在地图上绘制具有一定半径的圆圈 - 确保距离正确

Question

在R中，我试图在地图上绘制一个圆，在给定其质心为lat，long point的情况下绘制一定距离。我找到this thread并使用@lukeA的代码来实现我想要的。然而，似乎距离不对。我在某个纬度的两个经度之间得到的距离与绘制的不一致。可以用来衡量距离的网站是：http://www.stevemorse.org/nearest/distance.php

以下是代码。 spTransform中的单位指定为us-mi，因此我们应该能够以英里为单位给出圆直径。

我想要一个以lat = 45，long = -90为中心的圆圈。到lat = 45，long = -86的距离是~195 mi。因此直径等于2 * 195 = 390 mi。但绘制的圆圈远远不够。问题可能与预测有关。

有人可以帮助我，我错过了吗？

library(tidyverse)
library(data.table)
library(rgeos)
library(sp)

states = c('illinois', 'wisconsin', 'iowa', 'minnesota')
state_4s =  map_data('state') %>% data.table() %>% subset(region %in% states)
counties_4s = counties[region %in% states ]

map_4s <- ggplot(data = state_4s, 
                 mapping = aes(x = long, y = lat, group = group)) +
    geom_polygon(color = "black", fill = "gray", size = 0.1) +
    theme_bw()

map_4s = map_4s +
    geom_polygon(data = counties_4s, fill = NA, color = 'white', size = 0.1) + 
    geom_polygon(color = "black", fill = NA, size = 0.1) +
    coord_map("mercator")


long = c(-90)
lat = c(45)
center = data.frame(long, lat)


d <- SpatialPointsDataFrame(coords = center, 
                            data = center, 
                            proj4string = CRS("+init=epsg:4326"))



d_mrc <- spTransform(d, CRS("+proj=merc +init=epsg:4326 +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k_0=1.0 +units=us-mi +nadgrids=@null +no_defs"))


# Now, the width can be specified in miles:
d_mrc_bff_mrc <- gBuffer(d_mrc, byid = T, width = 195*2, capStyle = 'round')

d_mrc_bff <- spTransform(d_mrc_bff_mrc, CRS("+init=epsg:4326"))
d_mrc_bff_fort <- fortify(d_mrc_bff)

map_4s + 
    geom_point(data = center, aes(x = long, y = lat, group = 1)) + 
    geom_path(data=d_mrc_bff_fort, aes(long, lat, group=group), color="red") 

Answer 1

library(tidyverse)
library(data.table)
library(rgeos)
library(sp)

states = c('illinois', 'wisconsin', 'iowa', 'minnesota')
state_4s =  map_data('state') %>% data.table() %>% subset(region %in% states)

map_4s <- ggplot(data = state_4s, 
                 mapping = aes(x = long, y = lat, group = group)) +
    geom_polygon(color = "black", fill = "gray", size = 0.1) +
    theme_bw()



long = c(-90)
lat = c(45)
center = data.frame(long, lat)


d <- SpatialPointsDataFrame(coords = center, 
                            data = center, 
                            proj4string = CRS("+init=epsg:4326"))

long2UTMZone <- function(long) { (floor((long + 180)/6) %% 60) + 1 }

d_mrc <- spTransform(d, CRS(paste0("+proj=utm +zone=", long2UTMZone(long)," +datum=WGS84 +units=us-mi")))

# Now, the width can be specified in miles:
d_mrc_bff_mrc <- gBuffer(d_mrc, byid = T, width = 195, capStyle = 'round')

d_mrc_bff <- spTransform(d_mrc_bff_mrc, CRS("+init=epsg:4326"))
d_mrc_bff_fort <- fortify(d_mrc_bff)

map_4s + 
    geom_point(data = center, aes(x = long, y = lat, group = 1)) + 
    geom_path(data=d_mrc_bff_fort, aes(long, lat, group=group), color="red")