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Lucene Spatial shapes implemented using 3D planar geometry
/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.lucene.spatial3d.geom;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
/**
* Holds mathematical constants associated with the model of a planet.
* @lucene.experimental
*/
public class PlanetModel implements SerializableObject {
/** Planet model corresponding to sphere. */
public static final PlanetModel SPHERE = new PlanetModel(1.0,1.0);
/** Mean radius */
// see http://earth-info.nga.mil/GandG/publications/tr8350.2/wgs84fin.pdf
public static final double WGS84_MEAN = 6371008.7714;
/** Polar radius */
public static final double WGS84_POLAR = 6356752.314245;
/** Equatorial radius */
public static final double WGS84_EQUATORIAL = 6378137.0;
/** Planet model corresponding to WGS84 */
public static final PlanetModel WGS84 = new PlanetModel(WGS84_EQUATORIAL/WGS84_MEAN,
WGS84_POLAR/WGS84_MEAN);
// Surface of the planet:
// x^2/a^2 + y^2/b^2 + z^2/c^2 = 1.0
// Scaling factors are a,b,c. geo3d can only support models where a==b, so use ab instead.
/** The x/y scaling factor */
public final double ab;
/** The z scaling factor */
public final double c;
/** The inverse of ab */
public final double inverseAb;
/** The inverse of c */
public final double inverseC;
/** The square of the inverse of ab */
public final double inverseAbSquared;
/** The square of the inverse of c */
public final double inverseCSquared;
/** The flattening value */
public final double flattening;
/** The square ratio */
public final double squareRatio;
/** The scale of the planet */
public final double scale;
/** The inverse of scale */
public final double inverseScale;
// We do NOT include radius, because all computations in geo3d are in radians, not meters.
// Compute north and south pole for planet model, since these are commonly used.
/** North pole */
public final GeoPoint NORTH_POLE;
/** South pole */
public final GeoPoint SOUTH_POLE;
/** Min X pole */
public final GeoPoint MIN_X_POLE;
/** Max X pole */
public final GeoPoint MAX_X_POLE;
/** Min Y pole */
public final GeoPoint MIN_Y_POLE;
/** Max Y pole */
public final GeoPoint MAX_Y_POLE;
/** Minimum surface distance between poles */
public final double minimumPoleDistance;
/** Constructor.
* @param ab is the x/y scaling factor.
* @param c is the z scaling factor.
*/
public PlanetModel(final double ab, final double c) {
this.ab = ab;
this.c = c;
this.inverseAb = 1.0 / ab;
this.inverseC = 1.0 / c;
this.flattening = (ab - c) * inverseAb;
this.squareRatio = (ab * ab - c * c) / (c * c);
this.inverseAbSquared = inverseAb * inverseAb;
this.inverseCSquared = inverseC * inverseC;
this.NORTH_POLE = new GeoPoint(c, 0.0, 0.0, 1.0, Math.PI * 0.5, 0.0);
this.SOUTH_POLE = new GeoPoint(c, 0.0, 0.0, -1.0, -Math.PI * 0.5, 0.0);
this.MIN_X_POLE = new GeoPoint(ab, -1.0, 0.0, 0.0, 0.0, -Math.PI);
this.MAX_X_POLE = new GeoPoint(ab, 1.0, 0.0, 0.0, 0.0, 0.0);
this.MIN_Y_POLE = new GeoPoint(ab, 0.0, -1.0, 0.0, 0.0, -Math.PI * 0.5);
this.MAX_Y_POLE = new GeoPoint(ab, 0.0, 1.0, 0.0, 0.0, Math.PI * 0.5);
this.scale = (2.0 * ab + c)/3.0;
this.inverseScale = 1.0 / scale;
this.minimumPoleDistance = Math.min(surfaceDistance(NORTH_POLE, SOUTH_POLE), surfaceDistance(MIN_X_POLE, MAX_X_POLE));
}
/** Deserialization constructor.
* @param inputStream is the input stream.
*/
public PlanetModel(final InputStream inputStream) throws IOException {
this(SerializableObject.readDouble(inputStream), SerializableObject.readDouble(inputStream));
}
@Override
public void write(final OutputStream outputStream) throws IOException {
SerializableObject.writeDouble(outputStream, ab);
SerializableObject.writeDouble(outputStream, c);
}
/** Does this planet model describe a sphere?
*@return true if so.
*/
public boolean isSphere() {
return this.ab == this.c;
}
/** Find the minimum magnitude of all points on the ellipsoid.
* @return the minimum magnitude for the planet.
*/
public double getMinimumMagnitude() {
return Math.min(this.ab, this.c);
}
/** Find the maximum magnitude of all points on the ellipsoid.
* @return the maximum magnitude for the planet.
*/
public double getMaximumMagnitude() {
return Math.max(this.ab, this.c);
}
/** Find the minimum x value.
*@return the minimum X value.
*/
public double getMinimumXValue() {
return -this.ab;
}
/** Find the maximum x value.
*@return the maximum X value.
*/
public double getMaximumXValue() {
return this.ab;
}
/** Find the minimum y value.
*@return the minimum Y value.
*/
public double getMinimumYValue() {
return -this.ab;
}
/** Find the maximum y value.
*@return the maximum Y value.
*/
public double getMaximumYValue() {
return this.ab;
}
/** Find the minimum z value.
*@return the minimum Z value.
*/
public double getMinimumZValue() {
return -this.c;
}
/** Find the maximum z value.
*@return the maximum Z value.
*/
public double getMaximumZValue() {
return this.c;
}
/** Check if point is on surface.
* @param v is the point to check.
* @return true if the point is on the planet surface.
*/
public boolean pointOnSurface(final Vector v) {
return pointOnSurface(v.x, v.y, v.z);
}
/** Check if point is on surface.
* @param x is the x coord.
* @param y is the y coord.
* @param z is the z coord.
*/
public boolean pointOnSurface(final double x, final double y, final double z) {
// Equation of planet surface is:
// x^2 / a^2 + y^2 / b^2 + z^2 / c^2 - 1 = 0
return Math.abs(x * x * inverseAb * inverseAb + y * y * inverseAb * inverseAb + z * z * inverseC * inverseC - 1.0) < Vector.MINIMUM_RESOLUTION;
}
/** Check if point is outside surface.
* @param v is the point to check.
* @return true if the point is outside the planet surface.
*/
public boolean pointOutside(final Vector v) {
return pointOutside(v.x, v.y, v.z);
}
/** Check if point is outside surface.
* @param x is the x coord.
* @param y is the y coord.
* @param z is the z coord.
*/
public boolean pointOutside(final double x, final double y, final double z) {
// Equation of planet surface is:
// x^2 / a^2 + y^2 / b^2 + z^2 / c^2 - 1 = 0
return (x * x + y * y) * inverseAb * inverseAb + z * z * inverseC * inverseC - 1.0 > Vector.MINIMUM_RESOLUTION;
}
/** Compute a GeoPoint that's scaled to actually be on the planet surface.
* @param vector is the vector.
* @return the scaled point.
*/
public GeoPoint createSurfacePoint(final Vector vector) {
return createSurfacePoint(vector.x, vector.y, vector.z);
}
/** Compute a GeoPoint that's based on (x,y,z) values, but is scaled to actually be on the planet surface.
* @param x is the x value.
* @param y is the y value.
* @param z is the z value.
* @return the scaled point.
*/
public GeoPoint createSurfacePoint(final double x, final double y, final double z) {
// The equation of the surface is:
// (x^2 / a^2 + y^2 / b^2 + z^2 / c^2) = 1
// We will need to scale the passed-in x, y, z values:
// ((tx)^2 / a^2 + (ty)^2 / b^2 + (tz)^2 / c^2) = 1
// t^2 * (x^2 / a^2 + y^2 / b^2 + z^2 / c^2) = 1
// t = sqrt ( 1 / (x^2 / a^2 + y^2 / b^2 + z^2 / c^2))
final double t = Math.sqrt(1.0 / (x*x*inverseAbSquared + y*y*inverseAbSquared + z*z*inverseCSquared));
return new GeoPoint(t*x, t*y, t*z);
}
/** Compute a GeoPoint that's a bisection between two other GeoPoints.
* @param pt1 is the first point.
* @param pt2 is the second point.
* @return the bisection point, or null if a unique one cannot be found.
*/
public GeoPoint bisection(final GeoPoint pt1, final GeoPoint pt2) {
final double A0 = (pt1.x + pt2.x) * 0.5;
final double B0 = (pt1.y + pt2.y) * 0.5;
final double C0 = (pt1.z + pt2.z) * 0.5;
final double denom = inverseAbSquared * A0 * A0 +
inverseAbSquared * B0 * B0 +
inverseCSquared * C0 * C0;
if(denom < Vector.MINIMUM_RESOLUTION) {
// Bisection is undefined
return null;
}
final double t = Math.sqrt(1.0 / denom);
return new GeoPoint(t * A0, t * B0, t * C0);
}
/** Compute surface distance between two points.
* @param pt1 is the first point.
* @param pt2 is the second point.
* @return the adjusted angle, when multiplied by the mean earth radius, yields a surface distance. This will differ
* from GeoPoint.arcDistance() only when the planet model is not a sphere. @see {@link GeoPoint#arcDistance(Vector)}
*/
public double surfaceDistance(final GeoPoint pt1, final GeoPoint pt2) {
final double L = pt2.getLongitude() - pt1.getLongitude();
final double U1 = Math.atan((1.0-flattening) * Math.tan(pt1.getLatitude()));
final double U2 = Math.atan((1.0-flattening) * Math.tan(pt2.getLatitude()));
final double sinU1 = Math.sin(U1);
final double cosU1 = Math.cos(U1);
final double sinU2 = Math.sin(U2);
final double cosU2 = Math.cos(U2);
final double dCosU1CosU2 = cosU1 * cosU2;
final double dCosU1SinU2 = cosU1 * sinU2;
final double dSinU1SinU2 = sinU1 * sinU2;
final double dSinU1CosU2 = sinU1 * cosU2;
double lambda = L;
double lambdaP = Math.PI * 2.0;
int iterLimit = 0;
double cosSqAlpha;
double sinSigma;
double cos2SigmaM;
double cosSigma;
double sigma;
double sinAlpha;
double C;
double sinLambda, cosLambda;
do {
sinLambda = Math.sin(lambda);
cosLambda = Math.cos(lambda);
sinSigma = Math.sqrt((cosU2*sinLambda) * (cosU2*sinLambda) +
(dCosU1SinU2 - dSinU1CosU2 * cosLambda) * (dCosU1SinU2 - dSinU1CosU2 * cosLambda));
if (sinSigma==0.0) {
return 0.0;
}
cosSigma = dSinU1SinU2 + dCosU1CosU2 * cosLambda;
sigma = Math.atan2(sinSigma, cosSigma);
sinAlpha = dCosU1CosU2 * sinLambda / sinSigma;
cosSqAlpha = 1.0 - sinAlpha * sinAlpha;
cos2SigmaM = cosSigma - 2.0 * dSinU1SinU2 / cosSqAlpha;
if (Double.isNaN(cos2SigmaM))
cos2SigmaM = 0.0; // equatorial line: cosSqAlpha=0
C = flattening / 16.0 * cosSqAlpha * (4.0 + flattening * (4.0 - 3.0 * cosSqAlpha));
lambdaP = lambda;
lambda = L + (1.0 - C) * flattening * sinAlpha *
(sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1.0 + 2.0 * cos2SigmaM *cos2SigmaM)));
} while (Math.abs(lambda-lambdaP) >= Vector.MINIMUM_RESOLUTION && ++iterLimit < 100);
final double uSq = cosSqAlpha * this.squareRatio;
final double A = 1.0 + uSq / 16384.0 * (4096.0 + uSq * (-768.0 + uSq * (320.0 - 175.0 * uSq)));
final double B = uSq / 1024.0 * (256.0 + uSq * (-128.0 + uSq * (74.0 - 47.0 * uSq)));
final double deltaSigma = B * sinSigma * (cos2SigmaM + B / 4.0 * (cosSigma * (-1.0 + 2.0 * cos2SigmaM * cos2SigmaM)-
B / 6.0 * cos2SigmaM * (-3.0 + 4.0 * sinSigma * sinSigma) * (-3.0 + 4.0 * cos2SigmaM * cos2SigmaM)));
return c * inverseScale * A * (sigma - deltaSigma);
}
/** Compute new point given original point, a bearing direction, and an adjusted angle (as would be computed by
* the surfaceDistance() method above). The original point can be anywhere on the globe. The bearing direction
* ranges from 0 (due east at the equator) to pi/2 (due north) to pi (due west at the equator) to 3 pi/4 (due south)
* to 2 pi.
* @param from is the starting point.
* @param dist is the adjusted angle.
* @param bearing is the direction to proceed.
* @return the new point, consistent with the bearing direction and distance.
*/
public GeoPoint surfacePointOnBearing(final GeoPoint from, final double dist, final double bearing) {
// Algorithm using Vincenty's formulae (https://en.wikipedia.org/wiki/Vincenty%27s_formulae)
// which takes into account that planets may not be spherical.
//Code adaptation from http://www.movable-type.co.uk/scripts/latlong-vincenty.html
double lat = from.getLatitude();
double lon = from.getLongitude();
double sinα1 = Math.sin(bearing);
double cosα1 = Math.cos(bearing);
double tanU1 = (1.0 - flattening) * Math.tan(lat);
double cosU1 = 1.0 / Math.sqrt((1.0 + tanU1 * tanU1));
double sinU1 = tanU1 * cosU1;
double σ1 = Math.atan2(tanU1, cosα1);
double sinα = cosU1 * sinα1;
double cosSqα = 1.0 - sinα * sinα;
double uSq = cosSqα * squareRatio;
double A = 1.0 + uSq / 16384.0 * (4096.0 + uSq * (-768.0 + uSq * (320.0 - 175.0 * uSq)));
double B = uSq / 1024.0 * (256.0 + uSq * (-128.0 + uSq * (74.0 - 47.0 * uSq)));
double cos2σM;
double sinσ;
double cosσ;
double Δσ;
double σ = dist / (c * inverseScale * A);
double σʹ;
double iterations = 0;
do {
cos2σM = Math.cos(2.0 * σ1 + σ);
sinσ = Math.sin(σ);
cosσ = Math.cos(σ);
Δσ = B * sinσ * (cos2σM + B / 4.0 * (cosσ * (-1.0 + 2.0 * cos2σM * cos2σM) -
B / 6.0 * cos2σM * (-3.0 + 4.0 * sinσ * sinσ) * (-3.0 + 4.0 * cos2σM * cos2σM)));
σʹ = σ;
σ = dist / (c * inverseScale * A) + Δσ;
} while (Math.abs(σ - σʹ) >= Vector.MINIMUM_RESOLUTION && ++iterations < 100);
double x = sinU1 * sinσ - cosU1 * cosσ * cosα1;
double φ2 = Math.atan2(sinU1 * cosσ + cosU1 * sinσ * cosα1, (1.0 - flattening) * Math.sqrt(sinα * sinα + x * x));
double λ = Math.atan2(sinσ * sinα1, cosU1 * cosσ - sinU1 * sinσ * cosα1);
double C = flattening / 16.0 * cosSqα * (4.0 + flattening * (4.0 - 3.0 * cosSqα));
double L = λ - (1.0 - C) * flattening * sinα *
(σ + C * sinσ * (cos2σM + C * cosσ * (-1.0 + 2.0 * cos2σM * cos2σM)));
double λ2 = (lon + L + 3.0 * Math.PI) % (2.0 * Math.PI) - Math.PI; // normalise to -180..+180
return new GeoPoint(this, φ2, λ2);
}
@Override
public boolean equals(final Object o) {
if (!(o instanceof PlanetModel))
return false;
final PlanetModel other = (PlanetModel)o;
return ab == other.ab && c == other.c;
}
@Override
public int hashCode() {
return Double.hashCode(ab) + Double.hashCode(c);
}
@Override
public String toString() {
if (this.equals(SPHERE)) {
return "PlanetModel.SPHERE";
} else if (this.equals(WGS84)) {
return "PlanetModel.WGS84";
} else {
return "PlanetModel(ab="+ab+" c="+c+")";
}
}
}
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