# Ellipse fitting

Hallo,

I am investigating the JUniForm module of JAG3D, specifically the ellipse fitting function. Without more detailed descriptions I cannot understand the equation given under Properties > Feature. What approach/equation is the least square fit of an ellipse based on? Can you refer me to any relevant literature?

I would very much appreciate if you took the time to read and answer my question.

Thank you,
Antonio

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## Ellipse fitting

Hello Antonio,

What approach/equation is the least square fit of an ellipse based on? Can you refer me to any relevant literature?

Using 2D or 3D data?

Kind regards
Micha

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Using 2D data.

Kindly,
Antonio

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## Ellipse fitting

Hello,

the equation is given by

$\sum_{j=1}^2 s_j = 2a$

where

$s_j = |P_i - F_j|$

is the distance between the i-th point and the j-th focal point. Parameter a denotes the major semi-axis.

This model is also valid for the spatial case, cf. Lösler, M. and Nitschke, M., 2010. Bestimmung der Parameter einer Regressionsellipse in allgemeiner Raumlage. Allgemeine Vermessungs-Nachrichten, Vol. 117(3), pp. 113-117

and can be used to parametrize an elliptical cylinder, cf. Lösler, M. 2020. Modellierung und Bestimmung eines elliptischen Zylinders. Allgemeine Vermessungs-Nachrichten, Vol. 127(2), pp. 87-93

Kind regards
Micha

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Tags:
Ellipse, Fitting, Curve, JuniForm

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## Ellipse fitting

Micha,

the attached literature gives me all the answers.
Thank you for your help and responsiveness.

Antonio