Help for Excel Solver on a ellipse fit problem [URGENT]

[Corsa88]

Greetings guys

I have a set of scatter data x and y

x	y
0	0.0947
1	0.3099
2	0.6277
3	1.0481
4	1.5711
5	2.1967
6	2.9249
7	3.7557
8	4.6891
9	5.7251

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</tbody>

What I'm trying to do is to fit an ellipse through this data.

My approach is first to use the algebraic equation for an ellipse:

ax² + bxy + cy² + dx + ey + f = 0

I then created one additional column that allows me to compute the value of the ellipse equation for each pair of (x,y) coordinate. Also I assigned cells for the parameters in the ellipse equation: a, b, c, d, e, f

Then, to obtain the ellipse fit (which meant that I had to find the values of a,b,c,d,e,f which gave ellipse equation values = 0 for every pair of (x,y) point), what I did was to use the Solver feature in Excel:

such that:

Objective : Ellipse_equation value for first pair of (x,y) point = 0

While changing: a, b, c, d, e, f

Constraints: Ellipse_equation value for each and other pairs of (x,y) points = 0

However, the outcome of this process simply led the values of a,b,c,d,e,f = 0. I know this satisfies the condition, but it doesn't define an ellipse.

Anyone know what should I include in or edit the approach that I'm taking for this problem? Have been tearing out my hair in frustration on this one.

Thanks to everybody in advance. Would really appreciate your advice.

Thanks and regards
Corse

 

[shg]

... then rotate, then translate again, then rotate, then scale.

Delete that second rotation.

 

[Corsa88]

I'll put the current workbook up at the same link in a minute, and let you soldier on.

EDIT: Done.

For the Forward Transform =MMULT(MMULT(B22:D24, B27:D29), B32:D34) -> does this mean a rotation,translation and followed by a scaling operation?

So if I need to translate the point of pivot to the origin, would it imply that I would set dX =0, dY = 0?

 

[shg]

=MMULT(MMULT(B22:D24, B27:D29), B32:D34)

The resulting matrix performs the operations in the order in which they appear.

So if I need to translate the point of pivot to the origin, would it imply that I would set dX =0, dY = 0?

No, that doesn't do anything. If you want to move the point {x,y} to the origin, the translation is {-x,-y}

 

[Corsa88]

=MMULT(MMULT(B22:D24, B27:D29), B32:D34)

The resulting matrix performs the operations in the order in which they appear.


No, that doesn't do anything. If you want to move the point {x,y} to the origin, the translation is {-x,-y}

Oh i see, so i can manually override the translation parameters in that case. I'll try that to see if it would be able to define the best fit ellipse pivot point.