Optical Art with R

Last week, in a post entitled Bridget Riley exhibition in London, the author Markus Gesmann wrote an R script reproducing one of Riley's famous art pieces: Movement in Squares.

This reminded me of my own first "brush" with Op art. It was in art class years ago, our professor (Madame Vitré) had asked that we recreate an interesting piece. The concept in itself was easy: pick two points and draw a number of lines through each of them. Where they intersect, the two sets of lines create a multitude of polygons that can be filled in black or white alternatively, for quite a dramatic result.

As you can imagine, it was tedious work on paper. Years later, I'd get a thrill at doing it in just a couple minutes using Paint on Windows. Well, here I am again in 2012, now a grown-up programmer:

	optical.art <- function(P, N, colors = brewer.pal(P, "Greys")) {
	## This function creates an Op art figure as can be found on
	## http://r-de-jeu.blogspot.com/
	##
	## Inputs:
	## - P: (integer) number of starting points
	## - N: (integer) number of semi-lines starting from each point.
	## For best results, N should be a multiple of P
	## - colors: vector of colors for filling polygons.
	## For best results, you should use P colors
	require(sp)
	require(rgeos)
	require(RColorBrewer)
	# plot area
	plot(c(0, 1), c(0, 1), "n", axes=FALSE, xlab="", ylab="")
	create.polygon <- function(x, y) {
	pol <- Polygon(cbind(c(x, head(x, 1)), c(y, head(y, 1))))
	set <- Polygons(list(pol), "pol")
	spP <- SpatialPolygons(list(set))
	}
	plot.area <- create.polygon(x = c(0,1,1,0), y = c(0,0,1,1))
	polygons <- vector("list", length = P)
	for (p in 1:P) {
	# randomly select the coordinates of a point and the
	# angles of N semi-lines starting from that point
	center.x <- runif(1)
	center.y <- runif(1)
	angles <- 2*pi/N*(0:(N-1) + 2*pi*runif(1))
	# the semi-lines and frame will define N polygons
	polygons[[p]] <- vector("list", length = N)
	for (i in 1:N) {
	i1 <- i
	i2 <- ifelse((i + 1) > N, 1, i + 1)
	a1 <- angles[i1]
	a2 <- angles[i2]
	polygons[[p]][[i]] <-
	create.polygon(x = center.x + c(0, 2*cos(a1), 2*cos(a2), 0),
	y = center.y + c(0, 2*sin(a1), 2*sin(a2), 0))
	}
	}
	all.comb <- expand.grid(data.frame(replicate(P, 1:N)))
	for (k in 1:nrow(all.comb)) {
	# compute the intersection of the polygons
	poly <- plot.area
	for (i in 1:P) {
	poly <- gIntersection(poly, polygons[[i]][[all.comb[k,i]]])
	if (gIsEmpty(poly)) break
	}
	if (gIsEmpty(poly)) next
	# plot the polygon and fill it with the appropriate color
	coords <- poly@polygons[[1]]@Polygons[[1]]@coords
	polygon(coords[, 1], coords[, 2], border = NA,
	col = colors[1 + (sum(all.comb[k,]) %% length(colors))])
	}
	}

view raw optical.art.R hosted with ❤ by GitHub

The example above was run using P = 2, N = 30, and colors = c("black", "white"). And here is a nice series using three points and colors from the brewer palette:

P = 3, N = 12, colors = brewer.pal(3, "Reds")	P = 3, N = 15, colors = brewer.pal(3, "Purples")
P = 3, N = 15, colors = brewer.pal(3, "Blues")	P = 3, N = 9, colors = brewer.pal(3, "Greens")

Madame Vitré would be proud. (or horrified?)