PolarImagePlot()

PolarImagePlot.R

# by Tim Riffe, June 5th, 2012

# arguments:
# Mat, a matrix of z values as follows:
# leftmost edge of first column = 0 degrees, rightmost edge of last column = 360 degrees
# columns are distributed in cells equally over the range 0 to 360 degrees, like a grid prior to transform
# first row is innermost circle, last row is outermost circle

# outer.radius, By default everything scaled to unit circle 
# cols: color vector. default = rev(heat.colors(length(breaks)-1))
# breaks: manual breaks for colors. defaults to seq(min(Mat),max(Mat),length=nbreaks)
# nbreaks: how many color levels are desired?
# axes: should circular and radial axes be drawn? radial axes are drawn at 30 degree intervals only- this could be made more flexible.
# circle.rads: at which radii should circles be drawn? defaults to pretty(((0:ncol(Mat)) / ncol(Mat)) * outer.radius)

# TODO: add color strip legend. Contours.

PolarImagePlot <- function(Mat, outer.radius = 1, cols, ppa = 5, breaks, nbreaks = 51, axes = TRUE, circle.rads){
    
    # the image prep
    Mat      <- Mat[,ncol(Mat):1 ]
    radii    <- ((0:ncol(Mat)) / ncol(Mat)) * outer.radius
    
    # 5 points per arc will usually do
    Npts     <- ppa
    # all the angles for which a vertex is needed
    radians  <- 2 * pi * (0:(nrow(Mat) * Npts)) / (nrow(Mat) * Npts) + pi / 2
    # matrix where each row is the arc corresponding to a cell
    rad.mat  <- matrix(radians[-length(radians)], ncol = Npts, byrow = TRUE)[1:nrow(Mat), ]
    rad.mat  <- cbind(rad.mat, rad.mat[c(2:nrow(rad.mat), 1), 1])
    
    # the x and y coords assuming radius of 1
    y0 <- sin(rad.mat)
    x0 <- cos(rad.mat)
    
    # dimension markers
    nc <- ncol(x0)
    nr <- nrow(x0)
    nl <- length(radii)
    
    # make a copy for each radii, redimension in sick ways
    x1 <- aperm( x0 %o% radii, c(1, 3, 2))
    # the same, but coming back the other direction to close the polygon
    x2 <- x1[, , nc:1]
    #now stick together
    x.array <- abind:::abind(x1[, 1:(nl - 1), ], x2[, 2:nl, ], matrix(NA, ncol = (nl - 1), nrow = nr), along = 3)
    # final product, xcoords, is a single vector, in order, 
    # where all the x coordinates for a cell are arranged
    # clockwise. cells are separated by NAs- allows a single call to polygon()
    xcoords <- aperm(x.array, c(3, 1, 2))
    dim(xcoords) <- c(NULL)
    # repeat for y coordinates
    y1 <- aperm( y0 %o% radii,c(1, 3, 2))
    y2 <- y1[, , nc:1]
    y.array <- abind:::abind(y1[, 1:(length(radii) - 1), ], y2[, 2:length(radii), ], matrix(NA, ncol = (length(radii) - 1), nrow = nr), along = 3)
    ycoords <- aperm(y.array, c(3, 1, 2))
    dim(ycoords) <- c(NULL)
    
    # sort out colors and breaks:
    if (!missing(breaks) & !missing(cols)){
        if (length(breaks) - length(cols) != 1){
            stop("breaks must be 1 element longer than cols")
        }
    }
    if (missing(breaks) & !missing(cols)){
        breaks <- seq(min(Mat,na.rm = TRUE), max(Mat, na.rm = TRUE), length = length(cols) + 1)
    }
    if (missing(cols) & !missing(breaks)){
        cols <- rev(heat.colors(length(breaks) - 1))
    }
    if (missing(breaks) & missing(cols)){
        breaks <- seq(min(Mat,na.rm = TRUE), max(Mat, na.rm = TRUE), length = nbreaks)
        cols <- rev(heat.colors(length(breaks) - 1))
    }
    
    # get a color for each cell. Ugly, but it gets them in the right order
    cell.cols <- as.character(cut(as.vector(Mat[nrow(Mat):1,ncol(Mat):1]), breaks = breaks, labels = cols))
    
    # start empty plot
    plot(NULL, type = "n", ylim = c(-1, 1) * outer.radius, xlim = c(-1, 1) * outer.radius, asp = 1, axes = FALSE, xlab = "", ylab = "")
    # draw polygons with no borders:
    polygon(xcoords, ycoords, col = cell.cols, border = NA)
    
    if (axes){
        
        # a couple internals for axis markup
        RMat <- function(radians){
            matrix(c(cos(radians), sin(radians), -sin(radians), cos(radians)), ncol = 2)
        }
        
        circle <- function(x, y, rad = 1, nvert = 500){
            rads <- seq(0,2*pi,length.out = nvert)
            xcoords <- cos(rads) * rad + x
            ycoords <- sin(rads) * rad + y
            cbind(xcoords, ycoords)
        }
        # draw circles
        if (missing(circle.rads)){
            circle.rads <- pretty(radii)
        }
        for (i in circle.rads){
            lines(circle(0, 0, i), col = "#66666650")
        }
        
        # put on radial spoke axes:
        axis.rads <- c(0, pi / 6, pi / 3, pi / 2, 2 * pi / 3, 5 * pi / 6)
        r.labs <- c(90, 60, 30, 0, 330, 300)
        l.labs <- c(270, 240, 210, 180, 150, 120)
        
        for (i in 1:length(axis.rads)){ 
            endpoints <- zapsmall(c(RMat(axis.rads[i]) %*% matrix(c(1, 0, -1, 0) * outer.radius,ncol = 2)))
            segments(endpoints[1], endpoints[2], endpoints[3], endpoints[4], col = "#66666650")
            endpoints <- c(RMat(axis.rads[i]) %*% matrix(c(1.1, 0, -1.1, 0) * outer.radius, ncol = 2))
            lab1 <- bquote(.(r.labs[i]) * degree)
            lab2 <- bquote(.(l.labs[i]) * degree)
            text(endpoints[1], endpoints[2], lab1, xpd = TRUE)
            text(endpoints[3], endpoints[4], lab2, xpd = TRUE)
        }
        axis(2, pos = -1.2 * outer.radius, at = sort(union(circle.rads,-circle.rads)))
    }
    invisible(list(breaks = breaks, col = cols))
}


# example (ignore the interpolation part- do that some other way)
set.seed(1)
x <- runif(20, min = 0, max = 360)
y <- runif(20, min = 0, max = 40)
z <- rnorm(20)

Interp <- akima:::interp(x = x, y = y, z = z, 
        extrap = TRUE, 
        xo = seq(0, 360, length.out = 300), 
        yo = seq(0, 40, length.out = 100), 
        linear = FALSE)
Mat <- Interp[[3]]


PolarImagePlot(Mat)

Thanks a lot for sharing your script! This was very helpful for our bidirectional reflectance project!!!
I used your R script and added an Color Scale using the image.scale function from http://menugget.blogspot.de/2011/08/adding-scale-to-image-plot.html within the PolarImagePLot function:

PolarImagePlot <- function(Mat,theta, outer.radius = 1, ppa = 5, cols, breaks, nbreaks = 51, axes = TRUE, circle.rads,circle.labels, title=""){

make layout to add image.scale

layout(matrix(c(1,2), nrow=1, ncol=2),width=c(6,1), height=c(4,4))

first image

par(mar=c(1,1,2,1))

... your function

#Add scale
par(mar=c(1,1,1,5))
image.scale(Mat, col=cols, breaks=breaks, horiz=FALSE, yaxt="n", zlim=range(Mat, na.rm=TRUE))
axis(4,at=round(breaks[seq(1,length(breaks),length=10)], digits=2), las=2)
box()

}

Regards,
Clem

Thanks Tim and Clem for the scripts and ideas. @clem: I have problems with inserting a scale.

I run the image.scale function from menugget then I wrote this into my r console `PolarImagePlot <- function(Mat,theta, outer.radius = 1, ppa = 5, cols, breaks, nbreaks = 51, axes = TRUE, circle.rads,circle.labels, title=""){

make layout to add image.scalefollowed by thislayout(matrix(c(1,2), nrow=1, ncol=2),width=c(6,1), height=c(4,4))then the function from Tim # the image prep
Mat <- Mat[,ncol(Mat):1 ]
radii <- ((0:ncol(Mat)) / ncol(Mat)) * outer.radius

# 5 points per arc will usually do
Npts     <- ppa
# all the angles for which a vertex is needed
radians  <- 2 * pi * (0:(nrow(Mat) * Npts)) / (nrow(Mat) * Npts) + pi / 2
# matrix where each row is the arc corresponding to a cell
rad.mat  <- matrix(radians[-length(radians)], ncol = Npts, byrow = TRUE)[1:nrow(Mat), ]
rad.mat  <- cbind(rad.mat, rad.mat[c(2:nrow(rad.mat), 1), 1])

# the x and y coords assuming radius of 1
y0 <- sin(rad.mat)
x0 <- cos(rad.mat)

# dimension markers
nc <- ncol(x0)
nr <- nrow(x0)
nl <- length(radii)

# make a copy for each radii, redimension in sick ways
x1 <- aperm( x0 %o% radii, c(1, 3, 2))
# the same, but coming back the other direction to close the polygon
x2 <- x1[, , nc:1]
#now stick together
x.array <- abind:::abind(x1[, 1:(nl - 1), ], x2[, 2:nl, ], matrix(NA, ncol = (nl - 1), nrow = nr), along = 3)
# final product, xcoords, is a single vector, in order, 
# where all the x coordinates for a cell are arranged
# clockwise. cells are separated by NAs- allows a single call to polygon()
xcoords <- aperm(x.array, c(3, 1, 2))
dim(xcoords) <- c(NULL)
# repeat for y coordinates
y1 <- aperm( y0 %o% radii,c(1, 3, 2))
y2 <- y1[, , nc:1]
y.array <- abind:::abind(y1[, 1:(length(radii) - 1), ], y2[, 2:length(radii), ], matrix(NA, ncol = (length(radii) - 1), nrow = nr), along = 3)
ycoords <- aperm(y.array, c(3, 1, 2))
dim(ycoords) <- c(NULL)

# sort out colors and breaks:
if (!missing(breaks) & !missing(cols)){
    if (length(breaks) - length(cols) != 1){
        stop("breaks must be 1 element longer than cols")
    }
}
if (missing(breaks) & !missing(cols)){
    breaks <- seq(min(Mat,na.rm = TRUE), max(Mat, na.rm = TRUE), length = length(cols) + 1)
}
if (missing(cols) & !missing(breaks)){
    cols <- rev(heat.colors(length(breaks) - 1))
}
if (missing(breaks) & missing(cols)){
    breaks <- seq(min(Mat,na.rm = TRUE), max(Mat, na.rm = TRUE), length = nbreaks)
    cols <- rev(heat.colors(length(breaks) - 1))
}

# get a color for each cell. Ugly, but it gets them in the right order
cell.cols <- as.character(cut(as.vector(Mat[nrow(Mat):1,ncol(Mat):1]), breaks = breaks, labels = cols))

# start empty plot
plot(NULL, type = "n", ylim = c(-1, 1) * outer.radius, xlim = c(-1, 1) * outer.radius, asp = 1, axes = FALSE, xlab = "", ylab = "")
# draw polygons with no borders:
polygon(xcoords, ycoords, col = cell.cols, border = NA)

if (axes){
    
    # a couple internals for axis markup
    RMat <- function(radians){
        matrix(c(cos(radians), sin(radians), -sin(radians), cos(radians)), ncol = 2)
    }
    
    circle <- function(x, y, rad = 1, nvert = 500){
        rads <- seq(0,2*pi,length.out = nvert)
        xcoords <- cos(rads) * rad + x
        ycoords <- sin(rads) * rad + y
        cbind(xcoords, ycoords)
    }
    # draw circles
    if (missing(circle.rads)){
        circle.rads <- pretty(radii)
    }
    for (i in circle.rads){
        lines(circle(0, 0, i), col = "#66666650")
    }
    
    # put on radial spoke axes:
    axis.rads <- c(0, pi / 6, pi / 3, pi / 2, 2 * pi / 3, 5 * pi / 6)
    r.labs <- c(90, 60, 30, 0, 330, 300)
    l.labs <- c(270, 240, 210, 180, 150, 120)
    
    for (i in 1:length(axis.rads)){ 
        endpoints <- zapsmall(c(RMat(axis.rads[i]) %*% matrix(c(1, 0, -1, 0) * outer.radius,ncol = 2)))
        segments(endpoints[1], endpoints[2], endpoints[3], endpoints[4], col = "#66666650")
        endpoints <- c(RMat(axis.rads[i]) %*% matrix(c(1.1, 0, -1.1, 0) * outer.radius, ncol = 2))
        lab1 <- bquote(.(r.labs[i]) * degree)
        lab2 <- bquote(.(l.labs[i]) * degree)
        text(endpoints[1], endpoints[2], lab1, xpd = TRUE)
        text(endpoints[3], endpoints[4], lab2, xpd = TRUE)
    }
    axis(2, pos = -1.2 * outer.radius, at = sort(union(circle.rads,-circle.rads)))
}
invisible(list(breaks = breaks, col = cols))` and finally the last part of your comment `#Add scale

par(mar=c(1,1,1,5))
image.scale(Mat, col=cols, breaks=breaks, horiz=FALSE, yaxt="n", zlim=range(Mat, na.rm=TRUE))
axis(4,at=round(breaks[seq(1,length(breaks),length=10)], digits=2), las=2)
box()

}When I run this function with the provided example data from Tim# example (ignore the interpolation part- do that some other way)
set.seed(1)
x <- runif(20, min = 0, max = 360)
y <- runif(20, min = 0, max = 40)
z <- rnorm(20)

Interp <- akima:::interp(x = x, y = y, z = z,
extrap = TRUE,
xo = seq(0, 360, length.out = 300),
yo = seq(0, 40, length.out = 100),
linear = FALSE)
Mat <- Interp[[3]]

PolarImagePlot(Mat)I got the following Errormassage:Error in .External.graphics(C_layout, num.rows, num.cols, mat, as.integer(num.figures), :
invalid graphics state`
I am a R beginner and wnat to plot bidirectional data. Can you please give me hint what I am doing wrong in applying your code? sessioniInfo()

R version 3.4.0 Patched (2017-06-13 r72789)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1