I'm currently trying to animate a particle in 2D obeying a system of ODEs. I currently have the code below, based on examples online, but I really don't know how to proceed.
If anyone could offer assistance, I'd be most appreciative.
function Animation()
% Solving the systemP1 using ode45
sol=ode45(#systemP1,[0,0.0001],[10e-7,-1,10e-7,-1]);
t = linspace(0,0.0001)
p = deval(sol,t);
% Xposition
x = p(1,:)';
xdot = p(2,:)' ;
% Yposition
y = p(3,:)';
ydot = p(4,:)' ;
position = [x, y];
% Trajectory of the particle
path = plot(position(1,1), position(1,2),'k');
end
You almost have it correct. What you can do is put the plot in a for loop and plot each point individually. That way, you can see how the point moves in a more "real-time" sense. Make sure that at end of the for loop, add drawnow at the end of the iteration. It forces MATLAB to empty the graphic event queue. I also add pause at the end as well just in case the drawing goes too fast.
Make sure you have a hold on statement at the beginning before the for loop. I would also recommend freezing the axis to prevent auto scaling the axis when a new point is being the added. As such, your code would be modified to be:
function Animation()
% Solving the systemP1 using ode45
sol=ode45(#systemP1,[0,0.0001],[10e-7,-1,10e-7,-1]);
t = linspace(0,0.0001)
p = deval(sol,t);
% Xposition
x = p(1,:)';
xdot = p(2,:)' ;
% Yposition
y = p(3,:)';
ydot = p(4,:)' ;
position = [x, y];
%// Modifications start here
figure(1);
hold on;
%// Find limits of x and y axes
minX = min(x);
maxX = max(x);
minY = min(y);
maxY = max(y);
%// Prevent axis from auto-scaling
axis([minX maxX minY maxY]);
axis manual;
%//Plot each position vector over time
for idx = 1 : size(position,1)
%//Trajectory of the particle
plot(position(idx,1), position(idx,2),'k.', 'MarkerSize', 18);
pause(0.1); %// Pause 0.1 seconds to slow things down. Remove if necessary
drawnow;
end
end
The MarkerSize parameter changes the size of each point. I set it to 18 as it looks large enough on my machine. Make this larger or smaller according to your preference. I don't see why xdot and ydot are defined, so I left it out of the code. However, if you want to use these, basically replicate the same code I have above but for xdot and ydot. If you'd like me to do this for you, let me know in a comment and I'll modify my post.
Note
This post was inspired by Luis Mendo's post on plotting objects as animation. That post can be found here: Octave plot points as animation
Related
I have implemented the Hermite-Gaussian function in matlab for producing different modes. The light beam along z direction can be seen as a complex matrix in the plane.
The function for HG modes is as below.
%Hermite polynomial
function hk = HermitePoly(n)
if n==0
hk = 1;
elseif n==1
hk = [2 0];
else
hkm2 = zeros(1,n+1);
hkm2(n+1) = 1;
hkm1 = zeros(1,n+1);
hkm1(n) = 2;
for k=2:n
hk = zeros(1,n+1);
for e=n-k+1:2:n
hk(e) = 2*(hkm1(e+1) - (k-1)*hkm2(e));
end
hk(n+1) = -2*(k-1)*hkm2(n+1);
if k<n
hkm2 = hkm1;
hkm1 = hk;
end
end
end
% this is the function of HG modes in z position.
function [HGBeam,X,Y] = Hermite_Gaussian(N,hx,hy,w0,delta,lamda,z)
[X Y]=meshgrid((-N/2:N/2-1)*delta);
[theta,rad] = cart2pol(X,Y);
k=2*pi/lamda;
zr=pi*w0^2/lamda;
wz=w0*sqrt(1+(z/zr)^2);
qz=z+1i*zr;
q0=1i*zr;
if z==0
rz=Inf;
else
rz=z*(1+(zr/z)^2);
end
AmpLGB=sqrt(2/(2^(hx+hy)*pi*factorial(hx)*factorial(hy)*w0^2)).*(q0/qz).*(-conj(qz)/qz)^((hx+hy)/2).*exp(-(rad.*rad)/(wz)^2).*polyval(HermitePoly(hx),sqrt(2)*X/wz).*polyval(HermitePoly(hy),sqrt(2)*Y/wz);
PsLGB=exp(-1i*(k*(rad.*rad)/(2*rz)+k*z-(hx+hy+1)*atan(z/zr)));
HGBeam=AmpLGB.*PsLGB;
end
Now I plot one example for HG(2,0) as the following (example1):
clc
clear all;
close all;
lambda=809e-9; % optical wavelength
w0=0.025; %optical beam waist 15mm
k=2*pi/lambda; % optical wavenumber
Zr=pi*w0^2/lambda; % Rayleigh range
z0=0; % start position z=0; but careful 0*Inf is undefined, here 0*Inf=NAN
N=1024; % samples/side length at source plane
D1=0.25; % side length [m] at source plane
delta1=D1/N; % grid spacing [m]
x1=-D1/2:delta1:D1/2-delta1; % source plane x and y coordinates
y1=x1;
%% HG modes
HGx=2;
HGy=0;
HGintheory=Hermite_Gaussian(N,HGx,HGy,w0,delta1,lambda,z0);
h7=figure(7);
imagesc(x1,y1,abs(HGintheory).^2);
title(sprintf('z=%d; HG(%d,%d)',z0,HGx,HGy))
xlabel('x (m)'); ylabel('y (m)');
The plot of the light field will be as the following picture in the left side (its intensity):
We can use rot90() function to rotate matrix HGintheory (which is add one line code: HGintheory=rot90(HGintheory);) and then the field will rotate 90 degree (right side of the intensity plot).
Because I want to work with the light field. So the question is how can I rotate the complex matrix HGintheory in
arbitrary angle? For example 45 degree?
Does anyone knows how to rotate a complex matrix with big size? If something is wrong or unclear, please pointing out and Thank you in advance!
You can decompose your complex field into two real fields (amplitude and phase), rotate both with imrotate, and combine them afterwards pixel-wise
Hamp=abs(HGintheory);
Hphase=angle(HGintheory);
RotAngle=45;
HampRot=imrotate(Hamp,RotAngle,'bilinear','crop');
HphaseRot=imrotate(Hphase,RotAngle,'bilinear','crop');
HfullRot=HampRot.*exp(1i*HphaseRot);
figure(1);
imagesc(x1,y1,abs(HGintheory).^2);
figure(2);
imagesc(x1,y1,abs(HfullRot).^2);
You can rotate your initial meshgrid using:
[X,Y] = meshgrid(x1,y1)
xyc = [mean(x1), mean(y1)];
angel = 45;
R = [cosd(angel), -sind(angel); sind(angel), cosd(angel)];
XY = xyc' + R * ([X(:) Y(:)]-xyc)';
XR = reshape(XY(1,:),size(X));
YR = reshape(XY(2,:),size(Y));
and then use those transformed coordinates to plot:
imagesc(XR,YR,IntensityHGin);
I have a ball with these two equations:
x(t) = v0*cos(α)*t and
y(t) = h + v0*sin(α)*t− 1/2 gt^2 , where t ∈ [0,t final] is the time variable, h is the height, v0 is the initial speed, α is the angle made by v0 with the horizontal, g = 9.8 m/s^2. The floor is at y(x) = 0.
I need to draw a small animation of the ball moving on the plot. I now I should use for, plot, drawnow, but I don't know how to do it.
Can you tell me how to obain this animation?
First, here are some test variables to start with, including the acceleration due to gravity:
g = 9.8; %// m/s^2
v0 = 2; %// m/s
alpha = pi/6; %// Radians
h = 30; %// Start at 30 metres
t_final = 4.5; %// Seconds
t_vector = 0 : 0.01 : t_final;
t_vector in the last line of code creates a vector of points from the initial time of t = 0 up until our ending time in steps of 0.01. With these defined, our job is to go through each of these points in our vector and plot our ball. Next, let's create anonymous functions for each x and y to make our plotting easier:
x = #(t) v0*cos(alpha)*t;
y = #(t) h + v0*sin(alpha)*t - 0.5*g*t.^2;
What you can do next is use a for loop and go through each value of t_vector up until t_final and plot the individual point. You should probably make the point big so we can actually see what the ball looks like:
close all;
figure; hold on;
for t = t_vector
plot(x(t), y(t), 'b.', 'MarkerSize', 16);
axis([0 t_final 0 h]);
pause(0.01);
end
The above code will first close any figures we have open, spawn a new figure and use hold on so that we can call plot multiple times and append points to the graph without it erasing each time. Then, for each point in time, we plot the location on the graph as a blue dot, then make the size of the dot 16. We also make sure that the axis doesn't automatically adjust itself by enforcing that the x values are restricted between t = 0 up to t = t_final. We also restrict the y values from y = 0 up to the initial starting height, which is 30 in my example. At each point, we pause by 0.01 ms so you can see the drawing of the points.
As a bonus, this is what the figure looks like as an animated gif:
Hello and pardon me if my english is a bit rusty. I'm trying to create a circle that moves along a parametric function (coordinates are stored in vectors). I have written a function for drawing the circle and I know that you can use the axis equal command in matlab in order to create a circle shape and avoid an ellipse. My problem is that when I do this the figure window becomes very wide relative to the plotted graph. Any input is appreciated.
MAIN CODE:
t = linspace(0,3);
x = 30*cos(pi/4)/2*(1-exp(-0.5*t));
y = (30*sin(pi/4)/2 + 9.81/0.5^2)*(1-exp(0.5*t)) - 9.81*t/0.5;
for i = 1:length(t)
plot(x,y)
axis equal
hold on
cirkel(x(i),y(i),1,1,'r') % argument #3 is the radius #4 is 1 for fill
hold off
pause(0.01)
end
CIRCLE CODE:
function cirkel(x,y,r,f,c)
angle = linspace(0, 2*pi, 360);
xp = x + r*cos(angle);
yp = y + r*sin(angle);
plot(x,y)
if f == 1 && nargin == 5
fill(xp,yp,c)
end
When you call axis equal it makes one unit of the x axis be the same size as one unit of the y axis. You are seeing what you are because your y values span a much larger range than the x values.
One way to deal with this would be to query the aspect ratio and x/y limits of the current axes as shown in the second part of this answer. However, an easier approach is rather than using fill to plot your circle, you could instead use scatter with a circular marker which will be circular regardless of the aspect ratio of your axes.
t = linspace(0,3);
x = 30*cos(pi/4)/2*(1-exp(-0.5*t));
y = (30*sin(pi/4)/2 + 9.81/0.5^2)*(1-exp(0.5*t)) - 9.81*t/0.5;
% Plot the entire curve
hplot = plot(x, y);
hold on;
% Create a scatter plot where the area of the marker is 50. Store the handle to the plot
% in the variable hscatter so we can update the position inside of the loop
hscatter = scatter(x(1), y(1), 50, 'r', 'MarkerFaceColor', 'r');
for k = 1:length(t)
% Update the location of the scatter plot
set(hscatter, 'XData', x(k), ... % Set the X Position of the circle to x(k)
'YData', y(k)) % Set the Y Position of the circle to y(k)
% Refresh the plot
drawnow
end
As a side note, it is best to update existing plot objects rather than creating new ones.
If you want the small dot to appear circular, and you want to have a reasonable domain (x-axis extent), try this:
function cirkel(x,y,r,f,c)
angle = linspace(0, 2*pi, 360);
xp = x + 0.04*r*cos(angle); %% adding scale factor of 0.04 to make it appear circular
yp = y + r*sin(angle);
plot(x,y)
if f == 1 && nargin == 5
fill(xp,yp,c)
end
Note the addition of the scale factor in the computation of xp. If you want to automate this, you can add another parameter to cirkel(), let's call it s, that contains the scale factor. You can calculate the scale factor in your script by computing the ratio of the range to the domain (y extent divided by x extent).
I have to create some draggable points on an axes. However, this seems to be a very slow process, on my machine taking a bit more than a second when done like so:
x = rand(100,1);
y = rand(100,1);
tic;
for i = 1:100
h(i) = impoint(gca, x(i), y(i));
end
toc;
Any ideas on speed up would be highly appreciated.
The idea is simply to provide the user with the possibility to correct positions in a figure that have been previously calculated by Matlab, here exemplified by the random numbers.
You can use the the ginput cursor within a while loop to mark all points you want to edit. Afterwards just click outside the axes to leave the loop, move the points and accept with any key.
f = figure(1);
scatter(x,y);
ax = gca;
i = 1;
while 1
[u,v] = ginput(1);
if ~inpolygon(u,v,ax.XLim,ax.YLim); break; end;
[~, ind] = min(hypot(x-u,y-v));
h(i).handle = impoint(gca, x(ind), y(ind));
h(i).index = ind;
i = i + 1;
end
Depending on how you're updating your plot you can gain a general speedup by using functions like clf (clear figure) and cla (clear axes) instead of always opening a new figure window as explained in this answer are may useful.
Alternatively the following is a very rough idea of what I meant in the comments. It throws various errors and I don't have the time to debug it right now. But maybe it helps as a starting point.
1) Conventional plotting of data and activating of datacursormode
x = rand(100,1);
y = rand(100,1);
xlim([0 1]); ylim([0 1])
f = figure(1)
scatter(x,y)
datacursormode on
dcm = datacursormode(f);
set(dcm,'DisplayStyle','datatip','Enable','on','UpdateFcn',#customUpdateFunction)
2) Custom update function evaluating the chosen datatip and creating an impoint
function txt = customUpdateFunction(empt,event_obj)
pos = get(event_obj,'Position');
ax = get(event_obj.Target,'parent');
sc = get(ax,'children');
x = sc.XData;
y = sc.YData;
mask = x == pos(1) & y == pos(2);
x(mask) = NaN;
y(mask) = NaN;
set(sc, 'XData', x, 'YData', y);
set(datacursormode(gcf),'Enable','off')
impoint(ax, pos(1),pos(2));
delete(findall(ax,'Type','hggroup','HandleVisibility','off'));
txt = {};
It works for the, if you'd just want to move one point. Reactivating the datacursormode and setting a second point fails:
Maybe you can find the error.
I am looking to create a simple log(x) graph within MATLAB in which the model shows the point moving along the curve with time.
The overall aim is to have two of these graphs alongside one another and to apply an algorithm to them. I am really unsure where to start here.
I am relatively new at MATLAB coding so any help would be very useful!
Thanks
Luke
Here is a variation on #Jacob's solution. Instead of redrawing everything at each frame (clf) we simply update the point's location:
%# control animation speed
DELAY = 0.01;
numPoints = 600;
%# create data
x = linspace(0,10,numPoints);
y = log(x);
%# plot graph
figure('DoubleBuffer','on') %# no flickering
plot(x,y, 'LineWidth',2), grid on
xlabel('x'), ylabel('y'), title('y = log(x)')
%# create moving point + coords text
hLine = line('XData',x(1), 'YData',y(1), 'Color','r', ...
'Marker','o', 'MarkerSize',6, 'LineWidth',2);
hTxt = text(x(1), y(1), sprintf('(%.3f,%.3f)',x(1),y(1)), ...
'Color',[0.2 0.2 0.2], 'FontSize',8, ...
'HorizontalAlignment','left', 'VerticalAlignment','top');
%# infinite loop
i = 1; %# index
while true
%# update point & text
set(hLine, 'XData',x(i), 'YData',y(i))
set(hTxt, 'Position',[x(i) y(i)], ...
'String',sprintf('(%.3f,%.3f)',[x(i) y(i)]))
drawnow %# force refresh
%#pause(DELAY) %# slow down animation
i = rem(i+1,numPoints)+1; %# circular increment
if ~ishandle(hLine), break; end %# in case you close the figure
end
A simple solution is:
x = 1:100;
y = log(x);
DELAY = 0.05;
for i = 1:numel(x)
clf;
plot(x,y);
hold on;
plot(x(i),y(i),'r*');
pause(DELAY);
end
You may want to have a look at the COMET function, which will make an animation of the curve.
For example (using the same numbers as #Jacob)
x = 1:100;
y = log(x);
comet(x,y)
If you want to show the point moving on the line (not 'drawing' it), you simply plot the line before
x = 1:100;
y = log(x);
plot(x,y,'r')
hold on %# to keep the previous plot
comet(x,y,0) %# 0 hides the green tail
a little more complex solution along the same lines as #Jacob. Here I add some optimization using handle graphics and a MATLAB movie object for playback.
x=1:100;
y=log(x);
figure
plot(x,y);
hold on; % hold on so that the figure is not cleared
h=plot(x(1),y(1),'r*'); % plot the first point
DELAY=.05;
for i=1:length(x)
set(h,'xdata',x(i),'ydata',y(i)); % move the point using set
% to change the cooridinates.
M(i)=getframe(gcf);
pause(DELAY)
end
%% Play the movie back
% create figure and axes for playback
figure
hh=axes;
set(hh,'units','normalized','pos',[0 0 1 1]);
axis off
movie(M) % play the movie created in the first part
solution can be this way
x = .01:.01:3;
comet(x,log(x))