使用受约束的B样条曲线近似形状轮廓 [英] Approximate a shape outline using constrained B-splines

问题描述

我正在寻找一种生成受约束的样条曲线以逼近形状（在我的情况下为轮廓轮廓）的可能性。作为原始数据，我有一张包含数百个xy坐标对的表，这些对是从覆盖区边界收集的。样条线仅应近似于数据点（样条线不需要通过数据点）。我希望能够将花键平滑到一定程度。另外，我必须能够约束样条曲线：定义样条曲线必须通过的几个关键数据点。

R包 cobs（COnstrained B样条曲线） ，

解决方案

在注释主题之后，下面是一些图表。我使用

现在输入代码。

 ＃devtools :: install_github（ vbonhomme / Momocs）
库（ Momocs）＃版本1.0.3 
 
 xy<-结构（list（
 V1 = c（124.9，86.44，97.22，81.34，49.09，57.18，-77.6，-191.95，- 284.67，-383.18，-379.27，-492.85，-547.72，-600.67，-713.29，-814.36，-868.27，-926.99，-958.76，-1025.18，-1077.16，-1105.07，-1126.25，-1112.77，-1087.74， -989.56，-911.59，-859.61，-745.06，-656.5，-682.01，-637.25，-601.71，-539.09，-394.79，-219.17，-170.17，-201.48，-122.52，-43.56、127.97、344.42、539.09 ，686.11、987.63、1253.31、1283.15、1536.32、1741.34、1833.25、1700.3、1787.43、1911.31、2017.49、2097.81、2135.93、2093.73、2066.66、2063.78、2022.94、1978.69、1919.44、1904.3.1、1897.10、23.854。 ，1642.45，1553.96，1472.96，1396.04，1141.65，1085.82，1055.02，1358.24，1325.94，1031.91、1287.14、1265.36、931.15、872.12、811.48、755.65、738.32、697.41、682.49、647.35、647.65。 ，675.22，709.25，718.78，717.42，551.09，535.21，540.98，534.73，546.76，811.96，823.03，822.07，607.4，626.18，637.73，659.87，756.13，753.72，735.91，72.，57.72，579.71，72.79，57。 ，121.16、45.6、12.93，-9.87，-12.59、16、27.91、37.78、49.35、8.51、2.72，-1.02、59.22、58.2、51.73、54.45、0.96、10.59、138.62、149.69、144.87、142.26、146.34， 125.24、124.9、86.44、97.22、81.34、49.09、57.18，-77.6，-191.95，-284.67，-383.18，-379.27，-492.85，-547.72，-600.67，-713.29，-814.36，-868.27，-926.99， -958.76，-1025.18，-1077.16，-1105.07，-1126.25，-1112.77，-1087.74，-989.56，-911.59，-859.61，-745.06，-656.5，-682.01，-637.25，-601.71，-539.09，-394.79 ，-219.17，-170.17，-201.48，-122.52，-43.56，127.97，344.42，539.09，686.11，987.63，1253.31，1283.15，1536.32，1741.14，1832.35，1700.3，1787.43，1911.31，2017.49，2097.81， 2066.96、2063.78、2022.94、1978.69、1919.44、1904.03、1895.37、1854.22、1810.23、1771.09、1741.48、1642.45、1553.66、1472.96、1394.64、1 141.65，1085.82，1055.02，1358.24，1325.94，1031.91，1287.14，1265.36，931.15，872.12，811.48，755.65，738.32，697.41，682.49，647.35，628.25，620.09，629.62,78.21,718.615，675.22,718。 540.98、534.73、546.76、811.96、823.03、822.07、607.4、626.18、637.73、659.87、756.13、753.72、735.91、720.99、676.71、576.6、508.26、339.8、179.53、121.16、45.6、12.5.9- 16，27.91，37.78，49.35，8.51，2.72，-1.02，59.22，58.2，51.73，54.45，0.96，10.59，138.62，149.69，144.87，142.26，146.34，125.24），
 V2 = c（-446.8 ，-415.83，-394.43，-259.19，-104.69，-4.03，58.59，-80.26，52.11，-48.33，-142.23，-176.89，-233.68，-321.28，-416.57，-457.97，-458.93，-429.09， -422.35，-450.27，-431.98，-379.03，-260.63，-123.94，-2.65，269.76，455.55，548.92，616.3，691.38，756.84，888.72，1016.97，1157.18，1198.02，1101.37，1025.14，929.84，929.84 ，717.47，733.81，784.18，835.91，1225.63，1198.68，925.3，742.4，814.13，732.45，586.79，394.84，212.42，28.64，-111.58，-33 7.56，-490.03，-526.07，-528.82，-547.2，-551.97，-552.3，-585.51，-551.34，-543.16，-526.1，-494.11，-466.88，-355.93，-274.94，-215.04，-114.3， -194.21，-103.73，-3.62、104.2、230.8、154.25、380.55、416.62、260.07、295.75、295.75、251.47、220.67、225.96、180.72、121.52、4.14，-127.23，-176.24，-332.11，-408.35，- 494.11，-573.75，-582.62，-678.88，-730.38，-788.62，-831.94，-846.38，-895.95，-934.46，-968.15，-1033.12，-1097.62，-1150.08，-1157.3，-1254.04，-1340.2， -1441.75，-1500.47，-1550.52，-1605.39，-1681.44，-1709.84，-1715.22，-1672.34，-1607，-1522.59，-1440.57，-1421.18，-1345.62，-1247.95，-1190.77，-1181.58，-1071.65 ，-1037.62，-1010.39，-998.82，-986.57，-937.9，-887.29，-842.05，-831.46，-774.66，-703.91，-573.75，-533.59，-448.16，-446.8，-415.83，-394.43，- 259.19，-104.69，-4.03，58.59，-80.26，52.11，-48.33，-142.23，-176.89，-233.68，-321.28，-416.57，-457.97，-458.93，-429.09，-422.35，-450.27，-431.98 ，-379.03，-260.63，-123.94，-2.65，269.76，455.55，548.92，616.3 ，691.38，756.84，888.72，1016.97，1157.18，1198.02，1101.37，1025.14，929.84，852.25，766.48，717.47，733.81，784.18，835.91，1225.63，1198.68，925.3，742.4，48.2，798.2，798.13，586.2，768.2，394.2，586.2，394.2，586.23，586.2，394.24。 ，-111.58，-337.56，-490.03，-526.07，-528.82，-547.2，-551.97，-552.3，-585.51，-551.34，-543.16，-526.1，-494.11，-466.88，-355.93，-274.94，- 215.04，-114.3，-194.21，-103.73，-3.62、104.2、230.8、154.25、380.55、416.62、260.07、295.75、295.75、251.47、220.67、225.96、180.72、121.52、4.14，-127.23，-176.24，-332.11 ，-408.35，-494.11，-573.75，-582.62，-678.88，-730.38，-788.62，-831.94，-846.38，-895.95，-934.46，-968.15，-1033.12，-1097.62，-1150.08，-1157.3，- 1254.04，-1340.2，-1441.75，-1500.47，-1550.52，-1605.39，-1681.44，-1709.84，-1715.22，-1672.34，-1607，-1522.59，-1440.57，-1421.18，-1345.62，-1247.95，-1190.77， -1181.58，-1071.65，-1037.62，-1010.39，-998.82，-986.57，-937.9，-887.29，-842.05，-831.46，-774.66，-703.91，-573.75，-533.59，-448.16））.names = c（ V1， V2）， class = data.frame，row.names = c（NA，-280L））
 
 
 ###第一件事：双轮廓--------- ------------ 
 coo_plot（xy）
 ldk_labels（xy）＃由于叠加了
 coo_plot（xy [1：140，]，lwd = 3）而变得模糊＃第一个形状
 coo_draw（xy [-（1：140），]，border = white）＃第二个形状
 
＃从这里开始，我们将使用第一个形状的第140个点xy并命名为 shp以避免混淆
＃如果您对恐龙足迹感到厌倦，则可以使用带shp<-bot [9]的啤酒瓶来健走
 
 shp <-xy [1：140，] 
 
 ### 1.自然样条线--------------------- 
 
 shp_cumchord<-coo_perimcum（shp）＃等效cumchord 
 shp_spline<-cbind（spline（shp_cumchord，shp [，1]，method = natural，n = 120）$ y，
样条曲线（shp_cumchord，shp [，2]，method = natural，n = 120）$ y）
 
 coo_plot（shp，main =自然样条曲线，zoom = 1.2）
 coo_draw（shp_spline，border = blue，lwd = 2）
 
 ### 2.带有穗轴的B样条----------- ---------- 
库（cobs）
 
 shp_bspline<-cbind（cobs（shp_cumchord，shp [，1]，nknots = 50）$ fitted，
 cobs（shp_cumchord，shp [，2]，nknots = 50）$ fitted）
 
 coo_plot（shp，main = bspline，zoom = 1.2）
 coo_draw（shp_bspline， border = blue）
 
 ### 3.贝塞尔曲线--------------------- 
＃内置函数因此较短
 shp_bezier<-shp％&％; bezier（）％>％bezier_i（）
 
 coo_plot（shp，main = bezier，zoom = 1.2）
 coo_draw（shp_bezier，border = blue）
 
 
 ### 4.椭圆傅里叶变换------------------ --- 
＃另一个内置函数
 
 shp_eft<-shp％&％;％efourier（）％&％;％efourier_i（）
 
 coo_plot（shp ，main = bspline，zoom = 1.2）
 coo_draw（shp_eft，border = blue）
 
 ### 5.原始形状的面板和4种方法---- ----- 
 Out（列表（原始= shp，
 nat_spline = shp_spline，bspline = shp_bspline，
 bezier = shp_bezier，eft = shp_eft））％&g t;％
 panel（names = TRUE，dim = c（1，5））
  

I'm looking for a possibility to generate a constrained spline in order to approximate a shape (in my case, a footprint outline). As raw data, I have a table with several hundred xy-coordinate pairs, which have been collected from the boundary of the footprint. The spline should only approximate the data points (the spline does not need to pass the data points). I want to be able to smooth the spline to certain degrees. Also, I need to be able to constrain the spline: Defining several critical data points which the spline has to pass.

The R package "cobs" (COnstrained B-Splines, https://cran.r-project.org/web/packages/cobs/index.html) comes very close to providing a solution, offering parameters to constrain the spline as wanted. However, this package does not spline through an ordered sequence of data points, which of course is crucial when you want the spline to follow the boundary of a shape. I tried to spline x and y coordinates separately, but after recombining them two distinct shapes appear in the plot, so this does not seem to work (Or I got something wrong?). Is anybody aware of a solution?

---

Update: working example (dinosaur footprint outline)

data.txt:

structure(list(V1 = c(124.9, 86.44, 97.22, 81.34, 49.09, 57.18, 
-77.6, -191.95, -284.67, -383.18, -379.27, -492.85, -547.72, 
-600.67, -713.29, -814.36, -868.27, -926.99, -958.76, -1025.18, 
-1077.16, -1105.07, -1126.25, -1112.77, -1087.74, -989.56, -911.59, 
-859.61, -745.06, -656.5, -682.01, -637.25, -601.71, -539.09, 
-394.79, -219.17, -170.17, -201.48, -122.52, -43.56, 127.97, 
344.42, 539.09, 686.11, 987.63, 1253.31, 1283.15, 1536.32, 1741.14, 
1832.35, 1700.3, 1787.43, 1911.31, 2017.49, 2097.81, 2135.93, 
2093.73, 2066.96, 2063.78, 2022.94, 1978.69, 1919.44, 1904.03, 
1895.37, 1854.22, 1810.23, 1771.09, 1741.48, 1642.45, 1553.96, 
1472.96, 1396.04, 1141.65, 1085.82, 1055.02, 1358.24, 1325.94, 
1031.91, 1287.14, 1265.36, 931.15, 872.12, 811.48, 755.65, 738.32, 
697.41, 682.49, 647.35, 628.25, 620.09, 629.62, 675.22, 709.25, 
718.78, 717.42, 551.09, 535.21, 540.98, 534.73, 546.76, 811.96, 
823.03, 822.07, 607.4, 626.18, 637.73, 659.87, 756.13, 753.72, 
735.91, 720.99, 676.71, 576.6, 508.26, 339.8, 179.53, 121.16, 
45.6, 12.93, -9.87, -12.59, 16, 27.91, 37.78, 49.35, 8.51, 2.72, 
-1.02, 59.22, 58.2, 51.73, 54.45, 0.96, 10.59, 138.62, 149.69, 
144.87, 142.26, 146.34, 125.24, 124.9, 86.44, 97.22, 81.34, 49.09, 
57.18, -77.6, -191.95, -284.67, -383.18, -379.27, -492.85, -547.72, 
-600.67, -713.29, -814.36, -868.27, -926.99, -958.76, -1025.18, 
-1077.16, -1105.07, -1126.25, -1112.77, -1087.74, -989.56, -911.59, 
-859.61, -745.06, -656.5, -682.01, -637.25, -601.71, -539.09, 
-394.79, -219.17, -170.17, -201.48, -122.52, -43.56, 127.97, 
344.42, 539.09, 686.11, 987.63, 1253.31, 1283.15, 1536.32, 1741.14, 
1832.35, 1700.3, 1787.43, 1911.31, 2017.49, 2097.81, 2135.93, 
2093.73, 2066.96, 2063.78, 2022.94, 1978.69, 1919.44, 1904.03, 
1895.37, 1854.22, 1810.23, 1771.09, 1741.48, 1642.45, 1553.96, 
1472.96, 1396.04, 1141.65, 1085.82, 1055.02, 1358.24, 1325.94, 
1031.91, 1287.14, 1265.36, 931.15, 872.12, 811.48, 755.65, 738.32, 
697.41, 682.49, 647.35, 628.25, 620.09, 629.62, 675.22, 709.25, 
718.78, 717.42, 551.09, 535.21, 540.98, 534.73, 546.76, 811.96, 
823.03, 822.07, 607.4, 626.18, 637.73, 659.87, 756.13, 753.72, 
735.91, 720.99, 676.71, 576.6, 508.26, 339.8, 179.53, 121.16, 
45.6, 12.93, -9.87, -12.59, 16, 27.91, 37.78, 49.35, 8.51, 2.72, 
-1.02, 59.22, 58.2, 51.73, 54.45, 0.96, 10.59, 138.62, 149.69, 
144.87, 142.26, 146.34, 125.24), V2 = c(-446.8, -415.83, -394.43, 
-259.19, -104.69, -4.03, 58.59, -80.26, 52.11, -48.33, -142.23, 
-176.89, -233.68, -321.28, -416.57, -457.97, -458.93, -429.09, 
-422.35, -450.27, -431.98, -379.03, -260.63, -123.94, -2.65, 
269.76, 455.55, 548.92, 616.3, 691.38, 756.84, 888.72, 1016.97, 
1157.18, 1198.02, 1101.37, 1025.14, 929.84, 852.25, 766.48, 717.47, 
733.81, 784.18, 835.91, 1225.63, 1198.68, 925.3, 742.4, 814.13, 
732.45, 586.79, 394.84, 212.42, 28.64, -111.58, -337.56, -490.03, 
-526.07, -528.82, -547.2, -551.97, -552.3, -585.51, -551.34, 
-543.16, -526.1, -494.11, -466.88, -355.93, -274.94, -215.04, 
-114.3, -194.21, -103.73, -3.62, 104.2, 230.8, 154.25, 380.55, 
416.62, 260.07, 295.75, 295.75, 251.47, 220.67, 225.96, 180.72, 
121.52, 4.14, -127.23, -176.24, -332.11, -408.35, -494.11, -573.75, 
-582.62, -678.88, -730.38, -788.62, -831.94, -846.38, -895.95, 
-934.46, -968.15, -1033.12, -1097.62, -1150.08, -1157.3, -1254.04, 
-1340.2, -1441.75, -1500.47, -1550.52, -1605.39, -1681.44, -1709.84, 
-1715.22, -1672.34, -1607, -1522.59, -1440.57, -1421.18, -1345.62, 
-1247.95, -1190.77, -1181.58, -1071.65, -1037.62, -1010.39, -998.82, 
-986.57, -937.9, -887.29, -842.05, -831.46, -774.66, -703.91, 
-573.75, -533.59, -448.16, -446.8, -415.83, -394.43, -259.19, 
-104.69, -4.03, 58.59, -80.26, 52.11, -48.33, -142.23, -176.89, 
-233.68, -321.28, -416.57, -457.97, -458.93, -429.09, -422.35, 
-450.27, -431.98, -379.03, -260.63, -123.94, -2.65, 269.76, 455.55, 
548.92, 616.3, 691.38, 756.84, 888.72, 1016.97, 1157.18, 1198.02, 
1101.37, 1025.14, 929.84, 852.25, 766.48, 717.47, 733.81, 784.18, 
835.91, 1225.63, 1198.68, 925.3, 742.4, 814.13, 732.45, 586.79, 
394.84, 212.42, 28.64, -111.58, -337.56, -490.03, -526.07, -528.82, 
-547.2, -551.97, -552.3, -585.51, -551.34, -543.16, -526.1, -494.11, 
-466.88, -355.93, -274.94, -215.04, -114.3, -194.21, -103.73, 
-3.62, 104.2, 230.8, 154.25, 380.55, 416.62, 260.07, 295.75, 
295.75, 251.47, 220.67, 225.96, 180.72, 121.52, 4.14, -127.23, 
-176.24, -332.11, -408.35, -494.11, -573.75, -582.62, -678.88, 
-730.38, -788.62, -831.94, -846.38, -895.95, -934.46, -968.15, 
-1033.12, -1097.62, -1150.08, -1157.3, -1254.04, -1340.2, -1441.75, 
-1500.47, -1550.52, -1605.39, -1681.44, -1709.84, -1715.22, -1672.34, 
-1607, -1522.59, -1440.57, -1421.18, -1345.62, -1247.95, -1190.77, 
-1181.58, -1071.65, -1037.62, -1010.39, -998.82, -986.57, -937.9, 
-887.29, -842.05, -831.46, -774.66, -703.91, -573.75, -533.59, 
-448.16)), .Names = c("V1", "V2"), class = "data.frame", row.names = c(NA, 
-280L))

---

require(cobs)

xy <- dget(data.txt)

#Cumchord function (from Claude, 2008): Cumulative chordal distance vector
cumchord<-function(M)
{cumsum(sqrt(apply((M-rbind(M[1,],
M[-(dim(M)[1]),]))^2,1,sum)))}

z <- cumchord(xy)

#Calculating B-spline for x and y values separately
x <- cobs(z,xy[,1],nknots=50)
y <- cobs(z,xy[,2],nknots=50)

#Plot spline
plot(xy)
lines(x$fitted,y$fitted)

Image of resulting plot

解决方案

Following the comments thread, here are some graphs. I use Momocs since I'm familiar with it and it will shorten examples.

I brief, your problem is that there are two outlines in your outline.

I also include original use of spline by Julien Claude, and two additional examples with bezier curves and elliptic Fourier transforms. All 4 can be used to describe an outline (and reconstruct it) and it's probably worth gathering them here.

The picture gathers the original shape and these 4 methods

Now the code. It's not particularly long but quite repetitive.

# devtools::install_github("vbonhomme/Momocs")
library(Momocs) # version 1.0.3

xy <- structure(list(
  V1 = c(124.9, 86.44, 97.22, 81.34, 49.09, 57.18, -77.6, -191.95, -284.67, -383.18, -379.27, -492.85, -547.72, -600.67, -713.29, -814.36, -868.27, -926.99, -958.76, -1025.18, -1077.16, -1105.07, -1126.25, -1112.77, -1087.74, -989.56, -911.59, -859.61, -745.06, -656.5, -682.01, -637.25, -601.71, -539.09, -394.79, -219.17, -170.17, -201.48, -122.52, -43.56, 127.97, 344.42, 539.09, 686.11, 987.63, 1253.31, 1283.15, 1536.32, 1741.14, 1832.35, 1700.3, 1787.43, 1911.31, 2017.49, 2097.81, 2135.93, 2093.73, 2066.96, 2063.78, 2022.94, 1978.69, 1919.44, 1904.03, 1895.37, 1854.22, 1810.23, 1771.09, 1741.48, 1642.45, 1553.96, 1472.96, 1396.04, 1141.65, 1085.82, 1055.02, 1358.24, 1325.94, 1031.91, 1287.14, 1265.36, 931.15, 872.12, 811.48, 755.65, 738.32, 697.41, 682.49, 647.35, 628.25, 620.09, 629.62, 675.22, 709.25, 718.78, 717.42, 551.09, 535.21, 540.98, 534.73, 546.76, 811.96, 823.03, 822.07, 607.4, 626.18, 637.73, 659.87, 756.13, 753.72, 735.91, 720.99, 676.71, 576.6, 508.26, 339.8, 179.53, 121.16, 45.6, 12.93, -9.87, -12.59, 16, 27.91, 37.78, 49.35, 8.51, 2.72, -1.02, 59.22, 58.2, 51.73, 54.45, 0.96, 10.59, 138.62, 149.69, 144.87, 142.26, 146.34, 125.24, 124.9, 86.44, 97.22, 81.34, 49.09, 57.18, -77.6, -191.95, -284.67, -383.18, -379.27, -492.85, -547.72, -600.67, -713.29, -814.36, -868.27, -926.99, -958.76, -1025.18, -1077.16, -1105.07, -1126.25, -1112.77, -1087.74, -989.56, -911.59, -859.61, -745.06, -656.5, -682.01, -637.25, -601.71, -539.09, -394.79, -219.17, -170.17, -201.48, -122.52, -43.56, 127.97, 344.42, 539.09, 686.11, 987.63, 1253.31, 1283.15, 1536.32, 1741.14, 1832.35, 1700.3, 1787.43, 1911.31, 2017.49, 2097.81, 2135.93, 2093.73, 2066.96, 2063.78, 2022.94, 1978.69, 1919.44, 1904.03, 1895.37, 1854.22, 1810.23, 1771.09, 1741.48, 1642.45, 1553.96, 1472.96, 1396.04, 1141.65, 1085.82, 1055.02, 1358.24, 1325.94, 1031.91, 1287.14, 1265.36, 931.15, 872.12, 811.48, 755.65, 738.32, 697.41, 682.49, 647.35, 628.25, 620.09, 629.62, 675.22, 709.25, 718.78, 717.42, 551.09, 535.21, 540.98, 534.73, 546.76, 811.96, 823.03, 822.07, 607.4, 626.18, 637.73, 659.87, 756.13, 753.72, 735.91, 720.99, 676.71, 576.6, 508.26, 339.8, 179.53, 121.16, 45.6, 12.93, -9.87, -12.59, 16, 27.91, 37.78, 49.35, 8.51, 2.72, -1.02, 59.22, 58.2, 51.73, 54.45, 0.96, 10.59, 138.62, 149.69, 144.87, 142.26, 146.34, 125.24),
  V2 = c(-446.8, -415.83, -394.43, -259.19, -104.69, -4.03, 58.59, -80.26, 52.11, -48.33, -142.23, -176.89, -233.68, -321.28, -416.57, -457.97, -458.93, -429.09, -422.35, -450.27, -431.98, -379.03, -260.63, -123.94, -2.65, 269.76, 455.55, 548.92, 616.3, 691.38, 756.84, 888.72, 1016.97, 1157.18, 1198.02, 1101.37, 1025.14, 929.84, 852.25, 766.48, 717.47, 733.81, 784.18, 835.91, 1225.63, 1198.68, 925.3, 742.4, 814.13, 732.45, 586.79, 394.84, 212.42, 28.64, -111.58, -337.56, -490.03, -526.07, -528.82, -547.2, -551.97, -552.3, -585.51, -551.34, -543.16, -526.1, -494.11, -466.88, -355.93, -274.94, -215.04, -114.3, -194.21, -103.73, -3.62, 104.2, 230.8, 154.25, 380.55, 416.62, 260.07, 295.75, 295.75, 251.47, 220.67, 225.96, 180.72, 121.52, 4.14, -127.23, -176.24, -332.11, -408.35, -494.11, -573.75, -582.62, -678.88, -730.38, -788.62, -831.94, -846.38, -895.95, -934.46, -968.15, -1033.12, -1097.62, -1150.08, -1157.3, -1254.04, -1340.2, -1441.75, -1500.47, -1550.52, -1605.39, -1681.44, -1709.84, -1715.22, -1672.34, -1607, -1522.59, -1440.57, -1421.18, -1345.62, -1247.95, -1190.77, -1181.58, -1071.65, -1037.62, -1010.39, -998.82, -986.57, -937.9, -887.29, -842.05, -831.46, -774.66, -703.91, -573.75, -533.59, -448.16, -446.8, -415.83, -394.43, -259.19, -104.69, -4.03, 58.59, -80.26, 52.11, -48.33, -142.23, -176.89, -233.68, -321.28, -416.57, -457.97, -458.93, -429.09, -422.35, -450.27, -431.98, -379.03, -260.63, -123.94, -2.65, 269.76, 455.55, 548.92, 616.3, 691.38, 756.84, 888.72, 1016.97, 1157.18, 1198.02, 1101.37, 1025.14, 929.84, 852.25, 766.48, 717.47, 733.81, 784.18, 835.91, 1225.63, 1198.68, 925.3, 742.4, 814.13, 732.45, 586.79, 394.84, 212.42, 28.64, -111.58, -337.56, -490.03, -526.07, -528.82, -547.2, -551.97, -552.3, -585.51, -551.34, -543.16, -526.1, -494.11, -466.88, -355.93, -274.94, -215.04, -114.3, -194.21, -103.73, -3.62, 104.2, 230.8, 154.25, 380.55, 416.62, 260.07, 295.75, 295.75, 251.47, 220.67, 225.96, 180.72, 121.52, 4.14, -127.23, -176.24, -332.11, -408.35, -494.11, -573.75, -582.62, -678.88, -730.38, -788.62, -831.94, -846.38, -895.95, -934.46, -968.15, -1033.12, -1097.62, -1150.08, -1157.3, -1254.04, -1340.2, -1441.75, -1500.47, -1550.52, -1605.39, -1681.44, -1709.84, -1715.22, -1672.34, -1607, -1522.59, -1440.57, -1421.18, -1345.62, -1247.95, -1190.77, -1181.58, -1071.65, -1037.62, -1010.39, -998.82, -986.57, -937.9, -887.29, -842.05, -831.46, -774.66, -703.91, -573.75, -533.59, -448.16)), .Names = c("V1", "V2"), class = "data.frame", row.names = c(NA, -280L))


### First thing first: double outline ---------------------
coo_plot(xy)
ldk_labels(xy) # blurry since superimposed
coo_plot(xy[1:140, ], lwd=3) # first shape
coo_draw(xy[-(1:140), ], border="white") # second shape

# so from here, we will use the first 140th points from xy and name it 'shp' to avoid confusion
# if you're bored with dinos footprints, you can use beer bottles with shp <- bot[9] for a guinness

shp <- xy[1:140, ]

### 1.Natural splines ---------------------

shp_cumchord <- coo_perimcum(shp) # cumchord equivalent
shp_spline <- cbind(spline(shp_cumchord, shp[, 1], method="natural", n=120)$y,
                    spline(shp_cumchord, shp[, 2], method="natural", n=120)$y)

coo_plot(shp, main="natural spline", zoom=1.2)
coo_draw(shp_spline, border="blue", lwd=2)

### 2. B-splines with cobs ---------------------
library(cobs)

shp_bspline <- cbind(cobs(shp_cumchord, shp[, 1], nknots=50)$fitted,
                     cobs(shp_cumchord, shp[, 2], nknots=50)$fitted)

coo_plot(shp, main = "bspline", zoom=1.2)
coo_draw(shp_bspline, border="blue")

### 3. Bezier curves  ---------------------
# built in function so it's shorter
shp_bezier <- shp %>% bezier() %>% bezier_i()

coo_plot(shp, main = "bezier", zoom=1.2)
coo_draw(shp_bezier, border="blue")


### 4. elliptic Fourier transforms ---------------------
# another built in function

shp_eft <- shp %>% efourier() %>% efourier_i()

coo_plot(shp, main = "bspline", zoom=1.2)
coo_draw(shp_eft, border="blue")

### 5. A panel of original shape and 4 methods ---------
Out(list(original=shp,
         nat_spline=shp_spline, bspline=shp_bspline,
         bezier=shp_bezier, eft=shp_eft)) %>% 
panel(names=TRUE, dim=c(1, 5))

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