david fernandez
Multithread approach to 6DOF Mag Tracker
Revision 0:9621bbc04b9b, committed 2020-05-21
- Comitter:
- darkraxx
- Date:
- Thu May 21 13:10:58 2020 +0000
- Commit message:
- Multithread approach Mag Track
Changed in this revision
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/MadgwickAHRS.cpp Thu May 21 13:10:58 2020 +0000
@@ -0,0 +1,228 @@
+//=====================================================================================================
+// MadgwickAHRS.c
+//=====================================================================================================
+//
+// Implementation of Madgwick's IMU and AHRS algorithms.
+// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms
+//
+// Date Author Notes
+// 29/09/2011 SOH Madgwick Initial release
+// 02/10/2011 SOH Madgwick Optimised for reduced CPU load
+// 19/02/2012 SOH Madgwick Magnetometer measurement is normalised
+//
+//=====================================================================================================
+
+//---------------------------------------------------------------------------------------------------
+// Header files
+
+#include "MadgwickAHRS.h"
+#include <math.h>
+
+//---------------------------------------------------------------------------------------------------
+// Definitions
+
+#define sampleFreq 100.0f // sample frequency in Hz
+#define betaDef 10.0f // 2 * proportional gain
+
+//---------------------------------------------------------------------------------------------------
+// Variable definitions
+
+volatile float beta = betaDef; // 2 * proportional gain (Kp)
+volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame
+
+//---------------------------------------------------------------------------------------------------
+// Function declarations
+
+float invSqrt(float x);
+
+//====================================================================================================
+// Functions
+
+//---------------------------------------------------------------------------------------------------
+// AHRS algorithm update
+
+void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {
+ float recipNorm;
+ float s0, s1, s2, s3;
+ float qDot1, qDot2, qDot3, qDot4;
+ float hx, hy;
+ float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;
+
+ // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)
+ if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {
+ MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);
+ return;
+ }
+
+ // Rate of change of quaternion from gyroscope
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
+
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
+
+ // Normalise accelerometer measurement
+ recipNorm = invSqrt(ax * ax + ay * ay + az * az);
+ ax *= recipNorm;
+ ay *= recipNorm;
+ az *= recipNorm;
+
+ // Normalise magnetometer measurement
+ recipNorm = invSqrt(mx * mx + my * my + mz * mz);
+ mx *= recipNorm;
+ my *= recipNorm;
+ mz *= recipNorm;
+
+ // Auxiliary variables to avoid repeated arithmetic
+ _2q0mx = 2.0f * q0 * mx;
+ _2q0my = 2.0f * q0 * my;
+ _2q0mz = 2.0f * q0 * mz;
+ _2q1mx = 2.0f * q1 * mx;
+ _2q0 = 2.0f * q0;
+ _2q1 = 2.0f * q1;
+ _2q2 = 2.0f * q2;
+ _2q3 = 2.0f * q3;
+ _2q0q2 = 2.0f * q0 * q2;
+ _2q2q3 = 2.0f * q2 * q3;
+ q0q0 = q0 * q0;
+ q0q1 = q0 * q1;
+ q0q2 = q0 * q2;
+ q0q3 = q0 * q3;
+ q1q1 = q1 * q1;
+ q1q2 = q1 * q2;
+ q1q3 = q1 * q3;
+ q2q2 = q2 * q2;
+ q2q3 = q2 * q3;
+ q3q3 = q3 * q3;
+
+ // Reference direction of Earth's magnetic field
+ hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;
+ hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;
+ _2bx = sqrt(hx * hx + hy * hy);
+ _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;
+ _4bx = 2.0f * _2bx;
+ _4bz = 2.0f * _2bz;
+
+ // Gradient decent algorithm corrective step
+ s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
+ s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
+ s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
+ s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
+ s0 *= recipNorm;
+ s1 *= recipNorm;
+ s2 *= recipNorm;
+ s3 *= recipNorm;
+
+ // Apply feedback step
+ qDot1 -= beta * s0;
+ qDot2 -= beta * s1;
+ qDot3 -= beta * s2;
+ qDot4 -= beta * s3;
+ }
+
+ // Integrate rate of change of quaternion to yield quaternion
+ q0 += qDot1 * (1.0f / sampleFreq);
+ q1 += qDot2 * (1.0f / sampleFreq);
+ q2 += qDot3 * (1.0f / sampleFreq);
+ q3 += qDot4 * (1.0f / sampleFreq);
+
+ // Normalise quaternion
+ recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+ q0 *= recipNorm;
+ q1 *= recipNorm;
+ q2 *= recipNorm;
+ q3 *= recipNorm;
+}
+
+//---------------------------------------------------------------------------------------------------
+// IMU algorithm update
+
+void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) {
+ float recipNorm;
+ float s0, s1, s2, s3;
+ float qDot1, qDot2, qDot3, qDot4;
+ float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;
+
+ // Rate of change of quaternion from gyroscope
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);
+
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {
+
+ // Normalise accelerometer measurement
+ recipNorm = invSqrt(ax * ax + ay * ay + az * az);
+ ax *= recipNorm;
+ ay *= recipNorm;
+ az *= recipNorm;
+
+ // Auxiliary variables to avoid repeated arithmetic
+ _2q0 = 2.0f * q0;
+ _2q1 = 2.0f * q1;
+ _2q2 = 2.0f * q2;
+ _2q3 = 2.0f * q3;
+ _4q0 = 4.0f * q0;
+ _4q1 = 4.0f * q1;
+ _4q2 = 4.0f * q2;
+ _8q1 = 8.0f * q1;
+ _8q2 = 8.0f * q2;
+ q0q0 = q0 * q0;
+ q1q1 = q1 * q1;
+ q2q2 = q2 * q2;
+ q3q3 = q3 * q3;
+
+ // Gradient decent algorithm corrective step
+ s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;
+ s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;
+ s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;
+ s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude
+ s0 *= recipNorm;
+ s1 *= recipNorm;
+ s2 *= recipNorm;
+ s3 *= recipNorm;
+
+ // Apply feedback step
+ qDot1 -= beta * s0;
+ qDot2 -= beta * s1;
+ qDot3 -= beta * s2;
+ qDot4 -= beta * s3;
+ }
+
+ // Integrate rate of change of quaternion to yield quaternion
+ q0 += qDot1 * (1.0f / sampleFreq);
+ q1 += qDot2 * (1.0f / sampleFreq);
+ q2 += qDot3 * (1.0f / sampleFreq);
+ q3 += qDot4 * (1.0f / sampleFreq);
+
+ // Normalise quaternion
+ recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);
+ q0 *= recipNorm;
+ q1 *= recipNorm;
+ q2 *= recipNorm;
+ q3 *= recipNorm;
+}
+
+//---------------------------------------------------------------------------------------------------
+// Fast inverse square-root
+// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root
+
+float invSqrt(float x) {
+ float halfx = 0.5f * x;
+ float y = x;
+ long i = *(long*)&y;
+ i = 0x5f3759df - (i>>1);
+ y = *(float*)&i;
+ y = y * (1.5f - (halfx * y * y));
+ return y;
+}
+
+//====================================================================================================
+// END OF CODE
+//====================================================================================================
+
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/MadgwickAHRS.h Thu May 21 13:10:58 2020 +0000 @@ -0,0 +1,32 @@ +//===================================================================================================== +// MadgwickAHRS.h +//===================================================================================================== +// +// Implementation of Madgwick's IMU and AHRS algorithms. +// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms +// +// Date Author Notes +// 29/09/2011 SOH Madgwick Initial release +// 02/10/2011 SOH Madgwick Optimised for reduced CPU load +// +//===================================================================================================== +#ifndef MadgwickAHRS_h +#define MadgwickAHRS_h + +//---------------------------------------------------------------------------------------------------- +// Variable declaration + +extern volatile float beta; // algorithm gain +extern volatile float q0, q1, q2, q3; // quaternion of sensor frame relative to auxiliary frame + +//--------------------------------------------------------------------------------------------------- +// Function declarations + +void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz); +void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az); + +#endif +//===================================================================================================== +// End of file +//===================================================================================================== +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Mag_track.cpp Thu May 21 13:10:58 2020 +0000
@@ -0,0 +1,353 @@
+//=====================================================================================================
+// Mag_track.cpp
+//=====================================================================================================
+//
+// Implementation of Magnetic tracking algorithm.
+//
+// Date Author Notes
+// 30/01/2020 DAFG Initial release
+//
+//=====================================================================================================
+// Header files
+ #include "mbed.h"
+ #include "Mag_track.h"
+ #include <math.h>
+ #include "MadgwickAHRS.h"
+ #include "Scattered_interpolator.h"
+
+//----------------------------------------------------------------------------------------------------
+// Variable declaration
+ ///////////////////////////////////////////////////////////
+ // Filter Code Definitions
+ //////////////////////////////////////////////////////////////
+
+ // Maximum number of inputs that can be handled
+ // in one function call
+ #define MAX_INPUT_LEN 16
+ // Maximum length of filter than can be handled
+ #define MAX_FLT_LEN 84
+ // Buffer to hold all of the input samples
+ #define BUFFER_LEN (MAX_FLT_LEN + MAX_INPUT_LEN)
+
+ // Arrays to hold input samples
+ int16_t lp_insamp[ 3*BUFFER_LEN ];
+ int16_t insamp[ 3*BUFFER_LEN ];
+
+ #define FILTER_LEN_BP 71
+ // fs = 800 Hz; Band pass 85-115 Hz
+ int16_t coeffs_bp[ FILTER_LEN_BP ] =
+ {
+ 30, 0, -28, -39, -27, 0, 21, 21, 4, 0, 31, 81, 91, 0, -182, -340, -307, 0,
+ 465, 786, 653, 0, -861, -1371, -1079, 0, 1292, 1970, 1487, 0, -1648, -2421,
+ -1763, 0, 1823, 2588, 1823, 0, -1763, -2421, -1648, 0, 1487, 1970, 1292, 0,
+ -1079, -1371, -861, 0, 653, 786, 465, 0, -307, -340, -182, 0, 91, 81, 31, 0,
+ 4, 21, 21, 0, -27, -39, -28, 0, 30
+ };
+
+ #define FILTER_LEN_LP 82
+ // fs = 800 Hz; low pass fc 10-35 Hz
+ int16_t coeffs_lp[FILTER_LEN_LP] =
+ {
+ -7,-5,-7,-9,-11,-13,-15,-15,-15,-14,-11,-5,3,15,30,49,73,102,136,176,221,272,328,390,
+ 456,527,601,678,757,836,914,990,1064,1133,1197,1254,1303,1343,1374,1395,1406,1406,1395,
+ 1374,1343,1303,1254,1197,1133,1064,990,914,836,757,678,601,527,456,390,328,272,221,176,
+ 136,102,73,49,30,15,3,-5,-11,-14,-15,-15,-15,-13,-11,-9,-7,-5,-7
+ };
+ // I2C buffers
+ char data_write[2]; // 2 bytes for writing I2C
+ char data_read[12]; // 12 bytes for storing I2C sensor data
+ char rawData_a[6]; // x/y/z accel register data stored here
+ char rawData_g[6]; // x/y/z accel register data stored here
+ // Sensor Offsets
+ int16_t offset_mag[3] = {-226,-135,1506}; //{-267, -100, 1552};
+ int16_t offset_acc[3] = {-17,170,602};//{-123, 123, 760};
+ int16_t offset_gyr[3] = {-32,-42,-5};//{-40,-37,27};
+ // Sensor Settings Data
+ int KMX62_ADDR = 28; // KMX62 address
+ int MPU_ADDR = 208; // 0x68 = 104 *2
+ char REG_MPU[6] = {0x3b,0x43,0x1c,0x1b,0x1a,0x1d}; //Acc data, gyr data, acc_config, gyro_config, mpu_config
+ char REG[8] = {0x0A,0x10,0x38,0x3a,0x77,0x78,0x79,0x7E}; //Acc data, Mag data, ODC, Ctrl2 REG, buff_ctrl 1, 2 and 3, buff read
+ char set_up[5] = {0x77,0x1f,0x64,0x02,0x0E}; //ODC, Ctrl2, buff_ctrl set up
+ char set_up_mpu[4] = {0x08,0x10,0x00,0x00}; //Acc_config, gyro_config, set up and acc_config_2
+ // DSP buffers
+ double E_c[4] = {9.402,-4.057,0.8096,0.1276}; //Envelope extraction amplitude regularization coeff
+ int16_t E[3] = {0,0,0};
+ double E_D;
+ int16_t Test_point[2] ;
+ int16_t TRIAG = 0;
+ int16_t inter_p[2]={0,0};
+ // MCU ports setting
+ I2C i2c(I2C_SDA, I2C_SCL);
+ Serial PC(SERIAL_TX, SERIAL_RX);
+ DigitalOut myled(LED1);
+
+
+//---------------------------------------------------------------------------------------------------
+// Function declarations
+
+ /////// FIR init
+ void firFixedInit( void )
+ {
+ memset( insamp, 0, sizeof( insamp ) );
+ memset( lp_insamp, 0, sizeof( lp_insamp ) );
+ }
+
+ /////// the FIR filter function
+ void firFixed( int16_t *coeffs, int16_t *input, int16_t *output,
+ int length, int filterLength, int bias, int16_t *buffer )
+ {
+ int32_t acc; // accumulator for MACs
+ int16_t *coeffp; // pointer to coefficients
+ int16_t *inputp; // pointer to input samples
+ int16_t *bufferp; //pointer to input buffer
+ int n;
+ int k;
+
+ // put the new samples at the high end of the buffer
+ /*memcpy( &insamp[filterLength - 1 + bias*BUFFER_LEN], input,
+ length * sizeof(int16_t) );*/
+ bufferp=buffer;
+ memcpy( bufferp + filterLength - 1 + bias*BUFFER_LEN, input, length * sizeof(int16_t) );
+
+ // apply the filter to each input sample
+ for ( n = 0; n < length; n++ ) {
+ // calculate output n
+ coeffp = coeffs;
+ /*inputp = &insamp[filterLength - 1 + n + bias*BUFFER_LEN];*/
+ inputp = bufferp+filterLength - 1 + n + bias*BUFFER_LEN;
+ // load rounding constant
+ acc = 1 << 14;
+ // perform the multiply-accumulate
+ for ( k = 0; k < filterLength; k++ ) {
+ acc += (int32_t)(*coeffp++) * (int32_t)(*inputp--) ;
+ }
+ // saturate the result
+ if ( acc > 0x3fffffff ) {
+ acc = 0x3fffffff;
+ } else if ( acc < -0x40000000 ) {
+ acc = -0x40000000;
+ }
+ // convert from Q30 to Q15
+ output[n] = (int16_t)(acc >> 15);
+
+ }
+
+ // shift input samples back in time for next time
+ //memmove(&insamp[0+bias*BUFFER_LEN], &insamp[length + bias*BUFFER_LEN], (filterLength-1)*sizeof(int16_t));
+ memmove( bufferp + bias*BUFFER_LEN, bufferp+length + bias*BUFFER_LEN, (filterLength-1)*sizeof(int16_t));
+
+ }
+
+
+ /////// SIGN FUNCTION
+ int sign(int16_t x){
+ if (x>0) return 1;
+ if (x<0) return -1;
+ return 0;
+ }
+ /////// QUATERNION product FUNCTION
+ void Qprod(float *p, float *q, float *r ){
+ r[0]= p[0] * q[0] - p[1] * q[1] - p[2] * q[2] - p[3] * q[3];
+ r[1]= p[0]*q[1] + p[1]*q[0] + p[2]*q[3] - p[3]*q[2];
+ r[2]= p[0]*q[2] - p[1]*q[3] + p[2]*q[0] + p[3]*q[1];
+ r[3]= p[0]*q[3] + p[1]*q[2] - p[2]*q[1] + p[3]*q[0];
+ }
+ /////// QUATERNION rotation FUNCTION
+ void Qrotate(float *v, float *q, float *out ){
+
+ float v_1[4]= {0, v[0],v[1],v[2]};
+ float temp[4]={0,0,0,0};
+ Qprod(v_1,q,temp);
+ float q_conj[4]={q[0],-q[1],-q[2],-q[3]};
+ Qprod(q_conj,temp,v_1);
+ out[0]= v_1[1];
+ out[1]= v_1[2];
+ out[2]= v_1[3];
+ }
+ /////// Sensor set_up function
+ void sensor_setup(){
+ i2c.frequency(400000);
+ /*Configure MPU9250*/
+ data_write[0] = REG_MPU[4];
+ data_write[1] = set_up_mpu[2];
+ int status = i2c.write(MPU_ADDR, data_write, 2, false);
+ data_write[0] = REG_MPU[2];
+ data_write[1] = set_up_mpu[0];
+ status = i2c.write(MPU_ADDR, data_write, 2, false);
+ data_write[0] = REG_MPU[5];
+ data_write[1] = set_up_mpu[3];
+ status = i2c.write(MPU_ADDR, data_write, 2, false);
+ data_write[0] = REG_MPU[3];
+ data_write[1] = set_up_mpu[1];
+ status = i2c.write(MPU_ADDR, data_write, 2, false);
+ /*Configure KMX62 Sensor*/
+ // Ctrl Reg Set up
+ data_write[0] = REG[3];
+ data_write[1] = set_up[1];
+ status = i2c.write(KMX62_ADDR, data_write, 2, false);
+ if (status != 0) { // Error
+ while (status != 0) {
+ PC.printf("Error 1");
+ myled = !myled;
+ wait(1);
+ status = i2c.write(KMX62_ADDR, data_write, 2, false);
+ }
+ }
+ // ODC Reg Set up
+ data_write[0] = REG[2];
+ data_write[1] = set_up[0];
+ status = i2c.write(KMX62_ADDR, data_write, 2, false);
+ if (status != 0) { // Error
+ while (status != 0) {
+ PC.printf("Error 2");
+ myled = !myled;
+ wait(1);
+ status = i2c.write(KMX62_ADDR, data_write, 2, false);
+ }
+ }
+ // Buffer Reg Set up
+ int i;
+ for(i=0;i<3;i++) {
+ data_write[0] = REG[4+i];
+ data_write[1] = set_up[2+i];
+ status = i2c.write(KMX62_ADDR, data_write, 2, false);
+ if (status != 0) { // Error
+ while (status != 0) {
+ PC.printf("Error 3");
+ myled = !myled;
+ wait(1);
+ status = i2c.write(KMX62_ADDR, data_write, 2, false);
+ }
+ }
+ }
+ }
+
+ /////// MPU sensor axes alignment and offset correction
+ void MPUrot_offset(int16_t *Data, char *rawData, int16_t *offset){
+ int16_t Data_read[3];
+ Data_read[1] = -(((int16_t)rawData[0] << 8 | rawData[1])-offset[0]) ; // Turn the MSB and LSB into a signed 16-bit value
+ Data_read[0] = (((int16_t)rawData[2] << 8 | rawData[3])-offset[1] );
+ Data_read[2] = ((int16_t)rawData[4] << 8 | rawData[5])-offset[2] ;
+ Data[0]=Data_read[0]; Data[1]=Data_read[1]; Data[2]=Data_read[2];
+ }
+
+ /////// Magnetic sensor offset correction
+ void Mag_offset(int16_t *M_read, char *data, int16_t *offset){
+ M_read[0] = (((int16_t)data[7]<<8)|data[6]) - offset[0];
+ M_read[1] = (((int16_t)data[9]<<8)|data[8]) - offset[1];
+ M_read[2] = (((int16_t)data[11]<<8)|data[10]) - offset[2];
+ }
+ /////// Magnetic sensor reading
+ void Read_Mag(int16_t *M_read){
+ data_write[0] = REG[0];
+ i2c.write(KMX62_ADDR, data_write, 1, true); // no stop
+ i2c.read(KMX62_ADDR, data_read, 12, false);
+ Mag_offset(M_read, data_read, offset_mag);
+ }
+ /////// Acc sensor reading
+ void Read_Acc(int16_t *A_read){
+ data_write[0] = REG_MPU[0];
+ i2c.write(MPU_ADDR, data_write, 1, true); // no stop
+ i2c.read(MPU_ADDR, rawData_a, 6 ,false); // Read the six raw data registers into data array
+ MPUrot_offset(A_read, rawData_a, offset_acc);
+ }
+ /////// Gyr sensor reading
+ void Read_Gyr(int16_t *G_read){
+ data_write[0] = REG_MPU[1];
+ i2c.write(MPU_ADDR, data_write, 1, true); // no stop
+ i2c.read(MPU_ADDR, rawData_g, 6 ,false); // Read the six raw data registers into data array
+ MPUrot_offset(G_read, rawData_g, offset_gyr);
+ }
+
+ /////// Madgwick Quaternion update high-level function
+ void QUpdate(int32_t *q, float *m, float *a, float *g, int16_t *Mag, int16_t *Acc, int16_t *Gyr, float *Q_init, int32_t *Q_out){
+ float gRes = 0.0174533*0.0305175;//0.03*0.0175*2; //1/62.5; radianti, non gradi 500=0.016
+ float mRes = 0.000366; // G, non microT
+ float aRes = 0.00012207031; //1/8192;
+ float Q[4] = {0,0,0,0};
+ float Q_o[4] = {0,0,0,0};
+ //// scaling
+ m[0] = ((float) Mag[0])*mRes;
+ m[1] = ((float) Mag[1])*mRes;
+ m[2] = ((float) Mag[2])*mRes;
+ a[0] = ((float) Acc[0])*aRes;
+ a[1] = ((float) Acc[1])*aRes;
+ a[2] = ((float) Acc[2])*aRes;
+ g[0] = ((float) Gyr[0])*gRes;
+ g[1] = ((float) Gyr[1])*gRes;
+ g[2] = ((float) Gyr[2])*gRes;
+ //// quaternion calculation
+ MadgwickAHRSupdate(g[0], g[1], g[2], a[0], a[1], a[2], m[0], m[1], m[2]);
+ Q[0]=q0; Q[1]=q1; Q[2]=q2; Q[3]=q3;
+ Qprod(Q, Q_init, Q_o);
+ Q_out[0]=(int32_t)(Q_o[0]*(powf(2,30)));
+ Q_out[1]=(int32_t)(Q_o[1]*(powf(2,30)));
+ Q_out[2]=(int32_t)(Q_o[2]*(powf(2,30)));
+ Q_out[3]=(int32_t)(Q_o[3]*(powf(2,30)));
+ q[0]=(int32_t)(q0*(powf(2,30)));
+ q[1]=(int32_t)(q1*(powf(2,30)));
+ q[2]=(int32_t)(q2*(powf(2,30)));
+ q[3]=(int32_t)(q3*(powf(2,30)));
+ }
+
+ /////// Filtered magnetic signals envelope extraction
+ void Env_extraction(int16_t *P, int16_t *buffer_rot, int16_t *max, int16_t *p_i, double *R, double *ph, int16_t *S){
+ int16_t i, k;
+ for(i=0; i<3; i++){
+ max[2*i]=buffer_rot[i*8]; //maximum[i]=buffer_env[4+i*8];
+ max[2*i+1]=buffer_rot[i*8];
+ p_i[2*i]=0;
+ p_i[2*i+1]=0;
+
+ for(k=1;k<8;k++){
+ if ( buffer_rot[k + i*8] >= max[2*i] ){
+ max[2*i + 1] = max[2*i];
+ max[2*i] = buffer_rot[k + i*8];
+ p_i[2*i + 1]=p_i[2*i];
+ p_i[2*i]=k;
+ }
+ else {
+ if ( buffer_rot[k + i*8] >= max[2*i + 1] ){
+ max[2*i + 1] = buffer_rot[k + i*8];
+ p_i[2*i + 1]=k;
+ }
+ }
+ }
+ R[i]=((double)max[2*i])/((double)max[2*i + 1]);
+ E[i]=(int16_t)(((double)max[2*i])*(E_c[0]*exp(E_c[1]*R[i])+E_c[2]*exp(E_c[3]*R[i])));
+ if ( (p_i[2*i] == 0) && (p_i[2*i + 1] == 7) ){
+ p_i[2*i + 1] = -1;
+ }
+ if ( (p_i[2*i] == 7) && (p_i[2*i + 1] == 0) ){
+ p_i[2*i + 1] = 8;
+ }
+ //Phase update: Y phase is updated only if its Envelope is higher than 5.5 uT : 150
+ if (i == 1){
+ if(E[i]>=150){
+ ph[i]=((double)(p_i[2*i]+p_i[2*i + 1]))/2;
+ }
+ }
+ else{
+ ph[i]=((double)(p_i[2*i]+p_i[2*i + 1]))/2;
+ }
+ }
+ if (( fabs(ph[1]-ph[0]) >= 2 ) && ( fabs(ph[1]-ph[0]) <= 6)){
+ S[0]=-1;
+ }
+ else{
+ S[0]=1;
+ }
+ if (( fabs(ph[1]-ph[2]) >= 2 ) && ( fabs(ph[1]-ph[2]) <= 6)){
+ S[1]=-1;
+ }
+ else{
+ S[1]=1;
+ }
+ E_D = hypot( (double)E[0], (double)E[1] );
+ Test_point[0]= (int16_t)E_D;
+ Test_point[1]=S[1]*E[2];
+ TRIAG = Find_point(Test_point, TRIAG, SI_Points, SI_ConnectivityList, inter_p);
+ P[0]= S[0]*(int16_t)( (double)inter_p[0]*((double)E[0] / E_D));
+ P[1]= (int16_t)( (double)inter_p[0]*((double)E[1] / E_D));
+ P[2]=inter_p[1];
+ }
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Mag_track.h Thu May 21 13:10:58 2020 +0000 @@ -0,0 +1,66 @@ +//===================================================================================================== +// Mag_track.h +//===================================================================================================== +// +// Implementation of Magnetic tracking algorithm. +// +// Date Author Notes +// 30/01/2020 DAFG Initial release +// +//===================================================================================================== +#ifndef Mag_track_h +#define Mag_track_h +//---------------------------------------------------------------------------------------------------- +// Variable declaration + + // maximum number of inputs that can be handled + // in one function call + #define MAX_INPUT_LEN 16 + // maximum length of filter than can be handled + #define MAX_FLT_LEN 84 + // buffer to hold all of the input samples + #define BUFFER_LEN (MAX_FLT_LEN + MAX_INPUT_LEN) + extern int16_t lp_insamp[ 3*BUFFER_LEN ]; // Array to hold input samples LP + #define FILTER_LEN_LP 82 + // fs = 800 Hz; low pass fc 10-35 Hz + extern int16_t coeffs_lp[FILTER_LEN_LP]; + extern int16_t insamp[ 3*BUFFER_LEN ]; // Array to hold input samples BP + #define FILTER_LEN_BP 71 + // fs = 800 Hz; Band pass 85-115 Hz + extern int16_t coeffs_bp[ FILTER_LEN_BP ]; + + extern Serial PC; + extern DigitalOut myled; + +//--------------------------------------------------------------------------------------------------- +// Function declarations + + /////// FIR init + void firFixedInit( void ); + /////// the FIR filter function + void firFixed( int16_t *coeffs, int16_t *input, int16_t *output, + int length, int filterLength, int bias, int16_t *buffer ); + /////// SIGN FUNCTION + int sign(int16_t x); + /////// QUATERNION product FUNCTION + void Qprod(float *p, float *q, float *r ); + /////// QUATERNION rotation FUNCTION + void Qrotate(float *v, float *q, float *out ); + /////// Sensor set_up function + void sensor_setup(); + /////// MPU sensor axes alignment and offset correction + void MPUrot_offset(int16_t *Data, char *rawData, int16_t *offset); + /////// Magnetic sensor offset correction + void Mag_offset(int16_t *M_read, char *data, int16_t *offset); + /////// Sensors reading + void Read_Mag(int16_t *M_read); + void Read_Acc(int16_t *A_read); + void Read_Gyr(int16_t *G_read); + /////// Madgwick Quaternion update high-level function + void QUpdate(int32_t *q, float *m, float *a, float *g, int16_t *Mag, int16_t *Acc, int16_t *Gyr, float *Q_init, int32_t *Q_out); + /////// Filtered magnetic signals envelope extraction + void Env_extraction(int16_t *E, int16_t *buffer_rot, int16_t *max, int16_t *p_i, double *R, double *ph, int16_t *S); +#endif +//===================================================================================================== +// End of file +//===================================================================================================== \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Scattered_interpolator.cpp Thu May 21 13:10:58 2020 +0000
@@ -0,0 +1,132 @@
+#include "mbed.h"
+//Scattered Interpolations Points List and Connectivity List
+/*#define num_points 783
+#define num_triag 1514
+int16_t SI_Points[4*num_points]={
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+ };
+int16_t SI_ConnectivityList[6*num_triag]={
+ 157, 70, 258, 675, 223, 338, 302, 72, 254, 548, 595, 459, 27, 322, 697, 338, 514, 441, 405, 110, 688, 278, 7, 127, 33, 275, 97, 409, 15, 285, 170, 424, 364, 66, 25, 42, 180, 256, 292, 71, 89, 131, 443, 164, 213, 541, 460, 724, 26, 400, 619, 367, 79, 407, 401, 384, 486, 564, 589, 590, 614, 630, 572, 663, 684, 748, 711, 745, 675, 726, 585, 766, 752, 667, 659, 727, 734, 491, 623, 618, 616, 549, 583, 617, 648, 564, 535, 756, 578, 743, 474, 37, 19, 85, 21, 4, 47, 0, 34, 92, 48, 104, 117, 85, 101, 60, 159, 498, 165, 159, 344, 425, 493, 283, 434, 408, 117, 328, 170, 246, 151, 178, 211, 205, 205, 245, 257, 209, 351, 208, 297, 295, 432, 378, 305, 378, 396, 266, 320, 351, 315, 311, 311, 140, 162, 154, 190, 137, 209, 137, 266, 106, 112, 58, 116, 109, 23, 111, 162, 98, 212, 52, 95, 83, 50, 71, 119, 86, 86, 290, 131, 194, 318, 83, 171, 176, 124, 155, 131, 39, 148, 203, 231, 26, 177, 32, 32, 338, 336, 322, 135, 163, 240, 255, 55, 59, 329, 84, 358, 196, 233, 385, 389, 326, 369, 330, 254, 558, 273, 301, 188, 366, 334, 418, 463, 318, 313, 315, 377, 204, 181, 298, 304, 230, 272, 299, 171, 337, 289, 351, 345, 359, 368, 345, 451, 415, 471, 364, 422, 422, 450, 494, 454, 522, 356, 559, 582, 438, 354, 438, 430, 561, 501, 478, 687, 478, 632, 487, 601, 547, 604, 657, 541, 597, 533, 604, 630, 594, 618, 632, 672, 737, 745, 673, 738, 757, 704, 776, 760, 755, 757, 757, 757, 759, 766, 681, 621, 724, 723, 663, 612, 483, 672, 592, 634, 627, 618, 664, 652, 644, 655, 681, 665, 726, 748, 589, 614, 773, 753, 563, 623, 728, 706, 563, 557, 565, 602, 503, 475, 554, 583, 550, 575, 402, 392, 495, 476, 379, 447, 378, 388, 362, 262, 371, 442, 452, 462, 434, 549, 435, 476, 526, 587, 488, 565, 325, 452, 346, 512, 398, 386, 426, 453, 606, 596, 679, 556, 659, 660, 714, 649, 566, 581, 659, 611, 680, 714, 692, 671, 766, 754, 731, 746, 743, 772, 33, 6, 60, 46, 46, 217, 21, 21, 34, 13, 2, 4, 4, 7, 1, 2, 9, 25, 0, 24, 3, 25, 10, 48, 16, 37, 24, 61, 37, 62, 57, 34, 126, 48, 87, 29, 38, 76, 92, 127, 136, 69, 178, 80, 76, 76, 180, 180, 178, 76, 57, 28, 97, 46, 97, 61, 101, 185, 110, 165, 46, 227, 51, 51, 60, 60, 386, 184, 283, 147, 147, 185, 185, 293, 293, 205, 310, 220, 147, 346, 185, 386, 287, 185, 398, 260, 287, 413, 398, 394, 208, 310, 293, 331, 310, 275, 340, 262, 381, 352, 340, 294, 352, 352, 404, 352, 408, 327, 372, 333, 370, 370, 327, 189, 295, 284, 332, 332, 209, 294, 200, 245, 153, 284, 228, 234, 284, 284, 205, 234, 275, 153, 228, 238, 189, 189, 238, 238, 209, 160, 206, 161, 200, 152, 152, 152, 232, 192, 223, 192, 253, 200, 210, 210, 253, 206, 206, 252, 253, 297, 370, 362, 388, 333, 378, 321, 328, 370, 206, 253, 246, 285, 279, 321, 241, 232, 296, 257, 339, 339, 417, 392, 312, 296, 392, 379, 296, 288, 305, 274, 274, 320, 241, 247, 229, 274, 190, 182, 241, 211, 258, 229, 211, 175, 212, 179, 190, 197, 218, 169, 218, 186, 107, 169, 141, 137, 89, 141, 169, 141, 88, 128, 111, 133, 82, 123, 93, 130, 93, 137, 88, 140, 102, 113, 117, 117, 116, 112, 116, 116, 106, 118, 29, 102, 81, 106, 81, 118, 58, 93, 74, 82, 111, 58, 111, 72, 49, 48, 65, 65, 71, 25, 49, 35, 74, 63, 5, 0, 58, 35, 52, 30, 74, 42, 53, 63, 66, 44, 94, 78, 39, 43, 52, 44, 53, 40, 43, 43, 77, 64, 68, 64, 53, 75, 67, 78, 68, 95, 52, 66, 66, 77, 67, 77, 78, 94, 120, 98, 141, 169, 169, 224, 225, 187, 168, 193, 142, 95, 131, 115, 144, 197, 143, 191, 213, 156, 156, 156, 172, 172, 237, 188, 195, 164, 145, 163, 221, 188, 207, 230, 109, 129, 22, 157, 155, 155, 176, 156, 109, 71, 138, 138, 124, 129, 138, 156, 125, 125, 59, 18, 73, 22, 122, 36, 222, 54, 32, 22, 84, 149, 0, 26, 8, 55, 18, 5, 5, 149, 45, 26, 31, 45, 79, 214, 14, 91, 216, 135, 26, 149, 146, 201, 99, 222, 231, 90, 150, 277, 45, 375, 273, 84, 122, 282, 149, 122, 222, 99, 183, 233, 173, 5, 121, 73, 132, 99, 203, 5, 237, 164, 164, 183, 183, 250, 204, 242, 249, 276, 203, 291, 204, 323, 249, 292, 250, 353, 280, 329, 286, 280, 222, 292, 243, 222, 286, 201, 303, 231, 330, 215, 277, 273, 150, 215, 354, 269, 303, 231, 255, 349, 231, 314, 306, 373, 254, 349, 389, 174, 444, 385, 273, 441, 375, 375, 401, 349, 436, 457, 399, 324, 399, 403, 280, 369, 280, 280, 399, 369, 308, 353, 353, 367, 376, 318, 393, 367, 353, 353, 376, 301, 350, 383, 347, 334, 383, 377, 289, 343, 343, 343, 276, 317, 350, 317, 363, 363, 242, 265, 335, 335, 181, 265, 276, 242, 240, 240, 226, 272, 265, 230, 240, 271, 259, 259, 226, 226, 259, 236, 226, 191, 248, 236, 186, 218, 193, 218, 248, 219, 258, 267, 270, 264, 235, 288, 342, 271, 247, 300, 299, 300, 264, 264, 270, 299, 342, 382, 299, 342, 368, 342, 351, 392, 399, 399, 459, 430, 438, 397, 364, 399, 490, 490, 497, 497, 463, 448, 494, 480, 521, 471, 503, 480, 520, 510, 568, 529, 554, 570, 561, 553, 568, 568, 538, 513, 548, 513, 582, 542, 529, 500, 513, 548, 547, 542, 630, 610, 527, 582, 577, 572, 457, 470, 533, 502, 552, 527, 428, 436, 522, 522, 459, 469, 497, 497, 390, 390, 467, 467, 375, 470, 375, 436, 444, 416, 457, 373, 502, 444, 527, 532, 502, 533, 516, 492, 492, 533, 373, 492, 492, 492, 444, 482, 460, 336, 433, 433, 441, 389, 389, 374, 518, 429, 487, 433, 586, 460, 525, 478, 505, 629, 530, 607, 555, 622, 528, 567, 662, 528, 622, 600, 622, 567, 629, 592, 601, 601, 624, 612, 580, 634, 541, 541, 584, 551, 558, 609, 572, 577, 584, 559, 604, 560, 585, 585, 624, 609, 670, 653, 670, 646, 694, 694, 688, 711, 732, 711, 742, 736, 605, 605, 691, 662, 670, 709, 662, 662, 691, 685, 685, 704, 751, 738, 716, 669, 685, 685, 711, 736, 725, 751, 758, 747, 759, 767, 773, 774, 767, 767, 773, 781, 774, 774, 767, 765, 773, 771, 722, 751, 733, 737, 737, 756, 736, 738, 755, 742, 742, 745, 745, 771, 765, 707, 727, 748, 760, 717, 708, 742, 735, 676, 703, 701, 719, 672, 698, 688, 708, 720, 707, 656, 653, 657, 657, 600, 600, 674, 674, 609, 626, 607, 650, 631, 631, 634, 668, 687, 684, 643, 665, 624, 658, 631, 609, 645, 624, 643, 637, 644, 644, 652, 637, 640, 655, 640, 664, 681, 680, 678, 712, 652, 676, 687, 676, 700, 698, 698, 687, 719, 719, 705, 719, 727, 719, 744, 744, 623, 647, 696, 700, 538, 511, 603, 589, 521, 506, 554, 539, 570, 550, 599, 583, 718, 718, 678, 664, 680, 705, 628, 623, 664, 647, 562, 591, 628, 602, 517, 557, 545, 562, 640, 623, 515, 499, 491, 534, 509, 536, 498, 562, 509, 534, 536, 536, 455, 499, 462, 506, 545, 504, 515, 458, 517, 508, 531, 531, 550, 550, 554, 520, 554, 554, 521, 514, 508, 543, 504, 539, 503, 479, 508, 485, 447, 468, 504, 486, 463, 423, 383, 410, 448, 415, 431, 431, 450, 485, 376, 376, 431, 407, 357, 366, 377, 377, 411, 383, 427, 423, 427, 387, 451, 406, 450, 423, 425, 424, 396, 435, 424, 414, 432, 419, 340, 421, 361, 395, 370, 372, 442, 409, 405, 405, 404, 413, 473, 440, 484, 458, 473, 435, 419, 449, 449, 481, 495, 495, 458, 432, 435, 473, 440, 477, 593, 608, 588, 635, 536, 535, 606, 615, 546, 546, 565, 537, 472, 489, 565, 537, 563, 565, 507, 434, 476, 476, 395, 395, 434, 381, 344, 344, 426, 426, 381, 380, 489, 461, 461, 474, 488, 488, 489, 488, 445, 453, 386, 453, 493, 412, 496, 544, 544, 540, 493, 526, 581, 566, 540, 540, 540, 546, 540, 566, 544, 625, 606, 636, 639, 620, 636, 620, 651, 679, 613, 649, 679, 721, 683, 713, 679, 690, 639, 666, 606, 611, 620, 620, 642, 642, 593, 616, 616, 625, 635, 635, 654, 654, 660, 692, 712, 712, 639, 651, 682, 696, 697, 699, 679, 731, 699, 713, 713, 715, 699, 715, 729, 729, 748, 739, 702, 740, 752, 741, 775, 775, 761, 764, 763, 764, 690, 683, 740, 730, 740, 764, 772, 770, 772, 778, 776, 776,
+ 5, 82, 288, 671, 192, 277, 339, 82, 215, 538, 602, 437, 60, 277, 699, 385, 510, 518, 435, 217, 693, 262, 4, 136, 11, 261, 61, 408, 28, 311, 193, 451, 356, 49, 92, 35, 126, 272, 243, 83, 107, 115, 418, 5, 187, 580, 420, 720, 14, 354, 603, 358, 31, 431, 403, 415, 468, 575, 603, 573, 623, 618, 594, 668, 698, 739, 691, 738, 686, 735, 580, 762, 754, 664, 661, 723, 739, 517, 628, 626, 617, 575, 595, 635, 649, 545, 523, 752, 606, 740, 488, 24, 9, 46, 7, 9, 58, 3, 19, 69, 57, 153, 116, 165, 139, 85, 139, 523, 220, 97, 331, 455, 445, 260, 461, 404, 106, 321, 197, 285, 105, 189, 223, 159, 139, 284, 266, 199, 339, 180, 328, 321, 419, 365, 312, 355, 405, 279, 339, 337, 316, 339, 321, 152, 175, 179, 175, 128, 160, 123, 239, 72, 151, 35, 166, 25, 13, 123, 179, 119, 229, 66, 120, 86, 43, 75, 141, 115, 95, 317, 124, 219, 347, 108, 144, 155, 96, 168, 108, 29, 5, 204, 134, 8, 84, 55, 12, 214, 389, 216, 214, 5, 226, 268, 91, 36, 326, 36, 329, 90, 243, 460, 441, 367, 324, 254, 149, 516, 100, 276, 198, 357, 350, 391, 468, 291, 289, 345, 391, 195, 148, 316, 317, 256, 304, 270, 168, 342, 304, 359, 343, 368, 366, 366, 465, 422, 448, 314, 415, 448, 443, 510, 448, 497, 401, 560, 589, 436, 400, 401, 454, 582, 502, 441, 701, 518, 646, 530, 555, 522, 598, 629, 478, 610, 532, 586, 619, 610, 603, 571, 684, 751, 736, 674, 725, 765, 725, 775, 754, 762, 751, 762, 749, 765, 760, 665, 598, 709, 728, 650, 631, 530, 668, 530, 607, 619, 597, 655, 665, 658, 667, 667, 658, 727, 752, 590, 619, 771, 740, 556, 614, 739, 721, 588, 575, 591, 595, 479, 481, 570, 599, 564, 579, 423, 406, 484, 477, 351, 419, 388, 396, 328, 205, 327, 439, 426, 491, 472, 534, 440, 507, 566, 602, 496, 587, 184, 489, 260, 546, 346, 445, 446, 496, 596, 576, 690, 578, 639, 677, 728, 620, 596, 519, 638, 576, 682, 723, 700, 678, 763, 743, 739, 740, 752, 770, 21, 13, 33, 21, 28, 287, 15, 28, 23, 9, 9, 2, 15, 15, 6, 6, 13, 48, 1, 10, 6, 69, 13, 24, 13, 23, 16, 101, 38, 87, 38, 62, 153, 76, 139, 112, 57, 104, 105, 92, 105, 104, 136, 104, 57, 126, 205, 153, 127, 87, 37, 61, 159, 61, 101, 62, 87, 51, 60, 227, 85, 287, 110, 185, 147, 110, 325, 260, 287, 165, 227, 217, 283, 234, 307, 262, 331, 227, 217, 344, 103, 263, 283, 260, 394, 184, 331, 426, 446, 344, 228, 278, 310, 380, 293, 307, 310, 278, 340, 307, 307, 332, 319, 361, 361, 395, 371, 319, 332, 297, 372, 332, 284, 151, 253, 327, 327, 294, 245, 297, 206, 294, 208, 245, 208, 293, 275, 238, 180, 261, 228, 180, 189, 245, 199, 238, 228, 189, 166, 151, 167, 117, 161, 118, 192, 161, 200, 161, 232, 200, 246, 167, 209, 166, 210, 166, 210, 297, 295, 333, 362, 396, 355, 332, 348, 328, 362, 396, 246, 285, 279, 321, 311, 355, 257, 239, 266, 232, 348, 311, 410, 365, 305, 302, 379, 382, 305, 299, 296, 257, 305, 337, 258, 251, 258, 288, 211, 192, 223, 175, 241, 211, 182, 130, 190, 162, 212, 224, 186, 154, 212, 179, 128, 170, 133, 179, 114, 119, 133, 114, 123, 154, 128, 114, 72, 130, 72, 175, 128, 154, 102, 182, 106, 152, 118, 161, 160, 105, 112, 117, 113, 152, 25, 130, 102, 140, 106, 113, 65, 107, 89, 107, 93, 47, 81, 106, 47, 25, 58, 82, 25, 10, 41, 58, 70, 58, 25, 10, 29, 42, 42, 25, 66, 41, 43, 70, 52, 39, 77, 95, 30, 71, 44, 40, 44, 30, 40, 30, 78, 71, 64, 43, 68, 71, 68, 75, 75, 86, 67, 74, 77, 98, 78, 94, 98, 114, 119, 94, 170, 186, 193, 251, 194, 168, 171, 218, 120, 98, 142, 120, 171, 194, 172, 226, 176, 138, 191, 176, 207, 191, 198, 148, 132, 163, 5, 198, 230, 157, 221, 198, 129, 172, 12, 198, 131, 124, 138, 125, 83, 86, 124, 109, 109, 143, 125, 172, 129, 156, 32, 5, 122, 5, 84, 22, 146, 36, 59, 36, 134, 55, 25, 18, 5, 32, 12, 14, 8, 91, 91, 45, 56, 79, 135, 100, 45, 215, 135, 56, 91, 215, 122, 268, 146, 201, 196, 59, 216, 214, 150, 306, 174, 177, 146, 254, 90, 201, 268, 121, 233, 183, 146, 132, 183, 132, 183, 132, 158, 145, 202, 158, 202, 195, 132, 195, 145, 249, 250, 242, 202, 249, 203, 291, 242, 291, 249, 384, 222, 292, 243, 233, 173, 250, 195, 280, 292, 255, 349, 282, 390, 269, 135, 336, 269, 254, 322, 215, 255, 177, 303, 330, 303, 356, 354, 277, 330, 390, 309, 336, 373, 338, 214, 374, 354, 390, 356, 303, 428, 464, 367, 314, 369, 430, 324, 364, 326, 286, 403, 403, 347, 323, 358, 326, 347, 281, 358, 329, 376, 347, 363, 308, 377, 411, 308, 304, 357, 350, 313, 357, 313, 334, 308, 350, 334, 304, 335, 347, 276, 290, 301, 308, 221, 237, 237, 202, 221, 256, 240, 256, 256, 221, 259, 248, 289, 236, 236, 191, 264, 219, 213, 176, 219, 213, 218, 247, 224, 235, 225, 194, 267, 270, 271, 236, 267, 312, 315, 264, 270, 316, 300, 298, 298, 271, 300, 312, 368, 387, 315, 345, 359, 337, 379, 419, 422, 393, 454, 422, 397, 349, 403, 430, 459, 467, 490, 467, 456, 415, 471, 454, 543, 456, 494, 471, 514, 490, 548, 510, 573, 583, 547, 573, 589, 573, 529, 490, 529, 510, 561, 529, 542, 492, 542, 568, 561, 548, 626, 597, 547, 597, 594, 582, 416, 469, 527, 501, 547, 522, 470, 438, 501, 527, 467, 470, 469, 501, 397, 349, 438, 469, 416, 502, 428, 470, 400, 428, 400, 322, 500, 420, 533, 560, 533, 559, 482, 500, 532, 552, 420, 525, 444, 482, 482, 516, 385, 273, 460, 336, 487, 433, 336, 487, 541, 530, 518, 505, 558, 516, 560, 541, 516, 592, 487, 574, 518, 567, 483, 600, 691, 600, 629, 646, 592, 530, 601, 555, 607, 574, 631, 580, 612, 650, 551, 505, 586, 516, 585, 612, 577, 584, 577, 552, 584, 559, 586, 558, 604, 586, 646, 629, 673, 653, 693, 673, 698, 694, 720, 707, 732, 725, 632, 571, 670, 632, 691, 725, 641, 685, 711, 669, 704, 722, 757, 722, 695, 704, 691, 709, 720, 724, 709, 747, 759, 751, 758, 768, 779, 782, 773, 765, 774, 782, 780, 773, 771, 766, 775, 769, 737, 737, 716, 738, 722, 755, 732, 745, 756, 750, 735, 755, 750, 766, 762, 717, 734, 756, 762, 703, 701, 744, 734, 687, 707, 700, 726, 688, 708, 703, 719, 717, 703, 657, 646, 672, 656, 622, 567, 653, 673, 631, 621, 634, 668, 650, 645, 656, 672, 676, 668, 652, 676, 637, 665, 624, 604, 637, 621, 626, 621, 630, 643, 643, 626, 644, 658, 655, 667, 678, 675, 686, 723, 663, 668, 681, 665, 701, 684, 701, 689, 727, 718, 710, 708, 718, 710, 748, 739, 640, 655, 705, 689, 543, 484, 590, 573, 504, 477, 550, 521, 564, 545, 595, 575, 705, 710, 671, 647, 692, 700, 635, 602, 654, 635, 587, 615, 608, 587, 524, 579, 524, 579, 628, 608, 504, 477, 499, 549, 534, 557, 535, 557, 506, 524, 509, 534, 462, 524, 473, 524, 531, 486, 495, 447, 531, 485, 515, 539, 531, 539, 539, 538, 543, 553, 520, 494, 520, 538, 521, 543, 485, 456, 486, 468, 465, 450, 481, 465, 450, 427, 387, 392, 431, 384, 443, 407, 463, 479, 407, 391, 418, 391, 383, 368, 402, 383, 387, 366, 411, 402, 414, 382, 424, 382, 427, 411, 449, 414, 425, 455, 406, 382, 410, 392, 381, 413, 404, 434, 405, 371, 408, 372, 409, 372, 434, 360, 442, 409, 475, 465, 440, 409, 447, 455, 458, 465, 475, 481, 449, 417, 462, 499, 473, 499, 591, 587, 616, 628, 537, 556, 616, 591, 556, 578, 563, 536, 461, 523, 537, 507, 537, 562, 472, 395, 472, 439, 381, 352, 421, 360, 380, 394, 394, 380, 413, 426, 452, 421, 489, 512, 446, 474, 512, 526, 386, 398, 398, 446, 412, 445, 453, 466, 493, 496, 496, 546, 576, 540, 493, 526, 566, 566, 544, 576, 519, 596, 578, 616, 638, 581, 651, 611, 666, 649, 620, 666, 648, 729, 702, 715, 666, 697, 636, 690, 625, 642, 642, 649, 651, 666, 617, 639, 636, 651, 638, 617, 659, 638, 682, 686, 696, 705, 660, 677, 680, 692, 682, 696, 702, 728, 715, 729, 697, 699, 714, 728, 731, 743, 741, 731, 721, 743, 743, 731, 776, 769, 753, 754, 764, 753, 702, 706, 721, 721, 729, 763, 764, 764, 769, 770, 778, 772,
+ 148, 89, 267, 659, 232, 373, 320, 65, 149, 553, 614, 430, 17, 216, 682, 273, 494, 487, 425, 147, 674, 220, 11, 92, 17, 307, 46, 442, 19, 279, 197, 427, 314, 63, 112, 41, 139, 290, 250, 109, 114, 142, 423, 163, 219, 574, 482, 732, 8, 416, 599, 393, 20, 415, 437, 393, 465, 583, 597, 570, 627, 619, 577, 650, 688, 741, 694, 736, 671, 732, 551, 760, 760, 678, 675, 734, 744, 511, 640, 610, 593, 564, 599, 615, 613, 549, 556, 760, 588, 753, 512, 23, 15, 33, 11, 2, 63, 10, 28, 80, 76, 127, 167, 97, 87, 33, 101, 535, 159, 165, 287, 449, 412, 346, 472, 439, 29, 295, 171, 279, 136, 136, 241, 220, 159, 294, 296, 245, 365, 234, 295, 285, 410, 348, 288, 388, 425, 302, 351, 320, 300, 302, 348, 182, 190, 186, 211, 111, 199, 162, 279, 29, 160, 29, 167, 71, 19, 137, 137, 120, 235, 67, 115, 108, 53, 86, 144, 108, 115, 301, 108, 187, 353, 96, 170, 187, 108, 187, 115, 35, 109, 158, 177, 18, 122, 18, 22, 277, 244, 269, 56, 157, 259, 314, 26, 84, 286, 54, 323, 134, 286, 433, 309, 369, 326, 282, 196, 525, 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+ };*/
+
+#define num_points 784
+#define num_triag 1519
+int16_t SI_Points[4*num_points]={
+ 28120, 25954, 17028, 9063, 5343, 3387, 2250, 1557, 1107, 816, 617, 479, 378, 306, 253, 211, 180, 156, 136, 120, 108, 98, 90, 83, 77, 72, 68, 65, 25331, 22182, 15076, 9296, 5927, 3939, 2708, 1911, 1386, 1031, 784, 609, 483, 389, 319, 266, 225, 192, 167, 147, 130, 116, 105, 96, 89, 82, 77, 73, 16706, 15291, 11625, 8167, 5688, 3998, 2856, 2080, 1542, 1167, 897, 705, 562, 454, 373, 311, 263, 224, 194, 169, 149, 133, 120, 109, 100, 92, 85, 80, 10880, 10380, 8636, 6663, 4989, 3713, 2772, 2089, 1592, 1229, 964, 765, 616, 502, 414, 346, 292, 250, 216, 189, 166, 148, 133, 120, 110, 101, 93, 87, 7073, 7061, 6285, 5206, 4156, 3259, 2539, 1981, 1554, 1229, 981, 791, 645, 530, 442, 371, 315, 271, 234, 205, 181, 160, 144, 130, 118, 108, 100, 93, 4513, 4783, 4509, 3972, 3357, 2756, 2239, 1809, 1459, 1181, 962, 789, 652, 543, 456, 387, 331, 285, 247, 217, 192, 171, 153, 138, 125, 115, 106, 98, 2892, 3247, 3234, 2996, 2652, 2278, 1920, 1603, 1330, 1104, 917, 765, 641, 541, 460, 393, 338, 293, 256, 225, 200, 178, 160, 144, 131, 120, 111, 103, 1905, 2232, 2331, 2260, 2082, 1857, 1621, 1393, 1188, 1009, 856, 726, 618, 528, 453, 391, 339, 296, 260, 230, 205, 183, 165, 149, 136, 125, 115, 106, 1288, 1571, 1703, 1711, 1635, 1507, 1352, 1196, 1046, 907, 785, 677, 585, 506, 439, 384, 336, 295, 261, 232, 207, 186, 168, 153, 139, 128, 118, 110, 893, 1128, 1261, 1306, 1285, 1218, 1124, 1019, 910, 807, 710, 623, 546, 480, 421, 370, 328, 290, 259, 231, 207, 188, 170, 155, 142, 131, 120, 112, 637, 826, 947, 1007, 1015, 986, 933, 864, 787, 711, 637, 569, 505, 448, 399, 355, 316, 282, 253, 228, 206, 187, 170, 155, 142, 131, 122, 113, 466, 617, 723, 785, 810, 803, 774, 732, 680, 624, 568, 514, 464, 417, 375, 336, 303, 273, 246, 223, 203, 184, 169, 155, 143, 132, 122, 114, 349, 471, 561, 619, 650, 658, 645, 620, 586, 546, 504, 463, 423, 384, 349, 317, 288, 261, 237, 216, 197, 181, 166, 153, 142, 131, 123, 114, 268, 365, 442, 495, 528, 541, 540, 527, 505, 478, 447, 416, 384, 353, 323, 296, 271, 248, 228, 209, 192, 176, 163, 151, 140, 130, 122, 114, 211, 289, 354, 400, 432, 449, 454, 449, 436, 418, 396, 372, 348, 323, 299, 276, 255, 235, 217, 201, 185, 172, 159, 148, 138, 128, 120, 113, 169, 233, 286, 328, 357, 376, 385, 384, 378, 366, 351, 333, 314, 295, 276, 257, 239, 222, 206, 191, 178, 166, 154, 144, 135, 127, 119, 112, 138, 191, 236, 272, 299, 317, 327, 331, 328, 322, 311, 299, 284, 269, 254, 238, 223, 209, 196, 183, 171, 160, 150, 140, 132, 124, 116, 110, 115, 159, 197, 228, 252, 270, 281, 286, 287, 284, 277, 268, 257, 245, 233, 221, 209, 196, 184, 174, 163, 153, 144, 136, 128, 121, 114, 109, 98, 135, 166, 193, 216, 231, 243, 249, 252, 251, 247, 241, 233, 224, 215, 204, 194, 184, 175, 165, 156, 147, 139, 132, 124, 118, 112, 106, 85, 116, 143, 166, 186, 201, 211, 219, 222, 223, 221, 217, 212, 205, 198, 189, 181, 172, 164, 156, 148, 141, 133, 127, 121, 114, 109, 104, 75, 101, 124, 145, 162, 175, 186, 193, 197, 199, 198, 196, 192, 188, 182, 176, 169, 162, 155, 148, 141, 135, 128, 122, 116, 111, 106, 101, 67, 89, 109, 127, 142, 154, 164, 171, 175, 178, 179, 178, 175, 172, 168, 162, 157, 152, 146, 140, 134, 128, 123, 118, 113, 108, 103, 99, 61, 80, 97, 112, 126, 137, 146, 153, 157, 160, 162, 161, 160, 158, 155, 151, 147, 142, 137, 133, 127, 122, 118, 113, 109, 105, 100, 96, 57, 73, 87, 101, 112, 123, 131, 137, 142, 145, 147, 147, 147, 145, 143, 140, 137, 134, 129, 125, 121, 117, 113, 108, 105, 101, 97, 94, 52, 66, 80, 91, 101, 111, 118, 124, 129, 132, 134, 136, 135, 135, 133, 131, 128, 125, 122, 119, 115, 112, 108, 104, 101, 98, 94, 91, 50, 61, 73, 83, 93, 100, 107, 113, 118, 121, 123, 125, 125, 125, 124, 123, 120, 118, 115, 113, 109, 107, 103, 100, 97, 94, 91, 89, 47, 58, 67, 77, 85, 92, 98, 104, 108, 111, 114, 115, 116, 116, 115, 115, 113, 111, 109, 107, 104, 102, 99, 97, 94, 91, 89, 86, 45, 54, 63, 71, 79, 85, 91, 96, 100, 103, 105, 107, 108, 108, 108, 108, 106, 105, 103, 102, 99, 97, 95, 93, 90, 88, 86, 83,
+ 22973, 1678, -7370, -5167, -3767, -2873, -2210, -1714, -1348, -1076, -869, -711, -589, -492, -416, -355, -305, -264, -231, -203, -179, -159, -143, -128, -115, -105, -95, -87, 18855, 7465, -325, -1863, -1923, -1751, -1510, -1264, -1053, -875, -729, -611, -516, -439, -376, -324, -281, -246, -216, -191, -169, -151, -136, -123, -111, -101, -92, -85, 17033, 8876, 3019, 513, -417, -749, -835, -810, -738, -654, -572, -498, -432, -376, -328, -287, -252, -223, -197, -176, -157, -142, -128, -116, -105, -96, -88, -81, 12847, 7754, 3912, 1729, 598, 12, -276, -403, -443, -438, -413, -378, -342, -307, -274, -246, -219, -197, -177, -159, -144, -130, -118, -108, -98, -90, -83, -77, 9260, 6299, 3890, 2224, 1172, 522, 145, -72, -188, -243, -263, -264, -254, -238, -221, -202, -185, -169, -154, -141, -129, -118, -108, -99, -91, -84, -78, -72, 6969, 5141, 3545, 2316, 1432, 823, 427, 172, 15, -79, -132, -159, -170, -172, -167, -159, -151, -141, -131, -121, -113, -104, -97, -90, -84, -77, -72, -67, 5363, 4191, 3104, 2196, 1490, 969, 597, 339, 166, 51, -23, -69, -96, -111, -117, -119, -117, -113, -108, -102, -97, -91, -85, -80, -75, -70, -66, -62, 4170, 3402, 2655, 1993, 1443, 1012, 684, 444, 270, 148, 64, 6, -32, -57, -72, -81, -85, -86, -85, -84, -80, -77, -74, -70, -67, -63, -60, -56, 3271, 2762, 2245, 1760, 1341, 992, 713, 499, 336, 216, 128, 65, 20, -12, -33, -47, -56, -61, -65, -66, -65, -64, -62, -60, -58, -56, -53, -51, 2597, 2251, 1887, 1534, 1213, 936, 705, 521, 373, 261, 175, 110, 61, 26, 1, -18, -31, -39, -45, -49, -51, -51, -52, -51, -50, -49, -47, -45, 2081, 1843, 1585, 1325, 1080, 862, 676, 518, 389, 286, 205, 142, 93, 56, 28, 7, -8, -19, -28, -33, -38, -40, -41, -42, -42, -42, -41, -40, 1687, 1521, 1335, 1143, 956, 784, 632, 500, 389, 298, 223, 163, 117, 79, 51, 28, 10, -2, -12, -19, -25, -29, -32, -33, -34, -35, -35, -35, 1383, 1265, 1129, 983, 841, 706, 583, 474, 379, 299, 232, 177, 132, 96, 67, 44, 26, 12, 1, -7, -14, -19, -22, -25, -27, -28, -29, -30, 1146, 1059, 959, 849, 740, 633, 533, 442, 362, 293, 234, 184, 142, 108, 80, 57, 39, 24, 12, 3, -5, -10, -15, -18, -21, -23, -24, -25, 958, 895, 819, 735, 649, 565, 484, 409, 342, 282, 230, 186, 147, 116, 89, 67, 49, 34, 22, 12, 4, -2, -8, -12, -15, -17, -19, -20, 808, 760, 703, 639, 571, 503, 439, 376, 320, 269, 224, 183, 150, 120, 95, 74, 56, 42, 29, 19, 11, 4, -1, -6, -9, -12, -14, -16, 687, 650, 606, 556, 503, 449, 396, 345, 297, 254, 214, 179, 148, 122, 99, 79, 62, 47, 35, 25, 17, 10, 4, -1, -5, -8, -10, -13, 588, 560, 526, 487, 444, 401, 357, 315, 275, 237, 204, 173, 145, 121, 100, 81, 65, 52, 40, 30, 22, 15, 9, 4, 0, -4, -6, -9, 507, 485, 458, 427, 393, 358, 322, 286, 253, 221, 192, 165, 141, 119, 100, 83, 68, 55, 43, 34, 26, 19, 13, 8, 4, 0, -3, -6, 440, 422, 401, 376, 349, 320, 290, 261, 233, 206, 180, 157, 135, 116, 98, 82, 69, 56, 46, 37, 29, 22, 16, 11, 6, 3, 0, -3, 383, 370, 353, 332, 310, 287, 262, 238, 214, 191, 168, 148, 129, 112, 96, 82, 69, 58, 48, 39, 31, 25, 19, 13, 9, 6, 2, -1, 336, 325, 311, 295, 277, 257, 237, 216, 196, 176, 158, 139, 122, 107, 93, 80, 68, 58, 49, 40, 33, 26, 21, 16, 12, 8, 5, 2, 296, 287, 276, 262, 248, 231, 215, 197, 180, 163, 146, 130, 116, 102, 90, 78, 67, 57, 49, 41, 34, 28, 23, 17, 13, 10, 7, 4, 262, 255, 246, 234, 222, 208, 194, 179, 165, 150, 136, 122, 110, 97, 85, 75, 65, 56, 49, 41, 35, 29, 24, 19, 15, 11, 8, 5, 232, 227, 219, 210, 200, 189, 176, 164, 151, 139, 126, 114, 103, 92, 82, 72, 63, 55, 48, 41, 35, 29, 24, 20, 16, 13, 9, 7, 207, 203, 196, 189, 180, 170, 160, 150, 138, 128, 117, 107, 96, 87, 78, 69, 61, 54, 47, 41, 35, 29, 25, 21, 17, 13, 10, 8, 185, 182, 176, 170, 162, 155, 146, 137, 127, 118, 109, 100, 91, 82, 74, 66, 59, 52, 46, 40, 35, 29, 25, 21, 18, 14, 11, 8, 167, 163, 159, 153, 147, 140, 133, 125, 117, 109, 101, 92, 85, 77, 70, 63, 56, 50, 44, 39, 34, 30, 25, 21, 18, 15, 12, 9,
+ 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 1600, 1700, 1800, 1900, 2000, 2100, 2200, 2300, 2400, 2500, 2600, 2700, 2800, 2900, 3000,
+ 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 200, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 300, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 400, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 500, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 600, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 700, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 800, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 900, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1000, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1100, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1200, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1300, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1400, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1500, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1600, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1700, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1800, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 1900, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2000, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2100, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2200, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2300, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2400, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2500, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2600, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2700, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2800, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900, 2900,
+ };
+int16_t SI_ConnectivityList[6*num_triag]={
+ 580, 306, 742, 580, 756, 740, 779, 685, 768, 680, 730, 313, 729, 395, 92, 563, 731, 49, 567, 475, 203, 697, 611, 248, 783, 587, 444, 274, 662, 416, 470, 527, 497, 766, 698, 778, 724, 697, 611, 735, 772, 766, 722, 761, 729, 372, 594, 630, 653, 631, 601, 666, 695, 721, 581, 522, 411, 548, 625, 302, 212, 480, 645, 400, 450, 365, 701, 281, 392, 515, 256, 411, 262, 232, 122, 387, 124, 72, 39, 110, 412, 271, 185, 410, 329, 12, 234, 126, 151, 67, 92, 37, 172, 38, 142, 77, 755, 223, 223, 27, 109, 136, 222, 475, 416, 250, 362, 138, 307, 223, 164, 135, 221, 104, 136, 191, 132, 18, 50, 74, 186, 358, 361, 218, 242, 362, 471, 304, 360, 135, 219, 555, 418, 474, 390, 333, 416, 440, 498, 469, 524, 548, 412, 610, 557, 665, 666, 606, 525, 722, 641, 719, 666, 638, 667, 529, 419, 783, 753, 782, 139, 724, 781, 780, 670, 750, 779, 776, 772, 747, 777, 632, 767, 712, 764, 656, 761, 712, 764, 735, 761, 735, 762, 738, 763, 761, 651, 644, 504, 561, 672, 505, 477, 561, 616, 533, 707, 675, 648, 590, 622, 647, 626, 678, 740, 710, 647, 596, 394, 479, 449, 651, 458, 655, 519, 628, 624, 570, 456, 657, 603, 630, 520, 659, 684, 662, 606, 715, 632, 717, 580, 607, 608, 661, 551, 634, 552, 577, 606, 462, 597, 485, 596, 541, 408, 429, 461, 452, 400, 314, 348, 481, 507, 482, 564, 457, 538, 427, 479, 425, 481, 364, 421, 395, 398, 309, 337, 366, 338, 451, 454, 341, 425, 367, 365, 311, 338, 313, 177, 309, 146, 145, 116, 169, 140, 84, 85, 89, 114, 88, 141, 87, 58, 313, 371, 90, 116, 344, 398, 316, 367, 314, 341, 317, 317, 374, 315, 345, 235, 315, 343, 202, 177, 320, 542, 237, 295, 151, 149, 176, 93, 269, 494, 212, 239, 242, 268, 325, 487, 378, 404, 546, 464, 464, 432, 573, 574, 597, 571, 244, 353, 409, 462, 381, 489, 353, 378, 326, 324, 216, 269, 215, 213, 246, 159, 271, 187, 188, 131, 42, 129, 157, 42, 128, 153, 41, 127, 68, 68, 66, 39, 68, 96, 123, 211, 235, 264, 152, 123, 150, 94, 10, 92, 7, 63, 57, 53, 23, 25, 80, 22, 22, 132, 26, 52, 53, 51, 22, 82, 25, 81, 24, 25, 111, 55, 26, 54, 110, 110, 139, 223, 139, 54, 54, 81, 138, 109, 166, 137, 164, 137, 193, 223, 167, 279, 307, 279, 334, 278, 334, 250, 278, 279, 222, 221, 194, 194, 137, 80, 79, 138, 81, 108, 51, 20, 78, 47, 21, 20, 17, 49, 77, 20, 75, 48, 48, 107, 133, 107, 107, 192, 135, 163, 106, 73, 19, 19, 77, 48, 72, 76, 76, 104, 47, 43, 17, 246, 162, 160, 161, 161, 134, 219, 162, 160, 189, 192, 163, 247, 220, 247, 190, 160, 245, 276, 360, 245, 304, 305, 332, 274, 276, 246, 274, 277, 277, 248, 276, 221, 193, 249, 220, 247, 275, 192, 192, 248, 250, 307, 278, 363, 306, 278, 221, 447, 390, 391, 334, 447, 418, 500, 446, 444, 473, 443, 472, 332, 388, 415, 415, 361, 332, 331, 330, 302, 302, 331, 302, 301, 387, 358, 413, 356, 384, 386, 414, 331, 386, 357, 357, 387, 554, 469, 443, 415, 386, 384, 412, 467, 468, 413, 384, 442, 498, 498, 498, 468, 468, 583, 526, 555, 498, 554, 500, 526, 527, 470, 499, 556, 474, 471, 500, 555, 585, 582, 583, 499, 499, 583, 641, 638, 639, 586, 639, 611, 639, 556, 587, 585, 612, 558, 584, 558, 529, 530, 501, 502, 363, 531, 474, 446, 447, 391, 391, 474, 531, 474, 503, 502, 587, 559, 530, 531, 502, 586, 671, 614, 614, 559, 671, 558, 586, 615, 643, 587, 615, 727, 782, 726, 754, 669, 725, 83, 782, 753, 754, 697, 726, 614, 724, 642, 613, 668, 724, 669, 668, 780, 780, 754, 754, 725, 697, 778, 777, 723, 777, 695, 749, 748, 774, 747, 774, 719, 772, 721, 749, 694, 723, 720, 775, 720, 748, 664, 721, 611, 665, 637, 665, 665, 663, 664, 664, 720, 692, 692, 692, 720, 717, 716, 745, 745, 719, 745, 690, 688, 743, 770, 687, 713, 740, 766, 710, 711, 711, 715, 742, 743, 772, 743, 769, 773, 774, 771, 746, 744, 772, 745, 771, 766, 765, 738, 765, 741, 741, 732, 730, 732, 758, 734, 760, 758, 705, 758, 707, 701, 731, 27, 703, 701, 730, 703, 674, 701, 728, 702, 616, 673, 589, 505, 700, 674, 672, 646, 644, 590, 673, 647, 702, 703, 616, 592, 617, 617, 534, 534, 534, 533, 617, 618, 675, 649, 676, 733, 651, 677, 676, 703, 677, 704, 648, 675, 706, 705, 678, 705, 736, 679, 735, 736, 736, 656, 738, 711, 740, 658, 654, 710, 685, 685, 680, 625, 679, 682, 707, 708, 680, 680, 655, 681, 593, 619, 622, 649, 565, 590, 506, 478, 563, 507, 592, 535, 650, 650, 565, 591, 595, 621, 566, 592, 567, 593, 536, 563, 480, 478, 564, 508, 541, 594, 568, 595, 539, 564, 654, 599, 627, 601, 626, 653, 651, 652, 652, 626, 684, 629, 683, 656, 627, 627, 628, 574, 602, 602, 603, 550, 549, 520, 577, 522, 494, 493, 603, 633, 604, 605, 686, 605, 657, 657, 603, 631, 685, 715, 714, 632, 713, 741, 685, 712, 689, 688, 661, 661, 686, 714, 687, 687, 631, 659, 690, 609, 633, 661, 718, 718, 662, 690, 665, 610, 663, 664, 581, 636, 607, 635, 580, 608, 553, 553, 469, 468, 606, 635, 525, 496, 579, 579, 577, 578, 549, 523, 523, 468, 495, 495, 439, 493, 598, 599, 571, 545, 598, 572, 571, 516, 514, 543, 514, 460, 544, 490, 544, 462, 434, 461, 435, 458, 405, 349, 377, 346, 349, 292, 346, 346, 318, 347, 488, 433, 460, 431, 460, 460, 485, 459, 459, 404, 431, 376, 403, 403, 429, 375, 347, 319, 512, 486, 402, 456, 403, 401, 568, 569, 513, 510, 541, 541, 513, 513, 567, 595, 569, 543, 512, 565, 539, 566, 567, 512, 566, 510, 512, 511, 539, 484, 428, 455, 454, 510, 453, 453, 563, 537, 481, 508, 537, 511, 506, 480, 478, 449, 423, 450, 420, 420, 336, 395, 421, 453, 480, 450, 450, 426, 451, 423, 423, 421, 368, 309, 421, 395, 280, 396, 368, 342, 396, 395, 369, 396, 396, 370, 398, 342, 369, 424, 424, 456, 399, 370, 397, 374, 428, 402, 401, 429, 374, 428, 373, 344, 344, 310, 311, 283, 256, 255, 202, 227, 201, 254, 285, 254, 228, 253, 308, 254, 281, 253, 281, 252, 197, 226, 225, 225, 226, 143, 199, 197, 227, 198, 172, 143, 196, 112, 114, 113, 113, 113, 0, 29, 58, 57, 58, 29, 30, 1, 142, 115, 114, 59, 142, 197, 168, 168, 169, 169, 200, 200, 198, 198, 171, 171, 116, 88, 30, 174, 200, 144, 172, 147, 146, 117, 60, 257, 286, 201, 229, 311, 285, 282, 257, 200, 228, 255, 282, 257, 257, 365, 339, 284, 284, 339, 339, 340, 314, 258, 285, 258, 287, 257, 285, 289, 261, 316, 206, 317, 317, 343, 288, 317, 345, 318, 319, 289, 290, 207, 261, 232, 261, 203, 232, 203, 204, 287, 288, 231, 259, 258, 259, 202, 230, 86, 60, 148, 118, 145, 145, 147, 90, 264, 262, 207, 234, 347, 293, 319, 320, 294, 321, 321, 321, 237, 236, 205, 205, 176, 176, 238, 235, 118, 61, 180, 180, 206, 206, 182, 266, 181, 208, 323, 266, 295, 238, 264, 265, 269, 268, 267, 294, 155, 239, 266, 266, 242, 241, 270, 214, 327, 297, 325, 406, 351, 352, 436, 352, 380, 350, 352, 323, 377, 351, 434, 350, 376, 404, 489, 407, 407, 379, 377, 405, 491, 436, 517, 463, 437, 380, 381, 352, 491, 492, 438, 382, 546, 492, 516, 544, 489, 517, 518, 546, 544, 572, 572, 600, 546, 575, 519, 547, 492, 494, 494, 465, 465, 466, 466, 466, 356, 355, 384, 300, 357, 329, 382, 438, 216, 244, 272, 273, 356, 356, 327, 328, 243, 272, 325, 327, 297, 299, 437, 438, 326, 354, 381, 382, 271, 325, 409, 409, 325, 326, 297, 298, 269, 270, 182, 209, 154, 182, 154, 211, 98, 181, 184, 213, 241, 156, 212, 241, 241, 184, 210, 210, 189, 187, 159, 157, 187, 189, 216, 216, 160, 103, 44, 130, 101, 158, 129, 157, 101, 100, 74, 73, 101, 100, 103, 46, 46, 45, 74, 17, 43, 71, 45, 41, 101, 44, 70, 43, 97, 71, 157, 100, 128, 71, 156, 99, 126, 99, 125, 154, 12, 12, 69, 69, 66, 9, 37, 8, 36, 36, 94, 94, 92, 122, 96, 96, 66, 40, 96, 39, 126, 97, 182, 125, 152, 208, 179, 179, 151, 122, 92, 148, 123, 152, 152, 95, 93, 121, 119, 120, 62, 119, 148, 148, 118, 118, 91, 62, 32, 31, 91, 34, 62, 33, 61, 61, 34, 31, 33, 31, 34, 63, 63, 62, 35, 33, 4, 3, 2,
+ 608, 334, 741, 553, 728, 739, 780, 684, 767, 707, 729, 314, 728, 394, 119, 562, 703, 77, 595, 363, 204, 670, 583, 219, 777, 755, 472, 302, 661, 389, 442, 499, 496, 757, 699, 779, 751, 725, 584, 734, 756, 767, 750, 757, 756, 399, 621, 603, 626, 603, 574, 694, 696, 749, 582, 549, 439, 575, 598, 274, 239, 507, 646, 399, 449, 392, 728, 254, 420, 488, 229, 383, 289, 205, 149, 415, 96, 73, 11, 139, 384, 272, 157, 382, 330, 11, 206, 127, 123, 66, 64, 8, 144, 9, 115, 105, 783, 222, 783, 55, 108, 137, 250, 587, 417, 249, 333, 166, 335, 194, 165, 106, 249, 132, 108, 162, 104, 46, 79, 103, 214, 386, 389, 189, 214, 389, 444, 332, 359, 163, 190, 528, 391, 446, 389, 360, 444, 441, 471, 497, 523, 549, 413, 583, 584, 638, 693, 634, 497, 695, 640, 718, 667, 666, 668, 502, 391, 139, 725, 755, 783, 696, 782, 753, 671, 778, 752, 777, 757, 774, 778, 633, 766, 713, 737, 655, 733, 711, 736, 762, 759, 763, 761, 737, 761, 734, 679, 645, 505, 588, 728, 504, 476, 560, 617, 532, 706, 676, 621, 591, 649, 674, 627, 650, 712, 683, 648, 597, 366, 451, 476, 652, 485, 627, 492, 629, 597, 543, 484, 629, 575, 602, 548, 631, 711, 635, 578, 714, 660, 690, 552, 580, 636, 634, 523, 635, 524, 578, 579, 490, 598, 512, 623, 513, 407, 457, 488, 479, 373, 342, 347, 508, 534, 483, 536, 484, 537, 426, 506, 453, 482, 392, 448, 423, 426, 308, 364, 339, 310, 452, 455, 368, 452, 366, 393, 338, 365, 285, 205, 310, 174, 144, 115, 197, 168, 57, 84, 88, 86, 87, 113, 59, 30, 341, 399, 89, 144, 343, 370, 315, 339, 341, 313, 344, 316, 402, 287, 318, 236, 316, 344, 175, 178, 348, 515, 264, 323, 178, 148, 148, 65, 268, 466, 183, 238, 243, 240, 297, 459, 351, 403, 518, 437, 436, 404, 546, 575, 570, 599, 216, 354, 408, 435, 353, 488, 352, 406, 327, 296, 245, 241, 214, 185, 245, 130, 244, 186, 160, 102, 71, 157, 129, 14, 127, 154, 69, 126, 39, 40, 38, 10, 97, 124, 152, 238, 262, 291, 151, 94, 149, 65, 9, 63, 35, 34, 29, 24, 51, 23, 108, 51, 21, 103, 25, 51, 52, 79, 23, 53, 24, 52, 23, 53, 83, 26, 55, 83, 81, 111, 83, 167, 138, 82, 53, 110, 139, 138, 194, 166, 136, 165, 222, 195, 166, 223, 755, 307, 305, 306, 362, 279, 307, 250, 193, 193, 166, 165, 136, 79, 78, 109, 80, 79, 22, 49, 79, 75, 49, 19, 46, 78, 106, 48, 46, 77, 76, 135, 105, 106, 78, 163, 134, 134, 105, 101, 47, 18, 76, 47, 71, 104, 75, 75, 46, 44, 18, 218, 134, 132, 162, 133, 105, 191, 161, 161, 190, 191, 162, 219, 191, 218, 189, 188, 273, 247, 387, 246, 303, 304, 359, 275, 304, 275, 303, 305, 304, 276, 303, 192, 165, 248, 219, 276, 303, 164, 193, 249, 222, 306, 277, 335, 305, 249, 220, 419, 417, 362, 333, 446, 417, 473, 417, 445, 446, 444, 473, 360, 389, 416, 443, 360, 303, 359, 329, 331, 330, 330, 273, 329, 386, 385, 441, 357, 385, 387, 441, 358, 413, 358, 385, 414, 553, 442, 415, 414, 385, 412, 439, 440, 441, 412, 383, 470, 525, 470, 499, 469, 496, 555, 553, 527, 497, 527, 501, 499, 528, 471, 472, 529, 473, 472, 528, 556, 612, 555, 556, 500, 527, 584, 668, 611, 612, 613, 667, 612, 640, 584, 671, 613, 640, 585, 612, 557, 556, 529, 528, 503, 587, 503, 501, 419, 475, 363, 419, 503, 587, 475, 531, 530, 614, 558, 557, 530, 529, 614, 670, 642, 613, 587, 699, 559, 587, 643, 642, 643, 642, 755, 783, 727, 755, 670, 726, 783, 781, 726, 727, 698, 699, 641, 723, 641, 640, 696, 725, 696, 667, 781, 783, 753, 726, 724, 696, 780, 783, 750, 780, 722, 777, 776, 772, 775, 776, 746, 777, 722, 750, 695, 696, 748, 776, 721, 749, 692, 694, 638, 693, 638, 666, 692, 691, 691, 636, 747, 691, 720, 719, 719, 689, 744, 773, 718, 691, 717, 662, 715, 744, 743, 715, 741, 767, 738, 709, 738, 710, 743, 769, 771, 774, 770, 757, 774, 747, 772, 718, 772, 770, 772, 770, 764, 737, 766, 764, 768, 740, 731, 757, 759, 757, 761, 759, 759, 706, 731, 734, 729, 732, 783, 702, 674, 702, 675, 646, 673, 701, 674, 672, 645, 562, 532, 673, 647, 645, 619, 617, 562, 646, 619, 675, 704, 589, 619, 618, 645, 533, 506, 561, 560, 590, 619, 648, 621, 677, 732, 678, 704, 704, 731, 705, 732, 676, 703, 733, 732, 706, 733, 708, 706, 708, 737, 709, 684, 710, 684, 741, 631, 681, 711, 657, 658, 653, 597, 680, 709, 680, 709, 681, 708, 654, 709, 620, 647, 650, 677, 537, 618, 505, 477, 535, 506, 564, 534, 651, 678, 592, 619, 622, 649, 593, 620, 594, 621, 508, 591, 479, 505, 537, 507, 568, 622, 596, 623, 538, 592, 626, 598, 600, 629, 654, 681, 624, 653, 625, 598, 656, 628, 655, 628, 628, 655, 601, 546, 574, 575, 576, 523, 548, 519, 549, 495, 521, 520, 631, 606, 577, 578, 659, 577, 630, 658, 604, 659, 686, 742, 687, 605, 714, 742, 713, 740, 688, 661, 688, 633, 687, 715, 660, 688, 632, 660, 663, 637, 634, 662, 690, 691, 663, 691, 637, 582, 636, 637, 609, 637, 608, 636, 581, 609, 525, 526, 496, 495, 607, 608, 524, 523, 551, 552, 550, 551, 522, 496, 495, 440, 467, 468, 466, 492, 599, 600, 544, 518, 571, 544, 543, 488, 515, 516, 487, 461, 516, 518, 517, 434, 433, 460, 407, 430, 404, 321, 376, 347, 348, 265, 373, 345, 346, 348, 460, 405, 459, 430, 432, 433, 458, 432, 431, 376, 403, 348, 375, 376, 456, 347, 346, 291, 485, 459, 429, 483, 402, 373, 541, 570, 512, 483, 514, 542, 486, 514, 568, 596, 542, 515, 539, 593, 567, 594, 539, 484, 538, 482, 511, 510, 511, 483, 427, 483, 482, 537, 454, 480, 536, 509, 509, 536, 510, 483, 479, 453, 450, 448, 422, 422, 421, 448, 364, 422, 449, 481, 508, 451, 478, 398, 479, 424, 451, 422, 341, 336, 394, 367, 308, 368, 340, 369, 424, 368, 342, 369, 397, 371, 399, 370, 397, 425, 452, 429, 426, 398, 425, 401, 455, 401, 400, 401, 373, 400, 345, 372, 371, 309, 283, 284, 228, 228, 230, 200, 229, 255, 284, 227, 200, 280, 309, 282, 309, 254, 282, 280, 196, 225, 252, 224, 198, 144, 198, 224, 199, 197, 171, 115, 197, 84, 113, 85, 112, 86, 56, 1, 85, 84, 57, 28, 29, 0, 114, 87, 87, 31, 170, 198, 169, 196, 142, 170, 172, 173, 171, 199, 143, 144, 88, 60, 1, 173, 228, 145, 173, 174, 173, 89, 59, 230, 287, 202, 230, 310, 258, 283, 229, 201, 229, 283, 310, 284, 256, 338, 312, 311, 283, 340, 367, 313, 287, 286, 313, 259, 288, 258, 286, 261, 233, 289, 179, 289, 290, 315, 287, 318, 346, 291, 320, 262, 291, 234, 262, 233, 234, 231, 260, 176, 205, 260, 261, 232, 260, 231, 232, 203, 231, 59, 32, 147, 117, 146, 173, 119, 62, 263, 290, 235, 262, 320, 265, 292, 293, 293, 349, 293, 322, 209, 263, 206, 233, 177, 204, 210, 263, 90, 88, 208, 207, 207, 234, 209, 293, 209, 236, 295, 265, 267, 265, 237, 238, 296, 295, 295, 322, 183, 267, 267, 294, 271, 240, 242, 186, 355, 296, 352, 405, 324, 325, 408, 324, 379, 322, 351, 322, 405, 323, 406, 349, 377, 405, 462, 379, 406, 351, 378, 406, 463, 435, 490, 435, 409, 407, 380, 379, 464, 465, 410, 354, 519, 464, 517, 572, 490, 518, 519, 574, 545, 600, 573, 601, 547, 548, 520, 548, 493, 467, 493, 437, 438, 439, 465, 438, 355, 382, 356, 272, 356, 301, 410, 439, 244, 273, 300, 300, 328, 329, 300, 301, 244, 273, 326, 328, 298, 300, 410, 411, 354, 355, 354, 355, 298, 353, 381, 382, 298, 299, 270, 271, 242, 271, 210, 237, 182, 154, 183, 239, 70, 153, 185, 214, 213, 155, 213, 242, 212, 183, 211, 238, 188, 215, 158, 185, 188, 161, 188, 217, 131, 102, 16, 159, 130, 186, 158, 186, 129, 128, 73, 72, 100, 99, 74, 17, 45, 44, 45, 16, 15, 72, 16, 42, 72, 43, 42, 14, 98, 42, 128, 71, 99, 70, 127, 98, 98, 70, 126, 155, 41, 40, 40, 41, 37, 8, 36, 7, 64, 35, 66, 95, 93, 150, 68, 97, 67, 11, 67, 38, 125, 96, 153, 124, 180, 209, 180, 207, 150, 93, 121, 149, 124, 153, 123, 94, 122, 149, 92, 121, 91, 147, 120, 121, 119, 146, 90, 33, 31, 32, 62, 35, 61, 32, 60, 32, 6, 30, 5, 3, 5, 35, 64, 34, 7, 4, 3, 2, 1,
+ 581, 335, 769, 552, 672, 767, 752, 712, 769, 708, 757, 286, 756, 422, 120, 590, 730, 78, 568, 419, 176, 669, 610, 247, 756, 307, 445, 303, 689, 388, 469, 526, 524, 769, 671, 751, 752, 698, 583, 762, 777, 739, 723, 766, 757, 400, 622, 602, 625, 630, 573, 667, 668, 722, 554, 550, 412, 576, 597, 273, 240, 508, 618, 427, 477, 393, 729, 253, 393, 487, 228, 410, 290, 204, 150, 388, 95, 44, 10, 111, 411, 244, 156, 409, 302, 40, 233, 98, 150, 95, 63, 36, 171, 37, 114, 106, 223, 251, 167, 83, 137, 108, 251, 363, 389, 278, 361, 167, 363, 222, 136, 134, 250, 133, 107, 190, 103, 47, 51, 75, 215, 359, 362, 217, 213, 390, 443, 333, 387, 164, 218, 527, 390, 473, 417, 361, 417, 413, 470, 470, 551, 521, 385, 582, 585, 637, 694, 607, 524, 694, 668, 746, 639, 639, 640, 501, 418, 167, 752, 754, 83, 723, 754, 752, 643, 751, 751, 749, 756, 775, 750, 605, 769, 685, 736, 683, 760, 739, 763, 763, 757, 736, 763, 765, 766, 733, 652, 617, 477, 589, 700, 532, 504, 588, 589, 560, 734, 648, 620, 563, 650, 675, 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+ };
+
+ void vec(int16_t *a, int16_t *b, int16_t *v){
+ v[0] = a[0] - b[0];
+ v[1] = a[1] - b[1];
+ }
+
+float dot_prod(int16_t *a, int16_t *b){
+ return (double)a[0]*(double)b[0] + (double)a[1]*(double)b[1];
+}
+
+int Triangle_eval(int16_t *P, int16_t *A, int16_t *B, int16_t *C){
+ int16_t v0[2]={0,0};
+ int16_t v1[2]={0,0};
+ int16_t v2[2]={0,0};
+
+ float dot00, dot01, dot02, dot11, dot12, invDenom, u, v;
+
+ vec(C, A, v0);
+ vec(B, A, v1);
+ vec(P, A, v2);
+
+ dot00 = dot_prod(v0,v0);
+ dot01 = dot_prod(v0,v1);
+ dot02 = dot_prod(v0,v2);
+ dot11 = dot_prod(v1,v1);
+ dot12 = dot_prod(v1,v2);
+
+ invDenom = 1 / (dot00 * dot11 - dot01 * dot01);
+ u = (dot11 * dot02 - dot01 * dot12) * invDenom;
+ v = (dot00 * dot12 - dot01 * dot02) * invDenom;
+ //pc.printf("u = %.2f ",u); pc.printf("v = %.2f\n",v);
+ bool Tbool = ((u>=0) && (v>=0)) && (u+v<=1);
+
+ return (Tbool == true)?0:((u+v > 1)?1: (((v<0)&&(v<u))?2:3) );
+ }
+
+ float Triag_area(int16_t *A, int16_t *B, int16_t *C){
+ return ((float)A[0]*(float)B[1]+(float)B[0]*(float)C[1]+(float)A[1]*(float)C[0] - ( (float)C[0]*(float)B[1]+(float)B[0]*(float)A[1]+(float)A[0]*(float)C[1] ));
+ }
+
+ int16_t Find_point(int16_t *p, int16_t i_t, int16_t *P_S, int16_t *C_L, int16_t *inter_p){
+
+ int Eval=1;
+ int16_t triag = i_t;
+ int16_t t[3]={0,0,0};
+ int16_t A[2];
+ int16_t B[2];
+ int16_t C[2];
+
+ while (Eval > 0){
+
+ A[0]= P_S[0*num_points + C_L[0*num_triag + triag]]; A[1]= P_S[1*num_points + C_L[0*num_triag + triag]];
+ B[0]= P_S[0*num_points + C_L[1*num_triag + triag]]; B[1]= P_S[1*num_points + C_L[1*num_triag + triag]];
+ C[0]= P_S[0*num_points + C_L[2*num_triag + triag]]; C[1]= P_S[1*num_points + C_L[2*num_triag + triag]];
+
+ /*pc.printf("Point %d, ", p[0]);
+ pc.printf("%d\n", p[1]);
+ pc.printf("Triag = %d\n", triag);
+ pc.printf("A = %d ", A[0]); pc.printf("%d\n", A[1]);
+ pc.printf("B = %d ", B[0]); pc.printf("%d\n", B[1]);
+ pc.printf("C = %d ", C[0]); pc.printf("%d\n", C[1]);*/
+
+ Eval = Triangle_eval(p, A, B, C);
+ //pc.printf("Eval= %d\n",Eval);
+ if (Eval > 0) {
+ t[0]=t[1];t[1]=t[2];
+ t[2] = C_L[ (Eval+ 2)*num_triag + triag];
+ if (t[2]==t[0]){
+ if (Eval < 3){
+ t[2] = C_L[ (Eval+ 3)*num_triag + triag];
+ }
+ else{
+ t[2] = C_L[ (Eval)*num_triag + triag];
+ }
+ }
+ if (t[2] == -1){
+ Eval = 0;
+ }
+ else{
+ triag = t[2];
+ //pc.printf("Go to triag %d\n",triag);
+ }
+ }
+ }
+
+ A[0]= P_S[0*num_points + C_L[0*num_triag + triag]]; A[1]= P_S[1*num_points + C_L[0*num_triag + triag]];
+ B[0]= P_S[0*num_points + C_L[1*num_triag + triag]]; B[1]= P_S[1*num_points + C_L[1*num_triag + triag]];
+ C[0]= P_S[0*num_points + C_L[2*num_triag + triag]]; C[1]= P_S[1*num_points + C_L[2*num_triag + triag]];
+ float AT = Triag_area(A,B,C);
+ float A1 = Triag_area(p,B,C)/AT;
+ float A2 = Triag_area(A,p,C)/AT;
+ float A3 = Triag_area(A,B,p)/AT;
+
+ inter_p[0] = (int16_t)(A1*P_S[2*num_points + C_L[0*num_triag + triag]] + A2*P_S[2*num_points + C_L[1*num_triag + triag]] + A3*P_S[2*num_points + C_L[2*num_triag + triag]]);
+ inter_p[1] = (int16_t)(A1*P_S[3*num_points + C_L[0*num_triag + triag]] + A2*P_S[3*num_points + C_L[1*num_triag + triag]] + A3*P_S[3*num_points + C_L[2*num_triag + triag]]);
+ return triag;
+ }
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Scattered_interpolator.h Thu May 21 13:10:58 2020 +0000 @@ -0,0 +1,8 @@ +#ifndef Scattered_interpolator_h +#define Scattered_interpolator_h +#define num_points 784 +#define num_triag 1519 + extern int16_t SI_Points[4*num_points]; + extern int16_t SI_ConnectivityList[6*num_triag]; + int16_t Find_point(int16_t *p, int16_t i_t, int16_t *P_S, int16_t *C_L, int16_t *inter_p); +#endif \ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/main.cpp Thu May 21 13:10:58 2020 +0000
@@ -0,0 +1,252 @@
+#include "mbed.h"
+#include "rtos.h"
+#include <math.h>
+#include "MadgwickAHRS.h"
+#include "Mag_track.h"
+#include "Scattered_interpolator.h"
+
+//----------------------------------------------------------------------------------------------------
+// Global ariable declaration
+DigitalOut D_1(PA_7);
+DigitalOut D_2(PA_6);
+Thread thread;
+Ticker read_ticker;
+
+/////// Bounce button interrupt
+InterruptIn button1(USER_BUTTON);
+volatile bool button1_pressed = false; // Used in the main loop
+volatile bool button1_enabled = true; // Used for debouncing
+Timeout button1_timeout; // Used for debouncing
+
+/////// Flags
+bool flag = false;
+bool flag_data_ready = false;
+bool go_flag = false; // 10 sec flag for Qinit set up
+
+/////// External signal buffers
+int16_t Mag_read_buff[24];// 3*8 signed int_16 buffer read from sensor
+int16_t Acc_read[3]={0,0,0};
+int16_t Gyr_read[3]={0,0,0};
+float q_init[4]={1,0,0,0};
+float q_init_n[4]={1,0,0,0};//{-0.8489, 0.0046, -0.001, 0.5286};//{0,0,0,0}; //;
+
+/////// Counters
+int16_t count_1=1;
+int16_t count_2=1;
+
+
+
+//---------------------------------------------------------------------------------------------------
+// Function declarations
+
+// Enables button when bouncing is over
+void button1_enabled_cb(void)
+{
+ button1_enabled = true;
+}
+
+// ISR handling button pressed event
+void button1_onpressed_cb(void)
+{
+ if (button1_enabled) { // Disabled while the button is bouncing
+ button1_enabled = false;
+ button1_pressed = true; // To be read by the main loop
+ button1_timeout.attach(callback(button1_enabled_cb), 0.3); // Debounce time 300 ms
+ }
+}
+
+/////// Toggle flag
+void toggle_flag() {
+ flag = !flag;
+ //myled = !myled;
+}
+
+
+//////////////////////////////////////////////////////////////
+// Sensors reading thread
+//////////////////////////////////////////////////////////////
+void read_thread(){
+ PC.printf("Hello World 30/11/18 DAFG!\n");
+ int16_t i, j;
+ // Raw and Filtered signals buffers
+ memset( Mag_read_buff, 0, sizeof( Mag_read_buff ) );
+ int16_t Mag_filt[24]; // 24 signed int_16 output values from filter
+ int16_t Mag_filt_lp[24];// 24 signed int_16 output values from filter
+ int16_t M_LP[3]; // 3 signed int_16 output values from filter
+ // Quaternion update buffers
+ float a[3]={0,0,0};
+ float g[3]={0,0,0};
+ float m[3]={0,0,0};
+ int32_t q[4]={0, 0, 0, 0};
+ int32_t Q_out[4]={0, 0, 0, 0};
+ float Q[4]={0,0,0,0};
+ //Buffers for magnetic signal rotation
+ float v_I[3]={0,0,0};
+ float v_rotX[3]={0,0,0};
+ int16_t v_rotX_int[24];
+ memset( v_rotX_int, 0, sizeof( v_rotX_int ) );
+ float Mag_filt_f[3];
+ // Buffers for envelope extraction
+ int16_t maximum[6]={0,0,0,0,0,0};
+ int16_t peak_index[6]={0,0,0,0,0,0};
+ int16_t Env[3]={0,0,0};
+ double R[3]={0,0,0};
+ double phase[3]={0,0,0};
+ int16_t Sign[2]={1,1};
+ // ID word buffer
+ char data_out[4];
+ data_out[0] = 0xDA;
+ data_out[1] = 0x51; //DA51 = 55889
+ data_out[2] = 0xDA;
+ data_out[3] = 0xF6; // DAF6 = 56054
+
+
+
+
+ while (1) {
+ Thread::signal_wait(0x1);
+ D_2=1;
+ flag_data_ready = false;
+ ///////////////////////////////////////////////////////////
+ //// RUOTARE IL CAMPO
+ Q[0]=q0; Q[1]=-q1; Q[2]=-q2; Q[3]=-q3;
+ for(i=0;i<8;i++){
+ Mag_filt_f[0]= (float)Mag_read_buff[i]; Mag_filt_f[1]= (float)Mag_read_buff[8+i]; Mag_filt_f[2]= (float)Mag_read_buff[16+i];
+ Qrotate(Mag_filt_f,Q,v_I);
+ Qrotate(v_I,q_init,v_rotX);
+ v_rotX_int[i]=(int16_t)v_rotX[0]; v_rotX_int[8+i]=(int16_t)v_rotX[1]; v_rotX_int[16+i]=(int16_t)v_rotX[2];
+ }
+
+ ///////////////////////////////////////////////////////////
+ //Filter block
+ for(i=0;i<3;i++){
+ for(j=0;j<8;j++){
+ //Band-Pass
+ firFixed( coeffs_bp, &v_rotX_int[i*8 + j], &Mag_filt[i*8 + j], 1, FILTER_LEN_BP, i, insamp);
+ //Low-Pass
+ firFixed( coeffs_lp, &Mag_read_buff[i*8 + j], &Mag_filt_lp[i*8 + j], 1, FILTER_LEN_LP, i,lp_insamp);
+ }
+ M_LP[i]=Mag_filt_lp[i*8 + 4];
+ }
+
+ ///////////////////////////////////////////////////////////
+ /// ENVELOPE EXTRACTION
+
+ Env_extraction(Env, Mag_filt, maximum, peak_index, R, phase, Sign);
+
+ ///////////////////////////////////////////////////////////
+ /// Quaternion computing
+ QUpdate(q, m, a, g, M_LP, Acc_read, Gyr_read, q_init_n, Q_out);
+
+ ///////////////////////////////////////////////////////////
+ ///Send serial data: 20954 [1]| Envelope[3] | -2342 [1] | Quat [8]
+
+ if(go_flag){
+
+ for(i=0; i<2; i++){ //// PAROLA 20954
+ PC.printf("%c",data_out[i]);
+ }
+ for(i=0; i<3; i++){ // ENVELOPE
+ PC.printf("%c",(char)(Env[i] & 0xff));
+ PC.printf("%c",(char)(Env[i]>>8 & 0xff));
+ }
+ for(i=2; i<4; i++){ //// PAROLA -2342
+ PC.printf("%c",data_out[i]);
+ }
+ for(i=0;i<4;i++){
+ PC.printf("%c",(char)(Q_out[i] & 0xff));
+ PC.printf("%c",(char)(Q_out[i]>>8 & 0xff));
+ PC.printf("%c",(char)(Q_out[i]>>16 & 0xff));
+ PC.printf("%c",(char)(Q_out[i]>>24 & 0xff));
+ }
+
+ }
+ D_2=0;
+
+ }
+
+}
+
+
+//////////////////////////////////////////////////////////////
+// Main Code
+//////////////////////////////////////////////////////////////
+int main(){
+ PC.baud(921600); //115200 921600
+ /////// Internal signal buffers
+ int16_t Mag_read_in_buff[24];
+ memset( Mag_read_in_buff, 0, sizeof( Mag_read_in_buff ) );
+ int16_t Mag_in_read[3]={0,0,0};
+ int16_t Acc_in_read[3]={0,0,0};
+ int16_t Gyr_in_read[3]={0,0,0};
+ int i;
+ button1.fall(callback(button1_onpressed_cb)); // Attach ISR to handle button press event
+ // Init FIR filters
+ firFixedInit();
+ PC.printf("Press button start!\n");
+ D_1=0;
+ D_2=0;
+ while (!button1_pressed){
+ myled = !myled;
+ wait(0.1);
+ }
+ //Configure sensors
+ sensor_setup();
+ //Start sensor reading thread
+ thread.start(read_thread);
+ //Timer begins, Freq = 800
+ read_ticker.attach_us(&toggle_flag, 1250);
+ while(1){
+ if(flag){
+ D_1=1;
+ ///////////////////////////////////////////////////////////
+ // Read Mag register and Calibration Correction
+ Read_Mag(Mag_in_read);
+ ///////////////////////////////////////////////////////////
+ // Read acc + gyr register
+ if(count_1 == 1){
+ Read_Acc(Acc_in_read);
+ }
+ if(count_1 == 5){
+ Read_Gyr(Gyr_in_read);
+ }
+
+ ///////////////////////////////////////////////////////////
+ // Read Mag internal buffer fill
+ for(i=0;i<3;i++){
+ Mag_read_in_buff[8*i + count_1] = Mag_in_read[i];
+ }
+
+ ///////////////////////////////////////////////////////////
+ // External buffers updates and Signal Processing flag act
+ if(count_1 == 8){
+ count_1 = 0;
+ for(i=0;i<24;i++){
+ Mag_read_buff[i]=Mag_read_in_buff[i];
+ }
+ for(i=0;i<3;i++){
+ Acc_read[i]=Acc_in_read[i];
+ Gyr_read[i]=Gyr_in_read[i];
+ }
+ thread.signal_set(0x1);
+ }
+
+ ///////////////////////////////////////////////////////////
+ // Counter updates and flag management
+ count_1++;
+ if (count_2==8001){
+ go_flag=true;
+ beta = 0.1;//{-0.8489, 0.0046, -0.001, 0.5286}
+ q_init[0]=q0; q_init[1]=q1; q_init[2]=q2; q_init[3]=q3;
+ q_init_n[0]=q0; q_init_n[1]=-q1; q_init_n[2]=-q2; q_init_n[3]=-q3;
+ }
+ if (count_2 <=8001){
+ count_2++;
+ }
+
+ flag=0;
+ D_1=0;
+ }
+ }
+
+}
\ No newline at end of file
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/mbed-rtos.lib Thu May 21 13:10:58 2020 +0000 @@ -0,0 +1,1 @@ +https://os.mbed.com/users/mbed_official/code/mbed-rtos/#5713cbbdb706
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/mbed.bld Thu May 21 13:10:58 2020 +0000 @@ -0,0 +1,1 @@ +https://os.mbed.com/users/mbed_official/code/mbed/builds/65be27845400 \ No newline at end of file