# [R] Fitting a half-ellipse curve

From: Niklaus Hurlimann <niklaus.hurlimann_at_unil.ch>
Date: Wed, 29 Sep 2010 15:45:24 +0200

Dear mailing list,

I have following array:

```       X2                 Y2

[1,] 422.7900      6.0
[2,] 469.8007      10.5
[3,] 483.9428      11.0
[4,] 532.4917      25.5
[5,] 596.1942      33.5
[6,] 630.8496      40.5
[7,] 733.2996      45.0
[8,] 946.4779      32.0
[9,] 996.8068      35.5

```
[10,] 1074.3310 23.0

I do afterwards the following:

plot.new()

plot.window(xlim=c(min(X1)-50,max(X1)+50), ylim=c(min(Y1)-25,max(Y1)+25))

axis(2, cex.axis=1.2)
axis(1, cex.axis=1.2)

points(X2, Y2, type="p", pch=0, cex=1.2, col="black")

```title(main="Dyke Geometry Along Strike", cex.main=1.2, font.main=4)
title(xlab="distance [m]", cex.lab=1.2)
title(ylab="half-thickness [m]", cex.lab=1.2)

```

box()

I would like curve fitting where I proceeded with a non linear-regression with the according function below:

nls(formula = Y2 ~ abs(b*abs(1-X2^2/a^2)^(1/2)), start = list( a=282, b=40))

The formula should give the y-positive part of an ellipse in my opinion or I might be completely wrong.

In the end I would like to fit a curve of half an ellipse through the data. I might could do this as well with a 2nd order polynomial fit. I am grateful for any suggestions and comments to my problem.

Cheers

```--
Niklaus Hürlimann
Doctorant-PhD

Université de Lausanne
Institut de Minéralogie et Géochimie
L'Anthropole
CH-1015 Lausanne
Suisse

E-mail: Niklaus.Hurlimann_at_unil.ch
Tel:+41(0)21 692 4452

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