forked from rai-opensource/spatialmath-python
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy path3d_line.html
More file actions
1475 lines (1408 loc) · 105 KB
/
Copy path3d_line.html
File metadata and controls
1475 lines (1408 loc) · 105 KB
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
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE html>
<html class="writer-html5" lang="en" >
<head>
<meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<title>3D line — Spatial Maths package 0.12.0
documentation</title>
<link rel="stylesheet" href="_static/pygments.css" type="text/css" />
<link rel="stylesheet" href="_static/css/theme.css" type="text/css" />
<link rel="stylesheet" href="_static/graphviz.css" type="text/css" />
<link rel="shortcut icon" href="_static/favicon.ico"/>
<!--[if lt IE 9]>
<script src="_static/js/html5shiv.min.js"></script>
<![endif]-->
<script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
<script src="_static/jquery.js"></script>
<script src="_static/underscore.js"></script>
<script src="_static/doctools.js"></script>
<script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
<script type="text/x-mathjax-config">MathJax.Hub.Config({"TeX": {"Macros": {"presup": ["\\,{}^{\\scriptscriptstyle #1}\\!", 1], "SE": ["\\mathbf{SE}(#1)", 1], "SO": ["\\mathbf{SO}(#1)", 1], "se": ["\\mathbf{se}(#1)", 1], "so": ["\\mathbf{so}(#1)", 1], "vec": ["\\boldsymbol{#1}", 1], "dvec": ["\\dot{\\boldsymbol{#1}}", 1], "ddvec": ["\\ddot{\\boldsymbol{#1}}", 1], "fvec": ["\\presup{#1}\\boldsymbol{#2}", 2], "fdvec": ["\\presup{#1}\\dot{\\boldsymbol{#2}}", 2], "fddvec": ["\\presup{#1}\\ddot{\\boldsymbol{#2}}", 2], "norm": ["\\Vert #1 \\Vert", 1], "mat": ["\\mathbf{#1}", 1], "dmat": ["\\dot{\\mathbf{#1}}", 1], "fmat": ["\\presup{#1}\\mathbf{#2}", 2], "sk": ["\\left[#1\\right]", 1], "skx": ["\\left[#1\\right]_{\\times}", 1], "vex": ["\\vee\\left( #1\\right)", 1], "vexx": ["\\vee_{\\times}\\left( #1\\right)", 1], "q": "\\mathring{q}", "fq": ["\\presup{#1}\\mathring{q}", 1]}}})</script>
<script src="_static/js/theme.js"></script>
<link rel="index" title="Index" href="genindex.html" />
<link rel="search" title="Search" href="search.html" />
<link rel="next" title="Plane" href="3d_plane.html" />
<link rel="prev" title="Spatial inertia" href="6d_inertia.html" />
</head>
<body class="wy-body-for-nav">
<div class="wy-grid-for-nav">
<nav data-toggle="wy-nav-shift" class="wy-nav-side">
<div class="wy-side-scroll">
<div class="wy-side-nav-search" >
<a href="index.html" class="icon icon-home"> Spatial Maths package
<img src="_static/CartesianSnakes_LogoW.png" class="logo" alt="Logo"/>
</a>
<div class="version">
0.12
</div>
<div role="search">
<form id="rtd-search-form" class="wy-form" action="search.html" method="get">
<input type="text" name="q" placeholder="Search docs" />
<input type="hidden" name="check_keywords" value="yes" />
<input type="hidden" name="area" value="default" />
</form>
</div>
</div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="intro.html">Introduction</a></li>
<li class="toctree-l1 current"><a class="reference internal" href="spatialmath.html">Class reference</a><ul class="current">
<li class="toctree-l2 current"><a class="reference internal" href="spatialmath.html#d-space">3D-space</a><ul class="current">
<li class="toctree-l3"><a class="reference internal" href="spatialmath.html#pose-in-3d">Pose in 3D</a></li>
<li class="toctree-l3"><a class="reference internal" href="spatialmath.html#orientation-in-3d">Orientation in 3D</a></li>
<li class="toctree-l3"><a class="reference internal" href="spatialmath.html#d-spatial-vectors">6D spatial vectors</a></li>
<li class="toctree-l3 current"><a class="reference internal" href="spatialmath.html#geometry-in-3d">Geometry in 3D</a><ul class="current">
<li class="toctree-l4 current"><a class="current reference internal" href="#">3D line</a></li>
<li class="toctree-l4"><a class="reference internal" href="3d_plane.html">Plane</a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="spatialmath.html#supporting">Supporting</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="spatialmath.html#id1">2D-space</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="functions.html">Function reference</a></li>
<li class="toctree-l1"><a class="reference internal" href="indices.html">Indices</a></li>
</ul>
</div>
</div>
</nav>
<section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
<i data-toggle="wy-nav-top" class="fa fa-bars"></i>
<a href="index.html">Spatial Maths package</a>
</nav>
<div class="wy-nav-content">
<div class="rst-content">
<div role="navigation" aria-label="Page navigation">
<ul class="wy-breadcrumbs">
<li><a href="index.html" class="icon icon-home"></a> »</li>
<li><a href="spatialmath.html">Class reference</a> »</li>
<li>3D line</li>
<li class="wy-breadcrumbs-aside">
<a href="_sources/3d_line.rst.txt" rel="nofollow"> View page source</a>
</li>
</ul><div class="rst-breadcrumbs-buttons" role="navigation" aria-label="Sequential page navigation">
<a href="6d_inertia.html" class="btn btn-neutral float-left" title="Spatial inertia" accesskey="p"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
<a href="3d_plane.html" class="btn btn-neutral float-right" title="Plane" accesskey="n">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
</div>
<hr/>
</div>
<div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
<div itemprop="articleBody">
<section id="d-line">
<h1>3D line<a class="headerlink" href="#d-line" title="Permalink to this headline"></a></h1>
<p>A 3D line using Plücker coordinates.</p>
<dl class="py class">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Line3</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">spatialmath.baseposelist.BasePoseList</span></code></p>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.Alloc">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Alloc</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.Alloc" title="Permalink to this definition"></a></dt>
<dd><p>Construct an instance with N default values (BasePoseList superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>n</strong> (<em>int</em><em>, </em><em>optional</em>) – Number of values, defaults to 1</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>pose instance with <code class="docutils literal notranslate"><span class="pre">n</span></code> default values</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">X.Alloc(N)</span></code> creates an instance of the pose class <code class="docutils literal notranslate"><span class="pre">X</span></code> with <code class="docutils literal notranslate"><span class="pre">N</span></code>
default values, ie. <code class="docutils literal notranslate"><span class="pre">len(X)</span></code> will be <code class="docutils literal notranslate"><span class="pre">N</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">X</span></code> can be considered a vector of pose objects, and those elements
can be referenced <code class="docutils literal notranslate"><span class="pre">X[i]</span></code> or assigned to <code class="docutils literal notranslate"><span class="pre">X[i]</span> <span class="pre">=</span> <span class="pre">...</span></code>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The default value depends on the pose class and is the result
of the empty constructor. For <code class="docutils literal notranslate"><span class="pre">SO2</span></code>,
<code class="docutils literal notranslate"><span class="pre">SE2</span></code>, <code class="docutils literal notranslate"><span class="pre">SO3</span></code>, <code class="docutils literal notranslate"><span class="pre">SE3</span></code> it is an identity matrix, for a
twist class <code class="docutils literal notranslate"><span class="pre">Twist2</span></code> or <code class="docutils literal notranslate"><span class="pre">Twist3</span></code> it is a zero vector,
for a <code class="docutils literal notranslate"><span class="pre">UnitQuaternion</span></code> or <code class="docutils literal notranslate"><span class="pre">Quaternion</span></code> it is a zero
vector.</p>
</div>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">Alloc</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">10</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">X</span></code> is any of the SMTB classes.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.Empty">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Empty</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.Empty" title="Permalink to this definition"></a></dt>
<dd><p>Construct an empty instance (BasePoseList superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>pose instance with zero values</p>
</dd>
</dl>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">Empty</span><span class="p">()</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">0</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">X</span></code> is any of the SMTB classes.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.PointDir">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">PointDir</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">point</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dir</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.PointDir"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.PointDir" title="Permalink to this definition"></a></dt>
<dd><p>Create 3D line from a point and direction</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>point</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – A 3D point</p></li>
<li><p><strong>dir</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – Direction vector</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>3D line</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><code class="docutils literal notranslate"><span class="pre">Line3</span></code> instance</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">Line3.pointdir(P,</span> <span class="pre">W)</span></code> is a Plucker object that represents the
line containing the point <code class="docutils literal notranslate"><span class="pre">P</span></code> and parallel to the direction vector <code class="docutils literal notranslate"><span class="pre">W</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.TwoPoints" title="spatialmath.geom3d.Line3.TwoPoints"><code class="xref py py-meth docutils literal notranslate"><span class="pre">TwoPoints()</span></code></a> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.TwoPlanes" title="spatialmath.geom3d.Line3.TwoPlanes"><code class="xref py py-meth docutils literal notranslate"><span class="pre">TwoPlanes()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.TwoPlanes">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">TwoPlanes</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">pi1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pi2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.TwoPlanes"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.TwoPlanes" title="Permalink to this definition"></a></dt>
<dd><p>Create 3D line from intersection of two planes</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>pi1</strong> (array_like(4), or <code class="docutils literal notranslate"><span class="pre">Plane</span></code>) – First plane</p></li>
<li><p><strong>pi2</strong> (array_like(4), or <code class="docutils literal notranslate"><span class="pre">Plane</span></code>) – Second plane</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>3D line</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><code class="docutils literal notranslate"><span class="pre">Line3</span></code> instance</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">L</span> <span class="pre">=</span> <span class="pre">Plucker.planes(PI1,</span> <span class="pre">PI2)</span></code> is a Plucker object that represents
the line formed by the intersection of two planes <code class="docutils literal notranslate"><span class="pre">PI1</span></code> and <code class="docutils literal notranslate"><span class="pre">PI2</span></code>.</p>
<p>Planes are represented by the 4-vector <span class="math notranslate nohighlight">\([a, b, c, d]\)</span> which describes
the plane <span class="math notranslate nohighlight">\(\pi: ax + by + cz + d=0\)</span>.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.TwoPoints" title="spatialmath.geom3d.Line3.TwoPoints"><code class="xref py py-meth docutils literal notranslate"><span class="pre">TwoPoints()</span></code></a> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.PointDir" title="spatialmath.geom3d.Line3.PointDir"><code class="xref py py-meth docutils literal notranslate"><span class="pre">PointDir()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.TwoPoints">
<em class="property"><span class="pre">classmethod</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">TwoPoints</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">P</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">Q</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.TwoPoints"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.TwoPoints" title="Permalink to this definition"></a></dt>
<dd><p>Create 3D line from two 3D points</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>P</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – First 3D point</p></li>
<li><p><strong>Q</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – Second 3D point</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>3D line</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p><code class="docutils literal notranslate"><span class="pre">Line3</span></code> instance</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">Line3(P,</span> <span class="pre">Q)</span></code> create a <code class="docutils literal notranslate"><span class="pre">Line3</span></code> object that represents
the line joining the 3D points <code class="docutils literal notranslate"><span class="pre">P</span></code> (3,) and <code class="docutils literal notranslate"><span class="pre">Q</span></code> (3,). The direction
is from <code class="docutils literal notranslate"><span class="pre">Q</span></code> to <code class="docutils literal notranslate"><span class="pre">P</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3" title="spatialmath.geom3d.Line3"><code class="xref py py-meth docutils literal notranslate"><span class="pre">Line3()</span></code></a> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.PointDir" title="spatialmath.geom3d.Line3.PointDir"><code class="xref py py-meth docutils literal notranslate"><span class="pre">PointDir()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__eq__">
<span class="sig-name descname"><span class="pre">__eq__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__eq__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__eq__" title="Permalink to this definition"></a></dt>
<dd><p>Test if two lines are equivalent</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<code class="docutils literal notranslate"><span class="pre">Line3</span></code>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>lines are equivalent</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">L1</span> <span class="pre">==</span> <span class="pre">L2</span></code> is True if the <code class="docutils literal notranslate"><span class="pre">Line3</span></code> objects describe the same line in
space. Note that because of the over parameterization, lines can be
equivalent even if their coordinate vectors are different.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__ne__" title="spatialmath.geom3d.Line3.__ne__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__ne__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__init__">
<span class="sig-name descname"><span class="pre">__init__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">w</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__init__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__init__" title="Permalink to this definition"></a></dt>
<dd><p>Create a Line3 object</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>v</strong> (<em>array_like</em><em>(</em><em>6</em><em>) or </em><em>array_like</em><em>(</em><em>3</em><em>)</em>) – Plucker coordinate vector, or Plucker moment vector</p></li>
<li><p><strong>w</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em><em>, </em><em>optional</em>) – Plucker direction vector, optional</p></li>
</ul>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – bad arguments</p>
</dd>
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>3D line</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p><code class="docutils literal notranslate"><span class="pre">Line3</span></code> instance</p>
</dd>
</dl>
<p>A representation of a 3D line using Plucker coordinates.</p>
<ul class="simple">
<li><dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">Line3(P)</span></code> creates a 3D line from a Plucker coordinate vector <code class="docutils literal notranslate"><span class="pre">[v,</span> <span class="pre">w]</span></code></dt><dd><p>where <code class="docutils literal notranslate"><span class="pre">v</span></code> (3,) is the moment and <code class="docutils literal notranslate"><span class="pre">w</span></code> (3,) is the line direction.</p>
</dd>
</dl>
</li>
<li><p><code class="docutils literal notranslate"><span class="pre">Line3(v,</span> <span class="pre">w)</span></code> as above but the components <code class="docutils literal notranslate"><span class="pre">v</span></code> and <code class="docutils literal notranslate"><span class="pre">w</span></code> are
provided separately.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">Line3(L)</span></code> creates a copy of the <code class="docutils literal notranslate"><span class="pre">Line3</span></code> object <code class="docutils literal notranslate"><span class="pre">L</span></code>.</p></li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<ul class="simple">
<li><p>The <code class="docutils literal notranslate"><span class="pre">Line3</span></code> object inherits from <code class="docutils literal notranslate"><span class="pre">collections.UserList</span></code> and has list-like
behaviours.</p></li>
<li><p>A single <code class="docutils literal notranslate"><span class="pre">Line3</span></code> object contains a 1D array of Plucker coordinates.</p></li>
<li><p>The elements of the array are guaranteed to be Plucker coordinates.</p></li>
<li><p>The number of elements is given by <code class="docutils literal notranslate"><span class="pre">len(L)</span></code></p></li>
<li><p>The elements can be accessed using index and slice notation, eg. <code class="docutils literal notranslate"><span class="pre">L[1]</span></code> or
<code class="docutils literal notranslate"><span class="pre">L[2:3]</span></code></p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">Line3</span></code> instance can be used as an iterator in a for loop or list comprehension.</p></li>
<li><p>Some methods support operations on the internal list.</p></li>
</ul>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.TwoPoints" title="spatialmath.geom3d.Line3.TwoPoints"><code class="xref py py-meth docutils literal notranslate"><span class="pre">TwoPoints()</span></code></a> <code class="xref py py-meth docutils literal notranslate"><span class="pre">Planes()</span></code> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.PointDir" title="spatialmath.geom3d.Line3.PointDir"><code class="xref py py-meth docutils literal notranslate"><span class="pre">PointDir()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__mul__">
<span class="sig-name descname"><span class="pre">__mul__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__mul__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__mul__" title="Permalink to this definition"></a></dt>
<dd><p>Reciprocal product</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>left</strong> (<a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3" title="spatialmath.geom3d.Line3"><em>Line3</em></a>) – Left operand</p></li>
<li><p><strong>right</strong> (<a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3" title="spatialmath.geom3d.Line3"><em>Line3</em></a>) – Right operand</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>reciprocal product</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">left</span> <span class="pre">*</span> <span class="pre">right</span></code> is the scalar reciprocal product <span class="math notranslate nohighlight">\(\hat{w}_L \dot m_R + \hat{w}_R \dot m_R\)</span>.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<ul class="simple">
<li><p>Multiplication or composition of Plucker lines is not defined.</p></li>
<li><p>Pre-multiplication by an SE3 object is supported, see <code class="docutils literal notranslate"><span class="pre">__rmul__</span></code>.</p></li>
</ul>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__rmul__" title="spatialmath.geom3d.Line3.__rmul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__rmul__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__ne__">
<span class="sig-name descname"><span class="pre">__ne__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__ne__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__ne__" title="Permalink to this definition"></a></dt>
<dd><p>Test if two lines are not equivalent</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<code class="docutils literal notranslate"><span class="pre">Line3</span></code>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>lines are not equivalent</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">L1</span> <span class="pre">!=</span> <span class="pre">L2</span></code> is True if the Plucker objects describe different lines in
space. Note that because of the over parameterization, lines can be
equivalent even if their coordinate vectors are different.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__ne__" title="spatialmath.geom3d.Line3.__ne__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__ne__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__or__">
<span class="sig-name descname"><span class="pre">__or__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__or__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__or__" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded <code class="docutils literal notranslate"><span class="pre">|</span></code> operator tests for parallelism</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<code class="docutils literal notranslate"><span class="pre">Line3</span></code>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>lines are parallel</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">l1</span> <span class="pre">|</span> <span class="pre">l2</span></code> is an operator which is true if the two lines are parallel.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The <code class="docutils literal notranslate"><span class="pre">|</span></code> operator has low precendence.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.isparallel" title="spatialmath.geom3d.Line3.isparallel"><code class="xref py py-meth docutils literal notranslate"><span class="pre">isparallel()</span></code></a> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__xor__" title="spatialmath.geom3d.Line3.__xor__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__xor__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__rmul__">
<span class="sig-name descname"><span class="pre">__rmul__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">left</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__rmul__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__rmul__" title="Permalink to this definition"></a></dt>
<dd><p>Rigid-body transformation of 3D line</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>left</strong> (<a class="reference internal" href="3d_pose_SE3.html#spatialmath.pose3d.SE3" title="spatialmath.pose3d.SE3"><em>SE3</em></a>) – Rigid-body transform</p></li>
<li><p><strong>right</strong> (<em>Line</em>) – 3D line</p></li>
</ul>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>transformed 3D line</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>Line3 instance</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">T</span> <span class="pre">*</span> <span class="pre">line</span></code> is the line transformed by the rigid body transformation <code class="docutils literal notranslate"><span class="pre">T</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__mul__" title="spatialmath.geom3d.Line3.__mul__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__mul__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.__xor__">
<span class="sig-name descname"><span class="pre">__xor__</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.__xor__"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.__xor__" title="Permalink to this definition"></a></dt>
<dd><p>Overloaded <code class="docutils literal notranslate"><span class="pre">^</span></code> operator tests for intersection</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Plucker" title="spatialmath.geom3d.Plucker"><em>Plucker</em></a>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>lines intersect</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">l1</span> <span class="pre">^</span> <span class="pre">l2</span></code> is an operator which is true if the two lines intersect.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<ul class="simple">
<li><p>The <code class="docutils literal notranslate"><span class="pre">^</span></code> operator has low precendence.</p></li>
<li><p>Is <code class="docutils literal notranslate"><span class="pre">False</span></code> if the lines are equivalent since they would intersect at
an infinite number of points.</p></li>
</ul>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.intersects" title="spatialmath.geom3d.Line3.intersects"><code class="xref py py-meth docutils literal notranslate"><span class="pre">intersects()</span></code></a> <code class="xref py py-meth docutils literal notranslate"><span class="pre">parallel()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.append">
<span class="sig-name descname"><span class="pre">append</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.append"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.append" title="Permalink to this definition"></a></dt>
<dd><dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>x</strong> (<a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Plucker" title="spatialmath.geom3d.Plucker"><em>Plucker</em></a>) – Plucker object</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – Attempt to append a non Plucker object</p>
</dd>
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Plucker object with new Plucker line appended</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>Line3 instance</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.arghandler">
<span class="sig-name descname"><span class="pre">arghandler</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">arg</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">convertfrom</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">()</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.arghandler" title="Permalink to this definition"></a></dt>
<dd><p>Standard constructor support (BasePoseList superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>self</strong> – the instance to be initialized :type self: BasePoseList</p>
</dd>
</dl>
<p>instance :param arg: initial value :param convertfrom: list of classes
to accept and convert from :type: tuple of typles :param check: check
value is valid, defaults to True :type check: bool :raises ValueError:
bad type passed</p>
<p>The value <code class="docutils literal notranslate"><span class="pre">arg</span></code> can be any of:</p>
<ol class="arabic simple">
<li><p>None, an identity value is created</p></li>
<li><p>a numpy.ndarray of the appropriate shape and value which is valid for the subclass</p></li>
<li><p>a list whose elements all meet the criteria above</p></li>
<li><p>an instance of the subclass</p></li>
<li><p>a list whose elements are all singelton instances of the subclass</p></li>
</ol>
<p>For cases 2 and 3, a NumPy array or a list of NumPy array is passed.
Each NumPyarray is tested for validity (if <code class="docutils literal notranslate"><span class="pre">check</span></code> is False a cursory
check of shape is made, if <code class="docutils literal notranslate"><span class="pre">check</span></code> is True the numerical value is
inspected) and converted to the required internal format by the
<code class="docutils literal notranslate"><span class="pre">_import</span></code> method. The default <code class="docutils literal notranslate"><span class="pre">_import</span></code> method calls the <code class="docutils literal notranslate"><span class="pre">isvalid</span></code>
method for checking. This mechanism allows equivalent forms to be
passed, ie. 6x1 or 4x4 for an se(3).</p>
<p>If <code class="docutils literal notranslate"><span class="pre">self</span></code> is an instance of class <code class="docutils literal notranslate"><span class="pre">A</span></code>, and an instance of class
<code class="docutils literal notranslate"><span class="pre">B</span></code> is passed and <code class="docutils literal notranslate"><span class="pre">B</span></code> is an element of the <code class="docutils literal notranslate"><span class="pre">convertfrom</span></code> argument,
then <code class="docutils literal notranslate"><span class="pre">B.A()</span></code> will be invoked to perform the type conversion.</p>
<p>Examples:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">SE3</span><span class="p">()</span>
<span class="n">SE3</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="mi">4</span><span class="p">))</span>
<span class="n">SE3</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="mi">4</span><span class="p">)])</span>
<span class="n">SE3</span><span class="p">(</span><span class="n">SE3</span><span class="p">())</span>
<span class="n">SE3</span><span class="p">([</span><span class="n">SE3</span><span class="p">(),</span> <span class="n">SE3</span><span class="p">()])</span>
<span class="n">Twist3</span><span class="p">(</span><span class="n">SE3</span><span class="p">())</span>
</pre></div>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.binop">
<span class="sig-name descname"><span class="pre">binop</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">right</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">op</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">op2</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">list1</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.binop" title="Permalink to this definition"></a></dt>
<dd><p>Perform binary operation</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>left</strong> (<em>BasePoseList subclass</em>) – left operand</p></li>
<li><p><strong>right</strong> (<em>BasePoseList subclass</em><em>, </em><em>scalar</em><em> or </em><em>array</em>) – right operand</p></li>
<li><p><strong>op</strong> (<em>callable</em>) – binary operation</p></li>
<li><p><strong>op2</strong> (<em>callable</em>) – binary operation</p></li>
<li><p><strong>list1</strong> (<em>bool</em>) – return single array as a list, default True</p></li>
</ul>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – arguments are not compatible</p>
</dd>
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>list of values</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>list</p>
</dd>
</dl>
<p>The is a helper method for implementing binary operation with overloaded
operators such as <code class="docutils literal notranslate"><span class="pre">X</span> <span class="pre">*</span> <span class="pre">Y</span></code> where <code class="docutils literal notranslate"><span class="pre">X</span></code> and <code class="docutils literal notranslate"><span class="pre">Y</span></code> are both subclasses
of <code class="docutils literal notranslate"><span class="pre">BasePoseList</span></code>. Each operand has a list of one or more
values and this methods computes a list of result values according to:</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 16%" />
<col style="width: 17%" />
<col style="width: 7%" />
<col style="width: 60%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head" colspan="2"><p>Inputs</p></th>
<th class="head" colspan="2"><p>Output</p></th>
</tr>
<tr class="row-even"><th class="head"><p>len(left)</p></th>
<th class="head"><p>len(right)</p></th>
<th class="head"><p>len</p></th>
<th class="head"><p>operation</p></th>
</tr>
</thead>
<tbody>
<tr class="row-odd"><td><p>1</p></td>
<td><p>1</p></td>
<td><p>1</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ret</span> <span class="pre">=</span> <span class="pre">op(left,</span> <span class="pre">right)</span></code></p></td>
</tr>
<tr class="row-even"><td><p>1</p></td>
<td><p>M</p></td>
<td><p>M</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ret[i]</span> <span class="pre">=</span> <span class="pre">op(left,</span> <span class="pre">right[i])</span></code></p></td>
</tr>
<tr class="row-odd"><td><p>M</p></td>
<td><p>1</p></td>
<td><p>M</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ret[i]</span> <span class="pre">=</span> <span class="pre">op(left[i],</span> <span class="pre">right)</span></code></p></td>
</tr>
<tr class="row-even"><td><p>M</p></td>
<td><p>M</p></td>
<td><p>M</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ret[i]</span> <span class="pre">=</span> <span class="pre">op(left[i],</span> <span class="pre">right[i])</span></code></p></td>
</tr>
</tbody>
</table>
<p>The arguments to <code class="docutils literal notranslate"><span class="pre">op</span></code> are the internal numeric values, ie. as returned
by the <code class="docutils literal notranslate"><span class="pre">._A</span></code> property.</p>
<p>The result is always a list, except for the first case above and
<code class="docutils literal notranslate"><span class="pre">list1</span></code> is <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>
<p>If the right operand is not a <code class="docutils literal notranslate"><span class="pre">BasePoseList</span></code> subclass, but is a numeric
scalar or array then then <code class="docutils literal notranslate"><span class="pre">op2</span></code> is invoked</p>
<p>For example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">X</span><span class="o">.</span><span class="n">_binop</span><span class="p">(</span><span class="n">Y</span><span class="p">,</span> <span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">:</span> <span class="n">x</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span>
</pre></div>
</div>
<table class="docutils align-default">
<colgroup>
<col style="width: 19%" />
<col style="width: 8%" />
<col style="width: 73%" />
</colgroup>
<thead>
<tr class="row-odd"><th class="head"><p>Input</p></th>
<th class="head" colspan="2"><p>Output</p></th>
</tr>
<tr class="row-even"><th class="head"><p>len(left)</p></th>
<th class="head"><p>len</p></th>
<th class="head"><p>operation</p></th>
</tr>
</thead>
<tbody>
<tr class="row-odd"><td><p>1</p></td>
<td><p>1</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ret</span> <span class="pre">=</span> <span class="pre">op2(left,</span> <span class="pre">right)</span></code></p></td>
</tr>
<tr class="row-even"><td><p>M</p></td>
<td><p>M</p></td>
<td><p><code class="docutils literal notranslate"><span class="pre">ret[i]</span> <span class="pre">=</span> <span class="pre">op2(left[i],</span> <span class="pre">right)</span></code></p></td>
</tr>
</tbody>
</table>
<p>There is no check on the shape of <code class="docutils literal notranslate"><span class="pre">right</span></code> if it is an array.
The result is always a list, except for the first case above and
<code class="docutils literal notranslate"><span class="pre">list1</span></code> is <code class="docutils literal notranslate"><span class="pre">False</span></code>.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.clear">
<span class="sig-name descname"><span class="pre">clear</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">None</span> <span class="pre">--</span> <span class="pre">remove</span> <span class="pre">all</span> <span class="pre">items</span> <span class="pre">from</span> <span class="pre">S</span></span></span><a class="headerlink" href="#spatialmath.geom3d.Line3.clear" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.closest_to_line">
<span class="sig-name descname"><span class="pre">closest_to_line</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.closest_to_line"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.closest_to_line" title="Permalink to this definition"></a></dt>
<dd><p>Closest point between lines</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>other</strong> (<a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3" title="spatialmath.geom3d.Line3"><em>Line3</em></a>) – second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>nearest points and distance between lines at those points</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,N), ndarray(N)</p>
</dd>
</dl>
<p>There are four cases:</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">len(self)</span> <span class="pre">==</span> <span class="pre">len(other)</span> <span class="pre">==</span> <span class="pre">1</span></code> find the point on the first line closest to the second line, as well
as the minimum distance between the lines.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">len(self)</span> <span class="pre">==</span> <span class="pre">1,</span> <span class="pre">len(other)</span> <span class="pre">==</span> <span class="pre">N</span></code> find the point of intersection between the first
line and the <code class="docutils literal notranslate"><span class="pre">N</span></code> other lines, returning <code class="docutils literal notranslate"><span class="pre">N</span></code> intersection points and distances.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">len(self)</span> <span class="pre">==</span> <span class="pre">N,</span> <span class="pre">len(other)</span> <span class="pre">==</span> <span class="pre">1</span></code> find the point of intersection between the <code class="docutils literal notranslate"><span class="pre">N</span></code> first
lines and the other line, returning <code class="docutils literal notranslate"><span class="pre">N</span></code> intersection points and distances.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">len(self)</span> <span class="pre">==</span> <span class="pre">N,</span> <span class="pre">len(other)</span> <span class="pre">==</span> <span class="pre">M</span></code> for each of the <code class="docutils literal notranslate"><span class="pre">N</span></code> first
lines find the closest intersection with each of the <code class="docutils literal notranslate"><span class="pre">M</span></code> other lines, returning <code class="docutils literal notranslate"><span class="pre">N</span></code>
intersection points and distances.</p></li>
</ul>
<p>** this last one should be an option, default behavior would be to
test self[i] against line[i]
** maybe different function</p>
<p>For two sets of lines, of equal size, return an array of closest points
and distances.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">..</span> <span class="n">runblock</span><span class="p">::</span> <span class="n">pycon</span>
<span class="o">>>></span> <span class="kn">from</span> <span class="nn">spatialmath</span> <span class="kn">import</span> <span class="n">Plucker</span>
<span class="o">>>></span> <span class="n">line1</span> <span class="o">=</span> <span class="n">Plucker</span><span class="o">.</span><span class="n">TwoPoints</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
<span class="o">>>></span> <span class="n">line2</span> <span class="o">=</span> <span class="n">Plucker</span><span class="o">.</span><span class="n">TwoPoints</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">])</span>
<span class="o">>>></span> <span class="n">line1</span><span class="o">.</span><span class="n">closest_to_line</span><span class="p">(</span><span class="n">line2</span><span class="p">)</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Reference</dt>
<dd class="field-odd"><p><a class="reference external" href="https://web.cs.iastate.edu/~cs577/handouts/plucker-coordinates.pdf">Plucker coordinates</a></p>
</dd>
<dt class="field-even">Seealso</dt>
<dd class="field-even"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.distance" title="spatialmath.geom3d.Line3.distance"><code class="xref py py-meth docutils literal notranslate"><span class="pre">distance()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.closest_to_point">
<span class="sig-name descname"><span class="pre">closest_to_point</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.closest_to_point"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.closest_to_point" title="Permalink to this definition"></a></dt>
<dd><p>Point on line closest to given point</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>x</strong> (<em>array_like</em><em>(</em><em>3</em><em>)</em>) – An arbitrary 3D point</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Point on the line and distance to line</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3), float</p>
</dd>
</dl>
<p>Find the point on the line closest to <code class="docutils literal notranslate"><span class="pre">x</span></code> as well as the distance
at that closest point.</p>
<p>Example:</p>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="go"> File "<input>", line 1, in <module></span>
<span class="go">NameError: name 'Plucker' is not defined</span>
<span class="gt">Traceback (most recent call last):</span>
File <span class="nb">"<input>"</span>, line <span class="m">1</span>, in <span class="n"><module></span>
<span class="gr">NameError</span>: <span class="n">name 'line1' is not defined</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p>meth:<cite>point</cite></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.commonperp">
<span class="sig-name descname"><span class="pre">commonperp</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.commonperp"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.commonperp" title="Permalink to this definition"></a></dt>
<dd><p>Common perpendicular to two lines</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3" title="spatialmath.geom3d.Line3"><em>Line3</em></a>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Perpendicular line</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>Line3 instance or None</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">l1.commonperp(l2)</span></code> is the common perpendicular line between the two lines.
Returns <code class="docutils literal notranslate"><span class="pre">None</span></code> if the lines are parallel.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><code class="xref py py-meth docutils literal notranslate"><span class="pre">intersect()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.contains">
<span class="sig-name descname"><span class="pre">contains</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1.1102230246251565e-14</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.contains"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.contains" title="Permalink to this definition"></a></dt>
<dd><p>Test if points are on the line</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> (<em>3-element array_like</em><em>, or </em><em>numpy.ndarray</em><em>, </em><em>shape=</em><em>(</em><em>3</em><em>,</em><em>N</em><em>)</em>) – 3D point</p></li>
<li><p><strong>tol</strong> (<em>float</em><em>, </em><em>optional</em>) – Tolerance, defaults to 50*_eps</p></li>
</ul>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – Bad argument</p>
</dd>
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p>Whether point is on the line</p>
</dd>
<dt class="field-even">Return type</dt>
<dd class="field-even"><p>bool or numpy.ndarray(N) of bool</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">line.contains(X)</span></code> is true if the point <code class="docutils literal notranslate"><span class="pre">X</span></code> lies on the line defined by
the Plucker object self.</p>
<p>If <code class="docutils literal notranslate"><span class="pre">X</span></code> is an array with 3 rows, the test is performed on every column and
an array of booleans is returned.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.copy">
<span class="sig-name descname"><span class="pre">copy</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.copy" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.count">
<span class="sig-name descname"><span class="pre">count</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">integer</span> <span class="pre">--</span> <span class="pre">return</span> <span class="pre">number</span> <span class="pre">of</span> <span class="pre">occurrences</span> <span class="pre">of</span> <span class="pre">value</span></span></span><a class="headerlink" href="#spatialmath.geom3d.Line3.count" title="Permalink to this definition"></a></dt>
<dd></dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.distance">
<span class="sig-name descname"><span class="pre">distance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.distance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.distance" title="Permalink to this definition"></a></dt>
<dd><p>Minimum distance between lines</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<code class="docutils literal notranslate"><span class="pre">Line3</span></code>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Closest distance between lines</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
<p><a href="#id1"><span class="problematic" id="id2">``</span></a>l1.distance(l2) is the minimum distance between two lines.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.closest_to_line" title="spatialmath.geom3d.Line3.closest_to_line"><code class="xref py py-meth docutils literal notranslate"><span class="pre">closest_to_line()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.extend">
<span class="sig-name descname"><span class="pre">extend</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">iterable</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.extend" title="Permalink to this definition"></a></dt>
<dd><p>Extend sequence of values in an instance (BasePoseList superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>x</strong> (<em>instance of same type</em>) – the value to extend</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – incorrect type of appended object</p>
</dd>
</dl>
<p>Appends the argument’s values to the object’s internal list of values.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">Alloc</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">10</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">Alloc</span><span class="p">(</span><span class="mi">5</span><span class="p">))</span> <span class="c1"># extend the list</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">15</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">X</span></code> is any of the SMTB classes.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.index">
<span class="sig-name descname"><span class="pre">index</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="optional">[</span>, <em class="sig-param"><span class="n"><span class="pre">start</span></span></em><span class="optional">[</span>, <em class="sig-param"><span class="n"><span class="pre">stop</span></span></em><span class="optional">]</span><span class="optional">]</span><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">integer</span> <span class="pre">--</span> <span class="pre">return</span> <span class="pre">first</span> <span class="pre">index</span> <span class="pre">of</span> <span class="pre">value.</span></span></span><a class="headerlink" href="#spatialmath.geom3d.Line3.index" title="Permalink to this definition"></a></dt>
<dd><p>Raises ValueError if the value is not present.</p>
<p>Supporting start and stop arguments is optional, but
recommended.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.insert">
<span class="sig-name descname"><span class="pre">insert</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">i</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">item</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#spatialmath.geom3d.Line3.insert" title="Permalink to this definition"></a></dt>
<dd><p>Insert a value to an instance (BasePoseList superclass method)</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>i</strong> (<em>int</em>) – element to insert value before</p></li>
<li><p><strong>item</strong> (<em>instance of same type</em>) – the value to insert</p></li>
</ul>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>ValueError</strong> – incorrect type of inserted value</p>
</dd>
</dl>
<p>Inserts the argument into the object’s internal list of values.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">X</span><span class="o">.</span><span class="n">Alloc</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">10</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">X</span><span class="p">())</span> <span class="c1"># insert at start of list</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">11</span>
<span class="gp">>>> </span><span class="n">x</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span> <span class="n">X</span><span class="p">())</span> <span class="c1"># append to the list</span>
<span class="gp">>>> </span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="go">11</span>
</pre></div>
</div>
<p>where <code class="docutils literal notranslate"><span class="pre">X</span></code> is any of the SMTB classes.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>If <code class="docutils literal notranslate"><span class="pre">i</span></code> is beyond the end of the list, the item is appended
to the list</p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.intersect_plane">
<span class="sig-name descname"><span class="pre">intersect_plane</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">plane</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.intersect_plane"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.intersect_plane" title="Permalink to this definition"></a></dt>
<dd><p>Line intersection with a plane</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>plane</strong> (<em>array_like</em><em>(</em><em>4</em><em>) or </em><em>Plane</em>) – A plane</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Intersection point, λ</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3), float</p>
</dd>
</dl>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">P,</span> <span class="pre">λ</span> <span class="pre">=</span> <span class="pre">line.intersect_plane(plane)</span></code> is the point where the line
intersects the plane, and the corresponding λ value.
Return None, None if no intersection.</p></li>
</ul>
<p>The plane can be specified as:</p>
<blockquote>
<div><ul class="simple">
<li><p>a 4-vector <span class="math notranslate nohighlight">\([a, b, c, d]\)</span> which describes the plane <span class="math notranslate nohighlight">\(\pi: ax + by + cz + d=0\)</span>.</p></li>
<li><p>a <code class="docutils literal notranslate"><span class="pre">Plane</span></code> object</p></li>
</ul>
<p>The return value is a named tuple with elements:</p>
<blockquote>
<div><ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">.p</span></code> for the point on the line as a numpy.ndarray, shape=(3,)</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">.lam</span></code> the <cite>lambda</cite> value for the point on the line.</p></li>
</ul>
</div></blockquote>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">Sealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.point" title="spatialmath.geom3d.Line3.point"><code class="xref py py-meth docutils literal notranslate"><span class="pre">point()</span></code></a> <code class="xref py py-class docutils literal notranslate"><span class="pre">Plane</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.intersect_volume">
<span class="sig-name descname"><span class="pre">intersect_volume</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">bounds</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.intersect_volume"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.intersect_volume" title="Permalink to this definition"></a></dt>
<dd><p>Line intersection with a volume</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>bounds</strong> – Bounds of an axis-aligned rectangular cuboid</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>Intersection point, λ value</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3,N), ndarray(N)</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">P,</span> <span class="pre">λ</span> <span class="pre">=</span> <span class="pre">line.intersect_volume(bounds)</span></code> is a matrix (3xN) with columns
that indicate where the line intersects the faces of the volume and
the corresponding λ values.</p>
<p>The volume is specified by <code class="docutils literal notranslate"><span class="pre">bounds</span></code> = [xmin xmax ymin ymax zmin zmax].</p>
<p>The number of
columns N is either:</p>
<ul class="simple">
<li><p>0, when the line is outside the plot volume or,</p></li>
<li><p>2 when the line pierces the bounding volume.</p></li>
</ul>
<p>See also <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.plot" title="spatialmath.geom3d.Line3.plot"><code class="xref py py-meth docutils literal notranslate"><span class="pre">plot()</span></code></a> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.point" title="spatialmath.geom3d.Line3.point"><code class="xref py py-meth docutils literal notranslate"><span class="pre">point()</span></code></a></p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.intersects">
<span class="sig-name descname"><span class="pre">intersects</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.intersects"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.intersects" title="Permalink to this definition"></a></dt>
<dd><p>Intersection point of two lines</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<code class="docutils literal notranslate"><span class="pre">Line3</span></code>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>3D intersection point</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>ndarray(3) or None</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">l1.intersects(l2)</span></code> is the point of intersection of the two lines, or
<code class="docutils literal notranslate"><span class="pre">None</span></code> if the lines do not intersect or are equivalent.</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><code class="xref py py-meth docutils literal notranslate"><span class="pre">commonperp</span> <span class="pre">:meth:`eq()</span></code> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__xor__" title="spatialmath.geom3d.Line3.__xor__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__xor__()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.isparallel">
<span class="sig-name descname"><span class="pre">isparallel</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">2.220446049250313e-15</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.isparallel"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.isparallel" title="Permalink to this definition"></a></dt>
<dd><p>Test if lines are parallel</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>l2</strong> (<code class="docutils literal notranslate"><span class="pre">Line3</span></code>) – Second line</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>lines are parallel</p>
</dd>
<dt class="field-odd">Return type</dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<p><code class="docutils literal notranslate"><span class="pre">l1.isparallel(l2)</span></code> is true if the two lines are parallel.</p>
<p><code class="docutils literal notranslate"><span class="pre">l1</span> <span class="pre">|</span> <span class="pre">l2</span></code> as above but in binary operator form</p>
<dl class="field-list simple">
<dt class="field-odd">Seealso</dt>
<dd class="field-odd"><p><a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.__or__" title="spatialmath.geom3d.Line3.__or__"><code class="xref py py-meth docutils literal notranslate"><span class="pre">__or__()</span></code></a> <a class="reference internal" href="classes-3d.html#spatialmath.geom3d.Line3.intersects" title="spatialmath.geom3d.Line3.intersects"><code class="xref py py-meth docutils literal notranslate"><span class="pre">intersects()</span></code></a></p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="spatialmath.geom3d.Line3.isvalid">
<em class="property"><span class="pre">static</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">isvalid</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">check</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/geom3d.html#Line3.isvalid"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.geom3d.Line3.isvalid" title="Permalink to this definition"></a></dt>
<dd><p>A decorator indicating abstract staticmethods.</p>
<p>Similar to abstractmethod.</p>
<p>Usage:</p>
<blockquote>
<div><dl>
<dt>class C(metaclass=ABCMeta):</dt><dd><p>@abstractstaticmethod
def my_abstract_staticmethod(…):</p>
<blockquote>