在R中定位多边形质心最远边界点并绘制连线

步骤1：提取边界点并匹配最远点 #

假设你已拥有sf格式的邮编数据框postal_sf，先确保数据为多边形类型，执行以下操作：

• 计算每个区域的质心：postal_sf$centroid <- st_centroid(postal_sf)
• 将多边形转换为边界点集合：postal_sf$boundary_points <- st_cast(postal_sf, "POINT")
• 遍历每个区域，找到质心到边界的最远点：

for (i in 1:nrow(postal_sf)) {
  # 获取当前区域的质心与边界点
  cent <- postal_sf$centroid[i]
  bounds <- postal_sf$boundary_points[i]
  
  # 计算质心到所有边界点的距离
  dists <- st_distance(cent, bounds)
  
  # 定位最大距离对应的边界点并保存
  max_idx <- which.max(dists)
  postal_sf$farthest_point[i] <- bounds[max_idx,]
}

步骤2：生成质心到最远点的连线 #

将质心与最远点组合为线要素，绑定到原数据框：

# 批量生成连线的sf线对象
lines_list <- lapply(1:nrow(postal_sf), function(i) {
  st_sfc(st_linestring(rbind(st_coordinates(postal_sf$centroid[i]),
                             st_coordinates(postal_sf$farthest_point[i]))),
         crs = st_crs(postal_sf))
})

postal_sf$distance_line <- st_sfc(lines_list, crs = st_crs(postal_sf))

步骤3：绘制可视化地图 #

以tmap包为例，实现区域、质心、最远点及连线的叠加展示：

library(tmap)

tm_shape(postal_sf) +
  tm_polygons(col = "lightgray", alpha = 0.5) +  # 绘制邮编区域底色
  tm_shape(postal_sf) +
  tm_symbols(shape = 21, size = 0.1, col = "red", border.col = "black") +  # 标记质心
  tm_shape(postal_sf) +
  tm_symbols(shape = 21, size = 0.1, col = "blue", border.col = "black") +  # 标记最远点
  tm_shape(postal_sf) +
  tm_lines(col = "darkred", lwd = 0.5)  # 绘制质心到最远点的连线

优化提示 #

• 若数据为多部分多边形（MULTIPOLYGON），st_cast会自动提取所有部分的边界点，无需额外处理
• 确保所有要素的CRS一致，避免距离计算偏差
• 处理全德国邮编这类大数据时，用purrr替代循环提升效率：

library(purrr)

postal_sf <- postal_sf %>%
  mutate(
    centroid = st_centroid(geometry),
    boundary_points = st_cast(geometry, "POINT"),
    farthest_point = map2(centroid, boundary_points, function(c, b) {
      dists <- st_distance(c, b)
      b[which.max(dists),]
    }),
    distance_line = map2(centroid, farthest_point, function(c, fp) {
      st_linestring(rbind(st_coordinates(c), st_coordinates(fp)))
    }) %>% st_sfc(crs = st_crs(.))
  )

内容的提问来源于stack exchange，提问作者Marco