Java tutorial
/* * Copyright (C) 2009 The Android Open Source Project * * 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. */ package android.hardware; import java.util.GregorianCalendar; /** * Estimates magnetic field at a given point on * Earth, and in particular, to compute the magnetic declination from true * north. * * <p>This uses the World Magnetic Model produced by the United States National * Geospatial-Intelligence Agency. More details about the model can be found at * <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>. * This class currently uses WMM-2015 which is valid until 2020, but should * produce acceptable results for several years after that. Future versions of * Android may use a newer version of the model. */ public class GeomagneticField { // The magnetic field at a given point, in nanoteslas in geodetic // coordinates. private float mX; private float mY; private float mZ; // Geocentric coordinates -- set by computeGeocentricCoordinates. private float mGcLatitudeRad; private float mGcLongitudeRad; private float mGcRadiusKm; // Constants from WGS84 (the coordinate system used by GPS) static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f; static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523142f; static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f; // These coefficients and the formulae used below are from: // NOAA Technical Report: The US/UK World Magnetic Model for 2015-2020 static private final float[][] G_COEFF = new float[][] { { 0.0f }, { -29438.5f, -1501.1f }, { -2445.3f, 3012.5f, 1676.6f }, { 1351.1f, -2352.3f, 1225.6f, 581.9f }, { 907.2f, 813.7f, 120.3f, -335.0f, 70.3f }, { -232.6f, 360.1f, 192.4f, -141.0f, -157.4f, 4.3f }, { 69.5f, 67.4f, 72.8f, -129.8f, -29.0f, 13.2f, -70.9f }, { 81.6f, -76.1f, -6.8f, 51.9f, 15.0f, 9.3f, -2.8f, 6.7f }, { 24.0f, 8.6f, -16.9f, -3.2f, -20.6f, 13.3f, 11.7f, -16.0f, -2.0f }, { 5.4f, 8.8f, 3.1f, -3.1f, 0.6f, -13.3f, -0.1f, 8.7f, -9.1f, -10.5f }, { -1.9f, -6.5f, 0.2f, 0.6f, -0.6f, 1.7f, -0.7f, 2.1f, 2.3f, -1.8f, -3.6f }, { 3.1f, -1.5f, -2.3f, 2.1f, -0.9f, 0.6f, -0.7f, 0.2f, 1.7f, -0.2f, 0.4f, 3.5f }, { -2.0f, -0.3f, 0.4f, 1.3f, -0.9f, 0.9f, 0.1f, 0.5f, -0.4f, -0.4f, 0.2f, -0.9f, 0.0f } }; static private final float[][] H_COEFF = new float[][] { { 0.0f }, { 0.0f, 4796.2f }, { 0.0f, -2845.6f, -642.0f }, { 0.0f, -115.3f, 245.0f, -538.3f }, { 0.0f, 283.4f, -188.6f, 180.9f, -329.5f }, { 0.0f, 47.4f, 196.9f, -119.4f, 16.1f, 100.1f }, { 0.0f, -20.7f, 33.2f, 58.8f, -66.5f, 7.3f, 62.5f }, { 0.0f, -54.1f, -19.4f, 5.6f, 24.4f, 3.3f, -27.5f, -2.3f }, { 0.0f, 10.2f, -18.1f, 13.2f, -14.6f, 16.2f, 5.7f, -9.1f, 2.2f }, { 0.0f, -21.6f, 10.8f, 11.7f, -6.8f, -6.9f, 7.8f, 1.0f, -3.9f, 8.5f }, { 0.0f, 3.3f, -0.3f, 4.6f, 4.4f, -7.9f, -0.6f, -4.1f, -2.8f, -1.1f, -8.7f }, { 0.0f, -0.1f, 2.1f, -0.7f, -1.1f, 0.7f, -0.2f, -2.1f, -1.5f, -2.5f, -2.0f, -2.3f }, { 0.0f, -1.0f, 0.5f, 1.8f, -2.2f, 0.3f, 0.7f, -0.1f, 0.3f, 0.2f, -0.9f, -0.2f, 0.7f } }; static private final float[][] DELTA_G = new float[][] { { 0.0f }, { 10.7f, 17.9f }, { -8.6f, -3.3f, 2.4f }, { 3.1f, -6.2f, -0.4f, -10.4f }, { -0.4f, 0.8f, -9.2f, 4.0f, -4.2f }, { -0.2f, 0.1f, -1.4f, 0.0f, 1.3f, 3.8f }, { -0.5f, -0.2f, -0.6f, 2.4f, -1.1f, 0.3f, 1.5f }, { 0.2f, -0.2f, -0.4f, 1.3f, 0.2f, -0.4f, -0.9f, 0.3f }, { 0.0f, 0.1f, -0.5f, 0.5f, -0.2f, 0.4f, 0.2f, -0.4f, 0.3f }, { 0.0f, -0.1f, -0.1f, 0.4f, -0.5f, -0.2f, 0.1f, 0.0f, -0.2f, -0.1f }, { 0.0f, 0.0f, -0.1f, 0.3f, -0.1f, -0.1f, -0.1f, 0.0f, -0.2f, -0.1f, -0.2f }, { 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, -0.1f }, { 0.1f, 0.0f, 0.0f, 0.1f, -0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } }; static private final float[][] DELTA_H = new float[][] { { 0.0f }, { 0.0f, -26.8f }, { 0.0f, -27.1f, -13.3f }, { 0.0f, 8.4f, -0.4f, 2.3f }, { 0.0f, -0.6f, 5.3f, 3.0f, -5.3f }, { 0.0f, 0.4f, 1.6f, -1.1f, 3.3f, 0.1f }, { 0.0f, 0.0f, -2.2f, -0.7f, 0.1f, 1.0f, 1.3f }, { 0.0f, 0.7f, 0.5f, -0.2f, -0.1f, -0.7f, 0.1f, 0.1f }, { 0.0f, -0.3f, 0.3f, 0.3f, 0.6f, -0.1f, -0.2f, 0.3f, 0.0f }, { 0.0f, -0.2f, -0.1f, -0.2f, 0.1f, 0.1f, 0.0f, -0.2f, 0.4f, 0.3f }, { 0.0f, 0.1f, -0.1f, 0.0f, 0.0f, -0.2f, 0.1f, -0.1f, -0.2f, 0.1f, -0.1f }, { 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, -0.1f }, { 0.0f, 0.0f, 0.0f, -0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f } }; static private final long BASE_TIME = new GregorianCalendar(2015, 1, 1).getTimeInMillis(); // The ratio between the Gauss-normalized associated Legendre functions and // the Schmid quasi-normalized ones. Compute these once staticly since they // don't depend on input variables at all. static private final float[][] SCHMIDT_QUASI_NORM_FACTORS = computeSchmidtQuasiNormFactors(G_COEFF.length); /** * Estimate the magnetic field at a given point and time. * * @param gdLatitudeDeg * Latitude in WGS84 geodetic coordinates -- positive is east. * @param gdLongitudeDeg * Longitude in WGS84 geodetic coordinates -- positive is north. * @param altitudeMeters * Altitude in WGS84 geodetic coordinates, in meters. * @param timeMillis * Time at which to evaluate the declination, in milliseconds * since January 1, 1970. (approximate is fine -- the declination * changes very slowly). */ public GeomagneticField(float gdLatitudeDeg, float gdLongitudeDeg, float altitudeMeters, long timeMillis) { final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients. // We don't handle the north and south poles correctly -- pretend that // we're not quite at them to avoid crashing. gdLatitudeDeg = Math.min(90.0f - 1e-5f, Math.max(-90.0f + 1e-5f, gdLatitudeDeg)); computeGeocentricCoordinates(gdLatitudeDeg, gdLongitudeDeg, altitudeMeters); assert G_COEFF.length == H_COEFF.length; // Note: LegendreTable computes associated Legendre functions for // cos(theta). We want the associated Legendre functions for // sin(latitude), which is the same as cos(PI/2 - latitude), except the // derivate will be negated. LegendreTable legendre = new LegendreTable(MAX_N - 1, (float) (Math.PI / 2.0 - mGcLatitudeRad)); // Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in // 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times). float[] relativeRadiusPower = new float[MAX_N + 2]; relativeRadiusPower[0] = 1.0f; relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm; for (int i = 2; i < relativeRadiusPower.length; ++i) { relativeRadiusPower[i] = relativeRadiusPower[i - 1] * relativeRadiusPower[1]; } // Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N -- // this is much faster than calling Math.sin and Math.com MAX_N+1 times. float[] sinMLon = new float[MAX_N]; float[] cosMLon = new float[MAX_N]; sinMLon[0] = 0.0f; cosMLon[0] = 1.0f; sinMLon[1] = (float) Math.sin(mGcLongitudeRad); cosMLon[1] = (float) Math.cos(mGcLongitudeRad); for (int m = 2; m < MAX_N; ++m) { // Standard expansions for sin((m-x)*theta + x*theta) and // cos((m-x)*theta + x*theta). int x = m >> 1; sinMLon[m] = sinMLon[m - x] * cosMLon[x] + cosMLon[m - x] * sinMLon[x]; cosMLon[m] = cosMLon[m - x] * cosMLon[x] - sinMLon[m - x] * sinMLon[x]; } float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad); float yearsSinceBase = (timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f); // We now compute the magnetic field strength given the geocentric // location. The magnetic field is the derivative of the potential // function defined by the model. See NOAA Technical Report: The US/UK // World Magnetic Model for 2015-2020 for the derivation. float gcX = 0.0f; // Geocentric northwards component. float gcY = 0.0f; // Geocentric eastwards component. float gcZ = 0.0f; // Geocentric downwards component. for (int n = 1; n < MAX_N; n++) { for (int m = 0; m <= n; m++) { // Adjust the coefficients for the current date. float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m]; float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m]; // Negative derivative with respect to latitude, divided by // radius. This looks like the negation of the version in the // NOAA Techincal report because that report used // P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the // derivative with respect to theta is negated. gcX += relativeRadiusPower[n + 2] * (g * cosMLon[m] + h * sinMLon[m]) * legendre.mPDeriv[n][m] * SCHMIDT_QUASI_NORM_FACTORS[n][m]; // Negative derivative with respect to longitude, divided by // radius. gcY += relativeRadiusPower[n + 2] * m * (g * sinMLon[m] - h * cosMLon[m]) * legendre.mP[n][m] * SCHMIDT_QUASI_NORM_FACTORS[n][m] * inverseCosLatitude; // Negative derivative with respect to radius. gcZ -= (n + 1) * relativeRadiusPower[n + 2] * (g * cosMLon[m] + h * sinMLon[m]) * legendre.mP[n][m] * SCHMIDT_QUASI_NORM_FACTORS[n][m]; } } // Convert back to geodetic coordinates. This is basically just a // rotation around the Y-axis by the difference in latitudes between the // geocentric frame and the geodetic frame. double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad; mX = (float) (gcX * Math.cos(latDiffRad) + gcZ * Math.sin(latDiffRad)); mY = gcY; mZ = (float) (-gcX * Math.sin(latDiffRad) + gcZ * Math.cos(latDiffRad)); } /** * @return The X (northward) component of the magnetic field in nanoteslas. */ public float getX() { return mX; } /** * @return The Y (eastward) component of the magnetic field in nanoteslas. */ public float getY() { return mY; } /** * @return The Z (downward) component of the magnetic field in nanoteslas. */ public float getZ() { return mZ; } /** * @return The declination of the horizontal component of the magnetic * field from true north, in degrees (i.e. positive means the * magnetic field is rotated east that much from true north). */ public float getDeclination() { return (float) Math.toDegrees(Math.atan2(mY, mX)); } /** * @return The inclination of the magnetic field in degrees -- positive * means the magnetic field is rotated downwards. */ public float getInclination() { return (float) Math.toDegrees(Math.atan2(mZ, getHorizontalStrength())); } /** * @return Horizontal component of the field strength in nanoteslas. */ public float getHorizontalStrength() { return (float) Math.hypot(mX, mY); } /** * @return Total field strength in nanoteslas. */ public float getFieldStrength() { return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ); } /** * @param gdLatitudeDeg * Latitude in WGS84 geodetic coordinates. * @param gdLongitudeDeg * Longitude in WGS84 geodetic coordinates. * @param altitudeMeters * Altitude above sea level in WGS84 geodetic coordinates. * @return Geocentric latitude (i.e. angle between closest point on the * equator and this point, at the center of the earth. */ private void computeGeocentricCoordinates(float gdLatitudeDeg, float gdLongitudeDeg, float altitudeMeters) { float altitudeKm = altitudeMeters / 1000.0f; float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM; float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM; double gdLatRad = Math.toRadians(gdLatitudeDeg); float clat = (float) Math.cos(gdLatRad); float slat = (float) Math.sin(gdLatRad); float tlat = slat / clat; float latRad = (float) Math.sqrt(a2 * clat * clat + b2 * slat * slat); mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2) / (latRad * altitudeKm + a2)); mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg); float radSq = altitudeKm * altitudeKm + 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat + b2 * slat * slat) + (a2 * a2 * clat * clat + b2 * b2 * slat * slat) / (a2 * clat * clat + b2 * slat * slat); mGcRadiusKm = (float) Math.sqrt(radSq); } /** * Utility class to compute a table of Gauss-normalized associated Legendre * functions P_n^m(cos(theta)) */ static private class LegendreTable { // These are the Gauss-normalized associated Legendre functions -- that // is, they are normal Legendre functions multiplied by // (n-m)!/(2n-1)!! (where (2n-1)!! = 1*3*5*...*2n-1) public final float[][] mP; // Derivative of mP, with respect to theta. public final float[][] mPDeriv; /** * @param maxN * The maximum n- and m-values to support * @param thetaRad * Returned functions will be Gauss-normalized * P_n^m(cos(thetaRad)), with thetaRad in radians. */ public LegendreTable(int maxN, float thetaRad) { // Compute the table of Gauss-normalized associated Legendre // functions using standard recursion relations. Also compute the // table of derivatives using the derivative of the recursion // relations. float cos = (float) Math.cos(thetaRad); float sin = (float) Math.sin(thetaRad); mP = new float[maxN + 1][]; mPDeriv = new float[maxN + 1][]; mP[0] = new float[] { 1.0f }; mPDeriv[0] = new float[] { 0.0f }; for (int n = 1; n <= maxN; n++) { mP[n] = new float[n + 1]; mPDeriv[n] = new float[n + 1]; for (int m = 0; m <= n; m++) { if (n == m) { mP[n][m] = sin * mP[n - 1][m - 1]; mPDeriv[n][m] = cos * mP[n - 1][m - 1] + sin * mPDeriv[n - 1][m - 1]; } else if (n == 1 || m == n - 1) { mP[n][m] = cos * mP[n - 1][m]; mPDeriv[n][m] = -sin * mP[n - 1][m] + cos * mPDeriv[n - 1][m]; } else { assert n > 1 && m < n - 1; float k = ((n - 1) * (n - 1) - m * m) / (float) ((2 * n - 1) * (2 * n - 3)); mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m]; mPDeriv[n][m] = -sin * mP[n - 1][m] + cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m]; } } } } } /** * Compute the ration between the Gauss-normalized associated Legendre * functions and the Schmidt quasi-normalized version. This is equivalent to * sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)! */ private static float[][] computeSchmidtQuasiNormFactors(int maxN) { float[][] schmidtQuasiNorm = new float[maxN + 1][]; schmidtQuasiNorm[0] = new float[] { 1.0f }; for (int n = 1; n <= maxN; n++) { schmidtQuasiNorm[n] = new float[n + 1]; schmidtQuasiNorm[n][0] = schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n; for (int m = 1; m <= n; m++) { schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1] * (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1) / (float) (n + m)); } } return schmidtQuasiNorm; } }