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/*
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* Cresques Mapping Suite. Graphic Library for constructing mapping applications.
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*
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* Copyright (C) 2004-5.
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*
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* This program is free software; you can redistribute it and/or
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* modify it under the terms of the GNU General Public License
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* as published by the Free Software Foundation; either version 2
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* of the License, or (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307,USA.
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*
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* For more information, contact:
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*
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* cresques@gmail.com
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*/
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package org.cresques.cts; |
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import java.awt.geom.Point2D; |
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/**
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* Operaciones relacionadas con las proyecciones y sistemas
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* de coordenadas.
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* @author Luis W. Sevilla (sevilla_lui@gva.es)
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*/
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public class GeoCalc { |
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IProjection proj; |
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/**
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*
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* @param proj
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*/
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public GeoCalc(IProjection proj) {
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this.proj = proj;
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} |
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/**
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* Distancia entre dos puntos en la esfera.
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* Los puntos deben estar en coordenadas geogr?ficas
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* @param pt1
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* @param pt2
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* @return distancia en km.
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*/
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public double distanceGeo(Point2D pt1, Point2D pt2) { |
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double R2 = Math.pow(proj.getDatum().getESemiMajorAxis(), 2); |
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double dLat = Math.toRadians(pt2.getY() - pt1.getY()); |
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double dLong = Math.toRadians(pt2.getX() - pt1.getX()); |
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double alfa = Math.toRadians(pt1.getY()); |
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double alfa2 = Math.toRadians(pt2.getY()); |
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if (Math.abs(alfa2) < Math.abs(alfa)) { |
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alfa = alfa2; |
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} |
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double ds2 = (R2 * dLat * dLat) +
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(R2 * Math.cos(alfa) * Math.cos(alfa) * dLong * dLong); |
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return Math.sqrt(ds2); |
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} |
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/**
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* Distancia entre dos puntos en el elipsoide.
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* Los puntos deben estar en coordenadas geogr?ficas
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* ver http://www.codeguru.com/Cpp/Cpp/algorithms/general/article.php/c5115/
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* @param lat1
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* @param lon1
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* @param lat2
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* @param lon2
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* @return
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*/
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public double distanceEli(Point2D pt1, Point2D pt2) { |
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double lat1 = Math.toRadians(pt1.getY()); |
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double lon1 = -Math.toRadians(pt1.getX()); |
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double lat2 = Math.toRadians(pt2.getY()); |
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double lon2 = -Math.toRadians(pt2.getX()); |
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double F = (lat1 + lat2) / 2D; |
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double G = (lat1 - lat2) / 2D; |
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double L = (lon1 - lon2) / 2D; |
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double sing = Math.sin(G); |
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double cosl = Math.cos(L); |
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double cosf = Math.cos(F); |
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double sinl = Math.sin(L); |
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double sinf = Math.sin(F); |
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double cosg = Math.cos(G); |
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double flat = 1D / proj.getDatum().getEIFlattening(); |
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double S = (sing * sing * cosl * cosl) + (cosf * cosf * sinl * sinl);
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double C = (cosg * cosg * cosl * cosl) + (sinf * sinf * sinl * sinl);
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double W = Math.atan2(Math.sqrt(S), Math.sqrt(C)); |
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double R = Math.sqrt((S * C)) / W; |
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double H1 = ((3D * R) - 1D) / (2D * C); |
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double H2 = ((3D * R) + 1D) / (2D * S); |
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double D = 2D * W * proj.getDatum().getESemiMajorAxis(); |
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return (D * ((1D + (flat * H1 * sinf * sinf * cosg * cosg)) - |
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(flat * H2 * cosf * cosf * sing * sing))); |
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} |
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/**
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* Algrothims from Geocentric Datum of Australia Technical Manual
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*
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* http://www.anzlic.org.au/icsm/gdatum/chapter4.html
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*
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* This page last updated 11 May 1999
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*
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* Computations on the Ellipsoid
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*
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* There are a number of formulae that are available
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* to calculate accurate geodetic positions,
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* azimuths and distances on the ellipsoid.
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*
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* Vincenty's formulae (Vincenty, 1975) may be used
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* for lines ranging from a few cm to nearly 20,000 km,
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* with millimetre accuracy.
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* The formulae have been extensively tested
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* for the Australian region, by comparison with results
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* from other formulae (Rainsford, 1955 & Sodano, 1965).
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*
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* * Inverse problem: azimuth and distance from known
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* latitudes and longitudes
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* * Direct problem: Latitude and longitude from known
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* position, azimuth and distance.
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* * Sample data
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* * Excel spreadsheet
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*
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* Vincenty's Inverse formulae
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* Given: latitude and longitude of two points
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* (phi1, lembda1 and phi2, lembda2),
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* Calculate: the ellipsoidal distance (s) and
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* forward and reverse azimuths between the points (alpha12, alpha21).
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*/
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/**
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* Devuelve la distancia entre dos puntos usando las formulas
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* de vincenty.
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* @param pt1
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* @param pt2
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* @return
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*/
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public double distanceVincenty(Point2D pt1, Point2D pt2) { |
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return distanceAzimutVincenty(pt1, pt2).dist;
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} |
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/**
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* Returns the distance between two geographic points on the ellipsoid
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* and the forward and reverse azimuths between these points.
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* lats, longs and azimuths are in decimal degrees, distance in metres
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* Returns ( s, alpha12, alpha21 ) as a tuple
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* @param pt1
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* @param pt2
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* @return
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*/
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public GeoData distanceAzimutVincenty(Point2D pt1, Point2D pt2) { |
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GeoData gd = new GeoData(0, 0); |
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double f = 1D / proj.getDatum().getEIFlattening(); |
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double a = proj.getDatum().getESemiMajorAxis();
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double phi1 = pt1.getY();
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double lembda1 = pt1.getX();
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double phi2 = pt2.getY();
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double lembda2 = pt2.getX();
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if ((Math.abs(phi2 - phi1) < 1e-8) && |
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(Math.abs(lembda2 - lembda1) < 1e-8)) { |
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return gd;
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} |
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double piD4 = Math.atan(1.0); |
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double two_pi = piD4 * 8.0; |
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phi1 = (phi1 * piD4) / 45.0;
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lembda1 = (lembda1 * piD4) / 45.0; // unfortunately lambda is a key word! |
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phi2 = (phi2 * piD4) / 45.0;
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lembda2 = (lembda2 * piD4) / 45.0;
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double b = a * (1.0 - f); |
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double TanU1 = (1 - f) * Math.tan(phi1); |
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double TanU2 = (1 - f) * Math.tan(phi2); |
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double U1 = Math.atan(TanU1); |
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double U2 = Math.atan(TanU2); |
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double lembda = lembda2 - lembda1;
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double last_lembda = -4000000.0; // an impossibe value |
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double omega = lembda;
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// Iterate the following equations,
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// until there is no significant change in lembda
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double Sin_sigma = 0; |
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// Iterate the following equations,
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// until there is no significant change in lembda
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double Cos_sigma = 0; |
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double Cos2sigma_m = 0; |
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double alpha = 0; |
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double sigma = 0; |
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double sqr_sin_sigma = 0; |
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while ((last_lembda < -3000000.0) || |
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((lembda != 0) &&
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(Math.abs((last_lembda - lembda) / lembda) > 1.0e-9))) { |
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sqr_sin_sigma = Math.pow(Math.cos(U2) * Math.sin(lembda), 2) + |
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Math.pow(((Math.cos(U1) * Math.sin(U2)) - |
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(Math.sin(U1) * Math.cos(U2) * Math.cos(lembda))), |
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2);
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Sin_sigma = Math.sqrt(sqr_sin_sigma);
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Cos_sigma = (Math.sin(U1) * Math.sin(U2)) + |
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(Math.cos(U1) * Math.cos(U2) * Math.cos(lembda)); |
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sigma = Math.atan2(Sin_sigma, Cos_sigma);
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double Sin_alpha = (Math.cos(U1) * Math.cos(U2) * Math.sin(lembda)) / Math.sin(sigma); |
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alpha = Math.asin(Sin_alpha);
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Cos2sigma_m = Math.cos(sigma) -
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((2 * Math.sin(U1) * Math.sin(U2)) / Math.pow(Math.cos(alpha), |
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2));
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double C = (f / 16) * Math.pow(Math.cos(alpha), 2) * (4 + |
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(f * (4 - (3 * Math.pow(Math.cos(alpha), 2))))); |
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last_lembda = lembda; |
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lembda = omega + |
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((1 - C) * f * Math.sin(alpha) * (sigma + |
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(C * Math.sin(sigma) * (Cos2sigma_m +
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(C * Math.cos(sigma) * (-1 + |
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(2 * Math.pow(Cos2sigma_m, 2)))))))); |
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} |
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double u2 = (Math.pow(Math.cos(alpha), 2) * ((a * a) - (b * b))) / (b * b); |
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double A = 1 + |
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((u2 / 16384) * (4096 + |
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(u2 * (-768 + (u2 * (320 - (175 * u2))))))); |
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double B = (u2 / 1024) * (256 + |
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(u2 * (-128 + (u2 * (74 - (47 * u2)))))); |
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double delta_sigma = B * Sin_sigma * (Cos2sigma_m +
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((B / 4) * ((Cos_sigma * (-1 + |
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(2 * Math.pow(Cos2sigma_m, 2)))) - |
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((B / 6) * Cos2sigma_m * (-3 + |
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(4 * sqr_sin_sigma)) * (-3 + |
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(4 * Math.pow(Cos2sigma_m, 2))))))); |
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double s = b * A * (sigma - delta_sigma);
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double alpha12 = Math.atan2((Math.cos(U2) * Math.sin(lembda)), |
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((Math.cos(U1) * Math.sin(U2)) - |
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(Math.sin(U1) * Math.cos(U2) * Math.cos(lembda)))); |
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double alpha21 = Math.atan2((Math.cos(U1) * Math.sin(lembda)), |
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((-Math.sin(U1) * Math.cos(U2)) + |
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(Math.cos(U1) * Math.sin(U2) * Math.cos(lembda)))); |
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if (alpha12 < 0.0) { |
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alpha12 = alpha12 + two_pi; |
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} |
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if (alpha12 > two_pi) {
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alpha12 = alpha12 - two_pi; |
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} |
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alpha21 = alpha21 + (two_pi / 2.0);
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if (alpha21 < 0.0) { |
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alpha21 = alpha21 + two_pi; |
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} |
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if (alpha21 > two_pi) {
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alpha21 = alpha21 - two_pi; |
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} |
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alpha12 = (alpha12 * 45.0) / piD4;
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alpha21 = (alpha21 * 45.0) / piD4;
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return new GeoData(0, 0, s, alpha12, alpha21); |
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} |
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/**
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* Vincenty's Direct formulae
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* Given: latitude and longitude of a point (phi1, lembda1) and
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* the geodetic azimuth (alpha12)
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* and ellipsoidal distance in metres (s) to a second point,
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*
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* Calculate: the latitude and longitude of the second point (phi2, lembda2)
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* and the reverse azimuth (alpha21).
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*/
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/**
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* Returns the lat and long of projected point and reverse azimuth
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* given a reference point and a distance and azimuth to project.
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* lats, longs and azimuths are passed in decimal degrees.
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* Returns ( phi2, lambda2, alpha21 ) as a tuple
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* @param pt
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* @param azimut
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* @param dist
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* @return
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*/
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public GeoData getPointVincenty(Point2D pt, double azimut, double dist) { |
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GeoData ret = new GeoData(0, 0); |
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double f = 1D / proj.getDatum().getEIFlattening(); |
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double a = proj.getDatum().getESemiMajorAxis();
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double phi1 = pt.getY();
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double lembda1 = pt.getX();
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double alpha12 = azimut;
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double s = dist;
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double piD4 = Math.atan(1.0); |
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double two_pi = piD4 * 8.0; |
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phi1 = (phi1 * piD4) / 45.0;
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lembda1 = (lembda1 * piD4) / 45.0;
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alpha12 = (alpha12 * piD4) / 45.0;
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if (alpha12 < 0.0) { |
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alpha12 = alpha12 + two_pi; |
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} |
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if (alpha12 > two_pi) {
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alpha12 = alpha12 - two_pi; |
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} |
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double b = a * (1.0 - f); |
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double TanU1 = (1 - f) * Math.tan(phi1); |
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double U1 = Math.atan(TanU1); |
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double sigma1 = Math.atan2(TanU1, Math.cos(alpha12)); |
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double Sinalpha = Math.cos(U1) * Math.sin(alpha12); |
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double cosalpha_sq = 1.0 - (Sinalpha * Sinalpha); |
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double u2 = (cosalpha_sq * ((a * a) - (b * b))) / (b * b);
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double A = 1.0 + |
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((u2 / 16384) * (4096 + |
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(u2 * (-768 + (u2 * (320 - (175 * u2))))))); |
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double B = (u2 / 1024) * (256 + |
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(u2 * (-128 + (u2 * (74 - (47 * u2)))))); |
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// Starting with the approximation
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double sigma = (s / (b * A));
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double last_sigma = (2.0 * sigma) + 2.0; // something impossible |
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// Iterate the following three equations
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// until there is no significant change in sigma
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// two_sigma_m , delta_sigma
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double two_sigma_m = 0; |
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while (Math.abs((last_sigma - sigma) / sigma) > 1.0e-9) { |
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two_sigma_m = (2 * sigma1) + sigma;
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double delta_sigma = B * Math.sin(sigma) * (Math.cos(two_sigma_m) + |
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((B / 4) * (Math.cos(sigma) * ((-1 + |
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(2 * Math.pow(Math.cos(two_sigma_m), 2))) - |
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((B / 6) * Math.cos(two_sigma_m) * (-3 + |
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(4 * Math.pow(Math.sin(sigma), 2))) * (-3 + |
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(4 * Math.pow(Math.cos(two_sigma_m), 2)))))))); |
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last_sigma = sigma; |
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sigma = (s / (b * A)) + delta_sigma; |
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} |
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double phi2 = Math.atan2(((Math.sin(U1) * Math.cos(sigma)) + |
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(Math.cos(U1) * Math.sin(sigma) * Math.cos(alpha12))), |
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((1 - f) * Math.sqrt(Math.pow(Sinalpha, 2) + |
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Math.pow((Math.sin(U1) * Math.sin(sigma)) - |
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(Math.cos(U1) * Math.cos(sigma) * Math.cos(alpha12)), |
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2))));
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double lembda = Math.atan2((Math.sin(sigma) * Math.sin(alpha12)), |
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((Math.cos(U1) * Math.cos(sigma)) - |
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(Math.sin(U1) * Math.sin(sigma) * Math.cos(alpha12)))); |
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double C = (f / 16) * cosalpha_sq * (4 + (f * (4 - (3 * cosalpha_sq)))); |
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double omega = lembda -
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((1 - C) * f * Sinalpha * (sigma +
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(C * Math.sin(sigma) * (Math.cos(two_sigma_m) + |
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(C * Math.cos(sigma) * (-1 + |
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(2 * Math.pow(Math.cos(two_sigma_m), 2)))))))); |
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double lembda2 = lembda1 + omega;
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|
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double alpha21 = Math.atan2(Sinalpha, |
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((-Math.sin(U1) * Math.sin(sigma)) + |
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(Math.cos(U1) * Math.cos(sigma) * Math.cos(alpha12)))); |
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alpha21 = alpha21 + (two_pi / 2.0);
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|
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if (alpha21 < 0.0) { |
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alpha21 = alpha21 + two_pi; |
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} |
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|
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if (alpha21 > two_pi) {
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alpha21 = alpha21 - two_pi; |
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} |
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phi2 = (phi2 * 45.0) / piD4;
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lembda2 = (lembda2 * 45.0) / piD4;
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alpha21 = (alpha21 * 45.0) / piD4;
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|
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ret.pt = new Point2D.Double(lembda2, phi2); |
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ret.azimut = alpha21; |
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return ret;
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} |
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|
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/**
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* Superficie de un triangulo (esf?rico). Los puntos deben de estar
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* en coordenadas geogr?ficas.
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* @param pt1
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* @param pt2
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* @param pt3
|
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* @return
|
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*/
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public double surfaceSphere(Point2D pt1, Point2D pt2, Point2D pt3) { |
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double sup = -1; |
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double A = distanceGeo(pt1, pt2);
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double B = distanceGeo(pt2, pt3);
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double C = distanceGeo(pt3, pt1);
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sup = (((A + B + C) - Math.toRadians(180D)) * Math.PI * proj.getDatum() |
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.getESemiMajorAxis()) / Math.toRadians(180D); |
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|
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return sup;
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} |
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|
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/*
|
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* F?rmulas de Vincenty's.
|
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* (pasadas de http://wegener.mechanik.tu-darmstadt.de/GMT-Help/Archiv/att-8710/Geodetic_py
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* http://www.icsm.gov.au/icsm/gda/gdatm/index.html
|
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*/
|
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class GeoData { |
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Point2D pt;
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double azimut;
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double revAzimut;
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double dist;
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|
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public GeoData(double x, double y) { |
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pt = new Point2D.Double(x, y); |
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azimut = revAzimut = dist = 0;
|
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} |
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|
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public GeoData(double x, double y, double dist, double azi, double rAzi) { |
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pt = new Point2D.Double(x, y); |
458 |
azimut = azi; |
459 |
revAzimut = rAzi; |
460 |
this.dist = dist;
|
461 |
} |
462 |
} |
463 |
} |