MATLAB Answers

How to plot an Ellipse

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Dimitris Arapidis
Dimitris Arapidis on 8 Sep 2013
Commented: Image Analyst on 7 Jul 2020 at 15:03
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.

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muhammad  arfan
muhammad arfan on 18 Jun 2019
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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Accepted Answer

Roger Stafford
Roger Stafford on 8 Sep 2013
Edited: Cris LaPierre on 5 Apr 2019
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


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Kaleesh Bala
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
Walter Roberson on 27 Jul 2018
The foci are not enough information to determine the ellipse.
Image Analyst
Image Analyst on 7 Jul 2020 at 15:03
Here's a full demo:
% Define parameters.
fontSize = 15;
x1 = 1;
x2 = 20;
y1 = 2;
y2 = 8;
eccentricity = 0.85;
numPoints = 300; % Less for a coarser ellipse, more for a finer resolution.
% Make equations:
a = (1/2) * sqrt((x2 - x1) ^ 2 + (y2 - y1) ^ 2);
b = a * sqrt(1-eccentricity^2);
t = linspace(0, 2 * pi, numPoints); % Absolute angle parameter
X = a * cos(t);
Y = b * sin(t);
% Compute angles relative to (x1, y1).
angles = atan2(y2 - y1, x2 - x1);
x = (x1 + x2) / 2 + X * cos(angles) - Y * sin(angles);
y = (y1 + y2) / 2 + X * sin(angles) + Y * cos(angles);
% Plot the ellipse as a blue curve.
subplot(2, 1, 1);
plot(x,y,'b-', 'LineWidth', 2); % Plot ellipse
grid on;
axis equal
% Plot the two vertices with a red spot:
hold on;
plot(x1, y1, 'r.', 'MarkerSize', 25);
plot(x2, y2, 'r.', 'MarkerSize', 25);
caption = sprintf('Ellipse with vertices at (%.1f, %.1f) and (%.1f, %.1f)', x1, y1, x2, y2);
title(caption, 'FontSize', fontSize);
xlabel('x', 'FontSize', fontSize);
ylabel('y', 'FontSize', fontSize);
% Plot the x and y. x in blue and y in red.
subplot(2, 1, 2);
plot(t, x, 'b-', 'LineWidth', 2);
grid on;
hold on;
plot(t, y, 'r-', 'LineWidth', 2);
legend('x', 'y', 'Location', 'north');
title('x and y vs. t', 'FontSize', fontSize);
xlabel('t', 'FontSize', fontSize);
ylabel('x or y', 'FontSize', fontSize);
% Set up figure
g = gcf;
g.WindowState = 'maximized';
g.NumberTitle = 'off';
g.Name = 'Ellipse Demo by Roger Stafford and Image Analyst'

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More Answers (3)

Azzi Abdelmalek
Azzi Abdelmalek on 8 Sep 2013
Edited: Azzi Abdelmalek on 12 Jun 2015
a=5; % horizontal radius
b=10; % vertical radius
x0=0; % x0,y0 ellipse centre coordinates


Ivailo Ivanov
Ivailo Ivanov on 14 Jan 2016
It was very simple and comprehensible.
Cynthia Dickerson
Cynthia Dickerson on 27 Jun 2018
Thanks! This code worked for me perfectly. :)
Sandy M
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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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
Image Analyst on 25 Feb 2014
Perhaps of some interest, if you need to find the ellipse points:
Devi Satya Cheerla
Devi Satya Cheerla on 12 Jun 2015
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
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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Omar Maaroof
Omar Maaroof on 13 May 2019
you can use

  1 Comment

Walter Roberson
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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