旋转绘制的点以相对于另一组点重新投影 [英] Rotate plotted points to re-project relative to another set of points
本文介绍了旋转绘制的点以相对于另一组点重新投影的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！
问题描述
我有一个点的数据框，绘制两个多边形的轮廓，一个与另一个成直角，如下所示:
以下是绘制该图的数据:
概述 <-结构(列表(sample_ids = 结构(c(1L，1L，1L，1L，1L，1L，1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,1L, 1L, 1L, 1L, 1L, 1L, 1L), class = "factor", .Label = "MA15B1-1-5-C21"),伪地标 = 结构(1:205, .Label = c("C000-000",C000-001"、C000-002"、C000-003"、C000-004"、C000-005"、C000-006"、C000-007"、C000-008"、C000-009"、C000-010"、C000-011"、C000-012"、C000-013"、C000-014"、C000-015"、C000-016"、C000-017"、C000-018"、C000-019"、C000-020"、C000-021"、C000-022"、C000-023"、C000-024"、C000-025"、C000-026"、C000-027"、C000-028"、C000-029"、C000-030"、C000-031"、C000-032"、C000-033"、C000-034"、C000-035"、C000-036"、C000-037"、C000-038"、C000-039"、C000-040"、C001-000"、C001-001"、C001-002"、C001-003"、C001-004"、C001-005"、C001-006"、C001-007"、C001-008"、C001-009"、C001-010"、C001-011"、C001-012"、C001-013"、C001-014"、C001-015"、C001-016"、C001-017"、C001-018"、C001-019"、C001-020"、C001-021"、C001-022"、C001-023"、C001-024"、C001-025"、C001-026"、C001-027"、C001-028"、C001-029"、C001-030"、C001-031"、C001-032"、C001-033"、C001-034"、C001-035"、C001-036"、C001-037"、C001-038"、C001-039"、C001-040"、C002-000"、C002-001"、C002-002"、C002-003"、C002-004"、C002-005"、C002-006"、C002-007"、C002-008"、C002-009"、C002-010"、C002-011"、C002-012"、C002-013"、C002-014"、C002-015"、C002-016"、C002-017"、C002-018"、C002-019"、C002-020"、C002-021"、C002-022"、C002-023"、C002-024"、C002-025"、C002-026"、C002-027"、C002-028"、C002-029"、C002-030"、C002-031"、C002-032"、C002-033"、C002-034"、C002-035"、C002-036"、C002-037"、C002-038"、C002-039"、C002-040"、C003-000"、C003-001"、C003-002"、C003-003"、C003-004"、C003-005"、C003-006"、C003-007"、C003-008"、C003-009"、C003-010"、C003-011"、C003-012"、C003-013"、C003-014"、C003-015"、C003-016"、C003-017"、C003-018"、C003-019"、C003-020"、C003-021"、C003-022"、C003-023"、C003-024"、C003-025"、C003-026"、C003-027"、C003-028"、C003-029"、C003-030"、C003-031"、C003-032"、C003-033"、C003-034"、C003-035"、C003-036"、C003-037"、C003-038"、C003-039"、C003-040"、C004-000"、C004-001"、C004-002"、C004-003"、C004-004"、C004-005"、C004-006"、C004-007"、C004-008"、C004-009"、C004-010"、C004-011"、C004-012"、C004-013"、C004-014"、C004-015"、C004-016"、C004-017"、C004-018"、C004-019"、C004-020"、C004-021"、C004-022"、C004-023"、C004-024"、C004-025"、C004-026"、C004-027"、C004-028"、C004-029"、C004-030"、C004-031"、C004-032"、C004-033"、C004-034"、C004-035"、C004-036"、"C004-037", "C004-038", "C004-039", "C004-040"), class = "factor"),x = c(12.016122, 11.541907, 11.038835, 10.502722, 9.9116697,9.2927132、8.7031393、8.2882128、7.7682838、7.4592881、7.1727204、6.882329、6.5730295、6.2629328、5.974225、5.6768575、5.3772326、5.0374117、4.6981254、4.3568606、4.0674963、3.7128081、3.3609159、3.0815868、2.6982265、2.3401613、2.1256597、1.6268489、1.1917412、1.0033085, 0.88194823, 0.7922346, 0.65476406, 0.388096, 0.21852912,-0.060025979, -0.25463527, -0.43339792, -0.67199445, -0.74821764,-1.0261612, -1.0261612, -0.92627585, -0.61627114, -0.26953429,0.025590658、0.22602104、0.49005115、0.77080095、1.0086451、1.2377149、1.486245、1.7201869、1.973778、2.2724597、2.5824413、2.964093、3.2498548、3.5646105、3.9470801、4.323751、4.7156439、5.1217055、5.4455066、5.72192、6.0532079、6.4232531、6.8666763、7.2917495、7.7359419、8.1826134、8.6566973、9.1541157、9.6898823、10.248864、10.848221、11.471651、12.131388、12.808134、13.460155、14.156513、14.82901、14.82901、15.673672、16.729141、17.791584、18.740608、19.599586、20.401081、21.159971、21.838057、22.454126、22.9597、23.358027、23.555031、23.598192、23.432957、23.228603、23.358398、23.26931、23.070007、22.818201、22.594666、22.324627、22.001938、21.619722、21.251596、20.906891、20.514589、20.084562、19.653286、19.200079、18.76742、18.308954、17.817726、17.29768、16.733225、16.100943、15.422856、14.715117、13.926449、13.005936、12.016122、-13.766603、-13.935621、-14.166668、-14.608814、-14.919644、-14.839896、-12.870626、-10.359905、-5.3109751、1.5327182、5.367815、8.0128088、10.083024、11.875553、13.479352、15.080202、16.57955、18.080011、19.587444、21.106117、22.594666、24.057869、25.619652、27.149252、28.715357、30.36421、32.024361、33.747543、35.465405、37.282791、39.083374、40.917885、42.782429、44.547249、46.517342、48.3228、50.025127、51.226521、51.79425、51.81292、51.350864、51.350864、50.712288、49.727493、48.188499、46.295891、43.634846、39.408772、34.239418、29.100199、24.750076、20.78437、17.448862、14.623836、12.187436、10.035782、8.1002054、6.2869821、4.5976009、2.9719067、1.4258807、-0.022152033、-1.4664655, -2.8909578, -4.3156242, -5.6212177, -7.0099473,-8.3390236, -9.6840572, -10.756982, -11.072048, -11.078612,-11.288648, -11.518431, -11.715311, -12.164374, -12.689521,-12.874741、-12.984236、-13.186749、-13.325057、-13.766603), y = c(-29.035833, -29.341286, -29.524191, -29.617352,-29.582525、-29.559042、-29.727335、-30.435453、-30.877647、-31.823519、-32.774418、-33.682446、-34.534527、-35.375267、-36.243355, -37.097054, -37.951897, -38.769203, -39.605328,-40.459553, -41.383324, -42.267879, -43.180614, -44.17408,-45.114273, -46.101246, -47.206028, -48.160709, -49.188194,-50.379581、-51.624416、-52.90226、-54.175545、-55.411297、-56.715446, -57.996536, -59.338886, -60.712456, -62.08672,-63.551258, -64.960548, -64.960548, -66.095848, -67.283829,-68.451477, -69.582626, -70.686172, -71.78344, -72.867096,-73.942451、-75.013359、-76.076859、-77.141106、-78.198891、-79.238411, -80.269211, -81.259293, -82.296562, -83.31955,-84.296532, -85.274673, -86.239151, -87.189964, -88.227707,-89.338547, -90.414749, -91.467842, -92.440331, -93.458946,-94.472794, -95.514389, -96.540703, -97.558075, -98.525612,-99.472214, -100.33396, -101.13947, -101.80611, -102.3606,-103.02946, -103.25335, -103.3634, -103.3634, -103.23396,-101.97776, -99.767479, -97.053017, -94.317451, -91.671646,-89.110168, -86.560768, -84.055862, -81.558327, -79.093147,-76.637794, -74.252075, -71.948479, -69.772507, -67.696037,-65.677223, -63.73584, -61.868732, -60.046165, -58.283794,-56.586216, -54.961853, -53.364918, -51.774773, -50.241127,-48.760128, -47.291809, -45.853298, -44.371704, -42.896107,-41.429131, -39.946079, -38.466869, -37.086483, -35.756569,-34.21907, -32.492996, -30.540468, -29.035833, -64.279663,-64.431847, -64.572395, -64.716911, -64.756622, -64.598656,-63.945881、-63.02924、-61.699482、-60.840389、-60.469181、-60.270256, -60.174934, -60.11552, -60.097019, -60.055656,-60.050323, -60.042873, -60.036118, -60.031452, -60.046165,-60.07896, -60.085617, -60.114563, -60.141598, -60.151379,-60.169483、-60.178539、-60.202236、-60.205612、-60.228111、-60.25304, -60.282089, -60.357517, -60.381199, -60.472359,-60.610611, -60.919216, -61.434845, -62.125805, -62.965706,-62.965706, -62.721577, -62.7005, -62.964176, -63.475807,-64.327568, -65.531982, -66.759201, -67.726349, -68.583122,-69.032181、-69.287346、-69.39106、-69.402908、-69.362747、-69.289207, -69.224113, -69.148056, -69.087257, -69.023453,-68.941978, -68.890068, -68.853645, -68.838669, -68.784042,-68.784935, -68.770088, -68.771759, -68.66272, -68.247192,-67.730736, -67.32209, -66.940979, -66.564262, -66.290703,-66.0466, -65.689575, -65.31218, -64.962807, -64.588394,-64.279663), z = c(-11.640717, -12.212139, -12.790169, -13.404076,-14.090126, -14.849237, -15.624723, -16.223763, -16.94533,-17.385506、-17.770006、-18.141287、-18.529652、-18.912949、-19.258121、-19.616081、-19.978848、-20.412086、-20.848568、-21.292707, -21.653788, -22.129126, -22.603168, -22.961033,-23.492054、-23.98238、-24.24798、-24.95643、-25.557547、-25.78834, -25.931046, -26.042557, -26.233328, -26.602404,-26.848875, -27.232805, -27.515375, -27.78298, -28.115961,-28.284237, -28.652328, -28.652328, -28.618475, -28.382553,-28.104822、-27.870857、-27.725304、-27.513765、-27.281839、-27.089834, -26.904253, -26.696451, -26.501493, -26.284134,-26.017385, -25.736273, -25.376564, -25.116371, -24.823265,-24.455084、-24.090719、-23.707504、-23.306538、-22.99367、-22.731548, -22.407658, -22.039309, -21.587664, -21.154367,-20.697742, -20.23628, -19.742008, -19.219334, -18.651316,-18.054804, -17.410599, -16.73704, -16.020861, -15.284132,-14.572757、-13.813521、-13.082184、-13.082184、-11.836174、-10.371157, -8.9146891, -7.5984855, -6.3909879, -5.2539153,-4.1701441, -3.1843925, -2.2747555, -1.4981418, -0.85124946,-0.44579506, -0.22767115, -0.26378655, -0.35496628, -0.052757025,-0.018972158, -0.12546009, -0.30359784, -0.45423844, -0.66924334,-0.9572376, -1.3283906, -1.6891971, -2.0254967, -2.4296074,-2.8898013, -3.3561993, -3.856319, -4.3255644, -4.8272915,-5.3697472, -5.9422278, -6.5665784, -7.2926774, -8.0842562,-8.8555298, -9.6650724, -10.555345, -11.640717, -2.7672737,-2.1903069、-1.2737914、0.16836274、2.4672432、5.9690843、10.210753、15.91739、19.899754、14.792585、11.754315、9.7791786、8.1368742、6.8233938、5.5829773、4.618804、3.5732141、2.5846314、1.6089522, 0.62011236, -0.45423844, -1.6118737, -2.7228773,-3.9464815, -5.2166457, -6.505352, -7.8890376, -9.3358879,-10.906958, -12.543717, -14.332139, -16.252239, -18.320354,-20.591578、-22.985493、-25.616528、-28.454372、-31.466019、-34.491833, -37.347115, -39.844269, -39.844269, -40.963715,-42.466965, -44.281563, -46.622925, -49.180168, -50.47818,-50.001698, -48.150879, -47.208149, -44.766876, -42.444233,-40.224083、-38.183632、-36.332493、-34.635815、-33.141499、-31.745464, -30.478825, -29.272392, -28.079586, -26.989384,-25.958443、-24.988785、-23.958261、-23.041853、-22.102564、-21.195795, -20.102522, -18.509001, -16.776804, -15.243351,-13.770063, -12.316394, -11.027509, -9.7839518, -8.3760729,-6.9421391, -5.5482216, -4.1175952, -2.7672737)), .Names = c("sample_ids","伪地标", "x", "y", "z"), row.names = c(NA, -205L), class = "data.frame")以及上面 3d 绘图的代码:
图书馆(情节)plot_ly(轮廓，x = x，y = y，z = z，文本 = 伪地标，类型 = "scatter3d", 模式 = "标记",标记 = 列表(大小 = 2))现在我转换为数据框，并在 2d 中绘图
outlines_df <- data.frame(pseudolandmark = outlines[,2],x = as.numeric(outlines[,3]),y = as.numeric(outlines[,4]),z = as.numeric(outlines[,5]))ggplot(outlines_df, aes(x, z)) +geom_point() +coord_equal()这是轮廓之一的理想选择，就像视图直接垂直于轮廓的平面一样.这似乎是物体特定横截面的非常准确的表示.
但我坚持旋转数据集以将第二个轮廓投影到 2d 中，以便我将轮廓视为平面"，即.与第一个轮廓成 90 度.如果我只是使用 x 和 y 坐标而不是 x 和 z(如上)，结果会稍微倾斜(我希望将水平轮廓视为一条线，就像我在看它的细边缘一样):
这是第二个大纲本身
second_outline <- outlines_df[1:123, ]ggplot(second_outline, aes(x, z)) +geom_point() +coord_equal()结果就像我在 3d 空间中有一个特殊的切片.我想要的是一个看起来像这样的 2d 投影:
此视图显示轮廓平坦"，并与另一个轮廓垂直.
我
或者如果我将这个旋转应用到 y 轴，结果是不正确的:
ratio = diff(range(first_outline$x))/diff(range(first_outline$y))first_outline$ynew = ratio * first_outline$y - (ratio - 1) * mean(first_outline$y)ggplot(first_outline, aes(x, ynew)) +geom_point() +coord_equal()如何旋转数据以获得我想要的第二个轮廓的投影?
我在有关张量和惯性张量的文献中看到过，但我不确定如何开始使用它们.
解决方案
以下来自
蓝色是原始原始坐标，红色是 PCA 转换后的坐标.那个红色的轮廓看起来和我预期的一模一样，太棒了！
I have a data frame of points that plot outlines of two polygons, one at right angles to the other, like so:
Here are the data that make that plot:
outlines <-
structure(list(sample_ids = structure(c(1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 1L, 1L, 1L), class = "factor", .Label = "MA15B1-1-5-C21"),
pseudolandmark = structure(1:205, .Label = c("C000-000",
"C000-001", "C000-002", "C000-003", "C000-004", "C000-005",
"C000-006", "C000-007", "C000-008", "C000-009", "C000-010",
"C000-011", "C000-012", "C000-013", "C000-014", "C000-015",
"C000-016", "C000-017", "C000-018", "C000-019", "C000-020",
"C000-021", "C000-022", "C000-023", "C000-024", "C000-025",
"C000-026", "C000-027", "C000-028", "C000-029", "C000-030",
"C000-031", "C000-032", "C000-033", "C000-034", "C000-035",
"C000-036", "C000-037", "C000-038", "C000-039", "C000-040",
"C001-000", "C001-001", "C001-002", "C001-003", "C001-004",
"C001-005", "C001-006", "C001-007", "C001-008", "C001-009",
"C001-010", "C001-011", "C001-012", "C001-013", "C001-014",
"C001-015", "C001-016", "C001-017", "C001-018", "C001-019",
"C001-020", "C001-021", "C001-022", "C001-023", "C001-024",
"C001-025", "C001-026", "C001-027", "C001-028", "C001-029",
"C001-030", "C001-031", "C001-032", "C001-033", "C001-034",
"C001-035", "C001-036", "C001-037", "C001-038", "C001-039",
"C001-040", "C002-000", "C002-001", "C002-002", "C002-003",
"C002-004", "C002-005", "C002-006", "C002-007", "C002-008",
"C002-009", "C002-010", "C002-011", "C002-012", "C002-013",
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-6.9421391, -5.5482216, -4.1175952, -2.7672737)), .Names = c("sample_ids",
"pseudolandmark", "x", "y", "z"), row.names = c(NA, -205L), class = "data.frame")
And the code for the 3d plot above:
library(plotly)
plot_ly(outlines, x = x, y = y, z = z,
text = pseudolandmark,
type = "scatter3d", mode = "markers",
marker = list(size = 2))
Now I convert to a dataframe, and plot in 2d
outlines_df <- data.frame(pseudolandmark = outlines[,2],
x = as.numeric(outlines[,3]),
y = as.numeric(outlines[,4]),
z = as.numeric(outlines[,5]))
ggplot(outlines_df, aes(x, z)) +
geom_point() +
coord_equal()
This is ideal for one of the outlines, it's like the view is directly perpendicular to the plan of the outline. This seems like a very accurate representation of that particular cross-section of the object.
But I'm stuck at rotating the dataset to project the second outline into 2d so that I see the outline as 'flat', ie. at 90 degrees to the first outline. If I simply use x and y coords instead of x and z (as above), the result is slightly skewed (I want to see the horizontal outline as a single line, as if I am looking at its thin edge):
Here's the second outline by itself
second_outline <- outlines_df[1:123, ]
ggplot(second_outline, aes(x, z)) +
geom_point() +
coord_equal()
The result is as if I have a peculiar slice through the 3d space. What I want to get is a 2d projection that looks like this:
This view shows the outline 'flat', and perpendicular to the other outline.
I first thought that a simple rotation would solve the problem, but that's not quite right:
ratio = diff(range(first_outline$x))/diff(range(first_outline$z))
first_outline$znew = ratio * first_outline$z - (ratio - 1) * mean(first_outline$z)
ggplot(first_outline, aes(x, znew)) +
geom_point() +
coord_equal()
Or if I apply this rotation to the y-axis, the result is not right:
ratio = diff(range(first_outline$x))/diff(range(first_outline$y))
first_outline$ynew = ratio * first_outline$y - (ratio - 1) * mean(first_outline$y)
ggplot(first_outline, aes(x, ynew)) +
geom_point() +
coord_equal()
How can I rotate the data to get the projection that I want for the second outline?
I see in the literature about tensors and inertia tensors, but I'm not sure how to get started with those.
解决方案
Following from dww's helpful comments, here's a PCA of the coordinates:
# compute PCA...
first_outline_pca <- prcomp(first_outline[ , c('x', 'y', 'z')],
scores = TRUE,
cor = FALSE)
# extract PCs...
compscores <- data.frame(first_outline_pca$x[ ,1:3])
# plot to see what the result is...
ggplot() +
geom_point(data = compscores, aes(PC1, PC2), colour = "red") +
geom_point(data = compscores, aes(mean(PC1), mean(PC2)), colour = "green") +
geom_point(data = first_outline, aes(x, z), colour = "blue") +
geom_point(data = first_outline, aes(mean(x), mean(z)), colour = "green") +
coord_equal() +
theme_bw()
The blue is the original raw coords, and the red is the PCA-transformed coords. And that red outline looks pretty much exactly like what I was expecting, fantastic!
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