How to make your own 3-D sculpture with R

We've mentioned before how you can use R to design 3-D objects. Now, thanks to the latest version of the rgl package, you can produce real-world 3-D objects with R as well.

The rgl package has long made it possible to create virtual 3-D objects in R, and export them as animations like this:

 

But now, package author Duncan Murdoch has added the ability to export such 3-D objects in formats used by 3-D printers (such as STL, WebGL, PLY, and OBJ). Duncan used this feature to create the corresponding real-world sculpture below:

Duncan explained how he obtained the 3-D print via email:

I ordered it from shapeways.com, a service bureau that does 3D printing in a variety of materials. (They're in NYC, and were shut down for a few days by Hurricane Sandy, but still managed to get my print to me a day earlier than they promised to ship it!)  Including shipping to Canada, the cost was $22, and I had the print 11 days after I wrote the software.

The 3-D object file (in STL format) was created using just a few R commands and some elegant mathematics:

## Install rgl from R-forge with
## install.packages("rgl", repos="http://R-Forge.R-project.org")
 
library(rgl)
 
theta <- seq(0, 6*pi, len=2048)
sawtooth <- function(x) sin(x) + sin(2*x)/2
dsawtooth <- function(x) cos(x) + cos(2*x)
 
fb <- 21+1/3
x1 <- sawtooth(fb*theta)
dx1 <- dsawtooth(fb*theta)
 
offset <- 3*pi/3
y1 <- sawtooth(fb*theta - offset )
dy1 <- dsawtooth(fb*theta - offset)
 
r1 <- 0.1
r2 <- 0.4
 
k <- cylinder3d(cbind(sin(theta)+2*sin(2*theta), 2*sin(3*theta), cos(theta)-2*cos(2*theta)),
                      e1=cbind(cos(theta)+4*cos(2*theta), 6*cos(3*theta), sin(theta)+4*sin(2*theta)),
                      radius=0.8, closed=TRUE, keepVars=TRUE)
 
knot <- attr(k, "vars")
center <- cbind(0, x1, y1)*r2
e1 <- cbind(1, dx1, dy1)*r2
e2 <- cbind(rep(0, length(theta)), 1, 0)
for (i in 1:length(theta)) {
   trans <- cbind(knot$e1[i,], knot$e2[i,], knot$e3[i,])
   center[i,] <- knot$center[i,] + trans %*% center[i,]
   e1[i,] <- trans %*% e1[i,]
   e2[i,] <- trans %*% e2[i,]
}
 
braid <- addNormals(cylinder3d(center, e1=e1, e2=e2, radius=r1))
shade3d(braid, col="white")
writeSTL("braid.stl") 

Created by Pretty R at inside-R.org

Try it yourself! The package installed easily for me on a Mac running R 2.15.2, and I could also rotate the 3-D object interatively on-screen using the shade3d function. For more info, visit the rgl progect page linked below.

r-forge: rgl project page

Comments

[Nadra]

Great example of how additive manufacturing technologies can be applied to the world of art. Don't forget, Society of Manufacturing Engineers is seeking entries to the Contemporary Art Gallery which will open June 10-13 in Pittsburgh and display some masterpieces created with this new 3D imaging an 3D printing medium.

Here's the link to the art submission form: https://www.conferenceabstracts.com/cfp2/login.asp?EventKey=HZNJDBAF