Marc in the box - 7 months ago 103

R Question

I am hoping someone with experience can help in how one prepares the shape files from xyz data. A great example of a well-prepared dataset can be seen here for the comet Churyumovâ€“Gerasimenko, although the preceding steps in creating the shape file are not provided.

I'm trying to better understand how to apply a surface to a given set of XYZ coordinates. Using Cartesian coordinates is straight forward with the R package "rgl", however shapes that wrap around seem more difficult. I found the R package

`geometry`

`rgl`

`delaunayn`

`library(onion)`

library(rgl)

library(geometry)

data(bunny)

#XYZ point plot

open3d()

points3d(bunny, col=8, size=0.1)

#rgl.snapshot("3d_bunny_points.png")

#Facets following Delaunay triangulation

tc.bunny <- delaunayn(bunny)

open3d()

tetramesh(tc.bunny, bunny, alpha=0.25, col=8)

#rgl.snapshot("3d_bunny_facets.png")

This answer makes me believe that there might be a problem with the R implementation of Qhull. Also, I have now tried various settings (e.g.

`delaunayn(bunny, options="Qt")`

Here is an additional (simpler) example of a sphere. Even here, the calculation of facets does not always find the closest neighboring vertices (if you rotate the ball you will see some facets crossing through the interior).

`library(rgl)`

library(geometry)

set.seed(1)

n <- 10

rho <- 1

theta <- seq(0, 2*pi,, n) # azimuthal coordinate running from 0 to 2*pi

phi <- seq(0, pi,, n) # polar coordinate running from 0 to pi (colatitude)

grd <- expand.grid(theta=theta, phi=phi)

x <- rho * cos(grd$theta) * sin(grd$phi)

y <- rho * sin(grd$theta) * sin(grd$phi)

z <- rho * cos(grd$phi)

set.seed(1)

xyz <- cbind(x,y,z)

tbr = t(surf.tri(xyz, delaunayn(xyz)))

open3d()

rgl.triangles(xyz[tbr,1], xyz[tbr,2], xyz[tbr,3], col = 5, alpha=0.5)

rgl.snapshot("ball.png")

Answer

Here is an approach using kernel density estimation and the `contour3d`

function from `misc3d`

. I played around until I found a value for `levels`

that worked decently. It's not perfectly precise, but you may be able to tweak things to get a better, more accurate surface. If you have more than 8GB of memory, then you may be able to increase `n`

beyond what I did here.

```
library(rgl)
library(misc3d)
library(onion); data(bunny)
# the larger the n, the longer it takes, the more RAM you need
bunny.dens <- kde3d(bunny[,1],bunny[,2],bunny[,3], n=150,
lims=c(-.1,.2,-.1,.2,-.1,.2)) # I chose lim values manually
contour3d(bunny.dens$d, level = 600,
color = "pink", color2 = "green", smooth=500)
rgl.viewpoint(zoom=.75)
```

The image on the right is from the bottom, just to show another view.

You can use a larger value for `n`

in `kde3d`

but it will take longer, and you may run out of RAM if the array becomes too large. You could also try a different bandwidth (default used here). I took this approach from Computing and Displaying Isosurfaces in R - Feng & Tierney 2008.

Very similar isosurface approach using the `Rvcg`

package:

```
library(Rvcg)
library(rgl)
library(misc3d)
library(onion); data(bunny)
bunny.dens <- kde3d(bunny[,1],bunny[,2],bunny[,3], n=150,
lims=c(-.1,.2,-.1,.2,-.1,.2)) # I chose lim values manually
bunny.mesh <- vcgIsosurface(bunny.dens$d, threshold=600)
shade3d(vcgSmooth(bunny.mesh,"HC",iteration=3),col="pink") # do a little smoothing
```

Since it's a density estimation based approach, we can get a little more out of it by increasing the density of the bunny. I also use `n=400`

here. The cost is a significant increase in computation time, but the resulting surface is a *hare* better:

```
bunny.dens <- kde3d(rep(bunny[,1], 10), # increase density.
rep(bunny[,2], 10),
rep(bunny[,3], 10), n=400,
lims=c(-.1,.2,-.1,.2,-.1,.2))
bunny.mesh <- vcgIsosurface(bunny.dens$d, threshold=600)
shade3d(vcgSmooth(bunny.mesh,"HC",iteration=1), col="pink")
```

Better, more efficient surface reconstruction methods exist (e.g. power crust, Poisson surface reconstruction, ball-pivot algorithm), but I don't know that any have been implemented in R, yet.

Here's a relevant Stack Overflow post with some great information and links to check out (including links to code): robust algorithm for surface reconstruction from 3D point cloud?.