如何将2D图像投影为三维散点图中的曲面（在R中）？

Question

I'm working with 3 dimensional coordinates data, which i'm plotting in a scatterplot, i have ~30.000 datapoints, and i've included the first 10 here so that you can reproduce it

library(rgl)
library(plot3D)
library(car)

df <- data.frame(meanX = c(147.34694,
                       173.89244,
                       135.73004,
                       121.93766,
                       109.72152,
                       92.53709,
                       165.46588,
                       169.77744,
                       127.01796,
                       99.34347),
             meanY = c(140.40816,
                       110.99128,
                       134.56023,
                       164.18703,
                       166.04051,
                       155.97329,
                       105.29377,
                       104.42683,
                       130.17066,
                       155.99696),
             avgDist = c(40.788118,
                         12.957329,
                         14.24348,
                         39.10424,
                         34.694258,
                         25.532335,
                         21.491695,
                         23.528944,
                         9.309201,
                         31.916879))

I've been using the scatter3d function to plot this

scatter3d(x = df$meanX, y = df$meanY, z = df$avgDist, surface = FALSE)

Now my "problem", is that I would like to have a 2d surface with an external image file overlayed onto it at z=0, and as a bonus, if i could project a heatmap/contours from the scatterplot data (meanX and meanY used for the contours) over that image as well, that would be great.

This is the image i'd like to have draped at z = 0:

http://i.imgur.com/m6j4q3M.png

That image was made with this ggplot:

map.colors <- colorRampPalette(c("green","yellow","red"))

densityPlot <- ggplot(direData, aes(x = meanX, y = ,meanY)) + 
  stat_density2d(geom="tile", aes(fill=..density.., alpha=sqrt(sqrt(..density..))), contour=FALSE, n=100) +
  scale_alpha(range = c(0, 1.0)) + scale_fill_gradientn(colours = map.colors(5)) + 
  xlim(70,185) + ylim(70,185)

minimap <- readPNG('~/yasp/minimap.png')

densityPlot + annotation_raster(minimap, ymin = 70 ,ymax=185 ,xmin = 70,xmax = 185) + 
  stat_density2d(geom="tile", aes(fill=..density.., alpha=10*sqrt(..density..)), contour=FALSE, n=100)

Is there any way to do this? I've googled quite a bit for a solution but found no real way of doing this. I don't mind creating the image first in ggplot2 with the heatmap, saving that, and then using that as input for the surface draping, but it would of course be quite cool if it could all be done in one call to plot.

Answer 1

How about this?

I stored your lined image file in a png in the local directory, there is probably a way to do that without an intermediate file, but I would ask that as a separate question.

Note that this is actually a simple case of texture mapping. The texture is saved in the gameshot.png file you specified. You could warp the text around a more complicated object by adding more points to the geometry and adjusting the texture map coordinates accordingly.

While they should not have been absolutely necessary here, I added texture map coordinates as it looked like the file and the data were not aligned by default - and in fact the gameshot.png file was displaying reversed. It looks to me like the png file you specified does not quite match the data, I think there is an inversion somewhere before you saved it.

library(rgl)
library(plot3D)
library(car) 

df <- data.frame(meanX = c(147.34694, 173.89244, 135.73004, 121.93766,
                           109.72152,  92.53709, 165.46588, 169.77744,
                           127.01796,  99.34347),
                 meanY = c(140.40816, 110.99128, 134.56023, 164.18703,
                           166.04051, 155.97329, 105.29377, 104.42683,
                           130.17066, 155.99696),
                 avgDist = c(40.788118, 12.957329, 14.24348, 39.10424,
                             34.694258, 25.532335, 21.491695,23.528944,
                             9.309201,  31.916879))

car::scatter3d(x = df$meanX, y = df$meanY, z = df$avgDist, surface = FALSE)

xvek <- c(0,1)
yvek <- c(0,1)
lnx <- length(xvek)
lny <- length(yvek)
zmat <- matrix(0,lnx,lny)

# Setup the Texture coordinates - defaults seem to invert image
# tms <- matrix(c(0,0,1,1),lnx,lny) # generic case (xy-maped texture looks like png file)
# tmt <- matrix(c(0,1,0,1),lnx,lny)   

tmt <- matrix(c(1,1,0,0),lnx,lny) # "correct case" (ball density look more like picture)
tms <- matrix(c(1,0,1,0),lnx,lny) # I think the gameshot.png is in error  


# Texture file specified in question was stored locally in "gameshot.png"
surface3d(xvek,yvek,zmat,coord=c(3,1),texture_s=tms,texture_t=tmt,
          lit=F,fog=T,color="white",textype="rgb",texture="gameshot.png",add=T)

Yields this:

Answer 2

(2nd Edit) I try to write something better code and confirm two xy-coordinates are the same. ggplot2 theme with no axes or grid help me to plot only the panel region.

library(rgl); library(grid); library(gtable)

df <- data.frame(meanX = c(147.34694, 173.89244, 135.73004, 121.93766,
                           109.72152,  92.53709, 165.46588, 169.77744,
                           127.01796,  99.34347),
                 meanY = c(140.40816, 110.99128, 134.56023, 164.18703,
                           166.04051, 155.97329, 105.29377, 104.42683,
                           130.17066, 155.99696),
                 avgDist = c(40.788118, 12.957329, 14.24348, 39.10424,
                             34.694258, 25.532335, 21.491695,23.528944,
                             9.309201,  31.916879))

map.colors <- colorRampPalette(c("green","yellow","red"))

# set scale_*_continuous() to plot only the panel region. limits mean xlim (or ylim)
# change "tile" into "raster" because of making noise lines on my screen
densityPlot <- ggplot(df[,1:2], aes(x = meanX, y = ,meanY)) + 
  stat_density2d(geom="raster", aes(fill=..density.., alpha=sqrt(sqrt(..density..))), contour=FALSE, n=100) +
  scale_alpha(range = c(0, 1.0)) + scale_fill_gradientn(colours = map.colors(5)) + 
  scale_x_continuous(limits=c(70,185), expand = c(0,0)) + scale_y_continuous(limits=c(70,185), expand = c(0,0)) +
  geom_point(size=4)               # to test XY-coordinate (black points on the map)

open3d()
plot3d( df, type="s", radius=1, col="red", axes=F, 
        xlim = c(70,185), ylim = c(70,185),
        expand = 1 )
plot3d( df, type="h", col="blue", add=T )  # to test XY-coordinate (line segments from z = 0)
axes3d(c("x","y","z") )
show2d({                  # show2d uses 2D plot function's output as a texture on a box.
  grid.draw(gtable_filter(ggplotGrob(densityPlot), "panel"))
},
expand = 1 , texmipmap = F )   # texmipmap = F makes tone clear (not essential)

# I think this is clearly better than using a intermediate file,
# so I deleted related code. Thanks Mike !