旋转椭圆的绘制点以给出一个圆 [英] Rotate plotted points of an ellipse to give a circle
问题描述
我有一个椭圆形的分布，我认为这是圆锥截面.我想旋转这些点，以使分布变为圆形，就像我在看圆锥顶部上方的圆锥部分一样.
I have an ellipse-shaped distribution that I think is a conic section. I want to rotate the points so that the distribution becomes circular-shaped, as if I was looking at the conic section directly over the top of the cone.
Here's some example data (generated using the function here)
X_df <-
structure(list(x = c(550.685479223573, 411.808342674744, 125.337513241526,
-46.6813176776531, 54.1090479024869, 335.045593380922, 538.806846993829,
476.123346783785, 207.359201714354, -23.3704356149293, -1.06902389582398,
252.471032092766, 502.461757269191, 522.09464005165, 290.954504794153,
22.4116013413886, -37.4399705577234, 166.122770874069, 446.874779008936,
547.271442128866, 372.271299246978, 84.7905677157295, -50.074206596271,
90.757431249567, 378.201298931732, 547.145608993239, 443.947162007208,
161.476775837252, -38.5517112166543, 25.2627436553199, 296.503160027896,
524.775126009974, 500.784559912938, 245.712512645379, -4.31860487373257,
-21.9661658669887, 211.218663607589, 479.198761786515, 535.314989389215,
330.010941011427, 50.0215808044216, -46.3823119064223, 130.383487121344,
416.170638042649, 549.268852072098, 407.813005658263, 119.940919946473,
-46.978590114418, 57.7409750579334, 340.505587064792, 539.650771180236,
472.254339573695, 201.890629521184, -25.163386210777, 1.25193046435474,
256.776302252232, 506.305676724803, 520.004964534048, 284.257495593069,
18.8183745840118, -35.9075114459174, 172.662124500953, 452.343060560759,
546.468842888411, 367.193523099128, 81.9151159445705, -49.726312730029,
95.1883131124973, 382.503271032958, 548.377552998115, 439.474201456606,
157.248088356873, -39.8634174011649, 28.665422852919, 301.243788141946,
526.815879166266, 497.683488701185, 240.939374274905, -7.78381612220116,
-19.3411744866129, 217.640180353188, 483.134755325255, 534.947529479343,
324.801587123232, 45.3957868762181, -45.0069945691924, 134.781896592204,
420.833721926428, 550.278658272823, 403.464000037755, 116.273973349216,
-48.5483252399878, 62.3918399072614, 345.924165684106, 540.282415561272,
468.621672005007, 195.304995872248, -28.2738679786754, 4.25351768918281,
262.272866287766, 509.296144374104), y = c(150.522375543584,
317.792592638159, 332.783726315973, 177.890614907595, -1.30774215535761,
-41.9959828735621, 94.0557252742373, 281.491416261009, 347.931229803675,
232.411150772918, 41.2498141860971, -50.240758928064, 42.4333078345691,
233.202857825371, 347.930304275537, 279.801242902484, 93.7702821671593,
-42.9605564915062, -0.128821245055916, 179.228629398932, 331.853832274807,
317.39347890031, 147.731418574477, -19.2449921421865, -31.3298018420377,
123.222814177221, 301.499351173211, 340.662811705721, 204.270915882133,
17.5570334546183, -47.8527634953491, 69.1925023774197, 260.846781070028,
350.702299892942, 255.267980339802, 64.3048063206447, -47.7550214881633,
21.0575085383169, 209.247480999408, 342.716023607699, 298.578792586917,
118.053124236616, -33.3190320226709, -16.5618829502486, 154.097078032767,
319.940208485997, 330.141085013461, 175.063055837321, -4.17911647131882,
-40.77087978947, 96.7492568480405, 284.629419943293, 347.18869555741,
228.951107374031, 37.6230640656836, -49.9549156886126, 45.2896584936418,
236.96620488459, 349.2183672397, 277.259838492706, 88.5019845874813,
-43.1419505604449, 1.98249146234145, 183.766146834555, 334.721418603224,
314.869389642466, 144.917094343997, -21.0615467657252, -29.137753346726,
126.928148173889, 305.196445845808, 339.338402720207, 201.609402013064,
15.0779976117978, -47.1046400880924, 71.7191693530443, 263.543031729657,
350.145628648054, 252.792513384296, 61.2531942049295, -49.0697852698499,
24.2068045114243, 212.793083656477, 343.533262533366, 295.969945687212,
115.135250419503, -34.4145910896749, -14.7817206225652, 156.282366465729,
322.116360452784, 328.626788731125, 171.323808201914, -6.54021515590322,
-40.1360134761796, 101.492490333309, 286.854230399582, 347.010792855229,
226.829162028581, 35.3880363162166, -50.8418314561365, 48.893760376765
)), .Names = c("x", "y"), row.names = c(NA, -101L), class = "data.frame")
绘制椭圆，这类似于我的实际数据:
Plot the ellipse, this resembles my actual data:
ggplot(X_df, aes(x, y)) +
geom_point() +
coord_equal()
我想对xy坐标应用一个函数，以使椭圆围绕其长轴旋转，将椭圆的顶部移向我，椭圆的底部移离我，以获得类似的东西(尺寸相等)沿x轴(如上面的椭圆)，但沿y轴的尺寸不同):
I want to apply a function to the xy coords to rotate the ellipse around its long axis, moving the top of the ellipse towards me, and the bottom of the ellipse away from me, to get something like this (with equal dimension along the x-axis as the ellipse above, but different dimension along the y-axis):
我想像旋转椭圆一样旋转数据以生成圆，在该圆中，我看到形状的顶部和底部之间的最大距离(即，垂直于长轴的可能的最长轴)作为形状绕着它的长轴旋转.
I want to rotate my data like this ellipse is rotated to produce the circle, where I see the maximum distance between the top and bottom of the shape (ie. the longest possible axis perpendicular to the long axis), as the shape rotates around it long axis.
我该怎么做?
推荐答案
似乎您在说的是，如果我从x = -1000，y = 0的角度观察圆"边，会看到一条线从y轴逆时针旋转(超出xy平面).目标是将圆旋转回y轴.
It seems like what you're saying is that if I viewed the "circle" edge on from, say, x=-1000, y=0, I would see a line rotated counterclockwise (out of the xy-plane) away from the y axis. The goal is to rotate the circle back to the y-axis.
旋转角度为acos(1/ratio)(在这种情况下为0.839弧度或48.06度)，其中ratio为diff(range(X_df$x))/diff(range(X_df$y))(假设旋转轴在xy平面中且与x轴平行，并且数据包括圆的x轴上的点).
The angle of rotation is acos(1/ratio) (0.839 radians or 48.06 degrees in this case) where ratio is diff(range(X_df$x))/diff(range(X_df$y)) (assuming the axis of rotation is in the xy-plane and parallel to the x-axis and your data includes points on the x axis on both sides of the circle).
实际上，要将圆旋转回到xy平面，您可以将y点乘以ratio，然后为保持相同的中心，减去(ratio - 1) * mean(X_df$y)(这里我假设是数据点围绕圆均匀分布).
To, in effect, rotate the circle back to the xy-plane, you could just multiply the y points by ratio and then, to maintain the same center, subtract (ratio - 1) * mean(X_df$y) (where I've assumed the data points are evenly distributed about the circle).
换句话说(或实际上是用代码):
In other words (or in code, actually):
ratio = diff(range(X_df$x))/diff(range(X_df$y))
X_df$ynew = ratio * X_df$y - (ratio - 1) * mean(X_df$y)
ggplot(X_df, aes(x, ynew)) +
geom_point() +
coord_equal()
将原件与旋转"进行比较:
Compare original to "rotated":
这篇关于旋转椭圆的绘制点以给出一个圆的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！
