Recently I stumbled over the rgl-Package in R, which can be used to create interactive 3d plots. Now I want to visualize a set of boxes in one 3d plot. A Box B has cartesian coordinates B_coord=[x,y,z], which correspond to the lower left back corner and dimensions B_dim=[x1,y1,z1].
Apparently it is easy to draw, scale and position some cubes with the following exemplary code:
open3d()
printBox <- function(x,y,z,x1,y1,z1) {
mycube <- scale3d(cube3d(),x1,y1,z1)
wire3d(translate3d(mycube,x,y,z))
}
printBox(0,0,0,1,1,1)
With this code the boxes are moved to x,y,z and scaled to x1,y1,z1. My question is how to write a similar function with the same input which positions the boxes by the coordinates of their lower left back corner and draws a box with the dimensions x1, y1, z1. I am not tied to the rgl package and R, but I like its interactive 3d view.
Thank you for your ideas!
I think your code already does that. So as to make it more clear, and explain what those rgl functions do, I unrolled your function and commented it and put it in a more illustrative example.
library(rgl)
open3d()
# create and plot a box at (x,y,z) of size (x1,y1,z1)
printBox <- function(x, y, z, x1, y1, z1) {
mycube <- cube3d() # create a cube as mesh object
mycube <- scale3d(mycube, x1, y1, z1) # now scale that object by x1,y1,z1
mycube <- translate3d(mycube, x, y, z) # now move it to x,y,z
wire3d(mycube) # now plot it to rgl as a wireframe
}
# Display 5 boxes along a diagonal line
n <- 5
for (i in 1:n) {
x <- i/n
y <- i/n
z <- i/n
sz <- 1/(2*n)
printBox(x, y, z, sz,sz,sz )
}
axes3d() # add some axes
Related
I have two vectors representing x and y-coordinates in a scatter plot, and a thrid variable (z) for each (x,y)-coordinate representing the variable from which to draw contour lines. Example data are given as follows:
df<-data.frame(x=runif(n=30,min=-6,max=6),
y=runif(n=30,min=-6,max=10),
z=seq(1,100,length.out=30))
I use the R-package akima to generate the z-matrix for the contour plot
library(akima)
M1 <- interp(x=df$x,y=df$y,z=df$z)
contour(x=M1$x,y=M1$y,z=M1$z)
I now want to draw arrows perpendicular to the contourlines, preferably using something like the function "quiver" in the R-package pracma, with the origin of an arrow at every (x,y)-coordinate and with the arrow pointing in the direction of the gradient of the contourlines. Is there a way to do this?
My best idea so far is to somehow extract (x,y)-gradients of the contourlines and use these as velocities in the quiver function.
Grateful for any assistance.
The pracma package has a gradient function that can do this for you using the original M1$z values. For example, using your code to get M1 after set.seed(123):
contour(x=M1$x,y=M1$y,z=M1$z, asp = 1) # asp = 1 needed so things look perpendicular
library(pracma)
g <- gradient(M1$z, M1$x, M1$y)
x <- outer(M1$x, M1$y, function(x, y) x)
y <- outer(M1$x, M1$y, function(x, y) y)
quiver(x, y, g$Y, g$X, scale = 0.02, col = "blue")
Note that the gradient labels in the quiver plot have been swapped. Maybe I set up the x and y values transposed from the way the package expects. Here's what you get:
I want to plot a univariate normal density function of the normal distribution onto a (x,y,z) coordinate system.
The code I am using is:
library(rgl)
open3d()
x <- seq(0, 10, length=100)
y <- seq(0, 10, length=100)
z = outer(x,y, function(x,y) dnorm(x,2.5,1)*dnorm(y,2.5,1))
persp3d(x, y, z,col = rainbow(100))
The problem I an encountering is that I want the normal distribution not to be around its mean only but also to be on a straight line or a circle. In latter case, I would expect the output to be similar to a volcano. I guess I must first create some probabilities within a loop. How can I do this? Or should I also use some surface command to plot the output? I am pretty sure this has nothing to do with a bivariate normal though.
Best
Fuji
The first part is easy: just don't let your z depend on y for instance:
z = outer(x,y, function(x,y) dnorm(x,2.5,1))
persp3d(x, y, z,col = rainbow(100))
For the second part, you can imagine that the means of the normal distribution lie on the x^2+y^2=1 circle. You will have infinite normal distributions with radial directions. Try this:
#define the volcano function
volcano<-function(x,y,sigma=1/2) {
alpha<-atan(y/x)+pi*(x<0)
d<-sqrt((cos(alpha)-x)^2 + (sin(alpha)-y)^2)
dnorm(d,0,sigma)
}
x<-seq(-2,2,length.out=100)
y<-seq(-2,2,length.out=100)
z<-outer(x,y,volcano)
persp3d(x, y, z,col = rainbow(100))
I'm trying to make a 3D scatterplot with boudaries or zones based on combinations of 3 variables that return certain values. The variables each range between 0:1, and combine to make an index that ranges from -1:1 as follows:
f(x,y,z) = (x*y)-z
I'd like to create a visual representation that will highlight all combinations of variables that return a certain index value. As an example, I can easily show those variables where index > 0 using scatterplot3d (rgl would also work):
# Create imaginary dataset of 50 observations for each variable
x<-runif(50,0,1)
y<-runif(50,0,1)
z<-runif(50,0,1)
# Create subset where f(x,y,z) > 0
x1<-y1<-z1<-1
for (i in 1:length(x)){ if ((x[i]*y[i])-z[i] > 0) {
x1<-rbind(x1, x[i])
y1<-rbind(y1, y[i])
z1<-rbind(z1, z[i])}
}
s3d<-scatterplot3d(x,y,z) # Plot entire dataset
s3d$points3d(x1,y1,z1,pch=19, col="red") # Highlight subset where f(x,y,z) > 0
This gives me the following graph:
It seems fairly intuitive that there should be an easy way to plot either the surface (extending from top/right/back to bottom/left/front) separating the subset from the rest of the data, or else a volume/3D area within which these plots lie. E.g. my first instinct was to use something like surface3d, persp3d or planes3d. However, all attempts so far have only yielded error messages. Most solutions seem to use some form of z<-lm(y~x) but I obviously need something like q<-func((x*y)-z) for all values of x, y and z that yield q > 0.
I know I could calculate extreme points and use them as vertices for a 3D polygon, but that seems too "manual". It feels like I'm overlooking something fairly simple and obvious. I've looked at many similar questions on Stack but can't seem to find one that fits my particular problem. If I've missed any and this question has been answered already, please do point me in the right direction!
Here is a suggestion for an interactive 3D plot that is based on an example from the "R Graphics Cookbook" by Winston Chang.
set.seed(4321)
library(rgl)
interleave <- function(v1,v2) as.vector(rbind(v1,v2))
x <- runif(50)
y <- runif(50)
z <- runif(50)
plot3d(x, y, z, type="s", size=0.6, col=(2+(x*y<z)))
x0 <- y0 <- seq(0, 1, 0.1)
surface3d(x0, y0, outer(x0, y0), alpha=0.4) #plot the surface f(x,y)=x*y
x1 <- x[x * y > z] #select subset that is below the separating surface
y1 <- y[x * y > z]
z1 <- z[x * y > z]
segments3d(interleave(x1, x1), #highlight the distance of the points below the surface
interleave(y1, y1),
interleave(x1 * y1, z1), col="red", alpha=0.4)
If you don't like the red lines and only want the surface and the colored points, this will be sufficient:
plot3d(x,y,z,type="s",size=0.6,col=(2+(x*y<z)))
x0 <- y0 <- seq(0,1,0.1)
surface3d(x0,y0,outer(x0,y0),alpha=0.4)
Does this representation provide the information that you wanted to highlight?
The first thought was to see if the existing functions within scatterplot3d could handle the problem but I think not:
my.lm <- lm(z ~ I(x) * I(y)+0)
s3d$plane3d(my.lm, lty.box = "solid", col="red")
pkg:scatterplot3d doesn't really have a surface3d function so you will need to choose a package that provides that capability; say 'rgl', 'lattice', or 'plot3d'. Any of them should provide the needed facilities.
Is there any way to input a fixed vector of colours to any 3D rgl plots? If so it would be possible to extrude a map tile to a 3D surface based on a raster of the same area. But I'm finding the surface3d function behaves the same as raster::plot by insisting on mapping the input colour vector to the z variable. Is this beyond rgl's functionality at present?
I don't actually know if what you say about the coloring is correct for all rgl coloring functions, but it is not correct for rgl.surface(). This is a corruption of the example on the ?rgl.surface page. The color vector index was formed from the x-y (actually x-z) coordinates and gives a striping effect because they were modulo-ized to pull values from from a limited range.
library(rgl)
data(volcano)
y <- 2 * volcano
x <- 10 * (1:nrow(y))
z <- 10 * (1:ncol(y))
ylim <- range(y)
ylen <- ylim[2] - ylim[1] + 1
colorlut <- terrain.colors(ylen)
col <- colorlut[(x+length(x)*y +1)%%ylen ]
rgl.open()
rgl.surface(x, z, y, color=col, back="lines")
rgl.snapshot("striped_volcano.png")
I have a 3-tuple data set (X,Y,Z points) that I want to plot using R.
I want to create a surface plot from the data, and superimpose a contour map on the surface plot, so as to create the impression of the contour map being the "shadow" or projection from the surface plot. The contour map is to appear below the surface plot.
My data set looks somewhat like this:
Axis | Data Type
-------------------
X | Date value
Y | Float value
Z | Float value
How can I achieve this?
Edit:
I just saw that you pointed out one of your dimensions is a date. In that case, have a look at Jeff Ryan's chartSeries3d which is designed to chart 3-dimensional time series. Here he shows the yield curve over time:
Original Answer:
As I understand it, you want a countour map to be the projection on the plane beneath the 3D surface plot. I don't believe that there's an easy way to do this other than creating the two plots and then combining them. You may find the spatial view helpful for this.
There are two primary R packages for 3D plotting: rgl (or you can use the related misc3d package) and scatterplot3d.
rgl
The rgl package uses OpenGL to create interactive 3D plots (read more on the rgl website). Here's an example using the surface3d function:
library(rgl)
data(volcano)
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)
zlim <- range(z)
zlen <- zlim[2] - zlim[1] + 1
colorlut <- terrain.colors(zlen,alpha=0) # height color lookup table
col <- colorlut[ z-zlim[1]+1 ] # assign colors to heights for each point
open3d()
rgl.surface(x, y, z, color=col, alpha=0.75, back="lines")
The alpha parameter makes this surface partly transparent. Now you have an interactive 3D plot of a surface and you want to create a countour map underneath. rgl allows you add more plots to an existing image:
colorlut <- heat.colors(zlen,alpha=1) # use different colors for the contour map
col <- colorlut[ z-zlim[1]+1 ]
rgl.surface(x, y, matrix(1, nrow(z), ncol(z)),color=col, back="fill")
In this surface I set the heights=1 so that we have a plane underneath the other surface. This ends up looking like this, and can be rotated with a mouse:
scatterplot3d
scatterplot3d is a little more like other plotting functions in R (read the vignette). Here's a simple example:
temp <- seq(-pi, 0, length = 50)
x <- c(rep(1, 50) %*% t(cos(temp)))
y <- c(cos(temp) %*% t(sin(temp)))
z <- c(sin(temp) %*% t(sin(temp)))
scatterplot3d(x, y, z, highlight.3d=TRUE,
col.axis="blue", col.grid="lightblue",
main="scatterplot3d - 2", pch=20)
In this case, you will need to overlay the images. The R-Wiki has a nice post on creating a tanslucent background image.