**R – dahtah**, and kindly contributed to R-bloggers)

Stippling is the creation of a pattern simulating varying degrees of solidity or shading by using small dots (Wikipedia).StippleGen is a piece of software that renders images using stipple patterns, which I discovered on Xi’an’s blog a couple days ago.

StippleGen uses an algorithm by Adrian Secord (described here) that turns out to be related to a problem in spatial statistics, specifically how to mess with high-order statistics of point processes while controlling density. The algorithm is a variant of k-means and is extremely easy to implement in R.

library(imager) library(dplyr) library(purrr) stipple <- function(im,nPoints=1e3,gamma=2,nSteps=10) { dens <- (1-im)^gamma xy <- sample(nPix(im),nPoints,replace=TRUE,prob=dens) %>% coord.index(im,.) %>% select(x,y) for (ind in 1:nSteps) { xy <- cvt(xy,dens) plot(im); points(xy,col="red") } xy } plot.stipple <- function(im,out,cex=.25) { g <- imgradient(im,"xy") %>% map(~ interp(.,out)) plot(out,ylim=c(height(im),1),cex=cex,pch=19,axes=FALSE,xlab="",ylab="") } ##Compute Voronoi diagram of point set xy, ##and return center of mass of each cell (with density given by image im) cvt <- function(xy,im) { voronoi(xy,width(im),height(im)) %>% as.data.frame %>% mutate(vim=c(im)) %>% group_by(value) %>% dplyr::summarise(x=weighted.mean(x,w=vim),y=weighted.mean(y,w=vim)) %>% select(x,y) %>% filter(x %inr% c(1,width(im)),y %inr% c(1,height(im))) } ##Compute Voronoi diagram for points xy over image of size (w,h) ##Uses a distance transform followed by watershed voronoi <- function(xy,w,h) { v <- imfill(w,h) ind <- round(xy) %>% index.coord(v,.) v[ind] <- seq_along(ind) d <- distance_transform(v>0,1) watershed(v,-d,fill_lines=FALSE) } #image from original paper im <- load.image("http://dahtah.github.io/imager/images/stippling_leaves.png") out <- stipple(im,1e4,nSteps=5,gamma=1.5) plot.stipple(im,out)

TSP art is a variant where you solve a TSP problem to connect all the dots.

library(TSP) ##im is the original image (used only for its dimensions) ##out is the output of the stipple function (dot positions) draw.tsp <- function(im,out) { tour <- out %>% ETSP %>% solve_TSP plot(out[tour,],type="l",ylim=c(height(im),1),axes=FALSE,xlab="",ylab="") } ##Be careful, this is memory-heavy (also, slow) out <- stipple(im,4e3,gamma=1.5) draw.tsp(im,out)

I’ve written a more detailed explanation on the imager website, with other variants like stippling with line segments, and a mosaic filter.

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**R – dahtah**.

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