r - 如何绘制联锁环？

Question

如何在 R 中绘制互锁环面，如 this page for gnuplot 所示:

我在 R 中尝试了以下代码，但它们不起作用:

try_tori_1 = function(){
    library(rgl)
    xvec= yvec = seq(-pi,pi,by=0.1); 
    z <- outer(xvec,yvec,function(x,y) {sin(x)+.5*sin(x)*cos(y)} )
    persp3d(z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")
    z <- outer(xvec,yvec,function(x,y) {cos(x)+.5*cos(x)*cos(y)} )
    persp3d(z, theta = 30, phi = 30, expand = 0.5, col = "lightblue", add=T)
    z <- outer(xvec,yvec,function(x,y) {.5*sin(y)} )
    persp3d(z, theta = 30, phi = 30, expand = 0.5, col = "lightblue", add=T)
    z <- outer(xvec,yvec,function(x,y) {1+cos(x)+.5*cos(x)*cos(y)} )
    persp3d(z, theta = 30, phi = 30, expand = 0.5, col = "lightblue", add=T)
    z <- outer(xvec,yvec,function(x,y) {.5*sin(y)} )
    persp3d(z, theta = 30, phi = 30, expand = 0.5, col = "lightblue", add=T)
    z <- outer(xvec,yvec,function(x,y) {sin(x)+.5*sin(x)*cos(y)} )
    persp3d(z, theta = 30, phi = 30, expand = 0.5, col = "lightblue", add=T)
}

try_tori_2 = function(){
    library(rgl)
    u= v = seq(-pi,pi,by=0.1); 
    plot3d(cos(u)+.5*cos(u)*cos(v),sin(u)+.5*sin(u)*cos(v),.5*sin(v))
    plot3d(1+cos(u)+.5*cos(u)*cos(v),.5*sin(v),sin(u)+.5*sin(u)*cos(v))
}

Answer 1

我的回答是基于这两个网站的例子:

• 3D plots in R

• R: Fun with surf3D function

你是这样做的:

library(plot3D)
x <- seq(-pi,pi,by=0.1)
y <- seq(-pi,pi,by=0.1)
R = 1.0
r = 0.5
M <- mesh(x, y)
alpha <- M$x
beta <- M$y
surf3D(x = (R + r*cos(alpha)) * cos(beta), 
       y = (R + r*cos(alpha)) * sin(beta), 
       z = r * sin(alpha), 
       col="blue", colkey=FALSE, alpha = 0.3, border="black", 
       xlim=c(-0.5*pi,0.5*pi), ylim=c(-0.5*pi,0.5*pi), zlim=c(-0.5*pi,0.5*pi))
surf3D(x = R + cos(alpha) + r*cos(alpha) * cos(beta), 
       y = r*sin(beta), 
       z = sin(alpha)+ r * sin(alpha) * cos(beta), 
       col="red", colkey=FALSE, alpha = 0.3, border="black", add=T)

生成此图:

需要注意的重要事项是:

• 使用 surf3D 功能
• 使用 mesh
设置角度
• 要查看所有内容，请在第一个绘图中指定范围(xlim 等)
• 使用颜色和 alpha 进行绘图以获得您想要的颜色