如何计算r中椭圆交集的体积

Question

我想知道如何计算两个椭圆之间的交点，例如如下图所示，versicolor 和 virginca 交汇处的体积：这是基于此 tutorial:

使用以下 mwe 绘制的

data(iris)
log.ir <- log(iris[, 1:4])
ir.species <- iris[, 5]
ir.pca <- prcomp(log.ir, center = TRUE, scale. = TRUE)

library(ggbiplot)
g <- ggbiplot(ir.pca, obs.scale = 1, var.scale = 1, 
          groups = ir.species, ellipse = TRUE,
          circle = TRUE)
g <- g + scale_color_discrete(name = '')
g <- g + theme(legend.direction = 'horizontal', 
           legend.position = 'top')
print(g)

我得到椭圆的协方差和中心如下：

setosa.cov <- cov(ir.pca$x[ir.species=="setosa",])
versicolor.cov <- cov(ir.pca$x[ir.species=="versicolor",])
virginica.cov <- cov(ir.pca$x[ir.species=="virginica",])
setosa.centre <- colMeans(ir.pca$x[ir.species=="setosa",])
versicolor.centre <- colMeans(ir.pca$x[ir.species=="versicolor",])
virginica.centre <- colMeans(ir.pca$x[ir.species=="virginica",])

但后来我束手无策:-|

编辑： 按照下面@carl-witthoft的指示，这里有一个使用siar::overlap的例子：

library(siar)
setosa <- ir.pca$x[ir.species=="setosa",]
versicolor <- ir.pca$x[ir.species=="versicolor",]
virginica <- ir.pca$x[ir.species=="virginica",]

overlap.fun <- function(data.1, data.2){
   dimensions <- ncol(data.1)
   for(i in 1:(dimensions-1)){
      overlap.out <- overlap(data.1[,i], data.1[,i+1], data.2[,i], data.2[,i+1], steps = 5)
      out$overlap[i] <- overlap.out$overlap
      out$area1[i] <- overlap.out$area1
      out$area2[i] <- overlap.out$area2
   }
   return(out)
}

overlap.fun(versicolor, virginica)

returns:

$overlap
[1] 0.01587977 0.48477088 0.08375927
$area1
[1]1.020596 1.04614461 0.08758691                 
$area2
[1] 1.028594 1.1535106 0.1208483

奇怪的是，当我进行百分比计算时，这些值并不真正对应于 ggbiplot PCA 中的椭圆体：

tmp <- overlap(versicolor[,1], versicolor[,2], virginica[,1], virginica[,2], steps = 5)
virginica.percentage <- round(x=(tmp$overlap/tmp$area2*100), digits = 2)
versicolor.percentage <- round(x=(tmp$overlap/tmp$area1*100), digits = 2)
> virginica.percentage [1] 1.54
> versicolor.percentage[1] 1.56

这比上图 1 中显示的要少得多。但最好在 .

上打开另一个线程

Answer 1

可能的工具：

 spatstat::overlap.owin , geo::geointersect, siar::overlap .

你可能会问——你 应该问 ——“他怎么这么快就得到这些答案的？

为您获取包裹 sos 并输入 ???overlap

如何计算r中椭圆交集的体积

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