[R] ountour "resolution"

[David Winsemius]

On Sep 13, 2009, at 6:54 PM, (Ted Harding) wrote:

> Greetings all!
> I'm wanting to plot contours of a function, and I don't
> want to evaluate it at a dense grid of points (i.e. I don't
> want a huge array of values).
>
> Say I have a vector of x-values such as x <- 0.1*c(1:10),
> and the same for y <- 0.1*(0:10).
>
> I then evaluate a 10*10 matrix z of values of z = f(x,y).
>
> so I can then do
>
>  CL <- contourLines(x,y,z)
>
> and get a list of contour-lines, each list containing the
> x and y coordinates.
>
> When I look at the plot from contour(x,y,z), I see that the
> lines are (as expected) made up of straight-line segments.
> But the break-points between the segments seem to either have
> x-coords on the x-values in x, or have y-coords on the y-values
> in y. In other words, the breaks occur on the sides of the
> squares of the grid defined by x and y.
>
> So quite often the straight-line segments are quite long, and
> the resulting contours do not look at all smooth.
>
> An example of what I'm talking about can be seen from the
> following code:
>
>  n2 <- function(x,y){
>    dnorm(x,0.25,0.3)*dnorm(y,0.25,0.3) +
>    dnorm(x,0.75,0.3)*dnorm(y,0.75,0.3)
>    }
>
>  x <- y <- 0.1*(0:10)
>  z <- matrix(numeric(121),nrow=11)
>  for(i in (0:11)){ for(j in (1:11)){ z[i,j]<-n2(x[i],y[j]) } }
>
>  contour(x,y,z,nlevels=10)

Also, consider this Thin plate spline solution from Bill Dunlap  
earlier this year:

library(fields)
xy<-as.matrix(expand.grid(x=x,y=y))
contour(predict.surface(Tps(as.matrix(expand.grid(x=x, y=y)),  
as.vector(z) )))

-- 
David Winsemius

>  for(i in (1:11)) lines(c(x[i],x[i]),c(0,1))
>  for(i in (1:11)) lines(c(0,1),c(y[i],y[i]))
>
> I could get whatever minute difference between contour-levels
> I like by setting the nlevels or levels parameter. But there
> doesn't seem to be any way of achieving finer resolution in
> where the break-points occur. It is just as coarse, and always
> breaks on the grid-lines.
>
> Looking at the plot, it seems that this is due to an algorithm
> which linearly interpolates along the sides of the grid squares,
> and joins the resulting points by line segments.
>
> It seems that contourLines() generates the same breakpoints as
> occur in the plot from contour().
>
> I would be happy with the relatively few contour lines and the
> fairly coarse spacing between contour levels shown in the above
> plot, but would like to have smoother contours without having to
> use denser grid spacing such as
>
>  x <- y <- 0.005*(0:200)
>  z <- matrix(numeric(40401),nrow=201)
>  #etc
>
> Is there a function which, perhaps, produces contours by non-linear
> interpolation, and curved smoothing between interpolated points,
> to a specified resolution between break-points?
>
> I have had a poke under "functions" in the R-Site Help and Archive
> Search at http://finzi.psych.upenn.edu, searching on "contour",
> but nothing has leapt obviously to the eye amongst the 494 hits.
>
> With thanks,
> Ted.
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 13-Sep-09                                       Time: 23:49:06
> ------------------------------ XFMail ------------------------------
-- 
David Winsemius, MD
Heritage Laboratories
West Hartford, CT