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I am trying to plot a circle's equation-regression on x and y, but I do not know how to proceed. Any suggestions? (I want a circle to connect the points thru least square solution)
x = [5; 4; -1; 1];
y = [3; 5; 2; 1];
% circle's equation: x^2+y^2 = 2xc1+2yc2+c3
a = [2.*x,2.*y,ones(n,3)]
b = [x.^2 + y.^2];
c = a\b;
How do I plot the circle after this
There are a couple of ways how to plot a circle in matlab:
plot a line where the data points form a circle
use the 'o' marker in plot and the 'MarkerSize' name-value pair to set the radius of the circle
you can plot a circle image using the vscircle function
In your case, I would go with the first option, since you maintain in control of the circle size.
use the rectangle(...,'Curvature',[1 1]) function [EDITED: thx to #Cris Luengo]
So here is a plotting function
function circle(x,y,r)
%x and y are the coordinates of the center of the circle
%r is the radius of the circle
%0.01 is the angle step, bigger values will draw the circle faster but
%you might notice imperfections (not very smooth)
ang=0:0.01:2*pi+.01;
xp=r*cos(ang);
yp=r*sin(ang);
plot(x+xp,y+yp);
end
So with your (corrected) code, it looks like this
x = [5; 4; -1; 1];
y = [3; 5; 2; 1];
% circle's equation: x^2+y^2 = 2xc1+2yc2+c3
a = [2.*x,2.*y,ones(length(x),1)];
b = [x.^2 + y.^2];
c = a\b;
x_m = c(1)/2;
y_m = c(2)/2;
r = sqrt(x_m^2 + y_m^2 -c(3));
% plot data points
plot(x,y,'o')
hold on
% plot center
plot(x_m,y_m,'+')
% plot circle
circle(x_m,y_m,r)
hold off
The below code plots circles in Matlab. How can I specify the MarkerEdgeColor and MarkerFaceColor in it.
function plot_model
exit_agents=csvread('C:\Users\sony\Desktop\latest_mixed_crowds\December\exit_agents.csv');
%scatter(exit_agents(:,2),exit_agents(:,3),pi*.25^2,'filled');
for ii =1:size(exit_agents,1),
circle(exit_agents(ii,2),exit_agents(ii,3),0.25);
end
end
function h = circle(x,y,r)
hold on
th = 0:pi/50:2*pi;
xunit = r * cos(th) + x;
yunit = r * sin(th) + y;
h = plot(xunit, yunit);
hold off
end
Using plot and scatter scales them weirdly when zooming. This is not what I wish for.
There are various options to plot circles. The easiest is, to actually plot a filled rectangle with full curvature:
%// radius
r = 2;
%// center
c = [3 3];
pos = [c-r 2*r 2*r];
r = rectangle('Position',pos,'Curvature',[1 1], 'FaceColor', 'red', 'Edgecolor','none')
axis equal
With the update of the graphics engine with R2014b this is really smooth:
If you have an older version of Matlab than R2014b, you will need to stick with your trigonometric approach, but use fill to get it filled:
%// radius
r = 2;
%// center
c = [3 3];
%// number of points
n = 1000;
%// running variable
t = linspace(0,2*pi,n);
x = c(1) + r*sin(t);
y = c(2) + r*cos(t);
%// draw filled polygon
fill(x,y,[1,1,1],'FaceColor','red','EdgeColor','none')
axis equal
The "resolution" can be freely scaled by the number of points n.
Your function could then look like
function h = circle(x,y,r,MarkerFaceColor,MarkerEdgeColor)
hold on
c = [x y];
pos = [c-r 2*r 2*r];
r = rectangle('Position',pos,'Curvature',[1 1], ...
'FaceColor', MarkerFaceColor, 'Edgecolor',MarkerEdgeColor)
hold off
end
In the code below, I am attempting to move a ball from 90 degrees to 44 degrees and back to 90 degrees. I wanted to be able to track the position of the ball's center point. I am trying to do this by plotting a marker that follows the ball. I would also like to keep seeing the (x,y) position of the ball being updated as the ball moves.
Can you help me modify my code so that:
1. The marker remains in the center of the ball, and
2. Keep displaying the (x,y) position of the marker (ball's center) as it moves?
Here is what I have done so far:
close all; clc; clear;
% Define position of arm
theta=0:10:360; %theta is spaced around a circle (0 to 360).
r=0.04; %The radius of our circle.
%Define a circular magenta patch.
x=r*cosd(theta) + 0.075;
y=r*sind(theta) + 1;
% Size figure and draw arms
figure('position', [800, 300, 600, 550]);
point = plot(0.075,1, 'bo', 'markers', 3);
hold on
myShape2=patch(x,y,'m');
set(myShape2,'Xdata',x,'Ydata',y);
axis([-1.5 3 -1 3]); grid on;
n = 1;
T=0.15; %Delay between images
for theta = pi/2:-pi/90:0,
if theta >= pi/4;
theta = theta;
else
theta = pi/2 - theta;
end
Arot = [sin(theta) cos(theta); -cos(theta) sin(theta)];
xyRot = Arot * [x; y]; % rotates the points by theta
xyTrans = xyRot;
point = plot(xyTrans(1, n),xyTrans(2, n), 'bo', 'markers', 3);
hold on;
set(myShape2,'Xdata',(xyTrans(1, :)),'Ydata',(xyTrans(2, :)));
pause(T); %Wait T seconds
end
Thanks for your time and help!
close all; clc; clear;
% Define position of arm
theta=0:10:360; %theta is spaced around a circle (0 to 360).
r=0.04; %The radius of our circle.
%Define a circular magenta patch.
x=r*cosd(theta) + 0.075;
y=r*sind(theta) + 1;
% Size figure and draw arms
figure('position', [800, 300, 600, 550]);
hold on
myShape2=patch(x,y,'m');
set(myShape2,'Xdata',x,'Ydata',y);
point = plot(0.075,1, 'bo', 'markers', 1);
dim = [.2 .5 .3 .3];
axis([-1.5 3 -1 3]); grid on;
T=0.15;
% Create annotation object to display object center
ano = annotation('textbox',dim,'String',['center position: (','0.075, 1'],'FitBoxToText','on');
for theta = pi/2:-pi/90:0,
if theta >= pi/4;
theta = theta;
else
theta = pi/2 - theta;
end
Arot = [sin(theta) cos(theta); -cos(theta) sin(theta)];
xyTrans = Arot * [x; y];
% Remove plot and annotation object from previous frame
delete(point)
delete(ano)
set(myShape2,'Xdata',(xyTrans(1, :)),'Ydata',(xyTrans(2, :)));
% Calculate the center of the patch as mean x and y position
x_pos = mean(xyTrans(1, :));
y_pos = mean(xyTrans(2, :));
point = plot(x_pos, y_pos, 'bo', 'markers', 1);
ano = annotation('textbox',dim,'String',['center position: (',sprintf('%0.3f', x_pos),', ',...
sprintf('%0.3f', y_pos),')'],'FitBoxToText','on');
axis([-1.5 3 -1 3]); grid on;
pause(T);
end
I'm doing a mathematical experiment in Matlab and the result should be a circle in the x,y-plane. But sometimes, the circle starts spiraling. I'm now trying to bend the x,y-plane into a cylinder (as in the following picture). At the moment I only have the x and y coordinates of the points.
I've tried converting them into polar coordinates and then use some 'surf' commando's, but nothing works right now
(source: wtcoeselgem.be)
Edit: I've used the plot3 command, as suggested by Ander Biguri, resulting in the following figure.
(source: wtcoeselgem.be)
I will consider that you have a curve defined by x and y coordinates which you want to fold around a cylinder.
%% // Generate sample data
x = linspace(0,10*pi) ;
y2 = cos(x) ;
y1 = 10*cos(x/10) ;
y = y1+y2 ; y = y-min(y) ;
figure, plot(x,y,'-o') ;
This produces:
Next I define a basic cylinder, nothing original:
%% // Basic cylinder (just for background)
[Xc,Yc,Zc] = cylinder(1,100);
Zc = Zc * max(y) ;
hs = surf(Xc,Yc,Zc) ;
set(hs,'FaceColor',[.8 .8 .8],'FaceAlpha',0.5,'EdgeColor','none') ;
hold on
And here comes the interesting bit:
%% // Fold the points around the cylinder
Number_of_turn = 2 ;
xrange = [min(x),max(x)] ;
xspan = xrange(2)-xrange(1) ;
xc = x / xspan * 2*pi * Number_of_turn ;
Xp = cos(xc) ;
Zp = y ;
Yp = sin(xc) ;
hp = plot3(Xp,Yp,Zp,'-ok') ;
Which render:
For this example I assumed you wanted to wrap your curve around "2 turns" of the cylinder. This is easily changed with the Number_of_turn variable.
Note that you can also change the radius of the cylinder by multiplying the Xp and Yp coordinates by your radius.
The following seems to do more or less what you want
%// Data
xmin = -3;
xmax = 3; %// this piece will get folded into a cylinder
Rc = 5; %// cylinder radius
zmaxc = 5; %// cylinder max z
zminc = -5; %// cylinder min z
%// Spiral
t = linspace(0,1,1000);
r = 1+2*t;
theta = 2*pi*3*t;
x1 = r.*cos(theta);
y1 = r.*sin(theta); %// example spiral. Defined by x1, y1
%// Do the bending
z2 = y1;
phi = (x1-xmin)/(xmax-xmin)*2*pi;
x2 = Rc*cos(phi);
y2 = Rc*sin(phi);
%// Plot cylinder
[xc yc zc] = cylinder(Rc*ones(1,100),100);
zc = zminc + (zmaxc-zminc)*zc;
surf(xc,yc,zc)
shading flat
hold on
%// Plot bent spiral
plot3(x2,y2,z2, 'k.-');
Original spiral:
Two views of the result:
How do I draw an ellipse and an ellipsoid using MATLAB?
(x^2/a^2)+(y^2/b^2)=1
n=40;
a=0; b=2*pi;
c=0; d=2*pi;
for i=1:n
u=a+(b-a)*(i-1)/(n-1);
for j=1:m
v=a+(d-c)*(j-1)/(m-1);
x(i,j)=sin(u)*cos(v);
y(i,j)=sin(u)*sin(v);
z(i,j)=cos(u);
end
end
mesh(x,y,z);
But I want the shape?
Ellipse article on Wikipedia had a simple JavaScript code to draw ellipses.
It uses the parametric form:
x(theta) = a0 + ax*sin(theta) + bx*cos(theta)
y(theta) = b0 + ay*sin(theta) + by*cos(theta)
where
(a0,b0) is the center of the ellipse
(ax,ay) vector representing the major axis
(bx,by) vector representing the minor axis
I translated the code into a MATLAB function:
calculateEllipse.m
function [X,Y] = calculateEllipse(x, y, a, b, angle, steps)
%# This functions returns points to draw an ellipse
%#
%# #param x X coordinate
%# #param y Y coordinate
%# #param a Semimajor axis
%# #param b Semiminor axis
%# #param angle Angle of the ellipse (in degrees)
%#
narginchk(5, 6);
if nargin<6, steps = 36; end
beta = -angle * (pi / 180);
sinbeta = sin(beta);
cosbeta = cos(beta);
alpha = linspace(0, 360, steps)' .* (pi / 180);
sinalpha = sin(alpha);
cosalpha = cos(alpha);
X = x + (a * cosalpha * cosbeta - b * sinalpha * sinbeta);
Y = y + (a * cosalpha * sinbeta + b * sinalpha * cosbeta);
if nargout==1, X = [X Y]; end
end
and an example to test it:
%# ellipse centered at (0,0) with axes length
%# major=20, ,minor=10, rotated 50 degrees
%# (drawn using the default N=36 points)
p = calculateEllipse(0, 0, 20, 10, 50);
plot(p(:,1), p(:,2), '.-'), axis equal
The answers from Jacob and Amro are very good examples for computing and plotting points for an ellipse. I'll address some easy ways you can plot an ellipsoid...
First, MATLAB has a built-in function ELLIPSOID which generates a set of mesh points given the ellipsoid center and the semi-axis lengths. The following creates the matrices x, y, and z for an ellipsoid centered at the origin with semi-axis lengths of 4, 2, and 1 for the x, y, and z directions, respectively:
[x, y, z] = ellipsoid(0, 0, 0, 4, 2, 1);
You can then use the function MESH to plot it, returning a handle to the plotted surface object:
hMesh = mesh(x, y, z);
If you want to rotate the plotted ellipsoid, you can use the ROTATE function. The following applies a rotation of 45 degrees around the y-axis:
rotate(hMesh, [0 1 0], 45);
You can then adjust the plot appearance to get the following figure:
axis equal; %# Make tick mark increments on all axes equal
view([-36 18]); %# Change the camera viewpoint
xlabel('x');
ylabel('y');
zlabel('z');
Also, if you want to use the rotated plot points for further calculations, you can get them from the plotted surface object:
xNew = get(hMesh, 'XData'); %# Get the rotated x points
yNew = get(hMesh, 'YData'); %# Get the rotated y points
zNew = get(hMesh, 'ZData'); %# Get the rotated z points
I've adapted this excellent ellipse plotting script from MATLAB Central for your requirement of
function plotEllipse(a,b,C)
% range to plot over
%------------------------------------
N = 50;
theta = 0:1/N:2*pi+1/N;
% Parametric equation of the ellipse
%----------------------------------------
state(1,:) = a*cos(theta);
state(2,:) = b*sin(theta);
% Coordinate transform (since your ellipse is axis aligned)
%----------------------------------------
X = state;
X(1,:) = X(1,:) + C(1);
X(2,:) = X(2,:) + C(2);
% Plot
%----------------------------------------
plot(X(1,:),X(2,:));
hold on;
plot(C(1),C(2),'r*');
axis equal;
grid;
end
Note: change N to define the resolution of your ellipse
Here's an ellipse centered at (10,10) with a = 30 and b = 10
Ellipse article on Wikipedia and Rotation matrix.
Rewrite that functions:
rotate by rotAngle counter-clockwise around (0,0)
Coordinate transform to (cx, cy)
function [X,Y] = calculateEllipse(cx, cy, a, b, rotAngle)
%# This functions returns points to draw an ellipse
%#
%# #param x X coordinate
%# #param y Y coordinate
%# #param a Semimajor axis
%# #param b Semiminor axis
%# #param cx cetner x position
%# #param cy cetner y position
%# #param angle Angle of the ellipse (in degrees)
%#
steps = 30;
angle = linspace(0, 2*pi, steps);
% Parametric equation of the ellipse
X = a * cos(angle);
Y = b * sin(angle);
% rotate by rotAngle counter clockwise around (0,0)
xRot = X*cosd(rotAngle) - Y*sind(rotAngle);
yRot = X*sind(rotAngle) + Y*cosd(rotAngle);
X = xRot;
Y = yRot;
% Coordinate transform
X = X + cx;
Y = Y + cy;
end
and an example to test it:
[X,Y] = calculateEllipse(0, 0, 20, 10, 0);
plot(X, Y, 'b'); hold on; % blue
[X,Y] = calculateEllipse(0, 0, 20, 10, 45);
plot(X, Y, 'r'); hold on; % red
[X,Y] = calculateEllipse(30, 30, 20, 10, 135);
plot(X, Y, 'g'); % green
grid on;
Create two vectors, one of the x-coordinates of the points of the circumference of the ellipsoid, one of the y-coordinates. Make these vectors long enough to satisfy your accuracy requirements. Plot the two vectors as (x,y) pairs joined up. I'd drop the for loops from your code, much clearer if you use vector notation. Also I'd format your question using the SO markup for code to make it all clearer to your audience.
The simplest way might be to use the Matlab function
pdeellip(xc,yc,a,b,phi)
For example:
pdeellip(0,0,1,0.3,pi/4)
However, this is simple solution is good to have a quick glance how the ellipse looks like. If you want to have a nice plot, look at the other solutions.
I don't know in which version of Matlab this was added, but it's available at least from version R2012b on.