求外接多边形的圆的半径

Question

我正在尝试找到获取以下内容的最佳方法：从多边形中心到其边缘的最长直线的长度。

在下面的代码中，我下载了位于美国德克萨斯州的 75254 邮政编码的多边形数据。然后，我使用 sf::st_centroid() 确定其中心的位置，并使用 tmap 包绘制几何图形。

# Useful packages

library(dplyr)
library(sf)
library(tigris)
library(tmap)

# Download polygon data

geo <- tigris::zctas(cb = TRUE, starts_with = "75254")
geo <- st_as_sf(geo)

# Determine the location of the polygon's center

geo_center <- st_centroid(geo)

# Plot geometries

tm_shape(geo) +
  tm_polygons() +
  tm_shape(geo_center) +
  tm_dots(size = 0.1, col = "red")

再一次，是否有一种有效的方法来确定从多边形中心一直到多边形边缘最远点的直线长度？换句话说，如果圆和多边形都具有相同的中心，我如何找到完美外接多边形的圆的半径？

非常感谢您的帮助。

Answer 1

这里有一点，虽然我提到过，st_bbox 不会起作用，因为 bbox 的质心和你的形状不一样，因为质心是加权的。在这里看到一种基于到边界点的更远距离的方法，但是你需要投影你的形状（当前未投影）：

library(dplyr)
library(sf)
library(tigris)
library(tmap)

# Download polygon data
geo <- tigris::zctas(cb = TRUE, starts_with = "75254")
geo <- st_as_sf(geo)

st_crs(geo)
#> Coordinate Reference System:
#>   EPSG: 4269 
#>   proj4string: "+proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs"

#Need to project
geo=st_transform(geo,3857)

# Determine the location of the polygon's center

geo_center <- st_centroid(geo)
#> Warning in st_centroid.sf(geo): st_centroid assumes attributes are constant over
#> geometries of x

plot(st_geometry(geo))
plot(st_geometry(geo_center), col="blue", add=TRUE)

#Cast to points
geopoints=st_cast(geo,"POINT")
#> Warning in st_cast.sf(geo, "POINT"): repeating attributes for all sub-geometries
#> for which they may not be constant

r=max(st_distance(geo_center,geopoints))
r
#> 3684.917 [m]
buffer=st_buffer(geo_center,dist=r)
plot(st_geometry(buffer), add=TRUE, border="green")

Answer 2

OP 没有要求这样做，但如果有人想对多个形状执行此操作，这里有一个基于 dieghernan 示例的版本。

library(dplyr)
library(sf)
library(tigris)
library(tmap)

# Download polygon data
raw <- tigris::zctas(cb = TRUE, starts_with = "752")
geo <- raw %>% 
    st_as_sf() %>% 
    slice(1:5) %>%
    st_transform(3857) %>%
    arrange(GEOID10) # Sort on GEOID now so we don't have to worry about group_by resorting later

# Compute the convex hull
hull <- geo %>% st_convex_hull()

# Compute centroids
geo_center <- st_centroid(geo)

# Add centroid, then cast hull to points
hull_points <- hull %>% 
    mutate(centroid_geometry = geo_center$geometry) %>%
    st_cast("POINT")

# Compute distance from centroid to all points in hull
hull_points$dist_to_centroid <- as.numeric(hull_points %>% 
                                               st_distance(hull_points$centroid_geometry, by_element = TRUE))

# Pick the hull point the furthest distance from the centroid
hull_max <- hull_points %>% 
    arrange(GEOID10) %>%
    group_by(GEOID10) %>%
    summarize(max_dist = max(dist_to_centroid)) %>% 
    ungroup()

# Draw a circle using that distance
geo_circumscribed <- geo_center %>% st_buffer(hull_max$max_dist)

# Plot the shape, the hull, the centroids, and the circumscribed circles
tm_shape(geo) + 
    tm_borders(col = "red") + 
    tm_shape(hull) + 
    tm_borders(col = "blue", alpha = 0.5) + 
    tm_shape(geo_center) + 
    tm_symbols(col = "red", size = 0.1) + 
    tm_shape(geo_circumscribed) + 
    tm_borders(col = "green")

求外接多边形的圆的半径

Finding the radius of a circle that circumscribes a polygon

geometry

r

distance

geospatial

sf