如何绘制以不同角度对齐的点并用一条线连接它们？

Question

我正在尝试从 R 中的躯干部分模拟圆环的形状，但每次我想要接近真实形状时都会变得更加困难。我开始用四个半径测量来做这件事，我得到了一个很好的解决方案 ()。但是，现在我想绘制四个以上的半径但角度不同，并将这些点与模拟环的线连接起来，就像我做的这个草图一样：

我的第一个方法是旋转数据矩阵，但我无法使所有半径都从相同位置 (0,0) 开始。我也试过给坐标轴打分，但没有成功。

这就是为什么我想请教一些方向来做，最后计算出每个环的面积。
欢迎任何帮助

Answer 1

我正在使用 here 中的 spline.poly 函数。

spline.poly

spline.poly <- function(xy, vertices, k=3, ...) {
    # Assert: xy is an n by 2 matrix with n >= k.

    # Wrap k vertices around each end.
    n <- dim(xy)[1]
    if (k >= 1) {
        data <- rbind(xy[(n-k+1):n,], xy, xy[1:k, ])
    } else {
        data <- xy
    }

    # Spline the x and y coordinates.
    data.spline <- spline(1:(n+2*k), data[,1], n=vertices, ...)
    x <- data.spline$x
    x1 <- data.spline$y
    x2 <- spline(1:(n+2*k), data[,2], n=vertices, ...)$y

    # Retain only the middle part.
    cbind(x1, x2)[k < x & x <= n+k, ]
}

数据

df = data.frame(A = c(1, 4, 5, 8, 10),
                B = c(1, 3, 7, 9, 10),
                C = c(2, 6, 8, 9, 10),
                D = c(1, 3, 4, 7, 9),
                E = c(1, 2, 3, 4, 5))

绘图

#Calculate angles based on number of columns
angles = 0:(NCOL(df) - 1) * 2*pi/NCOL(df)

#Calculate x and y corresponding to each radial distance
toplot = lapply(1:NCOL(df), function(i){
    data.frame(x = df[,i]*cos(angles[i]),
               y = df[,i]*sin(angles[i]))
})

#Split toplot and merge back together the same rows
toplot2 = lapply(toplot, function(x) data.frame(x, ID = sequence(NROW(x))))
toplot2 = do.call(rbind, toplot2)
toplot2 = split(toplot2, toplot2$ID)

#Create empty plot    
graphics.off()
plot(do.call(rbind, toplot), type = "n", axes = FALSE, ann = FALSE, asp = 1)

#Allow drawing outside the plot region just in case
par(xpd = TRUE)

#Draw polygons
lapply(toplot2, function(a){
    polygon(spline.poly(xy = cbind(a$x, a$y), vertices = 100, k = 3))
})

#Draw points    
lapply(toplot, function(a){
    points(a)
})

#Draw radial lines    
lapply(toplot, function(a){
   lines(a)
})

面积

area_data = lapply(toplot2, function(a){
   spline.poly(xy = cbind(a$x, a$y), vertices = 100, k = 3)
})
library(geometry)
lapply(area_data, function(P) polyarea(P[,1], P[,2]))
#$`1`
#[1] 4.35568

#$`2`
#[1] 38.46985

#$`3`
#[1] 96.41331

#$`4`
#[1] 174.1584

#$`5`
#[1] 240.5837

如何绘制以不同角度对齐的点并用一条线连接它们？

How to plot points aligned at different angles and connect these by a line?

plot

r

polygon

area