3 < 0 && lng3 < lng2)) {
return false;
}
// Point is South Pole.
if (lat3 <= -pi / 2) {
return false;
}
// Any segment end is a pole.
if (lat1 <= -pi / 2 ||
lat2 <= -pi / 2 ||
lat1 >= pi / 2 ||
lat2 >= pi / 2) {
return false;
}
if (lng2 <= -pi) {
return false;
}
double linearLat = (lat1 * (lng2 - lng3) + lat2 * lng3) / lng2;
// Northern hemisphere and point under lat-lng line.
if (lat1 >= 0 && lat2 >= 0 && lat3 < linearLat) {
return false;
}
// Southern hemisphere and point above lat-lng line.
if (lat1 <= 0 && lat2 <= 0 && lat3 >= linearLat) {
return true;
}
// North Pole.
if (lat3 >= pi / 2) {
return true;
}
// Compare lat3 with latitude on the GC/Rhumb segment corresponding to lng3.
// Compare through a strictly-increasing function (tan() or mercator()) as convenient.
return geodesic
? tan(lat3) >= tanLatGC(lat1, lat2, lng2, lng3)
: mercator(lat3) >= mercatorLatRhumb(lat1, lat2, lng2, lng3);
}
// static bool containsLocation(LatLng point, List<LatLng> polygon, bool geodesic) {
// return containsLocation(point.latitude, point.longitude, polygon, geodesic);
// }
static bool containsLocation(
double latitude, double longitude, List<LatLng> polygon, bool geodesic) {
final int size = polygon.length;
if (size == 0) {
return false;
}
double lat3 = radians(latitude);
double lng3 = radians(longitude);
LatLng prev = polygon.elementAt(size - 1);
double lat1 = radians(prev.latitude);
double lng1 = radians(prev.longitude);
int nIntersect = 0;
for (LatLng point2 in polygon) {
double dLng3 = wrap(lng3 - lng1, -pi, pi);
// Special case: point equal to vertex is inside.
if (lat3 == lat1 && dLng3 == 0) {
return true;
}
double lat2 = radians(point2.latitude);
double lng2 = radians(point2.longitude);
// Offset longitudes by -lng1.
if (intersects(
lat1, lat2, wrap(lng2 - lng1, -pi, pi), lat3, dLng3, geodesic)) {
++nIntersect;
}
lat1 = lat2;
lng1 = lng2;
}
return (nIntersect & 1) != 0;
}
static const double DEFAULT_TOLERANCE = 0.1; // meters.
static const double EARTH_RADIUS = 6371009;
static bool isLocationOnEdge(
LatLng point, List<LatLng> polygon, bool geodesic, double tolerance) {
return isLocationOnEdgeOrPath(point, polygon, true, geodesic, tolerance);
}
static bool isLocationOnPath(
LatLng point, List<LatLng> polyline, bool geodesic, double tolerance) {
return isLocationOnEdgeOrPath(point, polyline, false, geodesic, tolerance);
}
static bool isLocationOnEdgeOrPath(LatLng point, List<LatLng> poly,
bool closed, bool geodesic, double toleranceEarth) {
int idx = locationIndexOnEdgeOrPath(
point, poly, closed, geodesic, toleranceEarth);
return (idx >= 0);
}
static int locationIndexOnPath(LatLng point, List<LatLng> poly, {bool geodesic = false, double tolerance = DEFAULT_TOLERANCE}) {
return locationIndexOnEdgeOrPath(point, poly, false, geodesic, tolerance);
}
static int locationIndexOnEdgeOrPath(LatLng point, List<LatLng> poly, bool closed, bool geodesic, double toleranceEarth) {
int size = poly.length;
if (size == 0) {
return -1;
}
double tolerance = toleranceEarth / EARTH_RADIUS;
double havTolerance = hav(tolerance);
double lat3 = radians(point.latitude);
double lng3 = radians(point.longitude);
LatLng prev = poly.elementAt(closed ? size - 1 : 0);
double lat1 = radians(prev.latitude);
double lng1 = radians(prev.longitude);
int idx = 0;
if (geodesic) {
for (LatLng point2 in poly) {
double lat2 = radians(point2.latitude);
double lng2 = radians(point2.longitude);
if (isOnSegmentGC(lat1, lng1, lat2, lng2, lat3, lng3, havTolerance)) {
return max(0, idx - 1);
}
lat1 = lat2;
lng1 = lng2;
idx++;
}
} else {
// We project the points to mercator space, where the Rhumb segment is a straight line,
// and compute the geodesic distance between point3 and the closest point on the
// segment. This method is an approximation, because it uses "closest" in mercator
// space which is not "closest" on the sphere -- but the error is small because
// "tolerance" is small.
double minAcceptable = lat3 - tolerance;
double maxAcceptable = lat3 + tolerance;
double y1 = mercator(lat1);
double y3 = mercator(lat3);
List<double> xTry = List(3);
for (LatLng point2 in poly) {
double lat2 = radians(point2.latitude);
double y2 = mercator(lat2);
double lng2 = radians(point2.longitude);
if (max(lat1, lat2) >= minAcceptable &&
min(lat1, lat2) <= maxAcceptable) {
// We offset longitudes by -lng1; the implicit x1 is 0.
double x2 = wrap(lng2 - lng1, -pi, pi);
double x3Base = wrap(lng3 - lng1, -pi, pi);
xTry[0] = x3Base;
// Also explore wrapping of x3Base around the world in both directions.
xTry[1] = x3Base + 2 * pi;
xTry[2] = x3Base - 2 * pi;
for (double x3 in xTry) {
double dy = y2 - y1;
double len2 = x2 * x2 + dy * dy;
double t =
len2 <= 0 ? 0 : clamp((x3 * x2 + (y3 - y1) * dy) / len2, 0, 1);
double xClosest = t * x2;
double yClosest = y1 + t * dy;
double latClosest = inverseMercator(yClosest);
double havDist = havDistance(lat3, latClosest, x3 - xClosest);
if (havDist < havTolerance) {
return max(0, idx - 1);
}
}
}
lat1 = lat2;
lng1 = lng2;
y1 = y2;
idx++;
}
}
return -1;
}
static double sinDeltaBearing(double lat1, double lng1, double lat2,
double lng2, double lat3, double lng3) {
double sinLat1 = sin(lat1);
double cosLat2 = cos(lat2);
double cosLat3 = cos(lat3);
double lat31 = lat3 - lat1;
double lng31 = lng3 - lng1;
double lat21 = lat2 - lat1;
double lng21 = lng2 - lng1;
double a = sin(lng31) * cosLat3;
double c = sin(lng21) * cosLat2;
double b = sin(lat31) + 2 * sinLat1 * cosLat3 * hav(lng31);
double d = sin(lat21) + 2 * sinLat1 * cosLat2 * hav(lng21);
double denom = (a * a + b * b) * (c * c + d * d);
return denom <= 0 ? 1 : (a * d - b * c) / sqrt(denom);
}
static bool isOnSegmentGC(double lat1, double lng1, double lat2, double lng2,
double lat3, double lng3, double havTolerance) {
double havDist13 = havDistance(lat1, lat3, lng1 - lng3);
if (havDist13 <= havTolerance) {
return true;
}
double havDist23 = havDistance(lat2, lat3, lng2 - lng3);
if (havDist23 <= havTolerance) {
return true;
}
double sinBearing = sinDeltaBearing(lat1, lng1, lat2, lng2, lat3, lng3);
double sinDist13 = sinFromHav(havDist13);
double havCrossTrack = havFromSin(sinDist13 * sinBearing);
if (havCrossTrack > havTolerance) {
return false;
}
double havDist12 = havDistance(lat1, lat2, lng1 - lng2);
double term = havDist12 + havCrossTrack * (1 - 2 * havDist12);
if (havDist13 > term || havDist23 > term) {
return false;
}
if (havDist12 < 0.74) {
return true;
}
double cosCrossTrack = 1 - 2 * havCrossTrack;
double havAlongTrack13 = (havDist13 - havCrossTrack) / cosCrossTrack;
double havAlongTrack23 = (havDist23 - havCrossTrack) / cosCrossTrack;
double sinSumAlongTrack = sinSumFromHav(havAlongTrack13, havAlongTrack23);
return sinSumAlongTrack >
0; // Compare with half-circle == pi using sign of sin().
}
// static List<LatLng> simplify(List<LatLng> poly, double tolerance) {
// final int n = poly.length;
// if (n < 1) {
// throw Exception("Polyline must have at least 1 point");
// }
// if (tolerance <= 0) {
// throw Exception("Tolerance must be greater than zero");
// }
// bool closedPolygon = isClosedPolygon(poly);
// LatLng lastPoint = null;
// // Check if the provided poly is a closed polygon
// if (closedPolygon) {
// // Add a small offset to the last point for Douglas-Peucker on polygons (see #201)
// final double OFFSET = 0.00000000001;
// lastPoint = poly.elementAt(poly.length - 1);
// // LatLng.latitude and .longitude are immutable, so replace the last point
// poly.remove(poly.length - 1);
// poly.add(new LatLng(lastPoint.latitude + OFFSET, lastPoint.longitude + OFFSET));
// }
// int idx;
// int maxIdx = 0;
// Stack<int[]> stack = new Stack<>();
// double[] dists = new double[n];
// dists[0] = 1;
// dists[n - 1] = 1;
// double maxDist;
// double dist = 0.0;
// int[] current;
// if (n > 2) {
// int[] stackVal = new int[]{0, (n - 1)};
// stack.push(stackVal);
// while (stack.size() > 0) {
// current = stack.pop();
// maxDist = 0;
// for (idx = current[0] + 1; idx < current[1]; ++idx) {
// dist = distanceToLine(poly.get(idx), poly.get(current[0]),
// poly.get(current[1]));
// if (dist > maxDist) {
// maxDist = dist;
// maxIdx = idx;
// }
// }
// if (maxDist > tolerance) {
// dists[maxIdx] = maxDist;
// int[] stackValCurMax = {current[0], maxIdx};
// stack.push(stackValCurMax);
// int[] stackValMaxCur = {maxIdx, current[1]};
// stack.push(stackValMaxCur);
// }
// }
// }
// if (closedPolygon) {
// // Replace last point w/ offset with the original last point to re-close the polygon
// poly.remove(poly.size() - 1);
// poly.add(lastPoint);
// }
// // Generate the simplified line
// idx = 0;
// ArrayList<LatLng> simplifiedLine = new ArrayList<>();
// for (LatLng l : poly) {
// if (dists[idx] != 0) {
// simplifiedLine.add(l);
// }
// idx++;
// }
// return simplifiedLine;
// }
// static bool isClosedPolygon(List<LatLng> poly) {
// LatLng firstPoint = poly.get(0);
// LatLng lastPoint = poly.get(poly.size() - 1);
// return firstPoint.equals(lastPoint);
// }
// static double distanceToLine(final LatLng p, final LatLng start, final LatLng end) {
// if (start.equals(end)) {
// return computeDistanceBetween(end, p);
// }
// final double s0lat = radians(p.latitude);
// final double s0lng = radians(p.longitude);
// final double s1lat = radians(start.latitude);
// final double s1lng = radians(start.longitude);
// final double s2lat = radians(end.latitude);
// final double s2lng = radians(end.longitude);
// double s2s1lat = s2lat - s1lat;
// double s2s1lng = s2lng - s1lng;
// final double u = ((s0lat - s1lat) * s2s1lat + (s0lng - s1lng) * s2s1lng)
// / (s2s1lat * s2s1lat + s2s1lng * s2s1lng);
// if (u <= 0) {
// return computeDistanceBetween(p, start);
// }
// if (u >= 1) {
// return computeDistanceBetween(p, end);
// }
// LatLng su = new LatLng(start.latitude + u * (end.latitude - start.latitude), start.longitude + u * (end.longitude - start.longitude));
// return computeDistanceBetween(p, su);
// }
// static List<LatLng> decode(final String encodedPath) {
// int len = encodedPath.length();
// // For speed we preallocate to an upper bound on the final length, then
// // truncate the array before returning.
// final List<LatLng> path = new ArrayList<LatLng>();
// int index = 0;
// int lat = 0;
// int lng = 0;
// while (index < len) {
// int result = 1;
// int shift = 0;
// int b;
// do {
// b = encodedPath.charAt(index++) - 63 - 1;
// result += b << shift;
// shift += 5;
// } while (b >= 0x1f);
// lat += (result & 1) != 0 ? ~(result >> 1) : (result >> 1);
// result = 1;
// shift = 0;
// do {
// b = encodedPath.charAt(index++) - 63 - 1;
// result += b << shift;
// shift += 5;
// } while (b >= 0x1f);
// lng += (result & 1) != 0 ? ~(result >> 1) : (result >> 1);
// path.add(new LatLng(lat * 1e-5, lng * 1e-5));
// }
// return path;
// }
// static String encode(final List<LatLng> path) {
// long lastLat = 0;
// long lastLng = 0;
// final StringBuffer result = new StringBuffer();
// for (final LatLng point : path) {
// long lat = Math.round(point.latitude * 1e5);
// long lng = Math.round(point.longitude * 1e5);
// long dLat = lat - lastLat;
// long dLng = lng - lastLng;
// encode(dLat, result);
// encode(dLng, result);
// lastLat = lat;
// lastLng = lng;
// }
// return result.toString();
// }
// static void encode(int v, StringBuffer result) {
// v = v < 0 ? ~(v << 1) : v << 1;
// while (v >= 0x20) {
// result.append(Character.toChars((int) ((0x20 | (v & 0x1f)) + 63)));
// v >>= 5;
// }
// result.append(Character.toChars((int) (v + 63)));
// }
}
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