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How to plot an Ellipse

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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
muhammad  arfan
muhammad arfan on 18 Jun 2019
dears!!!
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.
thanks
arfan khan
clc;
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;
disp('f');
disp(f);
end
% plot(f,'or')
plot(x,y, '*b');
x=((x(i)-x0)*cos(z)) - ((y(i)-y0)*sin(z))
y=(x(i)-x0)*sin(z)-(y(i)-y0)*cos(z)
xa(i)=rand(1)
x(i)= a+(b-a)*rand(1);
y(i)= rand(1);
for
m(i) = ((((x).^2)/a^2) + (((y).^2)/b^2)-1).^2
end
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);
plot(x,y,'y-')
axis equal
  10 Comments
Image Analyst
Image Analyst on 7 Jul 2020
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
y0=0;
t=-pi:0.01:pi;
x=x0+a*cos(t);
y=y0+b*sin(t);
plot(x,y)
  3 Comments
Sandy M
Sandy M on 27 Jul 2019
Hi, I do my ellipse graph
A=10;
B=7.5;
X=-10:.1:10;
Y=(7.5/10)*(1-x^2)^(1/2)
z=-(7.5/10)*(1-x^2)^(1/2)
Plot(x,y,x,z)
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
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?
  4 Comments
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
Ellipse2d
  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 https://www.mathworks.com/help/symbolic/mupad_ref/plot-ellipse2d.html 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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