mirror of
https://bitbucket.org/librepilot/librepilot.git
synced 2024-12-05 13:24:11 +01:00
511 lines
15 KiB
C
511 lines
15 KiB
C
/**
|
|
******************************************************************************
|
|
*
|
|
* @file CoordinateConversions.c
|
|
* @author The OpenPilot Team, http://www.openpilot.org Copyright (C) 2010.
|
|
* @brief General conversions with different coordinate systems.
|
|
* - all angles in deg
|
|
* - distances in meters
|
|
* - altitude above WGS-84 elipsoid
|
|
*
|
|
* @see The GNU Public License (GPL) Version 3
|
|
*
|
|
*****************************************************************************/
|
|
/*
|
|
* This program is free software; you can redistribute it and/or modify
|
|
* it under the terms of the GNU General Public License as published by
|
|
* the Free Software Foundation; either version 3 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* This program is distributed in the hope that it will be useful, but
|
|
* WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
|
|
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
|
|
* for more details.
|
|
*
|
|
* You should have received a copy of the GNU General Public License along
|
|
* with this program; if not, write to the Free Software Foundation, Inc.,
|
|
* 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
|
|
*/
|
|
|
|
#include <stdint.h>
|
|
#include <pios_math.h>
|
|
#include "inc/CoordinateConversions.h"
|
|
|
|
#define MIN_ALLOWABLE_MAGNITUDE 1e-30f
|
|
|
|
// Equatorial Radius
|
|
#define equatorial_radius 6378137.0d
|
|
|
|
// Eccentricity
|
|
#define eccentricity 8.1819190842622e-2d
|
|
#define equatorial_radius_sq (equatorial_radius * equatorial_radius)
|
|
#define eccentricity_sq (eccentricity * eccentricity)
|
|
|
|
// ****** convert Lat,Lon,Alt to ECEF ************
|
|
void LLA2ECEF(const int32_t LLAi[3], float ECEF[3])
|
|
{
|
|
double sinLat, sinLon, cosLat, cosLon;
|
|
double N;
|
|
double LLA[3] = {
|
|
((double)LLAi[0]) * 1e-7d,
|
|
((double)LLAi[1]) * 1e-7d,
|
|
((double)LLAi[2]) * 1e-4d
|
|
};
|
|
|
|
sinLat = sin(DEG2RAD_D(LLA[0]));
|
|
sinLon = sin(DEG2RAD_D(LLA[1]));
|
|
cosLat = cos(DEG2RAD_D(LLA[0]));
|
|
cosLon = cos(DEG2RAD_D(LLA[1]));
|
|
|
|
N = equatorial_radius / sqrt(1.0d - eccentricity_sq * sinLat * sinLat); // prime vertical radius of curvature
|
|
|
|
ECEF[0] = (float)((N + LLA[2]) * cosLat * cosLon);
|
|
ECEF[1] = (float)((N + LLA[2]) * cosLat * sinLon);
|
|
ECEF[2] = (float)(((1.0d - eccentricity_sq) * N + LLA[2]) * sinLat);
|
|
}
|
|
|
|
// ****** convert ECEF to Lat,Lon,Alt (ITERATIVE!) *********
|
|
void ECEF2LLA(const float ECEF[3], int32_t LLA[3])
|
|
{
|
|
/* b = math.sqrt( asq * (1-esq) )
|
|
bsq = b*b
|
|
|
|
ep = math.sqrt((asq - bsq)/bsq)
|
|
p = math.sqrt( math.pow(x,2) + math.pow(y,2) )
|
|
th = math.atan2(a*z, b*p)
|
|
|
|
lon = math.atan2(y,x)
|
|
lat = math.atan2( (z + ep*ep *b * math.pow(math.sin(th),3) ), (p - esq*a*math.pow(math.cos(th),3)) )
|
|
N = a/( math.sqrt(1-esq*math.pow(math.sin(lat),2)) )
|
|
alt = p / math.cos(lat) - N*/
|
|
|
|
const double x = ECEF[0], y = ECEF[1], z = ECEF[2];
|
|
|
|
const double b = sqrt(equatorial_radius_sq * (1 - eccentricity_sq));
|
|
const double bsq = b * b;
|
|
const double ep = sqrt((equatorial_radius_sq - bsq) / bsq);
|
|
|
|
const double p = sqrt(x * x + y * y);
|
|
const double th = atan2(equatorial_radius * z, b * p);
|
|
|
|
double lon = atan2(y, x);
|
|
|
|
const double lat = atan2(
|
|
(z + ep * ep * b * pow(sin(th), 3)),
|
|
(p - eccentricity_sq * equatorial_radius * pow(cos(th), 3))
|
|
);
|
|
const double N = equatorial_radius / (sqrt(1 - eccentricity_sq * pow(sin(lat), 2)));
|
|
const double alt = p / cos(lat) - N;
|
|
|
|
LLA[0] = (int32_t)(RAD2DEG_D(lat) * 1e7d);
|
|
LLA[1] = (int32_t)(RAD2DEG_D(lon) * 1e7d) % ((int32_t)(180 * 1e7d));
|
|
LLA[2] = (int32_t)(alt * 1e4d);
|
|
}
|
|
|
|
// ****** find ECEF to NED rotation matrix ********
|
|
void RneFromLLA(const int32_t LLAi[3], float Rne[3][3])
|
|
{
|
|
float sinLat, sinLon, cosLat, cosLon;
|
|
|
|
sinLat = sinf(DEG2RAD((float)LLAi[0] * 1e-7f));
|
|
sinLon = sinf(DEG2RAD((float)LLAi[1] * 1e-7f));
|
|
cosLat = cosf(DEG2RAD((float)LLAi[0] * 1e-7f));
|
|
cosLon = cosf(DEG2RAD((float)LLAi[1] * 1e-7f));
|
|
|
|
Rne[0][0] = -sinLat * cosLon;
|
|
Rne[0][1] = -sinLat * sinLon;
|
|
Rne[0][2] = cosLat;
|
|
Rne[1][0] = -sinLon;
|
|
Rne[1][1] = cosLon;
|
|
Rne[1][2] = 0;
|
|
Rne[2][0] = -cosLat * cosLon;
|
|
Rne[2][1] = -cosLat * sinLon;
|
|
Rne[2][2] = -sinLat;
|
|
}
|
|
|
|
// ****** find roll, pitch, yaw from quaternion ********
|
|
void Quaternion2RPY(const float q[4], float rpy[3])
|
|
{
|
|
float R13, R11, R12, R23, R33;
|
|
float q0s = q[0] * q[0];
|
|
float q1s = q[1] * q[1];
|
|
float q2s = q[2] * q[2];
|
|
float q3s = q[3] * q[3];
|
|
|
|
R13 = 2.0f * (q[1] * q[3] - q[0] * q[2]);
|
|
R11 = q0s + q1s - q2s - q3s;
|
|
R12 = 2.0f * (q[1] * q[2] + q[0] * q[3]);
|
|
R23 = 2.0f * (q[2] * q[3] + q[0] * q[1]);
|
|
R33 = q0s - q1s - q2s + q3s;
|
|
|
|
rpy[1] = RAD2DEG(asinf(-R13)); // pitch always between -pi/2 to pi/2
|
|
rpy[2] = RAD2DEG(atan2f(R12, R11));
|
|
rpy[0] = RAD2DEG(atan2f(R23, R33));
|
|
|
|
// TODO: consider the cases where |R13| ~= 1, |pitch| ~= pi/2
|
|
}
|
|
|
|
// ****** find quaternion from roll, pitch, yaw ********
|
|
void RPY2Quaternion(const float rpy[3], float q[4])
|
|
{
|
|
float phi, theta, psi;
|
|
float cphi, sphi, ctheta, stheta, cpsi, spsi;
|
|
|
|
phi = DEG2RAD(rpy[0] / 2);
|
|
theta = DEG2RAD(rpy[1] / 2);
|
|
psi = DEG2RAD(rpy[2] / 2);
|
|
cphi = cosf(phi);
|
|
sphi = sinf(phi);
|
|
ctheta = cosf(theta);
|
|
stheta = sinf(theta);
|
|
cpsi = cosf(psi);
|
|
spsi = sinf(psi);
|
|
|
|
q[0] = cphi * ctheta * cpsi + sphi * stheta * spsi;
|
|
q[1] = sphi * ctheta * cpsi - cphi * stheta * spsi;
|
|
q[2] = cphi * stheta * cpsi + sphi * ctheta * spsi;
|
|
q[3] = cphi * ctheta * spsi - sphi * stheta * cpsi;
|
|
|
|
if (q[0] < 0) { // q0 always positive for uniqueness
|
|
q[0] = -q[0];
|
|
q[1] = -q[1];
|
|
q[2] = -q[2];
|
|
q[3] = -q[3];
|
|
}
|
|
}
|
|
|
|
// ** Find Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
|
|
void Quaternion2R(float q[4], float Rbe[3][3])
|
|
{
|
|
const float q0s = q[0] * q[0], q1s = q[1] * q[1], q2s = q[2] * q[2], q3s = q[3] * q[3];
|
|
|
|
Rbe[0][0] = q0s + q1s - q2s - q3s;
|
|
Rbe[0][1] = 2 * (q[1] * q[2] + q[0] * q[3]);
|
|
Rbe[0][2] = 2 * (q[1] * q[3] - q[0] * q[2]);
|
|
Rbe[1][0] = 2 * (q[1] * q[2] - q[0] * q[3]);
|
|
Rbe[1][1] = q0s - q1s + q2s - q3s;
|
|
Rbe[1][2] = 2 * (q[2] * q[3] + q[0] * q[1]);
|
|
Rbe[2][0] = 2 * (q[1] * q[3] + q[0] * q[2]);
|
|
Rbe[2][1] = 2 * (q[2] * q[3] - q[0] * q[1]);
|
|
Rbe[2][2] = q0s - q1s - q2s + q3s;
|
|
}
|
|
|
|
|
|
// ** Find first row of Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
|
|
// ** This vector corresponds to the fuselage/roll vector xB **
|
|
void QuaternionC2xB(const float q0, const float q1, const float q2, const float q3, float x[3])
|
|
{
|
|
const float q0s = q0 * q0, q1s = q1 * q1, q2s = q2 * q2, q3s = q3 * q3;
|
|
|
|
x[0] = q0s + q1s - q2s - q3s;
|
|
x[1] = 2 * (q1 * q2 + q0 * q3);
|
|
x[2] = 2 * (q1 * q3 - q0 * q2);
|
|
}
|
|
|
|
|
|
void Quaternion2xB(const float q[4], float x[3])
|
|
{
|
|
QuaternionC2xB(q[0], q[1], q[2], q[3], x);
|
|
}
|
|
|
|
|
|
// ** Find second row of Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
|
|
// ** This vector corresponds to the spanwise/pitch vector yB **
|
|
void QuaternionC2yB(const float q0, const float q1, const float q2, const float q3, float y[3])
|
|
{
|
|
const float q0s = q0 * q0, q1s = q1 * q1, q2s = q2 * q2, q3s = q3 * q3;
|
|
|
|
y[0] = 2 * (q1 * q2 - q0 * q3);
|
|
y[1] = q0s - q1s + q2s - q3s;
|
|
y[2] = 2 * (q2 * q3 + q0 * q1);
|
|
}
|
|
|
|
|
|
void Quaternion2yB(const float q[4], float y[3])
|
|
{
|
|
QuaternionC2yB(q[0], q[1], q[2], q[3], y);
|
|
}
|
|
|
|
|
|
// ** Find third row of Rbe, that rotates a vector from earth fixed to body frame, from quaternion **
|
|
// ** This vector corresponds to the vertical/yaw vector zB **
|
|
void QuaternionC2zB(const float q0, const float q1, const float q2, const float q3, float z[3])
|
|
{
|
|
const float q0s = q0 * q0, q1s = q1 * q1, q2s = q2 * q2, q3s = q3 * q3;
|
|
|
|
z[0] = 2 * (q1 * q3 + q0 * q2);
|
|
z[1] = 2 * (q2 * q3 - q0 * q1);
|
|
z[2] = q0s - q1s - q2s + q3s;
|
|
}
|
|
|
|
|
|
void Quaternion2zB(const float q[4], float z[3])
|
|
{
|
|
QuaternionC2zB(q[0], q[1], q[2], q[3], z);
|
|
}
|
|
|
|
|
|
// ****** Express LLA in a local NED Base Frame ********
|
|
void LLA2Base(const int32_t LLAi[3], const float BaseECEF[3], float Rne[3][3], float NED[3])
|
|
{
|
|
float ECEF[3];
|
|
|
|
LLA2ECEF(LLAi, ECEF);
|
|
ECEF2Base(ECEF, BaseECEF, Rne, NED);
|
|
}
|
|
|
|
// ****** Express LLA in a local NED Base Frame ********
|
|
void Base2LLA(const float NED[3], const float BaseECEF[3], float Rne[3][3], int32_t LLAi[3])
|
|
{
|
|
float ECEF[3];
|
|
|
|
Base2ECEF(NED, BaseECEF, Rne, ECEF);
|
|
ECEF2LLA(ECEF, LLAi);
|
|
}
|
|
// ****** Express ECEF in a local NED Base Frame ********
|
|
void ECEF2Base(const float ECEF[3], const float BaseECEF[3], float Rne[3][3], float NED[3])
|
|
{
|
|
float diff[3];
|
|
|
|
diff[0] = (ECEF[0] - BaseECEF[0]);
|
|
diff[1] = (ECEF[1] - BaseECEF[1]);
|
|
diff[2] = (ECEF[2] - BaseECEF[2]);
|
|
|
|
NED[0] = Rne[0][0] * diff[0] + Rne[0][1] * diff[1] + Rne[0][2] * diff[2];
|
|
NED[1] = Rne[1][0] * diff[0] + Rne[1][1] * diff[1] + Rne[1][2] * diff[2];
|
|
NED[2] = Rne[2][0] * diff[0] + Rne[2][1] * diff[1] + Rne[2][2] * diff[2];
|
|
}
|
|
|
|
// ****** Express ECEF in a local NED Base Frame ********
|
|
void Base2ECEF(const float NED[3], const float BaseECEF[3], float Rne[3][3], float ECEF[3])
|
|
{
|
|
float diff[3];
|
|
|
|
diff[0] = Rne[0][0] * NED[0] + Rne[1][0] * NED[1] + Rne[2][0] * NED[2];
|
|
diff[1] = Rne[0][1] * NED[0] + Rne[1][1] * NED[1] + Rne[2][1] * NED[2];
|
|
diff[2] = Rne[0][2] * NED[0] + Rne[1][2] * NED[1] + Rne[2][2] * NED[2];
|
|
|
|
|
|
ECEF[0] = diff[0] + BaseECEF[0];
|
|
ECEF[1] = diff[1] + BaseECEF[1];
|
|
ECEF[2] = diff[2] + BaseECEF[2];
|
|
}
|
|
|
|
|
|
// ****** convert Rotation Matrix to Quaternion ********
|
|
// ****** if R converts from e to b, q is rotation from e to b ****
|
|
void R2Quaternion(float R[3][3], float q[4])
|
|
{
|
|
float m[4], mag;
|
|
uint8_t index, i;
|
|
|
|
m[0] = 1 + R[0][0] + R[1][1] + R[2][2];
|
|
m[1] = 1 + R[0][0] - R[1][1] - R[2][2];
|
|
m[2] = 1 - R[0][0] + R[1][1] - R[2][2];
|
|
m[3] = 1 - R[0][0] - R[1][1] + R[2][2];
|
|
|
|
// find maximum divisor
|
|
index = 0;
|
|
mag = m[0];
|
|
for (i = 1; i < 4; i++) {
|
|
if (m[i] > mag) {
|
|
mag = m[i];
|
|
index = i;
|
|
}
|
|
}
|
|
mag = 2 * sqrtf(mag);
|
|
|
|
if (index == 0) {
|
|
q[0] = mag / 4;
|
|
q[1] = (R[1][2] - R[2][1]) / mag;
|
|
q[2] = (R[2][0] - R[0][2]) / mag;
|
|
q[3] = (R[0][1] - R[1][0]) / mag;
|
|
} else if (index == 1) {
|
|
q[1] = mag / 4;
|
|
q[0] = (R[1][2] - R[2][1]) / mag;
|
|
q[2] = (R[0][1] + R[1][0]) / mag;
|
|
q[3] = (R[0][2] + R[2][0]) / mag;
|
|
} else if (index == 2) {
|
|
q[2] = mag / 4;
|
|
q[0] = (R[2][0] - R[0][2]) / mag;
|
|
q[1] = (R[0][1] + R[1][0]) / mag;
|
|
q[3] = (R[1][2] + R[2][1]) / mag;
|
|
} else {
|
|
q[3] = mag / 4;
|
|
q[0] = (R[0][1] - R[1][0]) / mag;
|
|
q[1] = (R[0][2] + R[2][0]) / mag;
|
|
q[2] = (R[1][2] + R[2][1]) / mag;
|
|
}
|
|
|
|
// q0 positive, i.e. angle between pi and -pi
|
|
if (q[0] < 0) {
|
|
q[0] = -q[0];
|
|
q[1] = -q[1];
|
|
q[2] = -q[2];
|
|
q[3] = -q[3];
|
|
}
|
|
}
|
|
|
|
// ****** Rotation Matrix from Two Vector Directions ********
|
|
// ****** given two vector directions (v1 and v2) known in two frames (b and e) find Rbe ***
|
|
// ****** solution is approximate if can't be exact ***
|
|
uint8_t RotFrom2Vectors(const float v1b[3], const float v1e[3], const float v2b[3], const float v2e[3], float Rbe[3][3])
|
|
{
|
|
float Rib[3][3], Rie[3][3];
|
|
float mag;
|
|
uint8_t i, j, k;
|
|
|
|
// identity rotation in case of error
|
|
for (i = 0; i < 3; i++) {
|
|
for (j = 0; j < 3; j++) {
|
|
Rbe[i][j] = 0;
|
|
}
|
|
Rbe[i][i] = 1;
|
|
}
|
|
|
|
// The first rows of rot matrices chosen in direction of v1
|
|
mag = VectorMagnitude(v1b);
|
|
if (fabsf(mag) < MIN_ALLOWABLE_MAGNITUDE) {
|
|
return -1;
|
|
}
|
|
for (i = 0; i < 3; i++) {
|
|
Rib[0][i] = v1b[i] / mag;
|
|
}
|
|
|
|
mag = VectorMagnitude(v1e);
|
|
if (fabsf(mag) < MIN_ALLOWABLE_MAGNITUDE) {
|
|
return -1;
|
|
}
|
|
for (i = 0; i < 3; i++) {
|
|
Rie[0][i] = v1e[i] / mag;
|
|
}
|
|
|
|
// The second rows of rot matrices chosen in direction of v1xv2
|
|
CrossProduct(v1b, v2b, &Rib[1][0]);
|
|
mag = VectorMagnitude(&Rib[1][0]);
|
|
if (fabsf(mag) < MIN_ALLOWABLE_MAGNITUDE) {
|
|
return -1;
|
|
}
|
|
for (i = 0; i < 3; i++) {
|
|
Rib[1][i] = Rib[1][i] / mag;
|
|
}
|
|
|
|
CrossProduct(v1e, v2e, &Rie[1][0]);
|
|
mag = VectorMagnitude(&Rie[1][0]);
|
|
if (fabsf(mag) < MIN_ALLOWABLE_MAGNITUDE) {
|
|
return -1;
|
|
}
|
|
for (i = 0; i < 3; i++) {
|
|
Rie[1][i] = Rie[1][i] / mag;
|
|
}
|
|
|
|
// The third rows of rot matrices are XxY (Row1xRow2)
|
|
CrossProduct(&Rib[0][0], &Rib[1][0], &Rib[2][0]);
|
|
CrossProduct(&Rie[0][0], &Rie[1][0], &Rie[2][0]);
|
|
|
|
// Rbe = Rbi*Rie = Rib'*Rie
|
|
for (i = 0; i < 3; i++) {
|
|
for (j = 0; j < 3; j++) {
|
|
Rbe[i][j] = 0;
|
|
for (k = 0; k < 3; k++) {
|
|
Rbe[i][j] += Rib[k][i] * Rie[k][j];
|
|
}
|
|
}
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
void Rv2Rot(float Rv[3], float R[3][3])
|
|
{
|
|
// Compute rotation matrix from a rotation vector
|
|
// To save .text space, uses Quaternion2R()
|
|
float q[4];
|
|
|
|
float angle = VectorMagnitude(Rv);
|
|
|
|
if (angle <= 0.00048828125f) {
|
|
// angle < sqrt(2*machine_epsilon(float)), so flush cos(x) to 1.0f
|
|
q[0] = 1.0f;
|
|
|
|
// and flush sin(x/2)/x to 0.5
|
|
q[1] = 0.5f * Rv[0];
|
|
q[2] = 0.5f * Rv[1];
|
|
q[3] = 0.5f * Rv[2];
|
|
// This prevents division by zero, while retaining full accuracy
|
|
} else {
|
|
q[0] = cosf(angle * 0.5f);
|
|
float scale = sinf(angle * 0.5f) / angle;
|
|
q[1] = scale * Rv[0];
|
|
q[2] = scale * Rv[1];
|
|
q[3] = scale * Rv[2];
|
|
}
|
|
|
|
Quaternion2R(q, R);
|
|
}
|
|
|
|
// ****** Vector Cross Product ********
|
|
void CrossProduct(const float v1[3], const float v2[3], float result[3])
|
|
{
|
|
result[0] = v1[1] * v2[2] - v2[1] * v1[2];
|
|
result[1] = v2[0] * v1[2] - v1[0] * v2[2];
|
|
result[2] = v1[0] * v2[1] - v2[0] * v1[1];
|
|
}
|
|
|
|
// ****** Vector Magnitude ********
|
|
float VectorMagnitude(const float v[3])
|
|
{
|
|
return sqrtf(v[0] * v[0] + v[1] * v[1] + v[2] * v[2]);
|
|
}
|
|
|
|
/**
|
|
* @brief Compute the inverse of a quaternion
|
|
* @param [in][out] q The matrix to invert
|
|
*/
|
|
void quat_inverse(float q[4])
|
|
{
|
|
q[1] = -q[1];
|
|
q[2] = -q[2];
|
|
q[3] = -q[3];
|
|
}
|
|
|
|
/**
|
|
* @brief Duplicate a quaternion
|
|
* @param[in] q quaternion in
|
|
* @param[out] qnew quaternion to copy to
|
|
*/
|
|
void quat_copy(const float q[4], float qnew[4])
|
|
{
|
|
qnew[0] = q[0];
|
|
qnew[1] = q[1];
|
|
qnew[2] = q[2];
|
|
qnew[3] = q[3];
|
|
}
|
|
|
|
/**
|
|
* @brief Multiply two quaternions into a third
|
|
* @param[in] q1 First quaternion
|
|
* @param[in] q2 Second quaternion
|
|
* @param[out] qout Output quaternion
|
|
*/
|
|
void quat_mult(const float q1[4], const float q2[4], float qout[4])
|
|
{
|
|
qout[0] = q1[0] * q2[0] - q1[1] * q2[1] - q1[2] * q2[2] - q1[3] * q2[3];
|
|
qout[1] = q1[0] * q2[1] + q1[1] * q2[0] + q1[2] * q2[3] - q1[3] * q2[2];
|
|
qout[2] = q1[0] * q2[2] - q1[1] * q2[3] + q1[2] * q2[0] + q1[3] * q2[1];
|
|
qout[3] = q1[0] * q2[3] + q1[1] * q2[2] - q1[2] * q2[1] + q1[3] * q2[0];
|
|
}
|
|
|
|
/**
|
|
* @brief Rotate a vector by a rotation matrix
|
|
* @param[in] R a three by three rotation matrix (first index is row)
|
|
* @param[in] vec the source vector
|
|
* @param[out] vec_out the output vector
|
|
*/
|
|
void rot_mult(float R[3][3], const float vec[3], float vec_out[3])
|
|
{
|
|
vec_out[0] = R[0][0] * vec[0] + R[0][1] * vec[1] + R[0][2] * vec[2];
|
|
vec_out[1] = R[1][0] * vec[0] + R[1][1] * vec[1] + R[1][2] * vec[2];
|
|
vec_out[2] = R[2][0] * vec[0] + R[2][1] * vec[1] + R[2][2] * vec[2];
|
|
}
|