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1612 dongfang 1
#include <stdlib.h>
2
#include <avr/io.h>
3
 
4
#include "attitude.h"
5
#include "dongfangMath.h"
2048 - 6
#include "commands.h"
1612 dongfang 7
 
1775 - 8
// For scope debugging only!
9
#include "rc.h"
10
 
1612 dongfang 11
// where our main data flow comes from.
12
#include "analog.h"
13
 
14
#include "configuration.h"
1775 - 15
#include "output.h"
1612 dongfang 16
 
17
// Some calculations are performed depending on some stick related things.
18
#include "controlMixer.h"
19
 
20
#define CHECK_MIN_MAX(value, min, max) {if(value < min) value = min; else if(value > max) value = max;}
21
 
22
/*
23
 * Gyro readings, as read from the analog module. It would have been nice to flow
24
 * them around between the different calculations as a struct or array (doing
25
 * things functionally without side effects) but this is shorter and probably
26
 * faster too.
27
 * The variables are overwritten at each attitude calculation invocation - the values
28
 * are not preserved or reused.
29
 */
1775 - 30
int16_t rate_ATT[2], yawRate;
1612 dongfang 31
 
32
// With different (less) filtering
1645 - 33
int16_t rate_PID[2];
34
int16_t differential[2];
1612 dongfang 35
 
36
/*
37
 * Gyro readings, after performing "axis coupling" - that is, the transfomation
38
 * of rotation rates from the airframe-local coordinate system to a ground-fixed
39
 * coordinate system. If axis copling is disabled, the gyro readings will be
40
 * copied into these directly.
41
 * These are global for the same pragmatic reason as with the gyro readings.
42
 * The variables are overwritten at each attitude calculation invocation - the values
43
 * are not preserved or reused.
44
 */
1645 - 45
int16_t ACRate[2], ACYawRate;
1612 dongfang 46
 
47
/*
48
 * Gyro integrals. These are the rotation angles of the airframe compared to the
49
 * horizontal plane, yaw relative to yaw at start.
50
 */
2048 - 51
int32_t attitude[2];
1612 dongfang 52
 
2048 - 53
//int readingHeight = 0;
1612 dongfang 54
 
1805 - 55
// Yaw angle and compass stuff.
2051 - 56
int32_t headingError;
1805 - 57
 
58
// The difference between the above 2 (heading - course) on a -180..179 degree interval.
59
// Not necessary. Never read anywhere.
60
// int16_t compassOffCourse = 0;
61
 
2051 - 62
uint16_t ignoreCompassTimer = 0;// 500;
1805 - 63
 
2048 - 64
int32_t heading; // Yaw Gyro Integral supported by compass
1775 - 65
int16_t yawGyroDrift;
1612 dongfang 66
 
1805 - 67
int16_t correctionSum[2] = { 0, 0 };
1612 dongfang 68
 
1775 - 69
// For NaviCTRL use.
1805 - 70
int16_t averageAcc[2] = { 0, 0 }, averageAccCount = 0;
1775 - 71
 
1612 dongfang 72
/*
73
 * Experiment: Compensating for dynamic-induced gyro biasing.
74
 */
1805 - 75
int16_t driftComp[2] = { 0, 0 }, driftCompYaw = 0;
1612 dongfang 76
// int16_t savedDynamicOffsetPitch = 0, savedDynamicOffsetRoll = 0;
77
// int32_t dynamicCalPitch, dynamicCalRoll, dynamicCalYaw;
78
// int16_t dynamicCalCount;
79
 
1980 - 80
uint16_t accVector;
81
 
1612 dongfang 82
/************************************************************************
83
 * Set inclination angles from the acc. sensor data.                    
84
 * If acc. sensors are not used, set to zero.                          
85
 * TODO: One could use inverse sine to calculate the angles more        
1616 dongfang 86
 * accurately, but since: 1) the angles are rather small at times when
87
 * it makes sense to set the integrals (standing on ground, or flying at  
1612 dongfang 88
 * constant speed, and 2) at small angles a, sin(a) ~= constant * a,    
89
 * it is hardly worth the trouble.                                      
90
 ************************************************************************/
91
 
1645 - 92
int32_t getAngleEstimateFromAcc(uint8_t axis) {
1991 - 93
  //int32_t correctionTerm = (dynamicParams.levelCorrection[axis] - 128) * 256L;
2048 - 94
  return (int32_t) GYRO_ACC_FACTOR * (int32_t) filteredAcc[axis]; // + correctionTerm;
2032 - 95
  // return 342L * filteredAcc[axis];
1612 dongfang 96
}
97
 
98
void setStaticAttitudeAngles(void) {
99
#ifdef ATTITUDE_USE_ACC_SENSORS
2048 - 100
  attitude[PITCH] = getAngleEstimateFromAcc(PITCH);
101
  attitude[ROLL] = getAngleEstimateFromAcc(ROLL);
1612 dongfang 102
#else
2048 - 103
  attitude[PITCH] = attitude[ROLL] = 0;
1612 dongfang 104
#endif
105
}
106
 
107
/************************************************************************
108
 * Neutral Readings                                                    
109
 ************************************************************************/
110
void attitude_setNeutral(void) {
1869 - 111
  // Servo_Off(); // disable servo output. TODO: Why bother? The servos are going to make a jerk anyway.
2032 - 112
  // dynamicParams.axisCoupling1 = dynamicParams.axisCoupling2 = 0;
1612 dongfang 113
 
1869 - 114
  driftComp[PITCH] = driftComp[ROLL] = yawGyroDrift = driftCompYaw = 0;
115
  correctionSum[PITCH] = correctionSum[ROLL] = 0;
1612 dongfang 116
 
1869 - 117
  // Calibrate hardware.
1961 - 118
  analog_setNeutral();
1612 dongfang 119
 
1869 - 120
  // reset gyro integrals to acc guessing
121
  setStaticAttitudeAngles();
2052 - 122
#ifdef USE_MK3MAG
2048 - 123
  attitude_resetHeadingToMagnetic();
2052 - 124
#endif
1869 - 125
  // Servo_On(); //enable servo output
1612 dongfang 126
}
127
 
128
/************************************************************************
129
 * Get sensor data from the analog module, and release the ADC          
130
 * TODO: Ultimately, the analog module could do this (instead of dumping
1645 - 131
 * the values into variables).
132
 * The rate variable end up in a range of about [-1024, 1023].
1612 dongfang 133
 *************************************************************************/
134
void getAnalogData(void) {
1869 - 135
  uint8_t axis;
1612 dongfang 136
 
1955 - 137
  analog_update();
138
 
1869 - 139
  for (axis = PITCH; axis <= ROLL; axis++) {
1963 - 140
    rate_PID[axis] = gyro_PID[axis] + driftComp[axis];
141
    rate_ATT[axis] = gyro_ATT[axis] + driftComp[axis];
1869 - 142
    differential[axis] = gyroD[axis];
143
    averageAcc[axis] += acc[axis];
144
  }
1775 - 145
 
1869 - 146
  averageAccCount++;
147
  yawRate = yawGyro + driftCompYaw;
1612 dongfang 148
}
149
 
150
/*
151
 * This is the standard flight-style coordinate system transformation
152
 * (from airframe-local axes to a ground-based system). For some reason
153
 * the MK uses a left-hand coordinate system. The tranformation has been
154
 * changed accordingly.
155
 */
156
void trigAxisCoupling(void) {
2048 - 157
  int16_t rollAngleInDegrees = attitude[ROLL] / GYRO_DEG_FACTOR_PITCHROLL;
158
  int16_t pitchAngleInDegrees = attitude[PITCH] / GYRO_DEG_FACTOR_PITCHROLL;
1866 - 159
 
2045 - 160
  int16_t cospitch = cos_360(pitchAngleInDegrees);
161
  int16_t cosroll = cos_360(rollAngleInDegrees);
162
  int16_t sinroll = sin_360(rollAngleInDegrees);
163
 
2048 - 164
  ACRate[PITCH] = (((int32_t) rate_ATT[PITCH] * cosroll
165
      - (int32_t) yawRate * sinroll) >> LOG_MATH_UNIT_FACTOR);
1866 - 166
 
2048 - 167
  ACRate[ROLL] = rate_ATT[ROLL]
168
      + (((((int32_t) rate_ATT[PITCH] * sinroll + (int32_t) yawRate * cosroll)
169
          >> LOG_MATH_UNIT_FACTOR) * tan_360(pitchAngleInDegrees))
170
          >> LOG_MATH_UNIT_FACTOR);
1866 - 171
 
2048 - 172
  ACYawRate =
173
      ((int32_t) rate_ATT[PITCH] * sinroll + (int32_t) yawRate * cosroll)
174
          / cospitch;
1612 dongfang 175
}
176
 
1775 - 177
// 480 usec with axis coupling - almost no time without.
1612 dongfang 178
void integrate(void) {
1869 - 179
  // First, perform axis coupling. If disabled xxxRate is just copied to ACxxxRate.
180
  uint8_t axis;
1872 - 181
 
2058 - 182
  if (staticParams.bitConfig & CFG_AXIS_COUPLING_ENABLED) {
1869 - 183
    trigAxisCoupling();
184
  } else {
185
    ACRate[PITCH] = rate_ATT[PITCH];
186
    ACRate[ROLL] = rate_ATT[ROLL];
187
    ACYawRate = yawRate;
188
  }
1612 dongfang 189
 
1869 - 190
  /*
191
   * Yaw
192
   * Calculate yaw gyro integral (~ to rotation angle)
2048 - 193
   * Limit heading proportional to 0 deg to 360 deg
1869 - 194
   */
2048 - 195
  heading += ACYawRate;
196
  intervalWrap(&heading, YAWOVER360);
2051 - 197
  headingError += ACYawRate;
198
 
1869 - 199
  /*
200
   * Pitch axis integration and range boundary wrap.
201
   */
202
  for (axis = PITCH; axis <= ROLL; axis++) {
2048 - 203
    attitude[axis] += ACRate[axis];
204
    if (attitude[axis] > PITCHROLLOVER180) {
205
      attitude[axis] -= PITCHROLLOVER360;
206
    } else if (attitude[axis] <= -PITCHROLLOVER180) {
207
      attitude[axis] += PITCHROLLOVER360;
1869 - 208
    }
209
  }
1612 dongfang 210
}
211
 
2062 - 212
void correctIntegralsByAcc0thOrder_old(void) {
213
  uint8_t axis;
214
  int32_t temp;
215
 
216
  uint8_t ca = controlActivity >> 8;
217
  uint8_t highControlActivity = (ca > staticParams.maxControlActivity);
218
 
219
  if (highControlActivity) {
220
    debugOut.digital[1] |= DEBUG_ACC0THORDER;
221
  } else {
222
    debugOut.digital[1] &= ~DEBUG_ACC0THORDER;
223
  }
224
 
225
  if (accVector <= staticParams.maxAccVector) {
226
    debugOut.digital[0] &= ~DEBUG_ACC0THORDER;
227
 
2065 - 228
    uint8_t permilleAcc = staticParams.zerothOrderCorrection / 8;
2062 - 229
    int32_t accDerived;
230
 
231
    /*
232
     if ((controlYaw < -64) || (controlYaw > 64)) { // reduce further if yaw stick is active
233
     permilleAcc /= 2;
234
     debugFullWeight = 0;
235
     }
236
 
237
     if ((maxControl[PITCH] > 64) || (maxControl[ROLL] > 64)) { // reduce effect during stick commands. Replace by controlActivity.
238
     permilleAcc /= 2;
239
     debugFullWeight = 0;
240
     */
241
 
242
    if (highControlActivity) { // reduce effect during stick control activity
243
      permilleAcc /= 4;
244
      if (controlActivity > staticParams.maxControlActivity * 2) { // reduce effect during stick control activity
245
        permilleAcc /= 4;
246
      }
247
    }
248
 
249
    /*
250
     * Add to each sum: The amount by which the angle is changed just below.
251
     */
252
    for (axis = PITCH; axis <= ROLL; axis++) {
253
      accDerived = getAngleEstimateFromAcc(axis);
254
      //debugOut.analog[9 + axis] = accDerived / (GYRO_DEG_FACTOR_PITCHROLL / 10);
255
      // 1000 * the correction amount that will be added to the gyro angle in next line.
256
      temp = attitude[axis];
257
      attitude[axis] = ((int32_t) (1000L - permilleAcc) * temp
258
          + (int32_t) permilleAcc * accDerived) / 1000L;
259
      correctionSum[axis] += attitude[axis] - temp;
260
    }
261
  } else {
262
    // experiment: Kill drift compensation updates when not flying smooth.
263
    // correctionSum[PITCH] = correctionSum[ROLL] = 0;
264
    debugOut.digital[0] |= DEBUG_ACC0THORDER;
265
  }
266
}
267
 
268
 
1612 dongfang 269
/************************************************************************
270
 * A kind of 0'th order integral correction, that corrects the integrals
271
 * directly. This is the "gyroAccFactor" stuff in the original code.
1646 - 272
 * There is (there) also a drift compensation
1612 dongfang 273
 * - it corrects the differential of the integral = the gyro offsets.
274
 * That should only be necessary with drifty gyros like ENC-03.
275
 ************************************************************************/
2059 - 276
#define LOG_DIVIDER 12
277
#define DIVIDER (1L << LOG_DIVIDER)
2062 - 278
void correctIntegralsByAcc0thOrder_new(void) {
1869 - 279
  // TODO: Consider changing this to: Only correct when integrals are less than ...., or only correct when angular velocities
280
  // are less than ....., or reintroduce Kalman.
281
  // Well actually the Z axis acc. check is not so silly.
282
  uint8_t axis;
283
  int32_t temp;
1908 - 284
 
2059 - 285
  uint16_t ca = controlActivity >> 6;
286
  uint8_t controlActivityWeighted = ca / staticParams.zerothOrderCorrectionControlTolerance;
287
  if (!controlActivityWeighted) controlActivityWeighted = 1;
288
  uint8_t accVectorWeighted = accVector / staticParams.zerothOrderCorrectionAccTolerance;
289
  if (!accVectorWeighted) accVectorWeighted = 1;
1988 - 290
 
2059 - 291
  uint8_t accPart = staticParams.zerothOrderCorrection;
292
  int32_t accDerived;
1988 - 293
 
2059 - 294
  debugOut.analog[14] = controlActivity;
295
  debugOut.analog[15] = accVector;
2048 - 296
 
2059 - 297
  /*
298
  if ((controlYaw < -64) || (controlYaw > 64)) { // reduce further if yaw stick is active
299
  permilleAcc /= 2;
300
  debugFullWeight = 0;
301
  }
1612 dongfang 302
 
2059 - 303
  if ((maxControl[PITCH] > 64) || (maxControl[ROLL] > 64)) { // reduce effect during stick commands. Replace by controlActivity.
304
  permilleAcc /= 2;
305
  debugFullWeight = 0;
306
  */
1953 - 307
 
2059 - 308
  debugOut.analog[20] = controlActivityWeighted;
309
  debugOut.analog[21] = accVectorWeighted;
310
  debugOut.analog[24] = accVector;
1953 - 311
 
2059 - 312
  accPart /=  controlActivityWeighted;
313
  accPart /=  accVectorWeighted;
314
  /*
315
   * Add to each sum: The amount by which the angle is changed just below.
316
   */
317
  for (axis = PITCH; axis <= ROLL; axis++) {
318
    accDerived = getAngleEstimateFromAcc(axis);
319
    //debugOut.analog[9 + axis] = accDerived / (GYRO_DEG_FACTOR_PITCHROLL / 10);
320
    // 1000 * the correction amount that will be added to the gyro angle in next line.
321
    temp = attitude[axis];
322
    attitude[axis] = ((int32_t) (DIVIDER - accPart) * temp + (int32_t)accPart * accDerived) >> LOG_DIVIDER;
323
    correctionSum[axis] += attitude[axis] - temp;
1869 - 324
  }
1612 dongfang 325
}
326
 
327
/************************************************************************
328
 * This is an attempt to correct not the error in the angle integrals
329
 * (that happens in correctIntegralsByAcc0thOrder above) but rather the
330
 * cause of it: Gyro drift, vibration and rounding errors.
331
 * All the corrections made in correctIntegralsByAcc0thOrder over
1646 - 332
 * DRIFTCORRECTION_TIME cycles are summed up. This number is
333
 * then divided by DRIFTCORRECTION_TIME to get the approx.
1612 dongfang 334
 * correction that should have been applied to each iteration to fix
335
 * the error. This is then added to the dynamic offsets.
336
 ************************************************************************/
1646 - 337
// 2 times / sec. = 488/2
338
#define DRIFTCORRECTION_TIME 256L
339
void driftCorrection(void) {
1869 - 340
  static int16_t timer = DRIFTCORRECTION_TIME;
341
  int16_t deltaCorrection;
1872 - 342
  int16_t round;
1869 - 343
  uint8_t axis;
1872 - 344
 
1869 - 345
  if (!--timer) {
346
    timer = DRIFTCORRECTION_TIME;
347
    for (axis = PITCH; axis <= ROLL; axis++) {
348
      // Take the sum of corrections applied, add it to delta
2048 - 349
      if (correctionSum[axis] >= 0)
1872 - 350
        round = DRIFTCORRECTION_TIME / 2;
351
      else
352
        round = -DRIFTCORRECTION_TIME / 2;
353
      deltaCorrection = (correctionSum[axis] + round) / DRIFTCORRECTION_TIME;
1869 - 354
      // Add the delta to the compensation. So positive delta means, gyro should have higher value.
1960 - 355
      driftComp[axis] += deltaCorrection / staticParams.driftCompDivider;
356
      CHECK_MIN_MAX(driftComp[axis], -staticParams.driftCompLimit, staticParams.driftCompLimit);
1869 - 357
      // DebugOut.Analog[11 + axis] = correctionSum[axis];
1955 - 358
      // DebugOut.Analog[16 + axis] = correctionSum[axis];
2035 - 359
      // debugOut.analog[28 + axis] = driftComp[axis];
1869 - 360
      correctionSum[axis] = 0;
361
    }
362
  }
1612 dongfang 363
}
364
 
1980 - 365
void calculateAccVector(void) {
2048 - 366
  int16_t temp;
367
  temp = filteredAcc[0] >> 3;
368
  accVector = temp * temp;
369
  temp = filteredAcc[1] >> 3;
370
  accVector += temp * temp;
371
  temp = filteredAcc[2] >> 3;
372
  accVector += temp * temp;
1980 - 373
}
374
 
2052 - 375
#ifdef USE_MK3MAG
2048 - 376
void attitude_resetHeadingToMagnetic(void) {
377
  if (commands_isCalibratingCompass())
378
    return;
379
 
380
  // Compass is off, skip.
2052 - 381
  if (!(staticParams.bitConfig & CFG_COMPASS_ENABLED))
2048 - 382
      return;
383
 
384
  // Compass is invalid, skip.
385
  if (magneticHeading < 0)
386
    return;
387
 
388
  heading = (int32_t) magneticHeading * GYRO_DEG_FACTOR_YAW;
2051 - 389
  //targetHeading = heading;
390
  headingError = 0;
2048 - 391
 
392
  debugOut.digital[0] ^= DEBUG_COMPASS;
393
}
394
 
395
void correctHeadingToMagnetic(void) {
396
  int32_t error;
397
 
2051 - 398
  if (commands_isCalibratingCompass()) {
2059 - 399
    //debugOut.analog[30] = -1;
2048 - 400
    return;
2051 - 401
  }
2048 - 402
 
403
  // Compass is off, skip.
404
  // Naaah this is assumed.
405
  // if (!(staticParams.bitConfig & CFG_COMPASS_ACTIVE))
406
  //     return;
407
 
408
  // Compass is invalid, skip.
2051 - 409
  if (magneticHeading < 0) {
2059 - 410
    //debugOut.analog[30] = -2;
2048 - 411
    return;
2051 - 412
  }
2048 - 413
 
414
  // Spinning fast, skip
2051 - 415
  if (abs(yawRate) > 128) {
2059 - 416
    // debugOut.analog[30] = -3;
2048 - 417
    return;
2051 - 418
  }
2048 - 419
 
420
  // Otherwise invalidated, skip
421
  if (ignoreCompassTimer) {
422
    ignoreCompassTimer--;
2059 - 423
    //debugOut.analog[30] = -4;
2048 - 424
    return;
425
  }
426
 
2059 - 427
  //debugOut.analog[30] = magneticHeading;
2058 - 428
 
2048 - 429
  // TODO: Find computational cost of this.
2051 - 430
  error = ((int32_t)magneticHeading*GYRO_DEG_FACTOR_YAW - heading);
431
  if (error <= -YAWOVER180) error += YAWOVER360;
432
  else if (error > YAWOVER180) error -= YAWOVER360;
2048 - 433
 
434
  // We only correct errors larger than the resolution of the compass, or else we would keep rounding the
435
  // better resolution of the gyros to the worse resolution of the compass all the time.
436
  // The correction should really only serve to compensate for gyro drift.
437
  if(abs(error) < GYRO_DEG_FACTOR_YAW) return;
438
 
2051 - 439
  int32_t correction = (error * staticParams.compassYawCorrection) >> 8;
2055 - 440
  //debugOut.analog[30] = correction;
2048 - 441
 
442
  // The correction is added both to current heading (the direction in which the copter thinks it is pointing)
2059 - 443
  // and to the heading error (the angle of yaw that the copter is off the set heading).
2048 - 444
  heading += correction;
2059 - 445
  headingError += correction;
2048 - 446
  intervalWrap(&heading, YAWOVER360);
447
 
2051 - 448
  // If we want a transparent flight wrt. compass correction (meaning the copter does not change attitude all
449
  // when the compass corrects the heading - it only corrects numbers!) we want to add:
450
  // This will however cause drift to remain uncorrected!
451
  // headingError += correction;
2055 - 452
  //debugOut.analog[29] = 0;
2048 - 453
}
2052 - 454
#endif
2048 - 455
 
1612 dongfang 456
/************************************************************************
457
 * Main procedure.
458
 ************************************************************************/
1805 - 459
void calculateFlightAttitude(void) {
1869 - 460
  getAnalogData();
1980 - 461
  calculateAccVector();
1869 - 462
  integrate();
1775 - 463
 
1612 dongfang 464
#ifdef ATTITUDE_USE_ACC_SENSORS
2062 - 465
  if (staticParams.maxControlActivity) {
466
    correctIntegralsByAcc0thOrder_old();
467
  } else {
468
    correctIntegralsByAcc0thOrder_new();
469
  }
1869 - 470
  driftCorrection();
1612 dongfang 471
#endif
2015 - 472
 
473
  // We are done reading variables from the analog module.
474
  // Interrupt-driven sensor reading may restart.
475
  startAnalogConversionCycle();
1612 dongfang 476
 
2052 - 477
#ifdef USE_MK3MAG
478
  if (staticParams.bitConfig & (CFG_COMPASS_ENABLED | CFG_GPS_ENABLED)) {
2048 - 479
    correctHeadingToMagnetic();
1869 - 480
  }
2052 - 481
#endif
1775 - 482
}
1612 dongfang 483
 
484
/*
485
 * This is part of an experiment to measure average sensor offsets caused by motor vibration,
486
 * and to compensate them away. It brings about some improvement, but no miracles.
487
 * As long as the left stick is kept in the start-motors position, the dynamic compensation
488
 * will measure the effect of vibration, to use for later compensation. So, one should keep
489
 * the stick in the start-motors position for a few seconds, till all motors run (at the wrong
490
 * speed unfortunately... must find a better way)
491
 */
492
/*
1805 - 493
 void attitude_startDynamicCalibration(void) {
494
 dynamicCalPitch = dynamicCalRoll = dynamicCalYaw = dynamicCalCount = 0;
495
 savedDynamicOffsetPitch = savedDynamicOffsetRoll = 1000;
496
 }
1612 dongfang 497
 
1805 - 498
 void attitude_continueDynamicCalibration(void) {
499
 // measure dynamic offset now...
500
 dynamicCalPitch += hiResPitchGyro;
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 dynamicCalRoll += hiResRollGyro;
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 dynamicCalYaw += rawYawGyroSum;
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 dynamicCalCount++;
504
 
505
 // Param6: Manual mode. The offsets are taken from Param7 and Param8.
506
 if (dynamicParams.UserParam6 || 1) { // currently always enabled.
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 // manual mode
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 driftCompPitch = dynamicParams.UserParam7 - 128;
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 driftCompRoll = dynamicParams.UserParam8 - 128;
510
 } else {
511
 // use the sampled value (does not seem to work so well....)
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 driftCompPitch = savedDynamicOffsetPitch = -dynamicCalPitch / dynamicCalCount;
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 driftCompRoll = savedDynamicOffsetRoll = -dynamicCalRoll / dynamicCalCount;
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 driftCompYaw = -dynamicCalYaw / dynamicCalCount;
515
 }
516
 
517
 // keep resetting these meanwhile, to avoid accumulating errors.
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 setStaticAttitudeIntegrals();
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 yawAngle = 0;
520
 }
521
 */