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From: =?UTF-8?Q?Hans-Bernhard_Br=c3=b6ker?= <HBBroeker@t-online.de>
Newsgroups: comp.graphics.apps.gnuplot
Subject: Re: gnuplot (fitting of ellipse)
Date: Sat, 25 Mar 2017 14:22:54 +0100
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Am 25.03.2017 um 01:55 schrieb vineeth25396@gmail.com:

> The reason why I use the
> formula cause I have a C++ code that gives the co-efficient of the
> ellipse in form of a,b,c,d,e,f. And I want to see if the co-efficents
> are matching. The link below will make more sense
> https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections

A large part of the problem with your description, and of the cause for 
the failures you've run across is sloppy use of terminology.

The equation you started out with isn't that of an ellipse.  It's not 
even really an equation.  It's the definition of a quadratic function of 
two variables.

What you're talking about is the implicit equation for an ellipse made 
by that function, by convention:

	f(x,y) = 0

gnuplot doesn't plot implicit equations just like that.  You have to 
plot intersection of the surface made up by points

	< x,y,f(x,y) >

with the implicit surface z=0.  As this is about surfaces, you have to 
use splot for this, plot.  Then see "help contour" about how to get just 
the intersection curve.

Or you could apply the math of conic sections to transform your 
impliciat equation into the explicit form of the elleipse, i.e. two new 
functions, x(t) and y(t) that trace the ellipse.  Written as 2D vectors, 
that explicit form will be of the general form

	X = X_0 + A * cos(t) + B * sin(t)  | t = 0 ... 2*pi

where vectors A and B are orthogonal to each other.  gnuplot can plot 
that in parametric mode.