Graphics3D作图中的一些疑惑

Question

points={{0., -0.000251202, -0.000529032}, {1.10231, 0.000415542, -0.000401279}, {2.20463, 0.000190039, 0.000459265}, {3.30694, -0.000494275, 0.000437368}, {4.40925, -0.000102353, -0.000343053}, {5.51157, 0.000508752, -0.000581533}, {6.61388, 0.000104944, 0.000324529}, {7.71619, -0.000562274, 0.000648002}, {8.81851, -0.000266506, -0.0000690501}, {9.92082, 0.00107397, -0.00135064}, {11.0231, -0.000304079, 0.000950942}, {12.1254, -0.000564895, 0.000337499}, {13.2278, -0.000715426, 0.000778095}, {14.3301, 0.0025422, -0.00314922}, {15.4324, -0.00134857, 0.00205102}, {16.5347, -0.00203807, 0.00228024}, {17.637, 0.00280885, -0.0037806}, {18.7393, 0.000179203, 0.000229882}, {19.8416, -0.00230704, 0.00287761}, {20.944, 0.000657987, -0.00122381}, {22.0463, 0.00152437, -0.00175613}, {23.1486, -0.000763421, 0.00129265}, {24.2509, -0.0010236, 0.00105839}, {25.3532, 0.000628783, -0.00110996}, {26.4555, 0.00079193, -0.000683648}, {27.5578, -0.000489561, 0.000921027}, {28.6601, -0.000722997, 0.000490829}, {29.7625, 0.000493335, -0.00082626}, {30.8648, 0.000516875, -0.000286298}, {31.9671, -0.000315666, 0.000676574}, {33.0694, -0.00043576, 0.000160529}, {34.1717, 0.0000717272, -0.000514237}, {35.274, 0.000569644, -0.000148825}, {36.3763, -4.2011*10^-6, 0.000459407}, {37.4786, -0.000693039, 0.000115991}, {38.581, 0.0000899994, -0.000461398}, {39.6833, 0.000536808, 0.0000206907}, {40.7856, 0.000177415, 0.000324643}, {41.8879, -0.000650534, -0.0000111144}, {42.9902, \ -0.000471991, -0.0002808}, {44.0925, 0.00112223, -7.76143*10^-6}, {45.1948, 0.000332232, 0.000333741}, {46.2972, -0.00142665, -0.0000845074}, {47.3995, 0.00015475, -0.000327102}, {48.5018, 0.00061099, 0.000152498}, {49.6041, 0.00153948, 0.000404216}, {50.7064, -0.00280842, -0.000413041}, {51.8087, \ -0.000728581, -0.00030234}, {52.911, 0.0049033, 0.000734964}, {54.0133, -0.00308278, -0.000180026}, {55.1157, \ -0.00251753, -0.000574611}, {56.218, 0.00374308, 0.000411023}, {57.3203, 0.000458707, 0.000318566}, {58.4226, -0.00289605, -0.000395305}, {59.5249, 0.000344923, -0.000192339}, {60.6272, 0.00205221, 0.000323567}, {61.7295, -0.000520311, 0.000175634}, {62.8319, -0.00149427, -0.000283173}, {63.9342, 0.000475274, -0.000209847}, {65.0365, 0.00120555, 0.000312492}, {66.1388, -0.000480506, 0.000184883}, {67.2411, -0.000954251, -0.000293577}, {68.3434, 0.000492957, -0.000161782}, {69.4457, 0.000615702, 0.000171733}, {70.548, -0.000248474, 0.000340461}, {71.6504, -0.00056659, -0.000253822}, {72.7527, 0.000123075, -0.000410786}, {73.855, 0.000607781, 0.000339281}, {74.9573, -0.000205068, 0.000395287}, {76.0596, -0.000389848, -0.00026001}, {77.1619, 7.09214*10^-6, -0.000612562}, {78.2642, 0.000381246, 0.000383311}, {79.3666, 0.000180368, 0.000801962}, {80.4689, -0.000596434, -0.000715059}, {81.5712, 4.50793*10^-6, -0.000579892}, {82.6735, 0.000392463, 0.000460566}, {83.7758, 0.000218127, 0.0010677}, {84.8781, -0.000528581, -0.000839554}, {85.9804, \ -0.000180597, -0.0011567}, {87.0827, 0.000273613, 0.000626851}, {88.1851, 0.00111911, 0.00312994}, {89.2874, -0.00187323, -0.00433953}, {90.3897, 0.000297288, -0.0000232473}, {91.492, 0.00160493, 0.00415162}, {92.5943, -0.00114087, -0.00218198}, {93.6966, \ -0.00073454, -0.00230623}, {94.7989, 0.00111195, 0.00236775}, {95.9012, 0.000215317, 0.00109847}, {97.0036, -0.00087867, -0.00192519}, {98.1059, 0.0000256054, -0.000559431}, {99.2082, 0.000673893, 0.00147724}, {100.311, -0.000144784, 0.000388606}, {101.413, -0.000516371, -0.00120696}, {102.515, 0.000206303, -0.000310655}, {103.617, 0.000400779, 0.00107811}, {104.72, -0.00023371, 0.0000921822}, {105.822, -0.000345513, -0.000687369}, {106.924, 0.000295295, -0.000229289}, {108.027, 0.000274134, 0.000527796}, {109.129, -0.00032854, 0.000384914}};
Graphics3D[{ Darker[Blue, 0.2], Thickness[0.002], Line[points] }]
(*这样的话,做出来的只有一条直线，不是三维图形*) 
Show[{ Graphics3D[{ Darker[Blue, 0.2], Thickness[0.002], Line[points]}]} , BoxRatios -> {3, 1, 1} , ImageSize -> 600] 
(*加上BoxRatios之后，才会显示出正确的图形*)

我想请教一下，这是为什么

Answer 1

实际上第一幅图也是三维图形，你可以把鼠标移到图形上，会出现旋转的图标。
第一幅图看起来像一条直线，问题就出在BoxRatios上，这个选项值默认为Automatic，会根据三维图形中的实际坐标值来确定边界框的比例。
我们来算下三个维度的最大值

ratio = Max /@ Array[points[[All, #]] &, 3]

得到{109.129,0.0049033,0.00415162}，以此作为BoxRatios的取值来画图

Graphics3D[{Darker[Blue, 0.2], Thickness[0.002], Line[points]}, 
 BoxRatios -> ratio]

发现这个图形跟第1幅图的样子差不多，其中1个轴的长度是其它2个轴的两万多倍，所以看起来像一条线。
调整一下3个轴的比例，比如像你取的{3,1,1}，这个相当于把另外两个维度的值放大了八千倍左右，这样产生的图形就是第2幅图，这是"失真"的图，但另两个维度的变化看得更清楚。

Comments

回答的非常好，谢谢您的解答