ardupilot/libraries/AP_Math/AP_Math.h

// -*- tab-width: 4; Mode: C++; c-basic-offset: 4; indent-tabs-mode: nil -*-

#ifndef AP_MATH_H
#define AP_MATH_H

// Assorted useful math operations for ArduPilot(Mega)

#include <AP_Common/AP_Common.h>
#include <AP_Param/AP_Param.h>
#include <math.h>
#ifdef __AVR__
# include "AP_Math_AVR_Compat.h"
#endif
#include <stdint.h>
#include "rotations.h"
#include "vector2.h"
#include "vector3.h"
#include "matrix3.h"
#include "quaternion.h"
#include "polygon.h"
#include "edc.h"
#include "float.h"
#include <AP_Param/AP_Param.h>

#ifndef M_PI_F
 #define M_PI_F 3.141592653589793f
#endif
#ifndef M_2PI_F
 #define M_2PI_F (2*M_PI_F)
#endif
#ifndef PI
 # define PI M_PI_F
#endif
#ifndef M_PI_2
 # define M_PI_2 1.570796326794897f
#endif
//Single precision conversions
#define DEG_TO_RAD 0.017453292519943295769236907684886f
#define RAD_TO_DEG 57.295779513082320876798154814105f

//GPS Specific double precision conversions
//The precision here does matter when using the wsg* functions for converting
//between LLH and ECEF coordinates. Test code in examlpes/location/location.pde
#if HAL_CPU_CLASS >= HAL_CPU_CLASS_75
	#define DEG_TO_RAD_DOUBLE 0.0174532925199432954743716805978692718781530857086181640625  // equals to (M_PI / 180.0)
	#define RAD_TO_DEG_DOUBLE 57.29577951308232286464772187173366546630859375               // equals to (180.0 / M_PI)
#endif

#define RadiansToCentiDegrees(x) ((x) * 5729.5779513082320876798154814105f)

// acceleration due to gravity in m/s/s
#define GRAVITY_MSS 9.80665f

// radius of earth in meters
#define RADIUS_OF_EARTH 6378100

#define ROTATION_COMBINATION_SUPPORT 0

// convert a longitude or latitude point to meters or centimeteres.
// Note: this does not include the longitude scaling which is dependent upon location
#define LATLON_TO_M  0.01113195f
#define LATLON_TO_CM 1.113195f

// Semi-major axis of the Earth, in meters.
#define WGS84_A 6378137.0
//Inverse flattening of the Earth
#define WGS84_IF 298.257223563
// The flattening of the Earth
#define WGS84_F (1/WGS84_IF)
// Semi-minor axis of the Earth in meters
#define WGS84_B (WGS84_A*(1-WGS84_F))
// Eccentricity of the Earth
#define WGS84_E (sqrt(2*WGS84_F - WGS84_F*WGS84_F))

// define AP_Param types AP_Vector3f and Ap_Matrix3f
AP_PARAMDEFV(Matrix3f, Matrix3f, AP_PARAM_MATRIX3F);
AP_PARAMDEFV(Vector3f, Vector3f, AP_PARAM_VECTOR3F);

// are two floats equal
static inline bool is_equal(const float fVal1, const float fVal2) { return fabsf(fVal1 - fVal2) < FLT_EPSILON ? true : false; }

// is a float is zero
static inline bool is_zero(const float fVal1) { return fabsf(fVal1) < FLT_EPSILON ? true : false; }

// a varient of asin() that always gives a valid answer.
float           safe_asin(float v);

// a varient of sqrt() that always gives a valid answer.
float           safe_sqrt(float v);

#if ROTATION_COMBINATION_SUPPORT
// find a rotation that is the combination of two other
// rotations. This is used to allow us to add an overall board
// rotation to an existing rotation of a sensor such as the compass
enum Rotation           rotation_combination(enum Rotation r1, enum Rotation r2, bool *found = NULL);
#endif

// longitude_scale - returns the scaler to compensate for shrinking longitude as you move north or south from the equator
// Note: this does not include the scaling to convert longitude/latitude points to meters or centimeters
float                   longitude_scale(const struct Location &loc);

// return distance in meters between two locations
float                   get_distance(const struct Location &loc1, const struct Location &loc2);

// return distance in centimeters between two locations
uint32_t                get_distance_cm(const struct Location &loc1, const struct Location &loc2);

// return bearing in centi-degrees between two locations
int32_t                 get_bearing_cd(const struct Location &loc1, const struct Location &loc2);

// see if location is past a line perpendicular to
// the line between point1 and point2. If point1 is
// our previous waypoint and point2 is our target waypoint
// then this function returns true if we have flown past
// the target waypoint
bool        location_passed_point(const struct Location & location,
                                  const struct Location & point1,
                                  const struct Location & point2);

/*
  return the proportion we are along the path from point1 to
  point2. This will be less than >1 if we have passed point2
 */
float location_path_proportion(const struct Location &location,
                               const struct Location &point1,
                               const struct Location &point2);

//  extrapolate latitude/longitude given bearing and distance
void        location_update(struct Location &loc, float bearing, float distance);

// extrapolate latitude/longitude given distances north and east
void        location_offset(struct Location &loc, float ofs_north, float ofs_east);

/*
  return the distance in meters in North/East plane as a N/E vector
  from loc1 to loc2
 */
Vector2f location_diff(const struct Location &loc1, const struct Location &loc2);

/*
  wrap an angle in centi-degrees
 */
int32_t wrap_360_cd(int32_t error);
int32_t wrap_180_cd(int32_t error);
float wrap_360_cd_float(float angle);
float wrap_180_cd_float(float angle);

/*
  wrap an angle defined in radians to -PI ~ PI (equivalent to +- 180 degrees)
 */
float wrap_PI(float angle_in_radians);

/*
 * check if lat and lng match. Ignore altitude and options
 */
bool locations_are_same(const struct Location &loc1, const struct Location &loc2);

/*
  print a int32_t lat/long in decimal degrees
 */
void print_latlon(AP_HAL::BetterStream *s, int32_t lat_or_lon);

#if HAL_CPU_CLASS >= HAL_CPU_CLASS_75
// Converts from WGS84 geodetic coordinates (lat, lon, height)
// into WGS84 Earth Centered, Earth Fixed (ECEF) coordinates
// (X, Y, Z)
void wgsllh2ecef(const Vector3d &llh, Vector3d &ecef);

// Converts from WGS84 Earth Centered, Earth Fixed (ECEF) 
// coordinates (X, Y, Z), into WHS84 geodetic 
// coordinates (lat, lon, height)
void wgsecef2llh(const Vector3d &ecef, Vector3d &llh);
#endif

// constrain a value
// constrain a value
static inline float constrain_float(float amt, float low, float high)
{
	// the check for NaN as a float prevents propogation of
	// floating point errors through any function that uses
	// constrain_float(). The normal float semantics already handle -Inf
	// and +Inf
	if (isnan(amt)) {
		return (low+high)*0.5f;
	}
	return ((amt)<(low)?(low):((amt)>(high)?(high):(amt)));
}
// constrain a int16_t value
static inline int16_t constrain_int16(int16_t amt, int16_t low, int16_t high) {
	return ((amt)<(low)?(low):((amt)>(high)?(high):(amt)));
}

// constrain a int32_t value
static inline int32_t constrain_int32(int32_t amt, int32_t low, int32_t high) {
	return ((amt)<(low)?(low):((amt)>(high)?(high):(amt)));
}

//matrix algebra
bool inverse(float x[], float y[], uint16_t dim);

// degrees -> radians
static inline float radians(float deg) {
	return deg * DEG_TO_RAD;
}

// radians -> degrees
static inline float degrees(float rad) {
	return rad * RAD_TO_DEG;
}

// square
static inline float sq(float v) {
	return v*v;
}

// 2D vector length
static inline float pythagorous2(float a, float b) {
	return sqrtf(sq(a)+sq(b));
}

// 3D vector length
static inline float pythagorous3(float a, float b, float c) {
	return sqrtf(sq(a)+sq(b)+sq(c));
}

#ifdef radians
#error "Build is including Arduino base headers"
#endif

/* The following three functions used to be arduino core macros */
#define max(a,b) ((a)>(b)?(a):(b))
#define min(a,b) ((a)<(b)?(a):(b))

static inline float maxf(float a, float b)
{
    return (a>b?a:b);
}

static inline float minf(float a, float b)
{
    return (a<b?a:b);
}

#undef INLINE
#endif // AP_MATH_H