MATLAB Answers


How to plot an Ellipse

Asked by Dimitris Arapidis on 8 Sep 2013
Latest activity Commented on by Sandy M
on 27 Jul 2019
I want to plot an Ellipse. I have the verticles for the major axis: d1(0,0.8736) d2(85.8024,1.2157) (The coordinates are taken from another part of code so the ellipse must be on the first quadrant of the x-y axis) I also want to be able to change the eccentricity of the ellipse.

  1 Comment

i have asigned to write a matlab code for 8 point to fit it in ellipse by using least square method..
i am new in using matlab and try my best but my points are not fit on ellipse. i use annealing method so that i have satisfied my teacher by my work. please chk my work and help me.
arfan khan
clear all;
close all;
r1 = rand(1);
r2 = [1+rand(1)]; % r2>r1
x0 = 0;
y0 = 0;
N = 8;
n= 100;
x1 = 1;
x2 = 2;
y1 = 1;
y2 = 2;
for i = 1:n
x = x1 +(x2-x1).*rand(N,1);
y = y1 +(y2-y1).*rand(N,1);
f = ((((x./r1).^2) +(y./r2).^2)-1).^2;
[m,l] = min(f);
z =.001* exp(10*(1-i/n));
v = z/2;
% disp('v');
% disp(v)
x1 = x(l)*v;
x2 = x(l)*v;
% disp('x1')
% disp(x1)
% disp('x2')
% disp(x2)
% ay = v./y(l);
% by = v./y(l);
% disp(v);
% % hold on;
% plot(f,'or')
plot(x,y, '*b');
x=((x(i)-x0)*cos(z)) - ((y(i)-y0)*sin(z))
x(i)= a+(b-a)*rand(1);
y(i)= rand(1);
m(i) = ((((x).^2)/a^2) + (((y).^2)/b^2)-1).^2
hold on;

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4 Answers

Answer by Roger Stafford on 8 Sep 2013
Edited by Cris LaPierre
on 5 Apr 2019
 Accepted Answer

Let (x1,y1) and (x2,y2) be the coordinates of the two vertices of the ellipse's major axis, and let e be its eccentricity.
a = 1/2*sqrt((x2-x1)^2+(y2-y1)^2);
b = a*sqrt(1-e^2);
t = linspace(0,2*pi);
X = a*cos(t);
Y = b*sin(t);
w = atan2(y2-y1,x2-x1);
x = (x1+x2)/2 + X*cos(w) - Y*sin(w);
y = (y1+y2)/2 + X*sin(w) + Y*cos(w);
axis equal


Walter Roberson
on 26 Jul 2018
If you already have the minor axis length then you can use that directly in b. If you do not have the minor axis length then you need to calculate it, and you need the information to calculate it; the main other way of characterizing it is to specify the eccentricity. If you do not know the minor axis length and you do not know the eccentricity, then what do you know?
Kaleesh Bala on 27 Jul 2018
ok fine let me put it in parametric type having two foci as x1 y1, x2 y2
determining r1,r2 to get the elliptical form? I think from r1 can get r2.
So how to determine r1.
xt = r1 * cos(t) + xc;
yt = r2 * sin(t) + yc;
Walter Roberson
on 27 Jul 2018
The foci are not enough information to determine the ellipse.

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Azzi Abdelmalek
Answer by Azzi Abdelmalek
on 8 Sep 2013
Edited by Azzi Abdelmalek
on 12 Jun 2015

a=5; % horizontal radius
b=10; % vertical radius
x0=0; % x0,y0 ellipse centre coordinates


It was very simple and comprehensible.
Thanks! This code worked for me perfectly. :)
Sandy M
on 27 Jul 2019
Hi, I do my ellipse graph
Its ok but i need it in cm units cause if i change properties of figure and paper to cm i get deference’s about 3 or 5 mm How can I justify the unit

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Answer by Kate
on 24 Feb 2014

how would you plot a ellipse with only knowing some co-ordinates on the curve and not knowing the y radius and x radius?


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Image Analyst
on 25 Feb 2014
Perhaps of some interest, if you need to find the ellipse points:
in the equation of ellipse X2/a2 + Y2/b2 = 1. knowing the points on ellipse, can find a and b. then enter the code below to mathematically compute y and to plot x,y.
x=(0:.01:a); # x value is from 0 to 'a' and discrete with 0.01 scale#
i=1:(a*100+1); # i is to calculate y at every discrete value. it should be for 1 i.e first x value to the last x value.. as it does not have a zero, add 1#
clear y # to clear any previous y value#
for i=1:(a*100+1)
y(i)=(b^2*(1-(x(i)^2)/a^2))^.5; #from the ellipse equation y=sqrt(b2(1-(x2/a2))#
hold on
hold on
hold on
Sandy M
on 27 Jul 2019
hi why u product the nmber with 100?
and, if i want the graph with cm units, what i do? cause i change garaph and paper properties but i still defreces about 4 mm when i prented it

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Answer by Omar Maaroof on 13 May 2019

you can use

  1 Comment

Walter Roberson
on 13 May 2019
MATLAB does not offer Ellipse2d plotting directly. Instead, the Symbolic Toolbox's engine, MuPAD, offers plot::Ellipse2d which can only be used from within a MuPAD notebook . R2018b was intended to be the last release that included the MuPAD notebook, but it was carried on to R2019a as well.

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