AHRS Library
Mahony.cpp@1:36bbe04e1f6f, 2018-10-26 (annotated)
- Committer:
- altb
- Date:
- Fri Oct 26 05:56:25 2018 +0000
- Revision:
- 1:36bbe04e1f6f
- Child:
- 3:6811c0ce95f6
Added Mahony Class
Who changed what in which revision?
User | Revision | Line number | New contents of line |
---|---|---|---|
altb | 1:36bbe04e1f6f | 1 | //============================================================================================= |
altb | 1:36bbe04e1f6f | 2 | // Mahony.c |
altb | 1:36bbe04e1f6f | 3 | //============================================================================================= |
altb | 1:36bbe04e1f6f | 4 | // |
altb | 1:36bbe04e1f6f | 5 | // Madgwick's implementation of Mayhony's AHRS algorithm. |
altb | 1:36bbe04e1f6f | 6 | // See: http://www.x-io.co.uk/open-source-imu-and-ahrs-algorithms/ |
altb | 1:36bbe04e1f6f | 7 | // |
altb | 1:36bbe04e1f6f | 8 | // From the x-io website "Open-source resources available on this website are |
altb | 1:36bbe04e1f6f | 9 | // provided under the GNU General Public Licence unless an alternative licence |
altb | 1:36bbe04e1f6f | 10 | // is provided in source." |
altb | 1:36bbe04e1f6f | 11 | // |
altb | 1:36bbe04e1f6f | 12 | // Date Author Notes |
altb | 1:36bbe04e1f6f | 13 | // 29/09/2011 SOH Madgwick Initial release |
altb | 1:36bbe04e1f6f | 14 | // 02/10/2011 SOH Madgwick Optimised for reduced CPU load |
altb | 1:36bbe04e1f6f | 15 | // |
altb | 1:36bbe04e1f6f | 16 | // Algorithm paper: |
altb | 1:36bbe04e1f6f | 17 | // http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=4608934&url=http%3A%2F%2Fieeexplore.ieee.org%2Fstamp%2Fstamp.jsp%3Ftp%3D%26arnumber%3D4608934 |
altb | 1:36bbe04e1f6f | 18 | // |
altb | 1:36bbe04e1f6f | 19 | //============================================================================================= |
altb | 1:36bbe04e1f6f | 20 | |
altb | 1:36bbe04e1f6f | 21 | //------------------------------------------------------------------------------------------- |
altb | 1:36bbe04e1f6f | 22 | // Header files |
altb | 1:36bbe04e1f6f | 23 | |
altb | 1:36bbe04e1f6f | 24 | #include "Mahony.h" |
altb | 1:36bbe04e1f6f | 25 | #include <math.h> |
altb | 1:36bbe04e1f6f | 26 | |
altb | 1:36bbe04e1f6f | 27 | //------------------------------------------------------------------------------------------- |
altb | 1:36bbe04e1f6f | 28 | // Definitions |
altb | 1:36bbe04e1f6f | 29 | |
altb | 1:36bbe04e1f6f | 30 | #define DEFAULT_SAMPLE_FREQ 100.0f // sample frequency in Hz |
altb | 1:36bbe04e1f6f | 31 | #define twoKpDef (2.0f * 0.5f) // 2 * proportional gain |
altb | 1:36bbe04e1f6f | 32 | #define twoKiDef (2.0f * 0.0f) // 2 * integral gain |
altb | 1:36bbe04e1f6f | 33 | |
altb | 1:36bbe04e1f6f | 34 | |
altb | 1:36bbe04e1f6f | 35 | //============================================================================================ |
altb | 1:36bbe04e1f6f | 36 | // Functions |
altb | 1:36bbe04e1f6f | 37 | |
altb | 1:36bbe04e1f6f | 38 | //------------------------------------------------------------------------------------------- |
altb | 1:36bbe04e1f6f | 39 | // AHRS algorithm update |
altb | 1:36bbe04e1f6f | 40 | |
altb | 1:36bbe04e1f6f | 41 | Mahony::Mahony() |
altb | 1:36bbe04e1f6f | 42 | { |
altb | 1:36bbe04e1f6f | 43 | twoKp = twoKpDef; // 2 * proportional gain (Kp) |
altb | 1:36bbe04e1f6f | 44 | twoKi = twoKiDef; // 2 * integral gain (Ki) |
altb | 1:36bbe04e1f6f | 45 | q0 = 1.0f; |
altb | 1:36bbe04e1f6f | 46 | q1 = 0.0f; |
altb | 1:36bbe04e1f6f | 47 | q2 = 0.0f; |
altb | 1:36bbe04e1f6f | 48 | q3 = 0.0f; |
altb | 1:36bbe04e1f6f | 49 | integralFBx = 0.0f; |
altb | 1:36bbe04e1f6f | 50 | integralFBy = 0.0f; |
altb | 1:36bbe04e1f6f | 51 | integralFBz = 0.0f; |
altb | 1:36bbe04e1f6f | 52 | anglesComputed = 0; |
altb | 1:36bbe04e1f6f | 53 | invSampleFreq = 1.0f / DEFAULT_SAMPLE_FREQ; |
altb | 1:36bbe04e1f6f | 54 | } |
altb | 1:36bbe04e1f6f | 55 | |
altb | 1:36bbe04e1f6f | 56 | void Mahony::update(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) |
altb | 1:36bbe04e1f6f | 57 | { |
altb | 1:36bbe04e1f6f | 58 | float recipNorm; |
altb | 1:36bbe04e1f6f | 59 | float q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3; |
altb | 1:36bbe04e1f6f | 60 | float hx, hy, bx, bz; |
altb | 1:36bbe04e1f6f | 61 | float halfvx, halfvy, halfvz, halfwx, halfwy, halfwz; |
altb | 1:36bbe04e1f6f | 62 | float halfex, halfey, halfez; |
altb | 1:36bbe04e1f6f | 63 | float qa, qb, qc; |
altb | 1:36bbe04e1f6f | 64 | |
altb | 1:36bbe04e1f6f | 65 | // Use IMU algorithm if magnetometer measurement invalid |
altb | 1:36bbe04e1f6f | 66 | // (avoids NaN in magnetometer normalisation) |
altb | 1:36bbe04e1f6f | 67 | if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { |
altb | 1:36bbe04e1f6f | 68 | updateIMU(gx, gy, gz, ax, ay, az); |
altb | 1:36bbe04e1f6f | 69 | return; |
altb | 1:36bbe04e1f6f | 70 | } |
altb | 1:36bbe04e1f6f | 71 | |
altb | 1:36bbe04e1f6f | 72 | // Convert gyroscope degrees/sec to radians/sec |
altb | 1:36bbe04e1f6f | 73 | // gx *= 0.0174533f; |
altb | 1:36bbe04e1f6f | 74 | // gy *= 0.0174533f; |
altb | 1:36bbe04e1f6f | 75 | // gz *= 0.0174533f; |
altb | 1:36bbe04e1f6f | 76 | |
altb | 1:36bbe04e1f6f | 77 | // Compute feedback only if accelerometer measurement valid |
altb | 1:36bbe04e1f6f | 78 | // (avoids NaN in accelerometer normalisation) |
altb | 1:36bbe04e1f6f | 79 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { |
altb | 1:36bbe04e1f6f | 80 | |
altb | 1:36bbe04e1f6f | 81 | // Normalise accelerometer measurement |
altb | 1:36bbe04e1f6f | 82 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); |
altb | 1:36bbe04e1f6f | 83 | ax *= recipNorm; |
altb | 1:36bbe04e1f6f | 84 | ay *= recipNorm; |
altb | 1:36bbe04e1f6f | 85 | az *= recipNorm; |
altb | 1:36bbe04e1f6f | 86 | |
altb | 1:36bbe04e1f6f | 87 | // Normalise magnetometer measurement |
altb | 1:36bbe04e1f6f | 88 | recipNorm = invSqrt(mx * mx + my * my + mz * mz); |
altb | 1:36bbe04e1f6f | 89 | mx *= recipNorm; |
altb | 1:36bbe04e1f6f | 90 | my *= recipNorm; |
altb | 1:36bbe04e1f6f | 91 | mz *= recipNorm; |
altb | 1:36bbe04e1f6f | 92 | |
altb | 1:36bbe04e1f6f | 93 | // Auxiliary variables to avoid repeated arithmetic |
altb | 1:36bbe04e1f6f | 94 | q0q0 = q0 * q0; |
altb | 1:36bbe04e1f6f | 95 | q0q1 = q0 * q1; |
altb | 1:36bbe04e1f6f | 96 | q0q2 = q0 * q2; |
altb | 1:36bbe04e1f6f | 97 | q0q3 = q0 * q3; |
altb | 1:36bbe04e1f6f | 98 | q1q1 = q1 * q1; |
altb | 1:36bbe04e1f6f | 99 | q1q2 = q1 * q2; |
altb | 1:36bbe04e1f6f | 100 | q1q3 = q1 * q3; |
altb | 1:36bbe04e1f6f | 101 | q2q2 = q2 * q2; |
altb | 1:36bbe04e1f6f | 102 | q2q3 = q2 * q3; |
altb | 1:36bbe04e1f6f | 103 | q3q3 = q3 * q3; |
altb | 1:36bbe04e1f6f | 104 | |
altb | 1:36bbe04e1f6f | 105 | // Reference direction of Earth's magnetic field |
altb | 1:36bbe04e1f6f | 106 | hx = 2.0f * (mx * (0.5f - q2q2 - q3q3) + my * (q1q2 - q0q3) + mz * (q1q3 + q0q2)); |
altb | 1:36bbe04e1f6f | 107 | hy = 2.0f * (mx * (q1q2 + q0q3) + my * (0.5f - q1q1 - q3q3) + mz * (q2q3 - q0q1)); |
altb | 1:36bbe04e1f6f | 108 | bx = sqrtf(hx * hx + hy * hy); |
altb | 1:36bbe04e1f6f | 109 | bz = 2.0f * (mx * (q1q3 - q0q2) + my * (q2q3 + q0q1) + mz * (0.5f - q1q1 - q2q2)); |
altb | 1:36bbe04e1f6f | 110 | |
altb | 1:36bbe04e1f6f | 111 | // Estimated direction of gravity and magnetic field |
altb | 1:36bbe04e1f6f | 112 | halfvx = q1q3 - q0q2; |
altb | 1:36bbe04e1f6f | 113 | halfvy = q0q1 + q2q3; |
altb | 1:36bbe04e1f6f | 114 | halfvz = q0q0 - 0.5f + q3q3; |
altb | 1:36bbe04e1f6f | 115 | halfwx = bx * (0.5f - q2q2 - q3q3) + bz * (q1q3 - q0q2); |
altb | 1:36bbe04e1f6f | 116 | halfwy = bx * (q1q2 - q0q3) + bz * (q0q1 + q2q3); |
altb | 1:36bbe04e1f6f | 117 | halfwz = bx * (q0q2 + q1q3) + bz * (0.5f - q1q1 - q2q2); |
altb | 1:36bbe04e1f6f | 118 | |
altb | 1:36bbe04e1f6f | 119 | // Error is sum of cross product between estimated direction |
altb | 1:36bbe04e1f6f | 120 | // and measured direction of field vectors |
altb | 1:36bbe04e1f6f | 121 | halfex = (ay * halfvz - az * halfvy) + (my * halfwz - mz * halfwy); |
altb | 1:36bbe04e1f6f | 122 | halfey = (az * halfvx - ax * halfvz) + (mz * halfwx - mx * halfwz); |
altb | 1:36bbe04e1f6f | 123 | halfez = (ax * halfvy - ay * halfvx) + (mx * halfwy - my * halfwx); |
altb | 1:36bbe04e1f6f | 124 | |
altb | 1:36bbe04e1f6f | 125 | // Compute and apply integral feedback if enabled |
altb | 1:36bbe04e1f6f | 126 | if(twoKi > 0.0f) { |
altb | 1:36bbe04e1f6f | 127 | // integral error scaled by Ki |
altb | 1:36bbe04e1f6f | 128 | integralFBx += twoKi * halfex * invSampleFreq; |
altb | 1:36bbe04e1f6f | 129 | integralFBy += twoKi * halfey * invSampleFreq; |
altb | 1:36bbe04e1f6f | 130 | integralFBz += twoKi * halfez * invSampleFreq; |
altb | 1:36bbe04e1f6f | 131 | gx += integralFBx; // apply integral feedback |
altb | 1:36bbe04e1f6f | 132 | gy += integralFBy; |
altb | 1:36bbe04e1f6f | 133 | gz += integralFBz; |
altb | 1:36bbe04e1f6f | 134 | } else { |
altb | 1:36bbe04e1f6f | 135 | integralFBx = 0.0f; // prevent integral windup |
altb | 1:36bbe04e1f6f | 136 | integralFBy = 0.0f; |
altb | 1:36bbe04e1f6f | 137 | integralFBz = 0.0f; |
altb | 1:36bbe04e1f6f | 138 | } |
altb | 1:36bbe04e1f6f | 139 | |
altb | 1:36bbe04e1f6f | 140 | // Apply proportional feedback |
altb | 1:36bbe04e1f6f | 141 | gx += twoKp * halfex; |
altb | 1:36bbe04e1f6f | 142 | gy += twoKp * halfey; |
altb | 1:36bbe04e1f6f | 143 | gz += twoKp * halfez; |
altb | 1:36bbe04e1f6f | 144 | } |
altb | 1:36bbe04e1f6f | 145 | |
altb | 1:36bbe04e1f6f | 146 | // Integrate rate of change of quaternion |
altb | 1:36bbe04e1f6f | 147 | gx *= (0.5f * invSampleFreq); // pre-multiply common factors |
altb | 1:36bbe04e1f6f | 148 | gy *= (0.5f * invSampleFreq); |
altb | 1:36bbe04e1f6f | 149 | gz *= (0.5f * invSampleFreq); |
altb | 1:36bbe04e1f6f | 150 | qa = q0; |
altb | 1:36bbe04e1f6f | 151 | qb = q1; |
altb | 1:36bbe04e1f6f | 152 | qc = q2; |
altb | 1:36bbe04e1f6f | 153 | q0 += (-qb * gx - qc * gy - q3 * gz); |
altb | 1:36bbe04e1f6f | 154 | q1 += (qa * gx + qc * gz - q3 * gy); |
altb | 1:36bbe04e1f6f | 155 | q2 += (qa * gy - qb * gz + q3 * gx); |
altb | 1:36bbe04e1f6f | 156 | q3 += (qa * gz + qb * gy - qc * gx); |
altb | 1:36bbe04e1f6f | 157 | |
altb | 1:36bbe04e1f6f | 158 | // Normalise quaternion |
altb | 1:36bbe04e1f6f | 159 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); |
altb | 1:36bbe04e1f6f | 160 | q0 *= recipNorm; |
altb | 1:36bbe04e1f6f | 161 | q1 *= recipNorm; |
altb | 1:36bbe04e1f6f | 162 | q2 *= recipNorm; |
altb | 1:36bbe04e1f6f | 163 | q3 *= recipNorm; |
altb | 1:36bbe04e1f6f | 164 | anglesComputed = 0; |
altb | 1:36bbe04e1f6f | 165 | } |
altb | 1:36bbe04e1f6f | 166 | |
altb | 1:36bbe04e1f6f | 167 | //------------------------------------------------------------------------------------------- |
altb | 1:36bbe04e1f6f | 168 | // IMU algorithm update |
altb | 1:36bbe04e1f6f | 169 | |
altb | 1:36bbe04e1f6f | 170 | void Mahony::updateIMU(float gx, float gy, float gz, float ax, float ay, float az) |
altb | 1:36bbe04e1f6f | 171 | { |
altb | 1:36bbe04e1f6f | 172 | float recipNorm; |
altb | 1:36bbe04e1f6f | 173 | float halfvx, halfvy, halfvz; |
altb | 1:36bbe04e1f6f | 174 | float halfex, halfey, halfez; |
altb | 1:36bbe04e1f6f | 175 | float qa, qb, qc; |
altb | 1:36bbe04e1f6f | 176 | |
altb | 1:36bbe04e1f6f | 177 | // Convert gyroscope degrees/sec to radians/sec |
altb | 1:36bbe04e1f6f | 178 | // gx *= 0.0174533f; |
altb | 1:36bbe04e1f6f | 179 | // gy *= 0.0174533f; |
altb | 1:36bbe04e1f6f | 180 | // gz *= 0.0174533f; |
altb | 1:36bbe04e1f6f | 181 | |
altb | 1:36bbe04e1f6f | 182 | // Compute feedback only if accelerometer measurement valid |
altb | 1:36bbe04e1f6f | 183 | // (avoids NaN in accelerometer normalisation) |
altb | 1:36bbe04e1f6f | 184 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { |
altb | 1:36bbe04e1f6f | 185 | |
altb | 1:36bbe04e1f6f | 186 | // Normalise accelerometer measurement |
altb | 1:36bbe04e1f6f | 187 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); |
altb | 1:36bbe04e1f6f | 188 | ax *= recipNorm; |
altb | 1:36bbe04e1f6f | 189 | ay *= recipNorm; |
altb | 1:36bbe04e1f6f | 190 | az *= recipNorm; |
altb | 1:36bbe04e1f6f | 191 | |
altb | 1:36bbe04e1f6f | 192 | // Estimated direction of gravity |
altb | 1:36bbe04e1f6f | 193 | halfvx = q1 * q3 - q0 * q2; |
altb | 1:36bbe04e1f6f | 194 | halfvy = q0 * q1 + q2 * q3; |
altb | 1:36bbe04e1f6f | 195 | halfvz = q0 * q0 - 0.5f + q3 * q3; |
altb | 1:36bbe04e1f6f | 196 | |
altb | 1:36bbe04e1f6f | 197 | // Error is sum of cross product between estimated |
altb | 1:36bbe04e1f6f | 198 | // and measured direction of gravity |
altb | 1:36bbe04e1f6f | 199 | halfex = (ay * halfvz - az * halfvy); |
altb | 1:36bbe04e1f6f | 200 | halfey = (az * halfvx - ax * halfvz); |
altb | 1:36bbe04e1f6f | 201 | halfez = (ax * halfvy - ay * halfvx); |
altb | 1:36bbe04e1f6f | 202 | |
altb | 1:36bbe04e1f6f | 203 | // Compute and apply integral feedback if enabled |
altb | 1:36bbe04e1f6f | 204 | if(twoKi > 0.0f) { |
altb | 1:36bbe04e1f6f | 205 | // integral error scaled by Ki |
altb | 1:36bbe04e1f6f | 206 | integralFBx += twoKi * halfex * invSampleFreq; |
altb | 1:36bbe04e1f6f | 207 | integralFBy += twoKi * halfey * invSampleFreq; |
altb | 1:36bbe04e1f6f | 208 | integralFBz += twoKi * halfez * invSampleFreq; |
altb | 1:36bbe04e1f6f | 209 | gx += integralFBx; // apply integral feedback |
altb | 1:36bbe04e1f6f | 210 | gy += integralFBy; |
altb | 1:36bbe04e1f6f | 211 | gz += integralFBz; |
altb | 1:36bbe04e1f6f | 212 | } else { |
altb | 1:36bbe04e1f6f | 213 | integralFBx = 0.0f; // prevent integral windup |
altb | 1:36bbe04e1f6f | 214 | integralFBy = 0.0f; |
altb | 1:36bbe04e1f6f | 215 | integralFBz = 0.0f; |
altb | 1:36bbe04e1f6f | 216 | } |
altb | 1:36bbe04e1f6f | 217 | |
altb | 1:36bbe04e1f6f | 218 | // Apply proportional feedback |
altb | 1:36bbe04e1f6f | 219 | gx += twoKp * halfex; |
altb | 1:36bbe04e1f6f | 220 | gy += twoKp * halfey; |
altb | 1:36bbe04e1f6f | 221 | gz += twoKp * halfez; |
altb | 1:36bbe04e1f6f | 222 | } |
altb | 1:36bbe04e1f6f | 223 | |
altb | 1:36bbe04e1f6f | 224 | // Integrate rate of change of quaternion |
altb | 1:36bbe04e1f6f | 225 | gx *= (0.5f * invSampleFreq); // pre-multiply common factors |
altb | 1:36bbe04e1f6f | 226 | gy *= (0.5f * invSampleFreq); |
altb | 1:36bbe04e1f6f | 227 | gz *= (0.5f * invSampleFreq); |
altb | 1:36bbe04e1f6f | 228 | qa = q0; |
altb | 1:36bbe04e1f6f | 229 | qb = q1; |
altb | 1:36bbe04e1f6f | 230 | qc = q2; |
altb | 1:36bbe04e1f6f | 231 | q0 += (-qb * gx - qc * gy - q3 * gz); |
altb | 1:36bbe04e1f6f | 232 | q1 += (qa * gx + qc * gz - q3 * gy); |
altb | 1:36bbe04e1f6f | 233 | q2 += (qa * gy - qb * gz + q3 * gx); |
altb | 1:36bbe04e1f6f | 234 | q3 += (qa * gz + qb * gy - qc * gx); |
altb | 1:36bbe04e1f6f | 235 | |
altb | 1:36bbe04e1f6f | 236 | // Normalise quaternion |
altb | 1:36bbe04e1f6f | 237 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); |
altb | 1:36bbe04e1f6f | 238 | q0 *= recipNorm; |
altb | 1:36bbe04e1f6f | 239 | q1 *= recipNorm; |
altb | 1:36bbe04e1f6f | 240 | q2 *= recipNorm; |
altb | 1:36bbe04e1f6f | 241 | q3 *= recipNorm; |
altb | 1:36bbe04e1f6f | 242 | anglesComputed = 0; |
altb | 1:36bbe04e1f6f | 243 | } |
altb | 1:36bbe04e1f6f | 244 | |
altb | 1:36bbe04e1f6f | 245 | //------------------------------------------------------------------------------------------- |
altb | 1:36bbe04e1f6f | 246 | // Fast inverse square-root |
altb | 1:36bbe04e1f6f | 247 | // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root |
altb | 1:36bbe04e1f6f | 248 | |
altb | 1:36bbe04e1f6f | 249 | float Mahony::invSqrt(float x) |
altb | 1:36bbe04e1f6f | 250 | { |
altb | 1:36bbe04e1f6f | 251 | float halfx = 0.5f * x; |
altb | 1:36bbe04e1f6f | 252 | float y = x; |
altb | 1:36bbe04e1f6f | 253 | long i = *(long*)&y; |
altb | 1:36bbe04e1f6f | 254 | i = 0x5f3759df - (i>>1); |
altb | 1:36bbe04e1f6f | 255 | y = *(float*)&i; |
altb | 1:36bbe04e1f6f | 256 | y = y * (1.5f - (halfx * y * y)); |
altb | 1:36bbe04e1f6f | 257 | y = y * (1.5f - (halfx * y * y)); |
altb | 1:36bbe04e1f6f | 258 | return y; |
altb | 1:36bbe04e1f6f | 259 | } |
altb | 1:36bbe04e1f6f | 260 | |
altb | 1:36bbe04e1f6f | 261 | //------------------------------------------------------------------------------------------- |
altb | 1:36bbe04e1f6f | 262 | |
altb | 1:36bbe04e1f6f | 263 | void Mahony::computeAngles() |
altb | 1:36bbe04e1f6f | 264 | { |
altb | 1:36bbe04e1f6f | 265 | roll = atan2f(q0*q1 + q2*q3, 0.5f - q1*q1 - q2*q2); |
altb | 1:36bbe04e1f6f | 266 | pitch = asinf(-2.0f * (q1*q3 - q0*q2)); |
altb | 1:36bbe04e1f6f | 267 | yaw = atan2f(q1*q2 + q0*q3, 0.5f - q2*q2 - q3*q3); |
altb | 1:36bbe04e1f6f | 268 | anglesComputed = 1; |
altb | 1:36bbe04e1f6f | 269 | } |
altb | 1:36bbe04e1f6f | 270 | |
altb | 1:36bbe04e1f6f | 271 | |
altb | 1:36bbe04e1f6f | 272 | //============================================================================================ |
altb | 1:36bbe04e1f6f | 273 | // END OF CODE |
altb | 1:36bbe04e1f6f | 274 | //============================================================================================ |
altb | 1:36bbe04e1f6f | 275 |