用rgl在球上填充一个区域

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英文:

Filling a region on a sphere with rgl

问题

这是世界首都的球面Voronoï镶嵌图:

用rgl在球上填充一个区域

我有定义每个国家边界的点的坐标。我想用颜色填充这些国家。动机是用与海洋相同的颜色绘制Voronoï边缘,这样我们在国家外部就看不到它们了。换句话说,我正在寻找一个类似于 polygon 函数但用于球面多边形的函数。


编辑

好的,我现在明白了。但出于某种原因,水的青色和Voronoï边缘的青色不同:

用rgl在球上填充一个区域

英文:

Here is the spherical Voronoï tessellation of the world capitals:

用rgl在球上填充一个区域

I have the coordinates of the points defining the boundary of each country. I'd like to fill the countries with a color. The motivation is to plot the Voronoï edges with the same color as the seas/oceans so that we will not see them outside the countries. In other words, I'm looking for a function similar to the polygon function but for spherical polygons.


Edit

Well, I get it now. But for some reason, the cyan color of the water and the cyan color of the Voronoï edges are different:

用rgl在球上填充一个区域

答案1

得分: 1

以下是代码的翻译部分:

# 载入地图库和数据
library(maps)
data(worldMapEnv)

# 创建一个填充国家的二维世界地图的PNG图像
world <- map("world", plot = FALSE, fill = TRUE, wrap = c(0, 360))

png("world2D.png", width = 1024L, height = 1024L)
opar <- par(mar = c(0, 0, 0, 0))
plot(world$x, world$y, type = "n", xlab = NA, ylab = NA, axes = FALSE,
     xaxs = "i", yaxs = "i", xlim = c(0, 360), ylim = c(-90, 90))
polygon(world$x, world$y, col="orangered", lwd = 2)
par(opar)
dev.off()
# 使用球面坐标创建单位球体的网格
library(cgalMeshes)
sphericalCoordinates <- function(θ, ϕ){
  x <- cos(θ) * sin(ϕ)
  y <- sin(θ) * sin(ϕ)
  z <- cos(ϕ)
  rbind(x, y, z)
}
rmesh <- parametricMesh(
  sphericalCoordinates, urange = c(0, 2*pi), vrange = c(0, pi),
  periodic = c(TRUE, TRUE), nu = 1024L, nv = 1024L
)
rmesh$normals <- rmesh$vb[-4L, ]

# 获取网格顶点的角度θ和ϕ
UV <- cooltools::car2sph(t(rmesh$vb[-4L, ]))
UV <- cbind(UV[, 3L], UV[, 2L])

# 现在加载PNG图像
library(imager)
img <- load.image("world2D.png")
# 获取r、g、b通道
r <- squeeze(R(img))
g <- squeeze(G(img))
b <- squeeze(B(img))

# 创建插值函数以获取UV点的颜色
library(cooltools) # 获取`approxfun2`函数
x_ <- seq(0, 2*pi, length.out = 1024L)
y_ <- seq(0, pi, length.out = 1024L)
f_r <- approxfun2(x_, y_, r)
f_g <- approxfun2(x_, y_, g)
f_b <- approxfun2(x_, y_, b)

# 插值r、g、b值
UV_r <- f_r(UV[, 1L], UV[, 2L])
UV_g <- f_g(UV[, 1L], UV[, 2L])
UV_b <- f_b(UV[, 1L], UV[, 2L])

# 将rgb转换为十六进制代码
clrs <- rgb(UV_r, UV_g, UV_b)
clrs[clrs == "#FFFFFF"] <- "cyan" # 用青色替换白色

# 将颜色分配给网格的顶点
# 我不知道为什么,但必须反转颜色
rmesh$material <- list(color = rev(clrs))

# 绘制
library(rgl)
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.7)
shade3d(rmesh, meshColor = "vertices")
snapshot3d("world3D.png", webshot = FALSE)

以上是代码的翻译部分。

英文:

Here is how to fill the countries.

library(maps)
data(worldMapEnv)

# make a PNG image of the world in 2D with filled countries
world &lt;- map(&quot;world&quot;, plot = FALSE, fill = TRUE, wrap = c(0, 360))

png(&quot;world2D.png&quot;, width = 1024L, height = 1024L)
opar &lt;- par(mar = c(0, 0, 0, 0))
plot(world$x, world$y, type = &quot;n&quot;, xlab = NA, ylab = NA, axes = FALSE,
     xaxs = &quot;i&quot;, yaxs = &quot;i&quot;, xlim = c(0, 360), ylim = c(-90, 90))
polygon(world$x, world$y, col=&quot;orangered&quot;, lwd = 2)
par(opar)
dev.off()

用rgl在球上填充一个区域

# use spherical coordinates to make a mesh of the unit sphere
library(cgalMeshes)
sphericalCoordinates &lt;- function(θ, ϕ){
  x &lt;- cos(θ) * sin(ϕ)
  y &lt;- sin(θ) * sin(ϕ)
  z &lt;- cos(ϕ)
  rbind(x, y, z)
}
rmesh &lt;- parametricMesh(
  sphericalCoordinates, urange = c(0, 2*pi), vrange = c(0, pi),
  periodic = c(TRUE, TRUE), nu = 1024L, nv = 1024L
)
rmesh$normals &lt;- rmesh$vb[-4L, ]

# get the angles θ and ϕ of the vertices of the mesh
UV &lt;- cooltools::car2sph(t(rmesh$vb[-4L, ]))
UV &lt;- cbind(UV[, 3L], UV[, 2L])


# now load the PNG image
library(imager)
img &lt;- load.image(&quot;world2D.png&quot;)
# take the r, g, b channels
r &lt;- squeeze(R(img))
g &lt;- squeeze(G(img))
b &lt;- squeeze(B(img))

# make interpolation functions to get the colors of the UV points
library(cooltools) # to get the `approxfun2` function
x_ &lt;- seq(0, 2*pi, length.out = 1024L)
y_ &lt;- seq(0, pi, length.out = 1024L)
f_r &lt;- approxfun2(x_, y_, r)
f_g &lt;- approxfun2(x_, y_, g)
f_b &lt;- approxfun2(x_, y_, b)

# now, interpolate the r, g, b values
UV_r &lt;- f_r(UV[, 1L], UV[, 2L])
UV_g &lt;- f_g(UV[, 1L], UV[, 2L])
UV_b &lt;- f_b(UV[, 1L], UV[, 2L])

# convert rgb to hex codes
clrs &lt;- rgb(UV_r, UV_g, UV_b)
clrs[clrs == &quot;#FFFFFF&quot;] &lt;- &quot;cyan&quot; # replace white with cyan


# assign the colors to the vertices of the mesh
# I don&#39;t know why, but one has to reverse the colors
rmesh$material &lt;- list(color = rev(clrs))


# plot
library(rgl)
open3d(windowRect = 50 + c(0, 0, 512, 512), zoom = 0.7)
shade3d(rmesh, meshColor = &quot;vertices&quot;)
snapshot3d(&quot;world3D.png&quot;, webshot = FALSE)

用rgl在球上填充一个区域

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  • 本文由 发表于 2023年6月22日 20:08:18
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