The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 1 | /* |
| 2 | * Copyright (C) 2009 The Android Open Source Project |
| 3 | * |
| 4 | * Licensed under the Apache License, Version 2.0 (the "License"); |
| 5 | * you may not use this file except in compliance with the License. |
| 6 | * You may obtain a copy of the License at |
| 7 | * |
| 8 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 9 | * |
| 10 | * Unless required by applicable law or agreed to in writing, software |
| 11 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 12 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 13 | * See the License for the specific language governing permissions and |
| 14 | * limitations under the License. |
| 15 | */ |
| 16 | |
| 17 | package android.hardware; |
| 18 | |
| 19 | import java.util.GregorianCalendar; |
| 20 | |
| 21 | /** |
Scott Main | 8edad6f | 2012-03-09 10:55:50 -0800 | [diff] [blame] | 22 | * Estimates magnetic field at a given point on |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 23 | * Earth, and in particular, to compute the magnetic declination from true |
| 24 | * north. |
| 25 | * |
| 26 | * <p>This uses the World Magnetic Model produced by the United States National |
| 27 | * Geospatial-Intelligence Agency. More details about the model can be found at |
| 28 | * <a href="http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml">http://www.ngdc.noaa.gov/geomag/WMM/DoDWMM.shtml</a>. |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 29 | * This class currently uses WMM-2015 which is valid until 2020, but should |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 30 | * produce acceptable results for several years after that. Future versions of |
| 31 | * Android may use a newer version of the model. |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 32 | */ |
| 33 | public class GeomagneticField { |
kopriva | b9cf1a1 | 2018-09-29 14:41:05 -0700 | [diff] [blame] | 34 | // The magnetic field at a given point, in nanoteslas in geodetic |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 35 | // coordinates. |
| 36 | private float mX; |
| 37 | private float mY; |
| 38 | private float mZ; |
| 39 | |
| 40 | // Geocentric coordinates -- set by computeGeocentricCoordinates. |
| 41 | private float mGcLatitudeRad; |
| 42 | private float mGcLongitudeRad; |
| 43 | private float mGcRadiusKm; |
| 44 | |
| 45 | // Constants from WGS84 (the coordinate system used by GPS) |
| 46 | static private final float EARTH_SEMI_MAJOR_AXIS_KM = 6378.137f; |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 47 | static private final float EARTH_SEMI_MINOR_AXIS_KM = 6356.7523142f; |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 48 | static private final float EARTH_REFERENCE_RADIUS_KM = 6371.2f; |
| 49 | |
| 50 | // These coefficients and the formulae used below are from: |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 51 | // NOAA Technical Report: The US/UK World Magnetic Model for 2015-2020 |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 52 | static private final float[][] G_COEFF = new float[][] { |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 53 | { 0.0f }, |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 54 | { -29438.5f, -1501.1f }, |
| 55 | { -2445.3f, 3012.5f, 1676.6f }, |
| 56 | { 1351.1f, -2352.3f, 1225.6f, 581.9f }, |
| 57 | { 907.2f, 813.7f, 120.3f, -335.0f, 70.3f }, |
| 58 | { -232.6f, 360.1f, 192.4f, -141.0f, -157.4f, 4.3f }, |
| 59 | { 69.5f, 67.4f, 72.8f, -129.8f, -29.0f, 13.2f, -70.9f }, |
| 60 | { 81.6f, -76.1f, -6.8f, 51.9f, 15.0f, 9.3f, -2.8f, 6.7f }, |
| 61 | { 24.0f, 8.6f, -16.9f, -3.2f, -20.6f, 13.3f, 11.7f, -16.0f, -2.0f }, |
| 62 | { 5.4f, 8.8f, 3.1f, -3.1f, 0.6f, -13.3f, -0.1f, 8.7f, -9.1f, -10.5f }, |
| 63 | { -1.9f, -6.5f, 0.2f, 0.6f, -0.6f, 1.7f, -0.7f, 2.1f, 2.3f, -1.8f, -3.6f }, |
| 64 | { 3.1f, -1.5f, -2.3f, 2.1f, -0.9f, 0.6f, -0.7f, 0.2f, 1.7f, -0.2f, 0.4f, 3.5f }, |
| 65 | { -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 } }; |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 66 | |
| 67 | static private final float[][] H_COEFF = new float[][] { |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 68 | { 0.0f }, |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 69 | { 0.0f, 4796.2f }, |
| 70 | { 0.0f, -2845.6f, -642.0f }, |
| 71 | { 0.0f, -115.3f, 245.0f, -538.3f }, |
| 72 | { 0.0f, 283.4f, -188.6f, 180.9f, -329.5f }, |
| 73 | { 0.0f, 47.4f, 196.9f, -119.4f, 16.1f, 100.1f }, |
| 74 | { 0.0f, -20.7f, 33.2f, 58.8f, -66.5f, 7.3f, 62.5f }, |
| 75 | { 0.0f, -54.1f, -19.4f, 5.6f, 24.4f, 3.3f, -27.5f, -2.3f }, |
| 76 | { 0.0f, 10.2f, -18.1f, 13.2f, -14.6f, 16.2f, 5.7f, -9.1f, 2.2f }, |
| 77 | { 0.0f, -21.6f, 10.8f, 11.7f, -6.8f, -6.9f, 7.8f, 1.0f, -3.9f, 8.5f }, |
| 78 | { 0.0f, 3.3f, -0.3f, 4.6f, 4.4f, -7.9f, -0.6f, -4.1f, -2.8f, -1.1f, -8.7f }, |
| 79 | { 0.0f, -0.1f, 2.1f, -0.7f, -1.1f, 0.7f, -0.2f, -2.1f, -1.5f, -2.5f, -2.0f, -2.3f }, |
| 80 | { 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 } }; |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 81 | |
| 82 | static private final float[][] DELTA_G = new float[][] { |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 83 | { 0.0f }, |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 84 | { 10.7f, 17.9f }, |
| 85 | { -8.6f, -3.3f, 2.4f }, |
| 86 | { 3.1f, -6.2f, -0.4f, -10.4f }, |
| 87 | { -0.4f, 0.8f, -9.2f, 4.0f, -4.2f }, |
| 88 | { -0.2f, 0.1f, -1.4f, 0.0f, 1.3f, 3.8f }, |
| 89 | { -0.5f, -0.2f, -0.6f, 2.4f, -1.1f, 0.3f, 1.5f }, |
| 90 | { 0.2f, -0.2f, -0.4f, 1.3f, 0.2f, -0.4f, -0.9f, 0.3f }, |
| 91 | { 0.0f, 0.1f, -0.5f, 0.5f, -0.2f, 0.4f, 0.2f, -0.4f, 0.3f }, |
| 92 | { 0.0f, -0.1f, -0.1f, 0.4f, -0.5f, -0.2f, 0.1f, 0.0f, -0.2f, -0.1f }, |
| 93 | { 0.0f, 0.0f, -0.1f, 0.3f, -0.1f, -0.1f, -0.1f, 0.0f, -0.2f, -0.1f, -0.2f }, |
| 94 | { 0.0f, 0.0f, -0.1f, 0.1f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, 0.0f, -0.1f, -0.1f }, |
| 95 | { 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 } }; |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 96 | |
| 97 | static private final float[][] DELTA_H = new float[][] { |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 98 | { 0.0f }, |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 99 | { 0.0f, -26.8f }, |
| 100 | { 0.0f, -27.1f, -13.3f }, |
| 101 | { 0.0f, 8.4f, -0.4f, 2.3f }, |
| 102 | { 0.0f, -0.6f, 5.3f, 3.0f, -5.3f }, |
| 103 | { 0.0f, 0.4f, 1.6f, -1.1f, 3.3f, 0.1f }, |
| 104 | { 0.0f, 0.0f, -2.2f, -0.7f, 0.1f, 1.0f, 1.3f }, |
| 105 | { 0.0f, 0.7f, 0.5f, -0.2f, -0.1f, -0.7f, 0.1f, 0.1f }, |
| 106 | { 0.0f, -0.3f, 0.3f, 0.3f, 0.6f, -0.1f, -0.2f, 0.3f, 0.0f }, |
| 107 | { 0.0f, -0.2f, -0.1f, -0.2f, 0.1f, 0.1f, 0.0f, -0.2f, 0.4f, 0.3f }, |
| 108 | { 0.0f, 0.1f, -0.1f, 0.0f, 0.0f, -0.2f, 0.1f, -0.1f, -0.2f, 0.1f, -0.1f }, |
| 109 | { 0.0f, 0.0f, 0.1f, 0.0f, 0.1f, 0.0f, 0.0f, 0.1f, 0.0f, -0.1f, 0.0f, -0.1f }, |
| 110 | { 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 } }; |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 111 | |
| 112 | static private final long BASE_TIME = |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 113 | new GregorianCalendar(2015, 1, 1).getTimeInMillis(); |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 114 | |
| 115 | // The ratio between the Gauss-normalized associated Legendre functions and |
| 116 | // the Schmid quasi-normalized ones. Compute these once staticly since they |
| 117 | // don't depend on input variables at all. |
| 118 | static private final float[][] SCHMIDT_QUASI_NORM_FACTORS = |
| 119 | computeSchmidtQuasiNormFactors(G_COEFF.length); |
| 120 | |
| 121 | /** |
| 122 | * Estimate the magnetic field at a given point and time. |
| 123 | * |
| 124 | * @param gdLatitudeDeg |
| 125 | * Latitude in WGS84 geodetic coordinates -- positive is east. |
| 126 | * @param gdLongitudeDeg |
| 127 | * Longitude in WGS84 geodetic coordinates -- positive is north. |
| 128 | * @param altitudeMeters |
| 129 | * Altitude in WGS84 geodetic coordinates, in meters. |
| 130 | * @param timeMillis |
| 131 | * Time at which to evaluate the declination, in milliseconds |
| 132 | * since January 1, 1970. (approximate is fine -- the declination |
| 133 | * changes very slowly). |
| 134 | */ |
| 135 | public GeomagneticField(float gdLatitudeDeg, |
| 136 | float gdLongitudeDeg, |
| 137 | float altitudeMeters, |
| 138 | long timeMillis) { |
| 139 | final int MAX_N = G_COEFF.length; // Maximum degree of the coefficients. |
| 140 | |
| 141 | // We don't handle the north and south poles correctly -- pretend that |
| 142 | // we're not quite at them to avoid crashing. |
| 143 | gdLatitudeDeg = Math.min(90.0f - 1e-5f, |
| 144 | Math.max(-90.0f + 1e-5f, gdLatitudeDeg)); |
| 145 | computeGeocentricCoordinates(gdLatitudeDeg, |
| 146 | gdLongitudeDeg, |
| 147 | altitudeMeters); |
| 148 | |
| 149 | assert G_COEFF.length == H_COEFF.length; |
| 150 | |
| 151 | // Note: LegendreTable computes associated Legendre functions for |
| 152 | // cos(theta). We want the associated Legendre functions for |
| 153 | // sin(latitude), which is the same as cos(PI/2 - latitude), except the |
| 154 | // derivate will be negated. |
| 155 | LegendreTable legendre = |
| 156 | new LegendreTable(MAX_N - 1, |
| 157 | (float) (Math.PI / 2.0 - mGcLatitudeRad)); |
| 158 | |
| 159 | // Compute a table of (EARTH_REFERENCE_RADIUS_KM / radius)^n for i in |
| 160 | // 0..MAX_N-2 (this is much faster than calling Math.pow MAX_N+1 times). |
| 161 | float[] relativeRadiusPower = new float[MAX_N + 2]; |
| 162 | relativeRadiusPower[0] = 1.0f; |
| 163 | relativeRadiusPower[1] = EARTH_REFERENCE_RADIUS_KM / mGcRadiusKm; |
| 164 | for (int i = 2; i < relativeRadiusPower.length; ++i) { |
| 165 | relativeRadiusPower[i] = relativeRadiusPower[i - 1] * |
| 166 | relativeRadiusPower[1]; |
| 167 | } |
| 168 | |
| 169 | // Compute tables of sin(lon * m) and cos(lon * m) for m = 0..MAX_N -- |
| 170 | // this is much faster than calling Math.sin and Math.com MAX_N+1 times. |
| 171 | float[] sinMLon = new float[MAX_N]; |
| 172 | float[] cosMLon = new float[MAX_N]; |
| 173 | sinMLon[0] = 0.0f; |
| 174 | cosMLon[0] = 1.0f; |
| 175 | sinMLon[1] = (float) Math.sin(mGcLongitudeRad); |
| 176 | cosMLon[1] = (float) Math.cos(mGcLongitudeRad); |
| 177 | |
| 178 | for (int m = 2; m < MAX_N; ++m) { |
| 179 | // Standard expansions for sin((m-x)*theta + x*theta) and |
| 180 | // cos((m-x)*theta + x*theta). |
| 181 | int x = m >> 1; |
| 182 | sinMLon[m] = sinMLon[m-x] * cosMLon[x] + cosMLon[m-x] * sinMLon[x]; |
| 183 | cosMLon[m] = cosMLon[m-x] * cosMLon[x] - sinMLon[m-x] * sinMLon[x]; |
| 184 | } |
| 185 | |
| 186 | float inverseCosLatitude = 1.0f / (float) Math.cos(mGcLatitudeRad); |
| 187 | float yearsSinceBase = |
| 188 | (timeMillis - BASE_TIME) / (365f * 24f * 60f * 60f * 1000f); |
| 189 | |
| 190 | // We now compute the magnetic field strength given the geocentric |
| 191 | // location. The magnetic field is the derivative of the potential |
| 192 | // function defined by the model. See NOAA Technical Report: The US/UK |
Peng Xu | 63bf36a | 2017-08-07 19:29:30 -0700 | [diff] [blame] | 193 | // World Magnetic Model for 2015-2020 for the derivation. |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 194 | float gcX = 0.0f; // Geocentric northwards component. |
| 195 | float gcY = 0.0f; // Geocentric eastwards component. |
| 196 | float gcZ = 0.0f; // Geocentric downwards component. |
| 197 | |
| 198 | for (int n = 1; n < MAX_N; n++) { |
| 199 | for (int m = 0; m <= n; m++) { |
| 200 | // Adjust the coefficients for the current date. |
| 201 | float g = G_COEFF[n][m] + yearsSinceBase * DELTA_G[n][m]; |
| 202 | float h = H_COEFF[n][m] + yearsSinceBase * DELTA_H[n][m]; |
| 203 | |
| 204 | // Negative derivative with respect to latitude, divided by |
| 205 | // radius. This looks like the negation of the version in the |
| 206 | // NOAA Techincal report because that report used |
| 207 | // P_n^m(sin(theta)) and we use P_n^m(cos(90 - theta)), so the |
| 208 | // derivative with respect to theta is negated. |
| 209 | gcX += relativeRadiusPower[n+2] |
| 210 | * (g * cosMLon[m] + h * sinMLon[m]) |
| 211 | * legendre.mPDeriv[n][m] |
| 212 | * SCHMIDT_QUASI_NORM_FACTORS[n][m]; |
| 213 | |
| 214 | // Negative derivative with respect to longitude, divided by |
| 215 | // radius. |
| 216 | gcY += relativeRadiusPower[n+2] * m |
| 217 | * (g * sinMLon[m] - h * cosMLon[m]) |
| 218 | * legendre.mP[n][m] |
| 219 | * SCHMIDT_QUASI_NORM_FACTORS[n][m] |
| 220 | * inverseCosLatitude; |
| 221 | |
| 222 | // Negative derivative with respect to radius. |
| 223 | gcZ -= (n + 1) * relativeRadiusPower[n+2] |
| 224 | * (g * cosMLon[m] + h * sinMLon[m]) |
| 225 | * legendre.mP[n][m] |
| 226 | * SCHMIDT_QUASI_NORM_FACTORS[n][m]; |
| 227 | } |
| 228 | } |
| 229 | |
| 230 | // Convert back to geodetic coordinates. This is basically just a |
| 231 | // rotation around the Y-axis by the difference in latitudes between the |
| 232 | // geocentric frame and the geodetic frame. |
| 233 | double latDiffRad = Math.toRadians(gdLatitudeDeg) - mGcLatitudeRad; |
| 234 | mX = (float) (gcX * Math.cos(latDiffRad) |
| 235 | + gcZ * Math.sin(latDiffRad)); |
| 236 | mY = gcY; |
| 237 | mZ = (float) (- gcX * Math.sin(latDiffRad) |
| 238 | + gcZ * Math.cos(latDiffRad)); |
| 239 | } |
| 240 | |
| 241 | /** |
| 242 | * @return The X (northward) component of the magnetic field in nanoteslas. |
| 243 | */ |
| 244 | public float getX() { |
| 245 | return mX; |
| 246 | } |
| 247 | |
| 248 | /** |
| 249 | * @return The Y (eastward) component of the magnetic field in nanoteslas. |
| 250 | */ |
| 251 | public float getY() { |
| 252 | return mY; |
| 253 | } |
| 254 | |
| 255 | /** |
| 256 | * @return The Z (downward) component of the magnetic field in nanoteslas. |
| 257 | */ |
| 258 | public float getZ() { |
| 259 | return mZ; |
| 260 | } |
| 261 | |
| 262 | /** |
| 263 | * @return The declination of the horizontal component of the magnetic |
| 264 | * field from true north, in degrees (i.e. positive means the |
| 265 | * magnetic field is rotated east that much from true north). |
| 266 | */ |
| 267 | public float getDeclination() { |
| 268 | return (float) Math.toDegrees(Math.atan2(mY, mX)); |
| 269 | } |
| 270 | |
| 271 | /** |
| 272 | * @return The inclination of the magnetic field in degrees -- positive |
| 273 | * means the magnetic field is rotated downwards. |
| 274 | */ |
| 275 | public float getInclination() { |
| 276 | return (float) Math.toDegrees(Math.atan2(mZ, |
| 277 | getHorizontalStrength())); |
| 278 | } |
| 279 | |
| 280 | /** |
kopriva | b9cf1a1 | 2018-09-29 14:41:05 -0700 | [diff] [blame] | 281 | * @return Horizontal component of the field strength in nanoteslas. |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 282 | */ |
| 283 | public float getHorizontalStrength() { |
Neil Fuller | 33253a4 | 2014-10-01 11:55:10 +0100 | [diff] [blame] | 284 | return (float) Math.hypot(mX, mY); |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 285 | } |
| 286 | |
| 287 | /** |
| 288 | * @return Total field strength in nanoteslas. |
| 289 | */ |
| 290 | public float getFieldStrength() { |
| 291 | return (float) Math.sqrt(mX * mX + mY * mY + mZ * mZ); |
| 292 | } |
| 293 | |
| 294 | /** |
| 295 | * @param gdLatitudeDeg |
| 296 | * Latitude in WGS84 geodetic coordinates. |
| 297 | * @param gdLongitudeDeg |
| 298 | * Longitude in WGS84 geodetic coordinates. |
| 299 | * @param altitudeMeters |
| 300 | * Altitude above sea level in WGS84 geodetic coordinates. |
| 301 | * @return Geocentric latitude (i.e. angle between closest point on the |
| 302 | * equator and this point, at the center of the earth. |
| 303 | */ |
| 304 | private void computeGeocentricCoordinates(float gdLatitudeDeg, |
| 305 | float gdLongitudeDeg, |
| 306 | float altitudeMeters) { |
| 307 | float altitudeKm = altitudeMeters / 1000.0f; |
| 308 | float a2 = EARTH_SEMI_MAJOR_AXIS_KM * EARTH_SEMI_MAJOR_AXIS_KM; |
| 309 | float b2 = EARTH_SEMI_MINOR_AXIS_KM * EARTH_SEMI_MINOR_AXIS_KM; |
| 310 | double gdLatRad = Math.toRadians(gdLatitudeDeg); |
| 311 | float clat = (float) Math.cos(gdLatRad); |
| 312 | float slat = (float) Math.sin(gdLatRad); |
| 313 | float tlat = slat / clat; |
| 314 | float latRad = |
| 315 | (float) Math.sqrt(a2 * clat * clat + b2 * slat * slat); |
| 316 | |
| 317 | mGcLatitudeRad = (float) Math.atan(tlat * (latRad * altitudeKm + b2) |
| 318 | / (latRad * altitudeKm + a2)); |
| 319 | |
| 320 | mGcLongitudeRad = (float) Math.toRadians(gdLongitudeDeg); |
| 321 | |
| 322 | float radSq = altitudeKm * altitudeKm |
| 323 | + 2 * altitudeKm * (float) Math.sqrt(a2 * clat * clat + |
| 324 | b2 * slat * slat) |
| 325 | + (a2 * a2 * clat * clat + b2 * b2 * slat * slat) |
| 326 | / (a2 * clat * clat + b2 * slat * slat); |
| 327 | mGcRadiusKm = (float) Math.sqrt(radSq); |
| 328 | } |
| 329 | |
| 330 | |
| 331 | /** |
| 332 | * Utility class to compute a table of Gauss-normalized associated Legendre |
| 333 | * functions P_n^m(cos(theta)) |
| 334 | */ |
| 335 | static private class LegendreTable { |
| 336 | // These are the Gauss-normalized associated Legendre functions -- that |
| 337 | // is, they are normal Legendre functions multiplied by |
| 338 | // (n-m)!/(2n-1)!! (where (2n-1)!! = 1*3*5*...*2n-1) |
| 339 | public final float[][] mP; |
| 340 | |
| 341 | // Derivative of mP, with respect to theta. |
| 342 | public final float[][] mPDeriv; |
| 343 | |
| 344 | /** |
| 345 | * @param maxN |
| 346 | * The maximum n- and m-values to support |
| 347 | * @param thetaRad |
| 348 | * Returned functions will be Gauss-normalized |
| 349 | * P_n^m(cos(thetaRad)), with thetaRad in radians. |
| 350 | */ |
| 351 | public LegendreTable(int maxN, float thetaRad) { |
| 352 | // Compute the table of Gauss-normalized associated Legendre |
| 353 | // functions using standard recursion relations. Also compute the |
| 354 | // table of derivatives using the derivative of the recursion |
| 355 | // relations. |
| 356 | float cos = (float) Math.cos(thetaRad); |
| 357 | float sin = (float) Math.sin(thetaRad); |
| 358 | |
| 359 | mP = new float[maxN + 1][]; |
| 360 | mPDeriv = new float[maxN + 1][]; |
| 361 | mP[0] = new float[] { 1.0f }; |
| 362 | mPDeriv[0] = new float[] { 0.0f }; |
| 363 | for (int n = 1; n <= maxN; n++) { |
John Spurlock | 8a985d2 | 2014-02-25 09:40:05 -0500 | [diff] [blame] | 364 | mP[n] = new float[n + 1]; |
The Android Open Source Project | 9066cfe | 2009-03-03 19:31:44 -0800 | [diff] [blame] | 365 | mPDeriv[n] = new float[n + 1]; |
| 366 | for (int m = 0; m <= n; m++) { |
| 367 | if (n == m) { |
| 368 | mP[n][m] = sin * mP[n - 1][m - 1]; |
| 369 | mPDeriv[n][m] = cos * mP[n - 1][m - 1] |
| 370 | + sin * mPDeriv[n - 1][m - 1]; |
| 371 | } else if (n == 1 || m == n - 1) { |
| 372 | mP[n][m] = cos * mP[n - 1][m]; |
| 373 | mPDeriv[n][m] = -sin * mP[n - 1][m] |
| 374 | + cos * mPDeriv[n - 1][m]; |
| 375 | } else { |
| 376 | assert n > 1 && m < n - 1; |
| 377 | float k = ((n - 1) * (n - 1) - m * m) |
| 378 | / (float) ((2 * n - 1) * (2 * n - 3)); |
| 379 | mP[n][m] = cos * mP[n - 1][m] - k * mP[n - 2][m]; |
| 380 | mPDeriv[n][m] = -sin * mP[n - 1][m] |
| 381 | + cos * mPDeriv[n - 1][m] - k * mPDeriv[n - 2][m]; |
| 382 | } |
| 383 | } |
| 384 | } |
| 385 | } |
| 386 | } |
| 387 | |
| 388 | /** |
| 389 | * Compute the ration between the Gauss-normalized associated Legendre |
| 390 | * functions and the Schmidt quasi-normalized version. This is equivalent to |
| 391 | * sqrt((m==0?1:2)*(n-m)!/(n+m!))*(2n-1)!!/(n-m)! |
| 392 | */ |
| 393 | private static float[][] computeSchmidtQuasiNormFactors(int maxN) { |
| 394 | float[][] schmidtQuasiNorm = new float[maxN + 1][]; |
| 395 | schmidtQuasiNorm[0] = new float[] { 1.0f }; |
| 396 | for (int n = 1; n <= maxN; n++) { |
| 397 | schmidtQuasiNorm[n] = new float[n + 1]; |
| 398 | schmidtQuasiNorm[n][0] = |
| 399 | schmidtQuasiNorm[n - 1][0] * (2 * n - 1) / (float) n; |
| 400 | for (int m = 1; m <= n; m++) { |
| 401 | schmidtQuasiNorm[n][m] = schmidtQuasiNorm[n][m - 1] |
| 402 | * (float) Math.sqrt((n - m + 1) * (m == 1 ? 2 : 1) |
| 403 | / (float) (n + m)); |
| 404 | } |
| 405 | } |
| 406 | return schmidtQuasiNorm; |
| 407 | } |
Rodrigo Damazio Bovendorp | 9119caa | 2010-03-15 21:19:59 -0300 | [diff] [blame] | 408 | } |