geo_mag_declination.cpp

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/**
* @file geo_mag_declination.cpp
*
* Calculation / lookup table for Earth's magnetic field declination (deg), inclination (deg) and strength (mTesla).
* Data generated by https://www.ngdc.noaa.gov/geomag-web/#igrfgrid IGRF calculator on 22 Jan 2018
*
* XXX Lookup table currently too coarse in resolution (only full degrees)
* and lat/lon res - needs extension medium term.
*
*/

#include "geo_mag_declination.h"

#include <mathlib/mathlib.h>

#include <math.h>
#include <stdint.h>

using math::constrain;

/** set this always to the sampling in degrees for the table below */
static constexpr float SAMPLING_RES = 10.0f;
static constexpr float SAMPLING_MIN_LAT = -60.0f;
static constexpr float SAMPLING_MAX_LAT = 60.0f;
static constexpr float SAMPLING_MIN_LON = -180.0f;
static constexpr float SAMPLING_MAX_LON = 180.0f;

// declination data in degrees
static constexpr const int8_t declination_table[13][37] = \
{
    { 47,46,45,43,42,41,39,37,33,29,23,16,10,4,-1,-6,-10,-15,-20,-27,-34,-42,-49,-56,-62,-67,-72,-74,-75,-73,-61,-22,26,42,47,48,47 },
    { 31,31,31,30,30,30,30,29,27,24,18,11,3,-4,-9,-13,-15,-18,-21,-27,-33,-40,-47,-52,-56,-57,-56,-52,-44,-30,-14,2,14,22,27,30,31 },
    { 22,23,23,23,22,22,22,23,22,19,13,5,-4,-12,-17,-20,-22,-22,-23,-25,-30,-36,-41,-45,-46,-44,-39,-31,-21,-11,-3,4,10,15,19,21,22 },
    { 17,17,17,18,17,17,17,17,16,13,8,-1,-10,-18,-22,-25,-26,-25,-22,-20,-21,-25,-29,-32,-31,-28,-23,-16,-9,-3,0,4,7,11,14,16,17 },
    { 13,13,14,14,14,13,13,12,11,9,3,-5,-14,-20,-24,-25,-24,-21,-17,-12,-9,-11,-14,-17,-18,-16,-12,-8,-3,-0,1,3,6,8,11,12,13 },
    { 11,11,11,11,11,10,10,10,9,6,-0,-8,-15,-21,-23,-22,-19,-15,-10,-5,-2,-2,-4,-7,-9,-8,-7,-4,-1,1,1,2,4,7,9,10,11 },
    { 10,9,9,9,9,9,9,8,7,3,-3,-10,-16,-20,-20,-18,-14,-9,-5,-2,1,2,0,-2,-4,-4,-3,-2,-0,0,0,1,3,5,7,9,10 },
    { 9,9,9,9,9,9,9,8,6,1,-4,-11,-16,-18,-17,-14,-10,-5,-2,-0,2,3,2,0,-1,-2,-2,-1,-0,-1,-1,-1,1,3,6,8,9 },
    { 8,9,9,10,10,10,10,8,5,0,-6,-12,-15,-16,-15,-11,-7,-4,-1,1,3,4,3,2,1,0,-0,-0,-1,-2,-3,-4,-2,0,3,6,8 },
    { 7,9,10,11,12,12,12,9,5,-1,-7,-13,-15,-15,-13,-10,-6,-3,0,2,3,4,4,4,3,2,1,0,-1,-3,-5,-6,-6,-3,0,4,7 },
    { 5,8,11,13,14,15,14,11,5,-2,-9,-15,-17,-16,-13,-10,-6,-3,0,3,4,5,6,6,6,5,4,2,-1,-5,-8,-9,-9,-6,-3,1,5 },
    { 3,8,11,15,17,17,16,12,5,-4,-12,-18,-19,-18,-16,-12,-8,-4,-0,3,5,7,9,10,10,9,7,4,-1,-6,-10,-12,-12,-9,-5,-1,3 },
    { 3,8,12,16,19,20,18,13,4,-8,-18,-24,-25,-23,-20,-16,-11,-6,-1,3,7,11,14,16,17,17,14,8,-0,-8,-13,-15,-14,-11,-7,-2,3 },
};

// inclination data in degrees
static constexpr const int8_t inclination_table[13][37] = \
{
    { -78,-76,-74,-72,-70,-68,-65,-63,-60,-57,-55,-54,-54,-55,-56,-57,-58,-59,-59,-59,-59,-60,-61,-63,-66,-69,-73,-76,-79,-83,-86,-87,-86,-84,-82,-80,-78 },
    { -72,-70,-68,-66,-64,-62,-60,-57,-54,-51,-49,-48,-49,-51,-55,-58,-60,-61,-61,-61,-60,-60,-61,-63,-66,-69,-72,-76,-78,-80,-81,-80,-79,-77,-76,-74,-72 },
    { -64,-62,-60,-59,-57,-55,-53,-50,-47,-44,-41,-41,-43,-47,-53,-58,-62,-65,-66,-65,-63,-62,-61,-63,-65,-68,-71,-73,-74,-74,-73,-72,-71,-70,-68,-66,-64 },
    { -55,-53,-51,-49,-46,-44,-42,-40,-37,-33,-30,-30,-34,-41,-48,-55,-60,-65,-67,-68,-66,-63,-61,-61,-62,-64,-65,-66,-66,-65,-64,-63,-62,-61,-59,-57,-55 },
    { -42,-40,-37,-35,-33,-30,-28,-25,-22,-18,-15,-16,-22,-31,-40,-48,-55,-59,-62,-63,-61,-58,-55,-53,-53,-54,-55,-55,-54,-53,-51,-51,-50,-49,-47,-45,-42 },
    { -25,-22,-20,-17,-15,-12,-10,-7,-3,1,3,2,-5,-16,-27,-37,-44,-48,-50,-50,-48,-44,-41,-38,-38,-38,-39,-39,-38,-37,-36,-35,-35,-34,-31,-28,-25 },
    { -5,-2,1,3,5,8,10,13,16,20,21,19,12,2,-10,-20,-27,-30,-30,-29,-27,-23,-19,-17,-17,-17,-18,-18,-17,-16,-16,-16,-16,-15,-12,-9,-5 },
    { 15,18,21,22,24,26,29,31,34,36,37,34,28,20,10,2,-3,-5,-5,-4,-2,2,5,7,8,7,7,6,7,7,7,6,5,6,8,11,15 },
    { 31,34,36,38,39,41,43,46,48,49,49,46,42,36,29,24,20,19,20,21,23,25,28,30,30,30,29,29,29,29,28,27,25,25,26,28,31 },
    { 43,45,47,49,51,53,55,57,58,59,59,56,53,49,45,42,40,40,40,41,43,44,46,47,47,47,47,47,47,47,46,44,42,41,40,42,43 },
    { 53,54,56,57,59,61,64,66,67,68,67,65,62,60,57,55,55,54,55,56,57,58,59,59,60,60,60,60,60,60,59,57,55,53,52,52,53 },
    { 62,63,64,65,67,69,71,73,75,75,74,73,70,68,67,66,65,65,65,66,66,67,68,68,69,70,70,71,71,70,69,67,65,63,62,62,62 },
    { 71,71,72,73,75,77,78,80,81,81,80,79,77,76,74,73,73,73,73,73,73,74,74,75,76,77,78,78,78,78,77,75,73,72,71,71,71 },
};

// strength data in micro-Tesla or centi-Gauss
static constexpr const int8_t strength_table[13][37] = \
{
    { 62,60,58,56,54,52,49,46,43,41,38,36,34,32,31,31,30,30,30,31,33,35,38,42,46,51,55,59,62,64,66,67,67,66,65,64,62 },
    { 59,56,54,52,50,47,44,41,38,35,32,29,28,27,26,26,26,25,25,26,28,30,34,39,44,49,54,58,61,64,65,66,65,64,63,61,59 },
    { 54,52,49,47,45,42,40,37,34,30,27,25,24,24,24,24,24,24,24,24,25,28,32,37,42,48,52,56,59,61,62,62,62,60,59,56,54 },
    { 49,47,44,42,40,37,35,33,30,28,25,23,22,23,23,24,25,25,26,26,26,28,31,36,41,46,51,54,56,57,57,57,56,55,53,51,49 },
    { 43,41,39,37,35,33,32,30,28,26,25,23,23,23,24,25,26,28,29,29,29,30,32,36,40,44,48,51,52,52,51,51,50,49,47,45,43 },
    { 38,36,35,33,32,31,30,29,28,27,26,25,24,24,25,26,28,30,31,32,32,32,33,35,38,42,44,46,47,46,45,45,44,43,41,40,38 },
    { 34,33,32,32,31,31,31,30,30,30,29,28,27,27,27,28,29,31,32,33,33,33,34,35,37,39,41,42,43,42,41,40,39,38,36,35,34 },
    { 33,33,32,32,33,33,34,34,35,35,34,33,32,31,30,30,31,32,33,34,35,35,36,37,38,40,41,42,42,41,40,39,37,36,34,33,33 },
    { 34,34,34,35,36,37,39,40,41,41,40,39,37,35,35,34,35,35,36,37,38,39,40,41,42,43,44,45,45,45,43,41,39,37,35,34,34 },
    { 37,37,38,39,41,42,44,46,47,47,46,45,43,41,40,39,39,40,41,41,42,43,45,46,47,48,49,50,50,50,48,46,43,41,39,38,37 },
    { 42,42,43,44,46,48,50,52,53,53,52,51,49,47,45,45,44,44,45,46,46,47,48,50,51,53,54,55,56,55,54,52,49,46,44,43,42 },
    { 48,48,49,50,52,53,55,56,57,57,56,55,53,51,50,49,48,48,48,49,49,50,51,53,55,56,58,59,60,60,58,56,54,52,50,49,48 },
    { 54,54,54,55,56,57,58,58,59,58,58,57,56,54,53,52,51,51,51,51,52,53,54,55,57,58,60,61,62,61,61,59,58,56,55,54,54 },
};

static unsigned
get_lookup_table_index(float *val, float min, float max)
{
    /* for the rare case of hitting the bounds exactly
     * the rounding logic wouldn't fit, so enforce it.
     */

    /* limit to table bounds - required for maxima even when table spans full globe range */
    /* limit to (table bounds - 1) because bilinear interpolation requires checking (index + 1) */
    *val = constrain(*val, min, max - SAMPLING_RES);

    return static_cast<unsigned>((-(min) + *val) / SAMPLING_RES);
}

static float
get_table_data(float lat, float lon, const int8_t table[13][37])
{
    /*
     * If the values exceed valid ranges, return zero as default
     * as we have no way of knowing what the closest real value
     * would be.
     */
    if (lat < -90.0f || lat > 90.0f ||
        lon < -180.0f || lon > 180.0f) {
        return 0.0f;
    }

    /* round down to nearest sampling resolution */
    float min_lat = floorf(lat / SAMPLING_RES) * SAMPLING_RES;
    float min_lon = floorf(lon / SAMPLING_RES) * SAMPLING_RES;

    /* find index of nearest low sampling point */
    unsigned min_lat_index = get_lookup_table_index(&min_lat, SAMPLING_MIN_LAT, SAMPLING_MAX_LAT);
    unsigned min_lon_index = get_lookup_table_index(&min_lon, SAMPLING_MIN_LON, SAMPLING_MAX_LON);

    const float data_sw = table[min_lat_index][min_lon_index];
    const float data_se = table[min_lat_index][min_lon_index + 1];
    const float data_ne = table[min_lat_index + 1][min_lon_index + 1];
    const float data_nw = table[min_lat_index + 1][min_lon_index];

    /* perform bilinear interpolation on the four grid corners */
    const float lat_scale = constrain((lat - min_lat) / SAMPLING_RES, 0.0f, 1.0f);
    const float lon_scale = constrain((lon - min_lon) / SAMPLING_RES, 0.0f, 1.0f);

    const float data_min = lon_scale * (data_se - data_sw) + data_sw;
    const float data_max = lon_scale * (data_ne - data_nw) + data_nw;

    return lat_scale * (data_max - data_min) + data_min;
}

float get_mag_declination(float lat, float lon)
{
    return get_table_data(lat, lon, declination_table);
}

float get_mag_inclination(float lat, float lon)
{
    return get_table_data(lat, lon, inclination_table);
}

float get_mag_strength(float lat, float lon)
{
    return get_table_data(lat, lon, strength_table);
}