R help - Feb 2003 - How to calculate the closest distance from a point to a curve?

Hely, R-list

Now I have non-parametric curve function, that is,
I only use N 2-Dimensional data points to represent
this curve, without explicit function formulation.

And given a new measurement (x1,x)', how can I calculate the shortese
Euclidean distance from this new
data point to the above curve?

Thanks a lot.

Fred

>Hely, R-list
>
>Now I have non-parametric curve function, that is,
>I only use N 2-Dimensional data points to represent
>this curve, without explicit function formulation.
>
(x,y) gives the points that define the curve (I've generated a circle 
centered at 0)
(a,b) is the point (I've set it to (2,2))

x<-seq(from=-1,to=+1,length=1000)
y<-sqrt(1-x^2)
x<-c(x,x)
y<-c(y,-y)
n<-length(x)
a<-2
b<-2

The code to find the closest point to (a,b) is:

minimo<-min((1:n)[sqrt((a-x)^2+(b-y)^2)==min(sqrt((a-x)^2+(b-y)^2))])
cat(x[minimo],y[minimo],"\n")

0.7077077 0.7065053 

Regards
Jose Lozano