R: 从x,y,z绘制三维曲面

如果x和y坐标不在网格上,则需要将x、y、z曲面插值到一个网格上。可以使用任何地质统计学软件包(geoR、gstat和其他软件包)或更简单的技术(如反距离加权)使用kriging来实现这一点。

我猜你提到的“interp”函数来自akima包。请注意,输出矩阵与输入点的大小无关。如果需要,可以在输入中有10000个点,并将其插值到10x10网格上。默认情况下,akima::interp在40x40网格上执行此操作:

> require(akima) ; require(rgl)
> x=runif(1000)
> y=runif(1000)
> z=rnorm(1000)
> s=interp(x,y,z)
> dim(s$z)
[1] 40 40
> surface3d(s$x,s$y,s$z)

因为它是随机的数据,所以看起来很糟糕。希望你的数据不是!

变量“b”和“s”可以是x或y。

require(lattice)

# begin generating my 3D shape
b <- seq(from=0, to=20,by=0.5)
s <- seq(from=0, to=20,by=0.5)
payoff <- expand.grid(b=b,s=s)
payoff$payoff <- payoff$b - payoff$s
payoff$payoff[payoff$payoff < -1] <- -1
# end generating my 3D shape


wireframe(payoff ~ s * b, payoff, shade = TRUE, aspect = c(1, 1),
    light.source = c(10,10,10), main = "Study 1",
    scales = list(z.ticks=5,arrows=FALSE, col="black", font=10, tck=0.5),
    screen = list(z = 40, x = -75, y = 0))

outer() 产生它。

看看这个函数的演示 persp() ,这是绘制曲面透视图的基本图形函数。

下面是他们的第一个例子:

x <- seq(-10, 10, length.out = 50)  
y <- x  
rotsinc <- function(x,y) {
    sinc <- function(x) { y <- sin(x)/x ; y[is.na(y)] <- 1; y }  
    10 * sinc( sqrt(x^2+y^2) )  
}

z <- outer(x, y, rotsinc)  
persp(x, y, z)

surface3d() :

require(rgl)  
surface3d(x, y, z)

rgl 很好,但是需要一些实验来确定轴的位置。

如果有很多点,为什么不从中随机抽取一个样本,然后绘制结果曲面。可以添加多个曲面,所有这些曲面都基于来自同一数据的采样,以查看采样过程是否对数据产生了可怕的影响。

所以,这里有一个非常糟糕的函数,但它做了我认为你希望它做的事情(但没有采样)。给定一个矩阵(x,y,z),其中z是它将绘制点和曲面的高度。限制是每个(x,y)对只能有一个z。所以那些在自身上循环的飞机会引起问题。

plot_points = T 将绘制生成曲面的各个点-这有助于检查曲面和点是否实际相交。这个 plot_contour = T 将在三维可视化下方绘制二维等高线图。设置颜色为 rainbow verbose = T 打印出大量的输出,用于在函数中断时调试它。

plot_rgl_model_a <- function(fdata, plot_contour = T, plot_points = T, 
                             verbose = F, colour = "rainbow", smoother = F){
  ## takes a model in long form, in the format
  ## 1st column x
  ## 2nd is y,
  ## 3rd is z (height)
  ## and draws an rgl model

  ## includes a contour plot below and plots the points in blue
  ## if these are set to TRUE

  # note that x has to be ascending, followed by y
  if (verbose) print(head(fdata))

  fdata <- fdata[order(fdata[, 1], fdata[, 2]), ]
  if (verbose) print(head(fdata))
  ##
  require(reshape2)
  require(rgl)
  orig_names <- colnames(fdata)
  colnames(fdata) <- c("x", "y", "z")
  fdata <- as.data.frame(fdata)

  ## work out the min and max of x,y,z
  xlimits <- c(min(fdata$x, na.rm = T), max(fdata$x, na.rm = T))
  ylimits <- c(min(fdata$y, na.rm = T), max(fdata$y, na.rm = T))
  zlimits <- c(min(fdata$z, na.rm = T), max(fdata$z, na.rm = T))
  l <- list (x = xlimits, y = ylimits, z = zlimits)
  xyz <- do.call(expand.grid, l)
  if (verbose) print(xyz)
  x_boundaries <- xyz$x
  if (verbose) print(class(xyz$x))
  y_boundaries <- xyz$y
  if (verbose) print(class(xyz$y))
  z_boundaries <- xyz$z
  if (verbose) print(class(xyz$z))
  if (verbose) print(paste(x_boundaries, y_boundaries, z_boundaries, sep = ";"))

  # now turn fdata into a wide format for use with the rgl.surface
  fdata[, 2] <- as.character(fdata[, 2])
  fdata[, 3] <- as.character(fdata[, 3])
  #if (verbose) print(class(fdata[, 2]))
  wide_form <- dcast(fdata, y ~ x, value_var = "z")
  if (verbose) print(head(wide_form))
  wide_form_values <- as.matrix(wide_form[, 2:ncol(wide_form)])  
  if (verbose) print(wide_form_values)
  x_values <- as.numeric(colnames(wide_form[2:ncol(wide_form)]))
  y_values <- as.numeric(wide_form[, 1])
  if (verbose) print(x_values)
  if (verbose) print(y_values)
  wide_form_values <- wide_form_values[order(y_values), order(x_values)]
  wide_form_values <- as.numeric(wide_form_values)
  x_values <- x_values[order(x_values)]
  y_values <- y_values[order(y_values)]
  if (verbose) print(x_values)
  if (verbose) print(y_values)

  if (verbose) print(dim(wide_form_values))
  if (verbose) print(length(x_values))
  if (verbose) print(length(y_values))

  zlim <- range(wide_form_values)
  if (verbose) print(zlim)
  zlen <- zlim[2] - zlim[1] + 1
  if (verbose) print(zlen)

  if (colour == "rainbow"){
    colourut <- rainbow(zlen, alpha = 0)
    if (verbose) print(colourut)
    col <- colourut[ wide_form_values - zlim[1] + 1]
    # if (verbose) print(col)
  } else {
    col <- "grey"
    if (verbose) print(table(col2))
  }


  open3d()
  plot3d(x_boundaries, y_boundaries, z_boundaries, 
         box = T, col = "black",  xlab = orig_names[1], 
         ylab = orig_names[2], zlab = orig_names[3])

  rgl.surface(z = x_values,  ## these are all different because
              x = y_values,  ## of the confusing way that 
              y = wide_form_values,  ## rgl.surface works! - y is the height!
              coords = c(2,3,1),
              color = col,
              alpha = 1.0,
              lit = F,
              smooth = smoother)

  if (plot_points){
    # plot points in red just to be on the safe side!
    points3d(fdata, col = "blue")
  }

  if (plot_contour){
    # plot the plane underneath
    flat_matrix <- wide_form_values
    if (verbose) print(flat_matrix)
    y_intercept <- (zlim[2] - zlim[1]) * (-2/3) # put the flat matrix 1/2 the distance below the lower height 
    flat_matrix[which(flat_matrix != y_intercept)] <- y_intercept
    if (verbose) print(flat_matrix)

    rgl.surface(z = x_values,  ## these are all different because
                x = y_values,  ## of the confusing way that 
                y = flat_matrix,  ## rgl.surface works! - y is the height!
                coords = c(2,3,1),
                color = col,
                alpha = 1.0,
                smooth = smoother)
  }
}

这个 add_rgl_model 在没有选项的情况下执行相同的操作,但会将曲面覆盖到现有的3dplot上。

add_rgl_model <- function(fdata){

  ## takes a model in long form, in the format
  ## 1st column x
  ## 2nd is y,
  ## 3rd is z (height)
  ## and draws an rgl model

  ##
  # note that x has to be ascending, followed by y
  print(head(fdata))

  fdata <- fdata[order(fdata[, 1], fdata[, 2]), ]

  print(head(fdata))
  ##
  require(reshape2)
  require(rgl)
  orig_names <- colnames(fdata)

  #print(head(fdata))
  colnames(fdata) <- c("x", "y", "z")
  fdata <- as.data.frame(fdata)

  ## work out the min and max of x,y,z
  xlimits <- c(min(fdata$x, na.rm = T), max(fdata$x, na.rm = T))
  ylimits <- c(min(fdata$y, na.rm = T), max(fdata$y, na.rm = T))
  zlimits <- c(min(fdata$z, na.rm = T), max(fdata$z, na.rm = T))
  l <- list (x = xlimits, y = ylimits, z = zlimits)
  xyz <- do.call(expand.grid, l)
  #print(xyz)
  x_boundaries <- xyz$x
  #print(class(xyz$x))
  y_boundaries <- xyz$y
  #print(class(xyz$y))
  z_boundaries <- xyz$z
  #print(class(xyz$z))

  # now turn fdata into a wide format for use with the rgl.surface
  fdata[, 2] <- as.character(fdata[, 2])
  fdata[, 3] <- as.character(fdata[, 3])
  #print(class(fdata[, 2]))
  wide_form <- dcast(fdata, y ~ x, value_var = "z")
  print(head(wide_form))
  wide_form_values <- as.matrix(wide_form[, 2:ncol(wide_form)])  
  x_values <- as.numeric(colnames(wide_form[2:ncol(wide_form)]))
  y_values <- as.numeric(wide_form[, 1])
  print(x_values)
  print(y_values)
  wide_form_values <- wide_form_values[order(y_values), order(x_values)]
  x_values <- x_values[order(x_values)]
  y_values <- y_values[order(y_values)]
  print(x_values)
  print(y_values)

  print(dim(wide_form_values))
  print(length(x_values))
  print(length(y_values))

  rgl.surface(z = x_values,  ## these are all different because
              x = y_values,  ## of the confusing way that 
              y = wide_form_values,  ## rgl.surface works!
              coords = c(2,3,1),
              alpha = .8)
  # plot points in red just to be on the safe side!
  points3d(fdata, col = "red")
}

所以我的方法是,试着用你所有的数据来做(我很容易画出从~15k点生成的曲面)。如果这样做不起作用,则取几个较小的样本,并使用这些函数一次绘制所有样本。

也许现在已经晚了,但是跟着Spacedman,你有没有尝试duplicate=“strip”或其他选项?

x=runif(1000)
y=runif(1000)
z=rnorm(1000)
s=interp(x,y,z,duplicate="strip")
surface3d(s$x,s$y,s$z,color="blue")
points3d(s)