[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

Re: Problem with Albers and Spherical Earth

John,

On Thu, Oct 8, 2009 at 6:45 PM, John Caron <address@hidden> wrote:
> Sorry, we only have the spherical case for Albers Equal Area. the
> closed-form elliptical looks pretty hairy. There are often good numerical
> solutions that are much faster, but i dont know of any java implementations.

What about this library:
http://www.jhlabs.com/java/maps/proj/index.html

It looks like the AlbersProjection.java handles non-spherical earth:

/*
Copyright 2006 Jerry Huxtable

Licensed 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.
*/

/*
 * This file was semi-automatically converted from the public-domain
USGS PROJ source.
 */
package com.jhlabs.map.proj;

import java.awt.geom.*;
import com.jhlabs.map.*;

public class AlbersProjection extends Projection {

        private final static double EPS10 = 1.e-10;
        private final static double TOL7 = 1.e-7;
        private double ec;
        private double n;
        private double c;
        private double dd;
        private double n2;
        private double rho0;
        private double phi1;
        private double phi2;
        private double[] en;

        private final static int N_ITER = 15;
        private final static double EPSILON = 1.0e-7;
        private final static double TOL = 1.0e-10;

        protected double projectionLatitude1 = MapMath.degToRad(45.5);
        protected double projectionLatitude2 = MapMath.degToRad(29.5);

        public AlbersProjection() {
                minLatitude = Math.toRadians(0);
                maxLatitude = Math.toRadians(80);
                initialize();
        }

        private static double phi1_(double qs, double Te, double Tone_es) {
                int i;
                double Phi, sinpi, cospi, con, com, dphi;

                Phi = Math.asin (.5 * qs);
                if (Te < EPSILON)
                        return( Phi );
                i = N_ITER;
                do {
                        sinpi = Math.sin (Phi);
                        cospi = Math.cos (Phi);
                        con = Te * sinpi;
                        com = 1. - con * con;
                        dphi = .5 * com * com / cospi * (qs / Tone_es -
                           sinpi / com + .5 / Te * Math.log ((1. - con) /
                           (1. + con)));
                        Phi += dphi;
                } while (Math.abs(dphi) > TOL && --i != 0);
                return( i != 0 ? Phi : Double.MAX_VALUE );
        }

        public Point2D.Double project(double lplam, double lpphi, 
Point2D.Double out) {
                double rho;
                if ((rho = c - (!spherical ? n * MapMath.qsfn(Math.sin(lpphi), 
e,
one_es) : n2 * Math.sin(lpphi))) < 0.)
                        throw new ProjectionException("F");
                rho = dd * Math.sqrt(rho);
                out.x = rho * Math.sin( lplam *= n );
                out.y = rho0 - rho * Math.cos(lplam);
                return out;
        }

        public Point2D.Double projectInverse(double xyx, double xyy,
Point2D.Double out) {
                double rho;
                if ((rho = MapMath.distance(xyx, xyy = rho0 - xyy)) != 0) {
                        double lpphi, lplam;
                        if (n < 0.) {
                                rho = -rho;
                                xyx = -xyx;
                                xyy = -xyy;
                        }
                        lpphi =  rho / dd;
                        if (!spherical) {
                                lpphi = (c - lpphi * lpphi) / n;
                                if (Math.abs(ec - Math.abs(lpphi)) > TOL7) {
                                        if ((lpphi = phi1_(lpphi, e, one_es)) 
== Double.MAX_VALUE)
                                                throw new 
ProjectionException("I");
                                } else
                                        lpphi = lpphi < 0. ? -MapMath.HALFPI : 
MapMath.HALFPI;
                        } else if (Math.abs(out.y = (c - lpphi * lpphi) / n2) 
<= 1.)
                                lpphi = Math.asin(lpphi);
                        else
                                lpphi = lpphi < 0. ? -MapMath.HALFPI : 
MapMath.HALFPI;
                        lplam = Math.atan2(xyx, xyy) / n;
                        out.x = lplam;
                        out.y = lpphi;
                } else {
                        out.x = 0.;
                        out.y = n > 0. ? MapMath.HALFPI : - MapMath.HALFPI;
                }
                return out;
        }

        public void initialize() {
                super.initialize();
                double cosphi, sinphi;
                boolean secant;

                phi1 = projectionLatitude1;
                phi2 = projectionLatitude2;

                if (Math.abs(phi1 + phi2) < EPS10)
                        throw new IllegalArgumentException("-21");
                n = sinphi = Math.sin(phi1);
                cosphi = Math.cos(phi1);
                secant = Math.abs(phi1 - phi2) >= EPS10;
                spherical = es > 0.0;
                if (!spherical) {
                        double ml1, m1;

                        if ((en = MapMath.enfn(es)) == null)
                                throw new IllegalArgumentException("0");
                        m1 = MapMath.msfn(sinphi, cosphi, es);
                        ml1 = MapMath.qsfn(sinphi, e, one_es);
                        if (secant) { /* secant cone */
                                double ml2, m2;

                                sinphi = Math.sin(phi2);
                                cosphi = Math.cos(phi2);
                                m2 = MapMath.msfn(sinphi, cosphi, es);
                                ml2 = MapMath.qsfn(sinphi, e, one_es);
                                n = (m1 * m1 - m2 * m2) / (ml2 - ml1);
                        }
                        ec = 1. - .5 * one_es * Math.log((1. - e) /
                                (1. + e)) / e;
                        c = m1 * m1 + n * ml1;
                        dd = 1. / n;
                        rho0 = dd * Math.sqrt(c - n * 
MapMath.qsfn(Math.sin(projectionLatitude),
                                e, one_es));
                } else {
                        if (secant) n = .5 * (n + Math.sin(phi2));
                        n2 = n + n;
                        c = cosphi * cosphi + n2 * sinphi;
                        dd = 1. / n;
                        rho0 = dd * Math.sqrt(c - n2 * 
Math.sin(projectionLatitude));
                }
        }

        /**
         * Returns true if this projection is equal area
         */
        public boolean isEqualArea() {
                return true;
        }

        public boolean hasInverse() {
                return true;
        }

        /**
         * Returns the ESPG code for this projection, or 0 if unknown.
         */
        public int getEPSGCode() {
                return 9822;
        }

        public String toString() {
                return "Albers Equal Area";
        }

/*
        public String toString() {
                return "Lambert Equal Area Conic";
        }
*/
}




-- 
Dr. Richard P. Signell   (508) 457-2229
USGS, 384 Woods Hole Rd.
Woods Hole, MA 02543-1598