Ok, I cannot assist you with shapes/drawing/geometric figures. I'm horrible with art and not much of a web/artistic designer.

If you did want an engine built that figures distances, or loops through possible combinations of points, I can do that.

If that doesn't help your cause, I understand. Reading what you just described, a java based calculator with a program that can build shapes and 3D-animation would be the way to go.

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Oh, I forgot to answer that question:

No, I am not at all interested in any graphics stuff! I just want the parameters for the ellipses. 5 numbers for each one of them.

I just drew those figures now in order to help explain the mathematical problem. That red-green-blue thing maybe was confusing. I did it just to explain that for each of the ellipse halves (the colored ones) there belongs a certain set of points. The points and ellipses and circles actually have no colors. They are just mathematical abstractions. The points are randomly distributed around each of their ellipse (half).
This part I don't understand. But it doesn't sound like anything I am interested in!

Please, before you put any work into this, please clear things out with me. It is so easy to misunderstand, especially since I am not used to strict mathematical language.

I want to put in 2D coordinates for two or three sets of points, together with radii and distances defining the circles' relations to each other, and get back the ellipse parameters that fits it best according to least square or something like that.

I guess one makes an initial guess for parameters of one of the ellipses, then uses the geometry of the circles to calculate which parameter this implies for the other ellispes. Then one calculates the fit (least square or something like that). Then iterates and refits until the fit is good enough. From the geometry of it, one needs to formulate some optimization function which hopefully can have its derivatives solved so that an efficient numerical method can be applied.

There is a duality between the 2D projection, where there exists ellipses and points; and the 3D physical world, where there exists circles. A certain angle in the 3D world, corresponds to the length of an ellipse axis in the 2D projection.

I'll think it through and make a better attempt at explaining things tomorrow.

I attached a shell program for you. It has 2 points you enter, radius lengths, and a filler loop program when you press the button.

It sounds like what you want to do is guess through scenarios until you meet a fit with the ellipses/circles.

If this is what you want, please supply me the equations for what you want to check.

Attached Files

Dirlewanger.xls (23.0 KB, 21 views)

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Well, I want a numerical method to efficiently find a good enough fit of ellispes to points. Much like this code does in Matlab:
MATLAB Central File Exchange - fit_ellipse
But for multiple related ellipses at once.

I'll solve the geometry and provide the equations, yes!

I see, you need 7 entry points, a,b,c,d,e and a 2D point. But you want to fit more than 1 ellipse at once. Got it.

Let's talk tomorrow when you are back online.

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You should be aware that if this is done in Matlab it will probably use a library
optimiser, and so not easily translated into another language. Though You
could probably produce something that could be called from another language
using the compiler.

RonL

But I can compile Matlab code and run it as a free standing program, right? If I get VBA source code that solves the problem, I'll look at it and try to write M-code that does the same thing.

I am on the way to formulate the restrictions which connect the ellipses which I want to fit simultaneously. Now I stumble on a part of that problem. Please consider this problem in isolation, which certainly must have a solution:


(Let C be the origo of a 3D coordinate system.)

V is constrained to the big circle with center M and known radius R = MB = MS = MV.
A is constrained to the small circle with center C and known radius r = CS = CA.
E is the intersection of lines CS and VB.
Angle AVE is known
What are the coordinates of point V?

M, C and B lie on a straight line.
Distances MC and CB are known.
Big circle and small circle intersect in point S (and a corresponing point one diameter away).
Big circle and small circle stand at a right angle to each other (angle MCS = pi/2).
Angle AEC = AES = AEV = pi/2.

The complication is, that as V is moved around its big circle, then not only does the distance VE change, but so does the distance AE too! For example, if V is placed in line with BCM, then AE = radius of the small circle.

Can someone crack the algebra of it? Or else I have to use a numerical method to find the coordinates of V, which must be done (twice) inside the iteration loop of the larger multi-ellipse fitting problem.

Dirlewanger,

I'm at work now, but I'll take a look at this during the week and see what I can do on Excel/VBA. I'll check back periodically to see if anybody else has answered this as well.

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