Welcome to mirror list, hosted at ThFree Co, Russian Federation.

segmented_shape.cpp « ArcWelder - github.com/FormerLurker/ArcWelderLib.git - Unnamed repository; edit this file 'description' to name the repository.
summaryrefslogtreecommitdiff
blob: 3da264cc526ad71f5e2f559e5ac4b0b28805a1af (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// Arc Welder: Anti-Stutter Library
//
// Compresses many G0/G1 commands into G2/G3(arc) commands where possible, ensuring the tool paths stay within the specified resolution.
// This reduces file size and the number of gcodes per second.
//
// Uses the 'Gcode Processor Library' for gcode parsing, position processing, logging, and other various functionality.
//
// Copyright(C) 2021 - Brad Hochgesang
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// This program is free software : you can redistribute it and/or modify
// it under the terms of the GNU Affero General Public License as published
// by the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.See the
// GNU Affero General Public License for more details.
//
//
// You can contact the author at the following email address: 
// FormerLurker@pm.me
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

#include "segmented_shape.h"
#include <stdio.h>
#include "utilities.h"
#include <cmath>
#include <iostream>
#pragma region Operators for Vector and Point

point operator +(point lhs, const vector rhs) {
  point p(
    lhs.x + rhs.x,
    lhs.y + rhs.y,
    lhs.z + rhs.z
  );
  return p;
}

point operator -(point lhs, const vector rhs) {
  return point(
    lhs.x - rhs.x,
    lhs.y - rhs.y,
    lhs.z - rhs.z
  );
} 
vector operator -(point& lhs, point& rhs) {
  return vector(
    lhs.x - rhs.x,
    lhs.y - rhs.y,
    lhs.z - rhs.z
  );
}

vector operator -(const point& lhs, const point& rhs) {
  return vector(
    lhs.x - rhs.x,
    lhs.y - rhs.y,
    lhs.z - rhs.z
  );
}

vector operator *(vector lhs, const double& rhs) {
  return vector(
    lhs.x * rhs,
    lhs.y * rhs,
    lhs.z * rhs
  );
}
#pragma endregion Operators for Vector and Point

#pragma region Point Functions
point point::get_midpoint(point p1, point p2)
{
  double x = (p1.x + p2.x) / 2.0;
  double y = (p1.y + p2.y) / 2.0;
  double z = (p1.z + p2.z) / 2.0;

  return point(x, y, z);
}

bool point::is_near_collinear(const point& p1, const point& p2, const point& p3, double tolerance)
{
  return utilities::abs((p1.y - p2.y) * (p1.x - p3.x) - (p1.y - p3.y) * (p1.x - p2.x)) <= 1e-9;
}

double point::cartesian_distance(const point& p1, const point& p2)
{
  return utilities::get_cartesian_distance(p1.x, p1.y, p2.x, p2.y);
}

#pragma endregion Point Functions

#pragma region Segment Functions
bool segment::get_closest_perpendicular_point(point c, point& d)
{
  return segment::get_closest_perpendicular_point(p1, p2, c, d);
}

bool segment::get_closest_perpendicular_point(const point& p1, const point& p2, const point& c, point& d)
{
  // [(Cx - Ax)(Bx - Ax) + (Cy - Ay)(By - Ay)] / [(Bx - Ax) ^ 2 + (By - Ay) ^ 2]
  double num = (c.x - p1.x) * (p2.x - p1.x) + (c.y - p1.y) * (p2.y - p1.y);
  double x_dif = p2.x - p1.x;
  double y_dif = p2.y - p1.y;
  double denom = (x_dif * x_dif) + (y_dif * y_dif);
  double t = num / denom;

  // We're considering this a failure if t == 0 or t==1 within our tolerance.  In that case we hit the endpoint, which is OK.
  // Why are we using the CIRCLE_GENERATION_A_ZERO_TOLERANCE tolerance here??
  if (utilities::less_than_or_equal(t, 0) || utilities::greater_than_or_equal(t, 1))
    return false;

  d.x = p1.x + t * (p2.x - p1.x);
  d.y = p1.y + t * (p2.y - p1.y);

  return true;
}

#pragma endregion

#pragma region Vector Functions
double vector::get_magnitude()
{
  return utilities::sqrt(x * x + y * y + z * z);
}

double vector::cross_product_magnitude(vector v1, vector v2)
{
  return (v1.x * v2.y - v1.y * v2.x);
}
#pragma endregion Vector Functions

#pragma region Distance Calculation Source
// Distance Calculation code taken from the following source:
// Copyright for distance calculations:
// Copyright 2001 softSurfer, 2012 Dan Sunday
// This code may be freely used, distributed and modified for any purpose
// providing that this copyright notice is included with it.
// SoftSurfer makes no warranty for this code, and cannot be held
// liable for any real or imagined damage resulting from its use.
// Users of this code must verify correctness for their application.
// dot product (3D) which allows vector operations in arguments
#define dot(u,v)   ((u).x * (v).x + (u).y * (v).y + (u).z * (v).z)
//#define dotxy(u,v)   ((u).x * (v).x + (u).y * (v).y)
//#define norm(v)     utilities::sqrt(dot(v,v))     // norm = length of  vector
//#define d(u,v)      norm(u-v)          // distance = norm of difference

#pragma endregion Distance Calculation Source


#pragma region Circle Functions

bool circle::try_create_circle(const point& p1, const point& p2, const point& p3, const double max_radius, circle& new_circle)
{
  if (point::is_near_collinear(p1,p2,p3, 0.001))
  {
    return false;
  }
  double x1 = p1.x;
  double y1 = p1.y;
  double x2 = p2.x;
  double y2 = p2.y;
  double x3 = p3.x;
  double y3 = p3.y;

  double a = x1 * (y2 - y3) - y1 * (x2 - x3) + x2 * y3 - x3 * y2;
  //  Take out to figure out how we handle very small values for a
  if (utilities::is_zero(a, 0.000000001))
  {
    return false;
  }
  double b = (x1 * x1 + y1 * y1) * (y3 - y2)
    + (x2 * x2 + y2 * y2) * (y1 - y3)
    + (x3 * x3 + y3 * y3) * (y2 - y1);

  double c = (x1 * x1 + y1 * y1) * (x2 - x3)
    + (x2 * x2 + y2 * y2) * (x3 - x1)
    + (x3 * x3 + y3 * y3) * (x1 - x2);

  double x = -b / (2.0 * a);
  double y = -c / (2.0 * a);

  double radius = utilities::get_cartesian_distance(x, y, x1, y1);
  if (radius > max_radius)
    return false;

  new_circle.center.x = x;
  new_circle.center.y = y;
  new_circle.center.z = p1.z;
  new_circle.radius = radius;

  return true;
}

bool circle::try_create_circle(const array_list<printer_point>& points, const double max_radius, const double resolution_mm, const double xyz_tolerance, bool allow_3d_arcs, circle& new_circle)
{
  int count = points.count();
  int middle_index = count / 2;
  int end_index = count - 1;
  

  
  if (circle::try_create_circle(points[0], points[middle_index], points[end_index], max_radius, new_circle) && !new_circle.is_over_deviation(points, resolution_mm, xyz_tolerance, allow_3d_arcs))
  {
    return true;
  }
  
       /*
  // This could be a near complete circle.  In that case, the endpoints might be too close together to generate an accurate circle with the 
  // precision we have to work with.  Let's adjust our circle into thirds and test those points as a last ditch effort.
  if (count > 5)
  {
    middle_index = count / 3;
    end_index = middle_index + middle_index;
    if (circle::try_create_circle(points[0], points[middle_index], points[end_index], max_radius, test_circle) && !test_circle.is_over_deviation(points, resolution_mm, xyz_tolerance, allow_3d_arcs))
    {
      new_circle = test_circle;
      return true;
    }
  }
  return false;
         */
  
  // Find the circle with the least deviation, if one exists.
  // Note, this could possibly take a LONG time in the worst case, but it's a pretty unlikely.
  // However, if the midpoint check doesn't pass, it's worth it to spend a bit more time 
  // finding the best fit for the circle (least squares deviation) 
  
  double least_deviation;
  bool found_circle=false;

  for (int index = 1; index < count - 1; index++)
  {
    
    if (index == middle_index)
    {
      // We already checked this one, and it failed, continue.
      continue;
    }
    circle test_circle;
    double current_deviation;
    if (circle::try_create_circle(points[0], points[index], points[count - 1], max_radius, test_circle) && test_circle.get_deviation_sum_squared(points, resolution_mm, xyz_tolerance, allow_3d_arcs, current_deviation))
    {
      
      if (!found_circle || current_deviation < least_deviation)
      {
        found_circle = true;
        least_deviation = current_deviation;
        new_circle = test_circle;
      }
    }
  }
  return found_circle;
  
}

double circle::get_polar_radians(const point& p1) const
{
  double polar_radians = utilities::atan2(p1.y - center.y, p1.x - center.x);
  if (polar_radians < 0)
    polar_radians = (2.0 * PI_DOUBLE) + polar_radians;
  return polar_radians;
}

bool circle::get_deviation_sum_squared(const array_list<printer_point>& points, const double resolution_mm, const double xyz_tolerance, const bool allow_3d_arcs, double &total_deviation)
{
  // We need to ensure that the Z steps are constand per linear travel unit
  double z_step_per_distance = 0;
  total_deviation = 0;
  // Skip the first and last points since they will fit perfectly.
  for (int index = 1; index < points.count() - 1; index++)
  {
    // Make sure the length from the center of our circle to the test point is 
    // at or below our max distance.
    double distance_from_center = utilities::get_cartesian_distance(points[index].x, points[index].y, center.x, center.y);
    if (allow_3d_arcs) {
      double z1 = points[index - 1].z;
      double z2 = points[index].z;

      double current_z_stepper_distance = (z2 - z1) / distance_from_center;
      if (index == 1) {
        z_step_per_distance = current_z_stepper_distance;
      }
      else if (!utilities::is_equal(z_step_per_distance, current_z_stepper_distance, xyz_tolerance))
      {
        // The z step is uneven, can't create arc				
        return false;
      }
    }
    double deviation = utilities::abs(distance_from_center - radius);
    total_deviation += deviation * deviation;
    if (deviation > resolution_mm)
    {
      // Too much deviation
      return false;
    }
  }
  // Check the point perpendicular from the segment to the circle's center, if any such point exists
  for (int index = 0; index < points.count() - 1; index++)
  {
    point point_to_test;
    if (segment::get_closest_perpendicular_point(points[index], points[index + 1], center, point_to_test))
    {
      double distance = utilities::get_cartesian_distance(point_to_test.x, point_to_test.y, center.x, center.y);
      double deviation = utilities::abs(distance - radius);
      total_deviation += deviation * deviation;
      if (deviation > resolution_mm)
      {
        return false;
      }
    }
  }
  return true;
}

bool circle::is_over_deviation(const array_list<printer_point>& points, const double resolution_mm, const double xyz_tolerance, const bool allow_3d_arcs)
{
  // We need to ensure that the Z steps are constand per linear travel unit
  double z_step_per_distance = 0;
  // shared point to test
  point point_to_test;
  int max_index = points.count() - 1;
  // Skip the first and last points since they will fit perfectly.
  for (int index = 0; index < max_index; index++)
  {
    point current_point(points[index]);
    if (index != 0)
    {
      // Make sure the length from the center of our circle to the test point is 
      // at or below our max distance.
      double distance_from_center = utilities::get_cartesian_distance(current_point.x, current_point.y, center.x, center.y);
      if (allow_3d_arcs) {
        double z1 = points[index - 1].z;
        double z2 = current_point.z;

        double current_z_stepper_distance = (z2 - z1) / distance_from_center;
        if (index == 1) {
          z_step_per_distance = current_z_stepper_distance;
        }
        else if (!utilities::is_equal(z_step_per_distance, current_z_stepper_distance, xyz_tolerance))
        {
          // The z step is uneven, can't create arc				
          return true;
        }
      }
      if (utilities::abs(distance_from_center - radius) > resolution_mm)
      {
        return true;
      }
    }
    
    // Check the point perpendicular from the segment to the circle's center, if any such point exists
    
    if (segment::get_closest_perpendicular_point(current_point, points[index + 1], center, point_to_test))
    {
      double distance = utilities::get_cartesian_distance(point_to_test.x, point_to_test.y, center.x, center.y);
      if (utilities::abs(distance - radius) > resolution_mm)
      {
       return true;
      }
    }
  }
  return false;
}
#pragma endregion Circle Functions

#pragma region Arc Functions
double arc::get_i() const
{
  return center.x - start_point.x;
}

double arc::get_j() const
{
  return center.y - start_point.y;
}

bool arc::try_create_arc(
  const circle& c,
  const printer_point& start_point,
  const printer_point& mid_point,
  const printer_point& end_point,
  arc& target_arc,
  double approximate_length,
  double resolution,
  double path_tolerance_percent,
  bool allow_3d_arcs)
{
  double polar_start_theta = c.get_polar_radians(start_point);
  double polar_mid_theta = c.get_polar_radians(mid_point);
  double polar_end_theta = c.get_polar_radians(end_point);

  // variable to hold radians
  double angle_radians = 0;
  DirectionEnum direction = DirectionEnum::UNKNOWN;  // 1 = counter clockwise, 2 = clockwise, 3 = unknown.
  // Determine the direction of the arc
  if (polar_end_theta > polar_start_theta)
  {
    if (polar_start_theta < polar_mid_theta && polar_mid_theta < polar_end_theta) {
      direction = DirectionEnum::COUNTERCLOCKWISE;
      angle_radians = polar_end_theta - polar_start_theta;
    }
    else if (
      (0.0 <= polar_mid_theta && polar_mid_theta < polar_start_theta) ||
      (polar_end_theta < polar_mid_theta && polar_mid_theta < (2.0 * PI_DOUBLE))
      )
    {
      direction = DirectionEnum::CLOCKWISE;
      angle_radians = polar_start_theta + ((2.0 * PI_DOUBLE) - polar_end_theta);
    }
  }
  else if (polar_start_theta > polar_end_theta)
  {
    if (
      (polar_start_theta < polar_mid_theta && polar_mid_theta < (2.0 * PI_DOUBLE)) ||
      (0.0 < polar_mid_theta && polar_mid_theta < polar_end_theta)
      )
    {
      direction = DirectionEnum::COUNTERCLOCKWISE;
      angle_radians = polar_end_theta + ((2.0 * PI_DOUBLE) - polar_start_theta);
    }
    else if (polar_end_theta < polar_mid_theta && polar_mid_theta < polar_start_theta)
    {
      direction = DirectionEnum::CLOCKWISE;
      angle_radians = polar_start_theta - polar_end_theta;
    }
  }

  // this doesn't always work..  in rare situations, the angle may be backward
  if (direction == 0 || utilities::is_zero(angle_radians)) return false;

  // Let's check the length against the original length
  // This can trigger simply due to the differing path lengths
  // but also could indicate that our vector calculation above
  // got the direction wrong
  double arc_length = c.radius * angle_radians;

  if (allow_3d_arcs)
  {
    // We may be traveling in 3 space, calculate the arc_length of the spiral
    if (start_point.z != end_point.z)
    {
      arc_length = utilities::hypot(arc_length, end_point.z - start_point.z);
    }
  }
  // Calculate the percent difference of the original path
  double path_difference_percent = utilities::get_percent_change(arc_length, approximate_length);
  if (!utilities::is_zero(path_difference_percent, path_tolerance_percent))
  {
    // So it's possible our vector calculation above got the direction wrong.
    // This can happen if there is a crazy arrangement of points
    // extremely close to eachother.  They have to be close enough to 
    // break our other checks.  However, we may be able to salvage this.
    // see if an arc moving in the opposite direction had the correct length.

    // Find the rest of the angle across the circle
    double test_radians = utilities::abs(angle_radians - 2 * PI_DOUBLE);
    // Calculate the length of that arc
    double test_arc_length = c.radius * test_radians;
    if (allow_3d_arcs)
    {
      // We may be traveling in 3 space, calculate the arc_length of the spiral
      if (start_point.z != end_point.z)
      {
        test_arc_length = utilities::hypot(test_arc_length, end_point.z - start_point.z);
      }
    }
    path_difference_percent = utilities::get_percent_change(test_arc_length,approximate_length);
    if (!utilities::is_zero(path_difference_percent, path_tolerance_percent))
    {
      return false;
    }
    // So, let's set the new length and flip the direction (but not the angle)!
    arc_length = test_arc_length;
    direction = direction == DirectionEnum::COUNTERCLOCKWISE ? DirectionEnum::CLOCKWISE : DirectionEnum::COUNTERCLOCKWISE;
  }

  if (allow_3d_arcs)
  {
    // Ensure the perimeter of the arc is less than that of a full circle
    double perimeter = utilities::hypot(c.radius * 2.0 * PI_DOUBLE, end_point.z - start_point.z);
    if (perimeter <= approximate_length) {
      return false;
    }

  }

  if (direction == 2) {
    angle_radians *= -1.0;
  }
  target_arc.direction = direction;
  target_arc.center.x = c.center.x;
  target_arc.center.y = c.center.y;
  target_arc.center.z = c.center.z;
  target_arc.radius = c.radius;
  target_arc.start_point = start_point;
  target_arc.end_point = end_point;
  target_arc.length = arc_length;
  target_arc.angle_radians = angle_radians;
  target_arc.polar_start_theta = polar_start_theta;
  target_arc.polar_end_theta = polar_end_theta;

  return true;

}

bool arc::try_create_arc(
  const array_list<printer_point>& points,
  arc& target_arc,
  double approximate_length,
  double max_radius_mm,
  double resolution_mm,
  double path_tolerance_percent,
  int min_arc_segments,
  double mm_per_arc_segment,
  double xyz_tolerance,
  bool allow_3d_arcs)
{
  circle test_circle = (circle)target_arc;

  if (!circle::try_create_circle(points, max_radius_mm, resolution_mm, xyz_tolerance, allow_3d_arcs, test_circle))
  {
    return false;
  }
  
  // We could save a bit of processing power and do our firmware compensation here, but we won't be able to track statistics for this easily.
  // moved check to segmented_arc.cpp
  int mid_point_index = ((points.count() - 2) / 2) + 1;
  arc test_arc;
  if (!arc::try_create_arc(test_circle, points[0], points[mid_point_index], points[points.count() - 1], test_arc, approximate_length, resolution_mm, path_tolerance_percent, allow_3d_arcs))
  {
    return false;
  }

  if (arc::are_points_within_slice(test_arc, points))
  {
    target_arc = test_arc;
    return true;
  }
  return false;
}

bool arc::are_points_within_slice(const arc& test_arc, const array_list<printer_point>& points)
{


  // Loop through the points and see if they fit inside of the angles
  double previous_polar = test_arc.polar_start_theta;
  bool will_cross_zero = false;
  bool crossed_zero = false;
  const int point_count = points.count();

  point start_norm((test_arc.start_point.x - test_arc.center.x) / test_arc.radius, (test_arc.start_point.y - test_arc.center.y) / test_arc.radius, 0.0);
  point end_norm((test_arc.end_point.x - test_arc.center.x) / test_arc.radius, (test_arc.end_point.y - test_arc.center.y) / test_arc.radius, 0.0);

  if (test_arc.direction == DirectionEnum::COUNTERCLOCKWISE)
  {
    will_cross_zero = test_arc.polar_start_theta > test_arc.polar_end_theta;
  }
  else
  {
    will_cross_zero = test_arc.polar_start_theta < test_arc.polar_end_theta;
  }

  // Need to see if point 1 to point 2 cross zero
  for (int index = point_count - 2; index < point_count; index++)
  {
    double polar_test;
    if (index < point_count - 1)
    {
      polar_test = test_arc.get_polar_radians(points[index]);
    }
    else
    {
      polar_test = test_arc.polar_end_theta;
    }

    // First ensure the test point is within the arc
    if (test_arc.direction == DirectionEnum::COUNTERCLOCKWISE)
    {
      // Only check to see if we are within the arc if this isn't the endpoint
      if (index < point_count - 1)
      {
        if (will_cross_zero)
        {
          if (!(polar_test > test_arc.polar_start_theta || polar_test < test_arc.polar_end_theta))
          {
            return false;
          }
        }
        else if (!(test_arc.polar_start_theta < polar_test && polar_test < test_arc.polar_end_theta))
        {
          return false;
        }
      }
      // Now make sure the angles are increasing
      if (previous_polar > polar_test)
      {
        if (!will_cross_zero)
        {
          return false;
        }

        // Allow the angle to cross zero once
        if (crossed_zero)
        {
          return false;
        }
        crossed_zero = true;
      }
    }
    else
    {
      if (index < point_count - 1)
      {
        if (will_cross_zero)
        {
          if (!(polar_test < test_arc.polar_start_theta || polar_test > test_arc.polar_end_theta))
          {
            return false;
          }
        }
        else if (!(test_arc.polar_start_theta > polar_test && polar_test > test_arc.polar_end_theta))
        {
          return false;
        }
      }
      // Now make sure the angles are decreasing
      if (previous_polar < polar_test)
      {
        if (!will_cross_zero)
        {
          return false;
        }
        // Allow the angle to cross zero once
        if (crossed_zero)
        {
          return false;
        }
        crossed_zero = true;
      }
    }

    // Now see if the segment intersects either of the vector from the center of the circle to the endpoints of the arc
    if ((index != 1 && ray_intersects_segment(test_arc.center, start_norm, points[index - 1], points[index])) || (index != point_count - 1 && ray_intersects_segment(test_arc.center, end_norm, points[index - 1], points[index])))
      return false;
    previous_polar = polar_test;
  }
  // Ensure that all arcs that cross zero do, and that all arcs that should not did not.
  if (will_cross_zero != crossed_zero)
  {
    return false;
  }

  return true;
}

// return the distance of ray origin to intersection point
bool arc::ray_intersects_segment(const point rayOrigin, const point rayDirection, const printer_point point1, const printer_point point2)
{
  vector v1 = rayOrigin - point1;
  vector v2 = point2 - point1;
  vector v3 = vector(-rayDirection.y, rayDirection.x, 0);

  double dot = dot(v2, v3);
  if (utilities::abs(dot) < 0.000001)
    return false;

  double t1 = vector::cross_product_magnitude(v2, v1) / dot;
  double t2 = dot(v1, v3) / dot;

  if (t1 >= 0.0 && (t2 >= 0.0 && t2 <= 1.0))
    return true;

  return false;
}

#pragma endregion

segmented_shape::segmented_shape(int min_segments, int max_segments, double resolution_mm, double path_tolerance_percnet, unsigned char default_xyz_precision, unsigned char default_e_precision) : points_(max_segments)
{

  set_xyz_precision(default_xyz_precision);
  e_precision_ = default_e_precision;
  max_segments_ = max_segments;
  path_tolerance_percent_ = path_tolerance_percnet;
  resolution_mm_ = resolution_mm / 2.0; // divide by 2 because it is + or - 1/2 of the desired resolution.
  e_relative_ = 0;
  is_shape_ = false;
  // min segments can never be lower than 3 (the default) else there could be no compression.
  if (min_segments < DEFAULT_MIN_SEGMENTS) min_segments_ = DEFAULT_MIN_SEGMENTS;
  else min_segments_ = min_segments;

  original_shape_length_ = 0;
  is_extruding_ = true;
}

segmented_shape::~segmented_shape()
{

}

unsigned char segmented_shape::get_xyz_precision() const
{
  return xyz_precision_;
}

double segmented_shape::get_xyz_tolerance() const
{
  return xyz_tolerance_;
}

unsigned char segmented_shape::get_e_precision() const
{
  return e_precision_;
}

void segmented_shape::set_xyz_precision(unsigned char precision)
{
  xyz_precision_ = precision;
  set_xyz_tolerance_from_precision();
}

void segmented_shape::set_xyz_tolerance_from_precision()
{
  xyz_tolerance_ = utilities::pow(10, -1.0 * static_cast<double>(xyz_precision_));
}

void segmented_shape::reset_precision()
{
  set_xyz_precision(DEFAULT_XYZ_PRECISION);
  e_precision_ = DEFAULT_E_PRECISION;
}

void segmented_shape::update_xyz_precision(unsigned char precision)
{
  if (xyz_precision_ < precision)
  {
    set_xyz_precision(precision);
  }
}

void segmented_shape::update_e_precision(unsigned char precision)
{
  if (e_precision_ < precision)
  {
    e_precision_ = precision;
  }

}

bool segmented_shape::is_extruding()
{
  return is_extruding_;
}

segmented_shape& segmented_shape::operator=(const segmented_shape& obj)
{
  points_.clear();
  if (obj.max_segments_ != max_segments_)
  {
    max_segments_ = obj.max_segments_;

    points_.resize(max_segments_);
  }
  points_.copy(obj.points_);

  original_shape_length_ = obj.original_shape_length_;
  e_relative_ = obj.e_relative_;
  is_shape_ = obj.is_shape_;
  max_segments_ = obj.max_segments_;
  resolution_mm_ = obj.resolution_mm_;
  return *this;
}

int segmented_shape::get_num_segments()
{
  return points_.count();
}

double segmented_shape::get_shape_length()
{
  return original_shape_length_;
}

double segmented_shape::get_shape_e_relative()
{
  return e_relative_;
}

void segmented_shape::clear()
{
  points_.clear();
  is_shape_ = false;
  e_relative_ = 0;
  original_shape_length_ = 0;
}
bool segmented_shape::is_shape() const
{
  // return the pre-calculated value.  This should be updated by the plugin
  return is_shape_;
}
void segmented_shape::set_is_shape(bool value)
{
  is_shape_ = value;
}

int segmented_shape::get_min_segments()
{
  return min_segments_;
}
int segmented_shape::get_max_segments()
{
  return max_segments_;
}

double segmented_shape::get_resolution_mm()
{
  return resolution_mm_;
}

double segmented_shape::get_path_tolerance_percent()
{
  return path_tolerance_percent_;
}

void segmented_shape::set_resolution_mm(double resolution_mm)
{
  resolution_mm_ = resolution_mm;

}
printer_point segmented_shape::pop_front()
{
  return points_.pop_front();
}
printer_point segmented_shape::pop_back()
{
  return points_.pop_back();
}

bool segmented_shape::try_add_point(printer_point p, double e_relative)
{
  throw std::exception();
}

std::string segmented_shape::get_shape_gcode_absolute(double e_abs_start)
{
  throw std::exception();
}

std::string segmented_shape::get_shape_gcode_relative()
{
  throw std::exception();
}