摘要：我认为在 R 中使用 gCentroid 会返回一组点的质心，但是我意识到由于某种原因它实际上返回的是几何平均值而不是质心
我想复制我在 R 中所做的质心计算：
gCentroid {rgeos}
这些点的质心：
34.7573, -86.678606
38.30088, -76.520266
38.712147, -77.158616
39.704905, -84.126463
... 使用 r 脚本 ...
require(rgdal)
require(rgeos)
no_am_eq_co <- "+proj=eqdc +lat_0=0 +lon_0=0 +lat_1=20 +lat_2=60 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs"
wgs84 <- "+proj=longlat +datum=WGS84"
df <- as.data.frame(list(c(34.7573,
38.30088,
38.712147,
39.704905),
c(-86.678606,
-76.520266,
-77.158616,
-84.126463)))
df$Name <- "points_A"
colnames(df) <- c("lat", "lon", "Name")
# FROM: Coordinates are geographic latitude/longitudes
coordinates(df) <- c("lon", "lat")
proj4string(df) <- CRS(wgs84)
# TO: Project into North America Equidistant Conic
df <- spTransform(df, CRS(no_am_eq_co))
# Get centroids
ctrs <- lapply(unique(df$Name),
function(x) gCentroid(SpatialPoints(df[df$Name==x,])))
ctrsout <- setNames( ctrs , unique(df$Name ) )
# Create data frame
df <- do.call(rbind, lapply(ctrsout, data.frame, stringsAsFactors=FALSE))
coordinates(df) <- c("x", "y")
proj4string(df) <- CRS(no_am_eq_co)
df <- as.data.frame(spTransform(df, CRS(wgs84)))
names(df) <- c("longitude", "latitude")
print(df$latitude)
print(df$longitude)
来到：
37.94873834, -81.18378815
我在 python 中构建了以下示例 - 我想复制计算，使用：
import numpy as np
from pyproj import Proj, transform
# Using: http://www.spatialreference.org/ref/esri/102010/ we get the Proj4js format
na_eq_co = "+proj=eqdc +lat_0=0 +lon_0=0 +lat_1=20 +lat_2=60 +x_0=0 +y_0=0 +ellps=GRS80 +datum=NAD83 +units=m +no_defs"
wgs84 = "+proj=longlat +datum=WGS84"
def proj_arr(points,proj_from,proj_to):
inproj = Proj(proj_from)
outproj = Proj(proj_to)
func = lambda x: transform(inproj,outproj,x[0],x[1])
return np.array(list(map(func, points)))
def get_polygon_centroid(polygon):
#https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon
pol = np.array(polygon)
if np.any(pol[-1] != pol[0]):
pol = np.append(pol,[pol[0]], axis=0)
pol_area = get_polygon_area(pol)
x = pol[:,0]
y = pol[:,1]
Cx = np.sum((x[:-1] + x[1:]) * ((x[:-1] * y[1:]) - (y[:-1] * x[1:]))) / (6. * pol_area)
Cy = np.sum((y[:-1] + y[1:]) * ((x[:-1] * y[1:]) - (y[:-1] * x[1:]))) / (6. * pol_area)
return np.array([Cx, Cy])
def get_polygon_area(polygon):
pol = np.array(polygon)
x = pol[:,0]
y = pol[:,1]
return np.sum( (x[:-1] * y[1:]) - (y[:-1] * x[1:]) ) / 2
def get_polygon_mean(polygon):
pol = np.array(polygon)
x = pol[:,0]
y = pol[:,1]
return np.array([np.mean(x),np.mean(y)])
def run_test(points):
points = points[:,::-1] #Flip-axis (so that longitude x-axis, latitude y-axis)
points_proj = proj_arr(points,wgs84,na_eq_co)
centroid_proj = get_polygon_centroid(points_proj)
mean_proj = get_polygon_mean(points_proj)
centroid = proj_arr([centroid_proj],na_eq_co,wgs84)
mean = proj_arr([mean_proj],na_eq_co,wgs84)
return (centroid[:,::-1][0], mean[:,::-1][0])
if __name__ == '__main__':
my_points = np.array([[34.7573,-86.678606],
[38.30088,-76.520266],
[38.712147,-77.158616],
[39.704905,-84.126463]])
test = run_test(my_points)
print("Centroid calculation: {0}\nMean calculation {1}".format(test[0],test[1]))
从这里我得到：
37.72876321 -82.35113685
不是：
37.94873834,-81.18378815
通过更多的挖掘，我添加了一个函数给我几何平均值：
Centroid calculation: [ 37.72876321 -82.35113685]
Mean calculation [ 37.94873834 -81.18378815]
我意识到由于某种原因，gCentroid 似乎在计算几何平均值而不是特征质心（我添加了一个均值函数，您可以看到它与 R 结果相匹配）
编辑：
我认为可能的原因是：因为我有一组点，而不是通过它们拟合一个随机多边形 - 就像我在例子中一样 - 甚至是一个凸包然后取其质心，该命令将默认为如果数据类型是“点”，则表示计算。所以我明确地传递了一个多边形：
x = readWKT(paste("POLYGON((-6424797.94257892 7164920.56353916,
-5582828.69570672 6739129.64644454,
-5583459.32266293 6808624.95123077,
-5855637.16642608 7316808.01148585,
-5941009.53089084 7067939.71641507,
-6424797.94257892 7164920.56353916))"))
python_cent = readWKT(paste("POINT(-5941009.53089084 7067939.71641507)"))
r_cent = gCentroid(x)
plot(x)
plot(r_cent,add=T,col='red')
plot(python_cent, add=T,col='green')
python质心在哪里：
centroid = get_polygon_centroid(np.array([[-6424797.94257892, 7164920.56353916],
[-5582828.69570672, 6739129.64644454],
[-5583459.32266293, 6808624.95123077],
[-5855637.16642608, 7316808.01148585],
[-6424797.94257892, 7164920.56353916]]))
然后用红色（-5875318 7010915 ）绘制它的质心，然后用绿色（ -5941009 7067939 ）绘制同一多边形（使用python）上的质心，用蓝色绘制简单平均值（-5974304 7038880）：
