
Hi,
I'm quite happy to find a library like this, providing a nice pack of functionality.
As I'm working in VB2008 and the examples are C++ or C# it is a bit troublesome to find the right entrance. May I ask for an example how to use UncertainMeasurementSample.FitToFunction properly in order to find a circle (X0, Y0, R) which fits to
a number of X,Y points?
It would be very helpful, thank you in advance!
Werner



Hi Werner,
There isn't a builtin function to do this, but it easy to do by defining a metric and adjusting the circle parameters to minimize it using FunctionMath.FindMinimum. Here is some example code:
' Define our test points
' These are some points on the circle with center (1, 3) and radius 5
Dim x = New Double() {1, 4, 5, 6, 5}
Dim y = New Double() {8, 7, 6, 3, 0}
' Computes the total squared distance of our test points
' from the circle with center at a(0), a(1) and radius a(2)
Function TotalSquaredDistance(a As Double()) As Double
Dim s As Double = 0.0
For i As Integer = 0 To 4
Dim dx As Double = x(i)  a(0)
Dim dy As Double = y(i)  a(1)
Dim d As Double = MoreMath.Hypot(dx, dy)
s = s + MoreMath.Pow(d  a(2), 2)
Next
Return s
End Function
Sub FitToCircle()
' Make an initial guess at center and radius parameters
Dim a = New Double() {0, 1, 2}
' Adjust parameters to minimize the total squared distance function
Dim result As SpaceExtremum = FunctionMath.FindMinimum(AddressOf TotalSquaredDistance, a)
' Report the parameters that mimimize the function; these are our bestfit parameters
Dim b As Double() = result.Location
Console.WriteLine("(x, y) = ({0}, {1}) R = {2}", b(0), b(1), b(2))
End Sub
BY the way, by differentiating the metric function wrt R, you can find an analytic expression for the bestfit R in terms of just the center parameters and the data. That allows you to further reduce a 3parameter minimization problem to a 2parameter minimization
problem.


Jul 16, 2013 at 2:53 PM
Edited Jul 16, 2013 at 3:35 PM

Hi,
great, hat's exactly what I am looking for.
Unfortunately I need to use c# and have some trouble expressing
"Function TotalSquaredDistance(a As Double()) As Double"
using Linq in order to pass it to FunctionMath.FindMinimum() Method.
I couldnt find any Examples concernig that.
May I please ask for a hint how to translate the example to c# or where I can find a c# example using FindMinimum()?
Thanks and best regards,
Martin



To answer my own question (hope it may be useful to others):
// some points to fit
double[,] sampleData = { { 1, 8 }, { 4, 7 }, { 5, 6 }, { 6, 3 }, { 5, 0 } };
// ' Make an initial guess at center and radius parameters
var initialGuess = new double[] { 0, 1, 2 };
FitToCircle(sampleData, initialGuess);
private static void FitToCircle(double[,] xy, double[] initialGuess)
{
var circle = FunctionMath.FindMinimum(
(double[] a) =>
{
Double s = 0.0;
int length = xy.GetLength(0);
for (int i = 0; i < length; i++)
{
Double dx = xy[i, 0]  a[0];
Double dy = xy[i, 1]  a[1];
Double d = Math.Sqrt(Math.Pow(dx, 2) + Math.Pow(dy, 2));
s = s + Math.Pow(d  a[2], 2);
}
return s;
}, initialGuess
);
}

