R：使用具有适当大小的persp将点添加到曲面图

Question

我想实现我添加到绘图中的点数已调整其大小以获得更好的3D印象。我知道我不得不使用返回的变换矩阵来计算与2d平面正交的矢量长度到3d中的相应点，但我不知道该怎么做。

以下是一个例子：

x1 <- rnorm(100)
x2 <- 4 + rpois(100, 4)
y <- 0.1*x1 + 0.2*x2 + rnorm(100)
dat <- data.frame(x1, x2, y)
m1 <- lm(y ~ x1 + x2, data=dat)

x1r <- range(dat$x1)
x1seq <- seq(x1r[1], x1r[2], length=30)
x2r <- range(dat$x2)
x2seq <- seq(x2r[1], x2r[2], length=30)
z <- outer(x1seq, x2seq, function(a,b){ 
           predict(m1, newdata=data.frame(x1=a, x2=b))
           })

res <- persp(x1seq, x2seq, z)
mypoints <- trans3d(dat$x1, dat$x2, dat$y, pmat=res)
points(mypoints, pch=1, col="red")

Answer 1

您可以使用显示的函数here来确定与观察者的距离，然后将点数（cex）缩放到该距离：

    # volcano data
z <- 2 * volcano        # Exaggerate the relief
x <- 10 * (1:nrow(z))   # 10 meter spacing (S to N)
y <- 10 * (1:ncol(z))   # 10 meter spacing (E to W)

# draw volcano and store transformation matrix
pmat <- persp(x, y, z, theta = 35, phi = 40, col = 'green4', scale = FALSE,
              ltheta = -120, shade = 0.75, border = NA, box = TRUE)

# take some xyz values from the matrix
s = sample(1:prod(dim(z)), size=500)
xx = x[row(z)[s] ]
yy = y[col(z)[s]]
zz = z[s] + 10

# depth calculation function (adapted from Duncan Murdoch at https://stat.ethz.ch/pipermail/r-help/2005-September/079241.html)
depth3d <- function(x,y,z, pmat, minsize=0.2, maxsize=2) {

  # determine depth of each point from xyz and transformation matrix pmat
  tr <- as.matrix(cbind(x, y, z, 1)) %*% pmat
  tr <- tr[,3]/tr[,4]

  # scale depth to point sizes between minsize and maxsize
  psize <- ((tr-min(tr) ) * (maxsize-minsize)) / (max(tr)-min(tr)) + minsize
  return(psize)
}

# determine distance to eye
psize = depth3d(xx,yy,zz,pmat,minsize=0.1, maxsize = 1)

# from 3D to 2D coordinates
mypoints <- trans3d(xx, yy, zz, pmat=pmat)

# plot in 2D space with pointsize related to distance
points(mypoints, pch=8, cex=psize, col=4)