[R] Fit a smooth closed shape through 4 points

[Paul Murrell]

Hi

If Xsplines give you the shape you want, then you can retrieve points on 
the boundary of the shape using xsplinePoints().  For example ...

shapepoints <- structure(list(x = c(8.9, 0, -7.7, 0, 8.9),
                               y = c(0, 2, 0, -3.8, 0)),
                          .Names = c("x", "y"),
                          row.names = c(NA, -5L),
                          class = "data.frame")

library(grid)
grid.newpage()
pushViewport(dataViewport(shapepoints[,1], shapepoints[,2]))
grid.points(shapepoints[,1], shapepoints[,2], default.units="native")
grid.xspline(shapepoints[-1,1], shapepoints[-1,2],
              default.units="native", shape=-1, open=FALSE)

xsg <- xsplineGrob(shapepoints[-1,1], shapepoints[-1,2],
                    default.units="native", shape=-1, open=FALSE)
# THIS is the information I think you want
trace <- xsplinePoints(xsg)
grid.points(trace$x, trace$y, default.units="native",
             size=unit(1, "mm"), pch=16)

Paul

On 22/03/16 03:04, Alexander Shenkin wrote:
> Thanks for your reply, Charles.  spline() doesn't seem to fit a closed
> shape; rather, it's producing a parabola.  Perhaps I'm missing an
> argument I should include?
>
> grid.xspline() seems to get close to what I need, but it returns a grob
> object - not sure how to work with those as shapes per se.
>
> My goal is to produce a 2D shape from which I can calculate area,
> average widths, and other such things.  The context is that we have
> measured tree crowns in a manner that has produced 4 points such as
> these from two offset axes.  We want to use the resulting shapes for our
> calculations.
>
> (incidentally, my original points were off - here are the correct ones)
>
> shapepoints = structure(list(x = c(8.9, 0, -7.7, 0, 8.9), y = c(0, 2, 0,
> -3.8,
> 0)), .Names = c("x", "y"), row.names = c(NA, -5L), class = "data.frame")
>
> plot(spline(shapepoints))
>
> Thanks,
> Allie
>
> On 3/21/2016 1:10 PM, Charles Determan wrote:
>> Hi Allie,
>>
>> What is you goal here?  Do you just want to plot a curve to the data?
>> Do you want a function to approximate the data?
>>
>> You may find the functions spline() and splinefun() useful.
>>
>> Quick point though, with so few points you are only going to get a very
>> rough approximation no matter the method used.
>>
>> Regards,
>> Charles
>>
>>
>> On Mon, Mar 21, 2016 at 7:59 AM, Alexander Shenkin <ashenkin at ufl.edu
>> <mailto:ashenkin at ufl.edu>> wrote:
>>
>>     Hello all,
>>
>>     I have sets of 4 x/y points through which I would like to fit
>>     closed, smoothed shapes that go through those 4 points exactly.
>>     smooth.spline doesn't like my data, since there are only 3 unique x
>>     points, and even then, i'm not sure smooth.spline likes making
>>     closed shapes.
>>
>>     Might anyone else have suggestions for fitting algorithms I could
>>     employ?
>>
>>     Thanks,
>>     Allie
>>
>>
>>     shapepoints = structure(c(8.9, 0, -7.7, 0, 0, 2, 0, 3.8), .Dim =
>> c(4L,
>>     2L), .Dimnames = list(NULL, c("x", "y")))
>>
>>     smooth.spline(shapepoints)
>>
>>     # repeat the first point to close the shape
>>     shapepoints = rbind(shapepoints, shapepoints[1,])
>>
>>     smooth.spline(shapepoints)
>>
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>>
>>
>
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.

-- 
Dr Paul Murrell
Department of Statistics
The University of Auckland
Private Bag 92019
Auckland
New Zealand
64 9 3737599 x85392
paul at stat.auckland.ac.nz
http://www.stat.auckland.ac.nz/~paul/