如何计算多边形质心和边缘之间的最大距离

Question

我有一个 SpatialPolygons(DataFrame) 对象，例如SpP

library(sp)    
Sr1 = Polygon(cbind(c(2,4,4,1,2),c(2,3,5,4,2)))
Sr2 = Polygon(cbind(c(5,4,2,5),c(2,3,2,2)))
Sr3 = Polygon(cbind(c(4,4,5,10,4),c(5,3,2,5,5)))
Sr4 = Polygon(cbind(c(5,6,6,5,5),c(4,4,3,3,4)), hole = TRUE)
Srs1 = Polygons(list(Sr1), "s1")
Srs2 = Polygons(list(Sr2), "s2")
Srs3 = Polygons(list(Sr3, Sr4), "s3/4")
SpP = SpatialPolygons(list(Srs1,Srs2,Srs3), 1:3)

我想为每个多边形计算其质心 (coordinates(SpP)) 与同一多边形内任何其他点之间的最大距离（我假设这个最远的点将在边缘上？）。

谁能教我怎么做？

Answer 1

这是我创建的一个简单函数，它为给定的多边形计算质心，并使用基本几何来查找离质心最远的点，并返回其坐标：

library(sp)
library(rgeos)
library(ggplot2)

Sr2 = Polygon(cbind(c(5,4,2,5),c(2,3,2,2)))
Srs2=Polygons(list(Sr2), "s2")
spPol=SpatialPolygons(list(Srs2))

find_furthest_point=function(polygon){
  coords=fortify(polygon)[,c(1:2)]  
  center=as.data.frame(gCentroid(polygon))
  longs=coords[,1]
  lats=coords[,2]

  dist_fx=function(long, lat, center=center){
    dist=sqrt((long-center[1])^2+(lat-center[2])^2)
    return(dist)
  }
  dists=mapply(dist_fx, longs, lats, MoreArgs=list(center))
  furthest_index=as.integer(which(dists==max(dists)))
  furthest=coords[furthest_index,]  
  return(furthest)
}

find_furthest_point(Sr2)