Hodograph drawing

February 8, 2014
By

(This article was first published on Dan Kelley Blog/R, and kindly contributed to R-bloggers)

Introduction

The polar graph known as a hodograph can be useful for vector plots, and also for showing varition within nearly-cyclical time series data. The Oce R package should have a function to create hodographs, but as usual my first step is to start by writing isolated code, testing to find the right match between the function and real-world needs.

The code chunk given below is such a test, with the build-in dataset named co2, which is a time-series starting in 1959. The hodograph is for the variation of CO2 from its value in 1959, so the data start at zero radius. Climatologists will why this makes sense, and climate-change deniars will think it’s part of a hoax.

I will leave documentation of the function for a later time, conscious of the fact that the argument list and the aesthtics of the output are likely to change with use.

Methods

First, define hodograph(), with arguments that suffice for a simple problem of a periodic signal x=x(t) to be plotted in polar fashion with radius indicating x and angle indicating t modulo 1 year.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
hodograph <- function(x, y, t, rings, ringlabels = TRUE, tcut = c("daily", "yearly"), 
    ...) {
    tcut <- match.arg(tcut)
    if (missing(t)) {
        stop("x-y method not coded yet\n")
    } else {
        if (!missing(y)) {
            stop("cannot give y if t is given\n")
        }
        if (tcut == "yearly") {
            ## x=x(t)
            t <- as.POSIXlt(t)
            start <- ISOdatetime(1900 + as.POSIXlt(t[1])$year, 1, 1, 0, 0, 0, 
                tz = attr(t, "tzone"))
            day <- as.numeric(julian(t, origin = start))
            xx <- x * cos(day/365 * 2 * pi)
            yy <- x * sin(day/365 * 2 * pi)
            ## axes
            if (missing(rings)) 
                rings <- pretty(sqrt(xx^2 + yy^2))
            rscale <- 1.04 * max(rings)
            theta <- seq(0, 2 * pi, length.out = 200)
            plot(xx, yy, asp = 1, xlim = rscale * c(-1.1, 1.1), ylim = rscale * 
                c(-1.1, 1.1), type = "n", xlab = "", ylab = "", axes = FALSE)
            ## month lines
            month <- c("Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", 
                "Sep", "Oct", "Nov", "Dec")
            day <- c(31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31)
            rscale <- max(rings)
            for (m in 1:12) {
                ## boundaries are for non leap years
                phi <- 2 * pi * (sum(day[1:m]) - day[1])/sum(day)
                lines(rscale * 1.1 * cos(phi) * c(0, 1), rscale * 1.1 * sin(phi) * 
                  c(0, 1), col = "gray")
                phi <- 2 * pi * (0.5/12 + (m - 1)/12)
                text(1.15 * rscale * cos(phi), 1.15 * rscale * sin(phi), month[m])
            }
            for (r in rings) {
                if (r > 0) {
                  gx <- r * cos(theta)
                  gy <- r * sin(theta)
                  lines(gx, gy, col = "gray")
                  if (ringlabels) 
                    text(gx[1], 0, format(r))
                }
            }
            points(xx, yy, ...)
        } else {
            stop("only tcut=\"yearly\" works at this time\n")
        }
    }
}

This may be tested as follows

1
2
3
4
5
6
data(co2)
year <- as.numeric(time(co2))
t0 <- as.POSIXlt("1959-01-01 00:00:00", tz = "UTC")
t <- t0 + (year - year[1]) * 365 * 86400
par(mar = rep(1, 4))
hodograph(x = co2 - co2[1], t = t, tcut = "yearly", type = "l", ringlabels = FALSE)

center

Results

The plot is informative. I’ve looked at the co2 data before, without really noticing the interannual variation, which is clearly seen as variation in the spacing of the spiraling data trace. For comparison, consider a conventional time-series plot.

1
plot(co2)

center

Conclusions

The function is useful as it is, but some improvements are indicated. For example, the ring labels are often over-written by the axes, and the only solution on offer presently is to skip the labels.

Resources

To leave a comment for the author, please follow the link and comment on their blog: Dan Kelley Blog/R.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Sponsors

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)