## Sunday, December 30, 2012

### Spirograph with R

Just had to figure out how to replicate this old toy of mine with R! I had no idea how long it's been around:

nor the mathematical basis behind it.

 Wikimedia Commons: HypotrochoidOutThreeFifths.gif

I especially like this one (A.RADIUS = 4.1, B.RADIUS = -6.165, BC = 2.3, A.REV = 100):

OK, enough playing ...

Spirograph function:

```#spirographR() will produce either a hypotrochoid or an epitrochoid.
#'A' is a circle of radius 'A.RADIUS'
#'B' is a circle of radius 'B.RADIUS' travelling around 'A'
#'C' is a point relative to the center of 'B' which rotates with the turning of 'B'.
#'BC' is the distance from the center of 'B' to 'C'
#'A.REV' is the number of revolutions that 'B' should travel around 'A'
#'N.PER.A.REV' is the number of radial increments to be calculated per revolution
#'A.CEN' is the position of the center of 'A'
#
#NOTE: A positive value for 'B' will result in a epitrochoid, while a negative value will result in a hypotrochoid.
#
spirographR <- function(
A.RADIUS=1,
B.RADIUS=-4,
BC=-2,
A.REV=4,
N.PER.A.REV=360,
A.CEN=list(x=0, y=0)){

B.CEN.START <- list(x=0, y=A.CEN\$y + A.RADIUS + B.RADIUS) #starting position of B circle
A.ANGLE <- seq(0, 2*pi*A.REV,, A.REV*N.PER.A.REV) #Radians around A for calculation
A.CIR <- 2*pi*A.RADIUS #Circumference of A
B.CIR <- 2*pi*B.RADIUS #Circumference of B

###Find position of B.CEN
B.CEN <- c()
HYP <- A.RADIUS + B.RADIUS
ADJ <- sin(A.ANGLE) * HYP
OPP <- cos(A.ANGLE) * HYP
B.CEN\$x <- A.CEN\$x + ADJ
B.CEN\$y <- A.CEN\$y + OPP

###Find position of C.POINT
C.POINT <- c()
A.CIR.DIST <- A.CIR * A.ANGLE / (2*pi)
B.POINT.ANGLE <- A.CIR.DIST / B.CIR * 2*pi
HYP <- BC
ADJ <- sin(B.POINT.ANGLE) * HYP
OPP <- cos(B.POINT.ANGLE) * HYP
C.POINT\$x <- B.CEN\$x + ADJ
C.POINT\$y <- B.CEN\$y + OPP

###Return trajectory of C
C.POINT
}```
Created by Pretty R at inside-R.org

To reproduce example:

```source("spirographR.R")

require(spatstat)

RES <- vector(mode="list", 100)
LIM <- c()
set.seed(1112)
for(i in seq(RES)){
#i=1
a.rad=sample(seq(1,10, 0.1),1)
b.rad=sample(seq(-3,10, 0.1),1)
bc=sample(seq(-10,10),1)
a.rev=least.common.multiple(abs(a.rad), abs(b.rad))
tmp <- runif(2, min=-100, max=100)
a.cen=list(x=tmp[1], y=tmp[2])
LIM <- range(c(LIM, unlist(a.cen)))
RES[[i]] <- spirographR(A.RADIUS=a.rad, B.RADIUS=b.rad, BC=bc, A.REV=a.rev, A.CEN=a.cen)
}

png("spirograph.png", width=4, height=4, units="in", res=600)
par(mar=c(0,0,0,0), bg=1)
for(i in seq(RES)){

if(i == 1){
plot(RES[[i]], t="n", xlim=LIM, ylim=LIM, asp=1)
}
lines(RES[[i]], col=rgb(runif(1), runif(1), runif(1), 0.8), lwd=0.3)
}
dev.off()```
Created by Pretty R at inside-R.org

#### 6 comments:

1. Very cool, thanks for sharing!

2. Hi Marc,
Great post, and a beautiful image.

One request: may I ask you to send the full post to the feed? (without the Read more added to it), so to make it easier to read on r-bloggers?

Yours,
Tal

3. That was great! Thanks for sharing.

4. Hi Tal, The reason I add the break to most of my posts is so that the main page doesn't get too long. This was an exceptionally short post though with mainly pictures, so I'll try to keep more before the break in the future. Cheers, Marc

5. Very nice of you to post this. I guess my two comments are pretty nitpicky: first, stop using FORTRAN formatting, i.e. capital names for all variables :-( ; second, I believe the only function you use from spatstat is the leastcommonmultiple, right? Just checking.

6. Hello cellocgw - Regarding your critiques: I don't even know FORTRAN, so my uncouth programming can only be attributed to me! :-) ; You're right on the second point - I tried using leastcommonmultiple to derive the number of revolutions that would complete the spirograph, but this doesn't seem to be correct. I didn't mean for people to have to download a new package actually - I thought this package was part of the recommended packages that comes with R, but I was wrong.