[R] computing the radius of an arc

[Nair, Murlidharan T]

Thanks, for all the suggestions. Indeed I am interested in computing curvature (http://en.wikipedia.org/wiki/Curvature) of the curve that is given as a discrete set of points. I have the curve in 3D but I can certainly write it in 2D as well. Code is given at the bottom. I will try with the suggestions you have given, but if anyone has done this before, I would appreciate your help.
Cheers../Murli

#Here is a sample set of points I have
#==================================================
crv.data<-structure(list(x = c(0, -0.0306853139578441, -0.276628790412316,
-0.859263925181012, -1.62257352572431, -2.54180446175123, -3.58311939939041,
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153.181154659904, 151.187404301975, 149.102695344265)), .Names = c("x",
"y", "z"), row.names = c(NA, -250L), class = "data.frame")

angle<- 26.565 #degrees
angle<-angle*pi/180
proj2D.x<- (crv.data$x -crv.data$z)*cos(angle)
proj2D.y<-(crv.data$y +crv.data$x+crv.data$z) *sin(0.46365)
proj2d.xy<-cbind(proj2D.x,proj2D.y)
colnames(proj2d.xy)<-c("x","y")

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Hans W Borchers
Sent: Friday, July 24, 2009 5:41 AM
To: r-help at stat.math.ethz.ch
Subject: Re: [R] computing the radius of an arc

Nair, Murlidharan T <mnair <at> iusb.edu> writes:

>
> Hi!!
>
> I am interesting in computing the radius of an arc that best approximates
> a curve. Is there an R function that I can use to draw an arc?
> Nothing useful came up when I searched help.search.  Does anyone have any
> suggestion to do this?
> Thanks ../Murli
>

If you are looking for some formulas to calculate the center and radius
of such a circle/arc, search for 'curvature' in Wikipedia or MathWorld.
Formulas are a bit involved, and you will need to be able to compute
first and second derivatives of the curve.

In case the curve is given as a set of discrete points, you could apply
some polynomial, spline, etc., interpolation.

If you _then_ apply 'draw.arc', watch out to set the aspect ratio to 1,
otherwise your circle may appear to be incorrect.

    library(plotrix)
    curve(sin(x), 0, pi, col="blue", asp=1)
    draw.arc(pi/2, 0, 1, deg1=45, deg2=135, col="red")

Physical meaning of the curvature (and thus the approximation) is that
an observer moving on the curve will feel the same centrifugal forces
as if moving on the circle, at that moment.

Regards
Hans Werner

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