quick code to draw points with a blur parameter that scales to some notion of a standard deviation.

blurpoint.R

# blur point.
add_alpha <- function(col, alpha = .5){
	if (all(col %in% colors())){
		r.g.b. <- t(col2rgb(col))/255
	} else {
		r.g.b. <- as.matrix(colorspace::hex2RGB(col, gamma = FALSE)@coords)
	}
	cola <- apply(r.g.b., 1, 
			function(x) 
				rgb(x[1], x[2], x[3], alpha=alpha))  
	cola
}

get_asp <- function(){
	diff(par("usr")[1:2]) / diff(par("usr")[3:4]) *
			par("pin")[2] / par("pin")[1]
}
blurpoint <- function(
  x, 
  y, 
  col,               # color: named or hex (alpha ignored and reapplied using alpha arg)
  sd = 1,            # standard deviation
  cex = 1,           # standard cex (relative to unit circle)
  N = 500,           # Number of verticies
  maxq = 1,          # blur out to 100% quantile? 1 = Inf, so this means until .99 in practice.
  asp.adjust = TRUE, # adjust for non-unity aspect so that circles guaranteed?
  alpha = .01,       # alpha as prop. 
  ci95 = TRUE,       # draw ring at 95ci
  ctr = FALSE){        # add point to centroid?
	# x,y centroid
	# col = base color, to interoplate toward bg
	# sd, standard dev to represent as blur
	# cex = common multiplier of point size
	# N, how many vertices
	
	# radians
	rads  <- c(seq(0, 2 * pi, length = N - 1), 2 * pi)
	ux    <- cos(rads)
	uy    <- sin(rads)
	radii <- qnorm(seq(.5, maxq, length = 100),sd=sd)[-100]
	xx    <- outer(ux, radii) * cex + x
	# adjust for non-unity aspect ratio, so that circles always circles?
	asp   <- ifelse(asp.adjust, 1/get_asp(),1)
	yy    <- outer(uy, radii) * cex * asp + y
	cola <- add_alpha(col, alpha=alpha)
	for (i in 1:ncol(xx)){
		polygon(xx[, i], yy[, i], border = FALSE, col = cola)
	}
	# ring as 95%
	if (ci95){
		r95 <- qnorm(.975, sd = sd) * cex
		polygon(x = (ux * r95) + x, 
				y = (uy * r95 * asp) + y,
				border = col,
				lwd = .8)
	}
	if (ctr){
		points(x,y,cex=.5,pch=16,col=col)
	}
}



plot(NULL, type = 'n', xlim = c(0,35), ylim = c(0,55), asp=2, ann = FALSE, las = 1)
blurpoint(15,15,col="#FF0000",sd=.5,cex=2,ci95=FALSE)
blurpoint(5,15,col="#FF0000",sd=1,cex=1,ci95=FALSE,ctr=TRUE)