[R] Fit a smooth closed shape through 4 points

[Thierry Onkelinx]

Dear Allie,

You could use elliptic fourier analysis

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")

shapepoints$Theta <- seq(0, 2 * pi, length = nrow(shapepoints))
model <- lm(cbind(x, y) ~ I(sin(Theta)) + I(cos(Theta)), data = shapepoints)
model2 <- lm(cbind(x, y) ~ I(sin(Theta)) + I(cos(Theta)) + I(sin(2 *
Theta)) + I(cos(2 * Theta)), data = shapepoints)

newdata <- data.frame(Theta = seq(0, 2 * pi, length = 41))
plot(predict(model, newdata = newdata), type = "l", xlim = c(-10, 10), ylim
= c(-10, 10))
points(shapepoints, col = "red")
plot(predict(model2, newdata = newdata), type = "l", xlim = c(-10, 10),
ylim = c(-10, 10))
points(shapepoints, col = "red")

Best regards,

Thierry

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

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2016-03-21 15:04 GMT+01:00 Alexander Shenkin <ashenkin op ufl.edu>:

> 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 op ufl.edu
>> <mailto:ashenkin op 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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