I'm trying to simulate the movement of a target in Matlab, whose initial x and y co-ordinates, true bearing and speed (in m/s) are specified. I am wondering if there is a way to simply draw a straight line, at the specified bearing angle to show the path taken by the target (as shown in the image below)
Thanks in advance!
Your best bet is to rely on one of the built-in polar plotting functions to do this. I think the one that is most similar to your needs would be compass. It essentially plots an arrow pointing from the center to a point (defined in cartesian coordinates) on a polar plot.
theta = deg2rad(130);
% Your speed in m/s
speed = 5;
hax = axes();
c = compass(hax, speed * cos(theta), speed * sin(theta));
% Change the view to orient the axes the way you've drawn
view([90 -90])
Then in order to change the bearing and speed, you simply call the compass function again with your new bearing/speed.
new_theta = deg2rad(new_angle_degrees);
c = compass(hax, new_speed * cos(new_theta), new_speed * sin(new_theta));
Other polar plotting options include polar and polarplot which accept polar coordinates but don't have an arrow head. If you don't like the polar plot you could always go with quiver on a cartesian axes (making sure you specify the same axes).
Edit
Based on your feedback and request, below is an example of a polar plot of the distance traveled.
% Speed in m/s
speed = 5;
% Time in seconds
time = 1.5;
% Bearing in degrees
theta = 130;
hax = axes();
% Specify polar line from origin (0,0) to target position (bearing, distance)
hpolar = polar(hax, [0 deg2rad(theta)], [0 speed * time], '-o');
% Ensure the axis looks as you mentioned in your question
view([90 -90]);
Now to update this plot with a new bearing, speed, time you would simply call polar again specifying the axes.
hpolar = polar(hax, [0 theta], [0 speed], '-o');
I am not sure if I got it correctly, here is my solution:
figure;hold on; % Create figure
x_start = 10;% Starting position
y_start = 20;
plot(x_start+[-1 1],[y_start y_start],'k');% Plot crosshairs
plot([x_start x_start],y_start+[-1 1],'k');
angle = -(130-90)*pi/180; % Bearing angle 130° like in your graph
x_target = x_start+10*cos(angle); % Calculation of target position
y_target = y_start+10*sin(angle);
plot(x_target+[-1 1],[y_target y_target],'k');% Plot crosshairs
plot([x_target x_target],y_target+[-1 1],'k');
% Draw line between start and target
plot([x_start x_target],[y_start y_target],'g');
set(gca,'xlim',[0 30],'ylim',[0 30]); % Adjust axes
text(x_start+1,y_start,'Start'); % Write text to points
text(x_target+1,y_target,'End');
Related
I want to convert an image from Cartesian to Polar and to use it for opengl texture.
So I used matlab referring to the two articles below.
Link 1
Link 2
My code is exactly same with Link 2's anwser
% load image
img = imread('my_image.png');
% convert pixel coordinates from cartesian to polar
[h,w,~] = size(img);
[X,Y] = meshgrid((1:w)-floor(w/2), (1:h)-floor(h/2));
[theta,rho] = cart2pol(X, Y);
Z = zeros(size(theta));
% show pixel locations (subsample to get less dense points)
XX = X(1:8:end,1:4:end);
YY = Y(1:8:end,1:4:end);
tt = theta(1:8:end,1:4:end);
rr = rho(1:8:end,1:4:end);
subplot(121), scatter(XX(:),YY(:),3,'filled'), axis ij image
subplot(122), scatter(tt(:),rr(:),3,'filled'), axis ij square tight
% show images
figure
subplot(121), imshow(img), axis on
subplot(122), warp(theta, rho, Z, img), view(2), axis square
The result was exactly what I wanted, and I was very satisfied except for one thing. It's the area (red circled area) in the picture just below. Considering that the opposite side (blue circled area) is not, I think this part should also be filled. Because of this part is empty, so there is a problem when using it as a texture.
And I wonder how I can fill this part. Thank you.
(little difference from Link 2's answer code like degree<->radian and axis values. but i think it is not important.)
Those issues you show in your question happen because your algorithm is wrong.
What you did (push):
throw a grid on the source image
transform those points
try to plot these colored points and let MATLAB do some magic to make it look like a dense picture
Do it the other way around (pull):
throw a grid on the output
transform that backwards
sample the input at those points
The distinction is called "push" (into output) vs "pull" (from input). Only Pull gives proper results.
Very little MATLAB code is necessary. You just need pol2cart and interp2, and a meshgrid.
With interp2 you get to choose the interpolation (linear, cubic, ...). Nearest-neighbor interpolation leaves visible artefacts.
im = im2single(imread("PQFax.jpg"));
% center of polar map, manually picked
cx = 10 + 409/2;
cy = 7 + 413/2;
% output parameters
radius = 212;
dRho = 1;
dTheta = 2*pi / (2*pi * radius);
Thetas = pi/2 - (0:dTheta:2*pi);
Rhos = (0:dRho:radius);
% polar mesh
[Theta, Rho] = meshgrid(Thetas, Rhos);
% transform...
[Xq,Yq] = pol2cart(Theta, Rho);
% translate to sit on the circle's center
Xq = Xq + cx;
Yq = Yq + cy;
% sample image at those points
Ro = interp2(im(:,:,1), Xq,Yq, "cubic");
Go = interp2(im(:,:,2), Xq,Yq, "cubic");
Bo = interp2(im(:,:,3), Xq,Yq, "cubic");
Vo = cat(3, Ro, Go, Bo);
Vo = imrotate(Vo, 180);
imshow(Vo)
The other way around (get a "torus" from a "ribbon") is quite similar. Throw a meshgrid on the torus space, subtract center, transform from cartesian to polar, and use those to sample from the "ribbon" image into the "torus" image.
I'm more familiar with OpenCV than with MATLAB. Perhaps MATLAB has something like OpenCV's warpPolar(), or a generic remap(). In any case, the operation is trivial to do entirely "by hand" but there are enough supporting functions to take the heavy lifting off your hands (interp2, pol2cart, meshgrid).
1.- The white arcs tell that the used translation pol-cart introduces significant errors.
2.- Reversing the following script solves your question.
It's a script that goes from cart-pol without introducing errors or ignoring input data, which is what happens when such wide white arcs show up upon translation apparently correct.
clear all;clc;close all
clc,cla;
format long;
A=imread('shaffen dass.jpg');
[sz1 sz2 sz3]=size(A);
szx=sz2;szy=sz1;
A1=A(:,:,1);A2=A(:,:,2);A3=A(:,:,3); % working with binary maps or grey scale images this wouldn't be necessary
figure(1);imshow(A);
hold all;
Cx=floor(szx/2);Cy=floor(szy/2);
plot(Cx,Cy,'co'); % because observe image centre not centered
Rmin=80;Rmax=400; % radius search range for imfindcircles
[centers, radii]=imfindcircles(A,[Rmin Rmax],... % outer circle
'ObjectPolarity','dark','Sensitivity',0.9);
h=viscircles(centers,radii);
hold all; % inner circle
[centers2, radii2]=imfindcircles(A,[Rmin Rmax],...
'ObjectPolarity','bright');
h=viscircles(centers2,radii2);
% L=floor(.5*(radii+radii2)); % this is NOT the length X that should have the resulting XY morphed graph
L=floor(2*pi*radii); % expected length of the morphed graph
cx=floor(.5*(centers(1)+centers2(1))); % coordinates of averaged circle centres
cy=floor(.5*(centers(2)+centers2(2)));
plot(cx,cy,'r*'); % check avg centre circle is not aligned to figure centre
plot([cx 1],[cy 1],'r-.');
t=[45:360/L:404+1-360/L]; % if step=1 then we only get 360 points but need an amount of L points
% if angle step 1/L over minute waiting for for loop to finish
R=radii+5;x=R*sind(t)+cx;y=R*cosd(t)+cy; % build outer perimeter
hL1=plot(x,y,'m'); % axis equal;grid on;
% hold all;
% plot(hL1.XData,hL1.YData,'ro');
x_ref=hL1.XData;y_ref=hL1.YData;
% Sx=zeros(ceil(R),1);Sy=zeros(ceil(R),1);
Sx={};Sy={};
for k=1:1:numel(hL1.XData)
Lx=floor(linspace(x_ref(k),cx,ceil(R)));
Ly=floor(linspace(y_ref(k),cy,ceil(R)));
% plot(Lx,Ly,'go'); % check
% plot([cx x(k)],[cy y(k)],'r');
% L1=unique([Lx;Ly]','rows');
Sx=[Sx Lx'];Sy=[Sy Ly'];
end
sx=cell2mat(Sx);sy=cell2mat(Sy);
[s1 s2]=size(sx);
B1=uint8(zeros(s1,s2));
B2=uint8(zeros(s1,s2));
B3=uint8(zeros(s1,s2));
for n=1:1:s2
for k=1:1:s1
B1(k,n)=A1(sx(k,n),sy(k,n));
B2(k,n)=A2(sx(k,n),sy(k,n));
B3(k,n)=A3(sx(k,n),sy(k,n));
end
end
C=uint8(zeros(s1,s2,3));
C(:,:,1)=B1;
C(:,:,2)=B2;
C(:,:,3)=B3;
figure(2);imshow(C);
the resulting
3.- let me know if you'd like some assistance writing pol-cart from this script.
Regards
John BG
I am looking to create a simple circle graph within MATLAB in which the model shows the point moving along the circle with radius and angular velocity defined by the user.
Angular velocity in RADIANS/SEC
I am relatively new at MATLAB coding so any help would be very useful!
I tried this code:
r=1;
t = 0:.01:2*pi;
x = r*cos(t);
y = r*sin(t);
comet(x,y);
But when I change the 0.01 value the point doesn't move faster, it just skips more of the curve, also i'm unsure if the increments are in radians.
Thanks for your time
Edited version: See edit history for previous version.
Radius = 10;
AngularVelocity = 5; % in deg / s
AngleStep = 0.1
Angles = AngleStep : AngleStep : 2*pi;
CircleX = [Radius]; % empty array
CircleY = [0]; % empty array
%Initial zero-angle plot whose data we'll keep updating in the for loop:
a = plot([CircleX,CircleX], [CircleY,CircleY], 'r:');
hold on;
b = plot(CircleX, CircleY, 'o', 'markeredgecolor', 'k', 'markerfacecolor','g');
axis([-Radius, +Radius, -Radius, +Radius]); % make sure the axis is fixed
axis equal; % make x and y pixels of equal size so it "looks" a circle!
hold off;
for t = Angles
CircleX(end+1) = Radius * cos (t); % append point at end of CircleX array
CircleY(end+1) = Radius * sin (t); % append point at end of Circley array
set(a,'xdata',CircleX,'ydata',CircleY); % update plot 'a' data
set(b,'xdata', CircleX(end), 'ydata', CircleY(end)); % update plot 'b' data
drawnow; % ensure intermediate frames are shown!
pause(AngleStep/AngularVelocity) % pause the right amount of time!
end
This edit has made two changes compared to the previous version:
Instead of redrawing, now we're updating the data of an existing plot. This is generally faster as matlab doesn't have to redraw axes objects (i.e. the containers that hold the plot)
I increased AngleStep from 0.01 to 0.1. This means there's 10 times less angles to draw, so you can afford to draw then 10 times slower, therefore it becomes less likely that matlab will be unable to draw because of overhead. Having said that, this is at the cost of a less perfect circle. Try with AngleStep=1 to see what I mean.
My goal is to continuously plot the position & orientation of camera relative to marker using MATLAB.
There are three thing to plot.(1)camera (2)all circle points (3)origin point '*'
Both the camera and points will be moving in each frame.I plotted all these three things in a static figure i.e. using hold on. as shown in the attached figure.
Now i want to plot them all continuously (real time) in the same figure as the values change.Till now i have only been able to dynamically update only one of these things i.e. the circular points for some random values. If I add another plot ,it conflicts.Can you please tell me how to update multiple plots in same figure and the plotCamera.
hF = figure;
hAx = gca;
im_pt_2world=rand(3,3);
x_o=im_pt_2world(1,1); y_o=im_pt_2world(1,2); %origin of the calibrated world points
x_ip=im_pt_2world(:,1); y_ip=im_pt_2world(:,2);
hpoints = plot3(x_ip, y_ip,zeros(size(im_pt_2world, 1),1),'ro');
% I added the "ishandle" so the program will end in case u closed the figure
while (1) & ishandle(hpoints)
%instead of using plot I directly change the data in the line
% this is faster the plot if only because you don't need to reedefine the limits and labels...
im_pt_2world=rand(3,3);
x_ip=im_pt_2world(:,1); y_ip=im_pt_2world(:,2);
set(hpoints,'ydata',y_ip);
set(hpoints,'xdata',x_ip);
drawnow %updates the display
end
The plotCamera function (Computer Vision System Toolbox) returns a handle to the graphical object, which you can manipulate programmatically. Changing the object's properties, such as Location and Orientation will move the camera in the plot. The help example for plotCamera shows how to make the camera fly in a circle:
% Plot a camera pointing along the Y-axis
R = [1 0 0;
0 0 -1;
0 1 0];
% Setting opacity of the camera to zero for faster animation.
cam = plotCamera('Location', [10 0 20], 'Orientation', R, 'Opacity', 0);
% Set view properties
grid on
axis equal
axis manual
% Make the space large enough for the animation.
xlim([-15, 20]);
ylim([-15, 20]);
zlim([15, 25]);
% Make the camera fly in a circle
for theta = 0:pi/64:10*pi
% Rotation about cameras y-axis
T = [cos(theta) 0 sin(theta);
0 1 0;
-sin(theta) 0 cos(theta)];
cam.Orientation = T * R;
cam.Location = [10 * cos(theta), 10 * sin(theta), 20];
drawnow();
end
If you really want to have fun with this, you can supply a function handle to be called when you click on the camera. For example, the function can display the image that the camera sees.
i just started with my master thesis and i already am in trouble with my capability/understanding of matlab.
The thing is, i have a trajectory on a surface of a planet/moon whatever (a .mat with the time, and the coordinates. Then i have some .mat with time and the measurement at that time.
I am able to plot this as a color coded trajectory (using the measurement and the coordinates) in scatter(). This works awesomely nice.
However my problem is that i need something more sophisticated.
I now need to take the trajectory and instead of color-coding it, i am supposed to add the graph (value) of the measurement (which is given for each point) to the trajectory (which is not always a straight line). I will added a little sketch to explain what i want. The red arrow shows what i want to add to my plot and the green shows what i have.
You can always transform your data yourself: (using the same notation as #Shai)
x = 0:0.1:10;
y = x;
m = 10*sin(x);
So what you need is the vector normal to the curve at each datapoint:
dx = diff(x); % backward finite differences for 2:end points
dx = [dx(1) dx]; % forward finite difference for 1th point
dy = diff(y);
dy = [dy(1) dy];
curve_tang = [dx ; dy];
% rotate tangential vectors 90° counterclockwise
curve_norm = [-dy; dx];
% normalize the vectors:
nrm_cn = sqrt(sum(abs(curve_norm).^2,1));
curve_norm = curve_norm ./ repmat(sqrt(sum(abs(curve_norm).^2,1)),2,1);
Multiply that vector with the measurement (m), offset it with the datapoint coordinates and you're done:
mx = x + curve_norm(1,:).*m;
my = y + curve_norm(2,:).*m;
plot it with:
figure; hold on
axis equal;
scatter(x,y,[],m);
plot(mx,my)
which is imo exactly what you want. This example has just a straight line as coordinates, but this code can handle any curve just fine:
x=0:0.1:10;y=x.^2;m=sin(x);
t=0:pi/50:2*pi;x=5*cos(t);y=5*sin(t);m=sin(5*t);
If I understand your question correctly, what you need is to rotate your actual data around an origin point at a certain angle. This is pretty simple, as you only need to multiply the coordinates by a rotation matrix. You can then use hold on and plot to overlay your plot with the rotated points, as suggested in the comments.
Example
First, let's generate some data that resembles yours and create a scatter plot:
% # Generate some data
t = -20:0.1:20;
idx = (t ~= 0);
y = ones(size(t));
y(idx) = abs(sin(t(idx)) ./ t(idx)) .^ 0.25;
% # Create a scatter plot
x = 1:numel(y);
figure
scatter(x, x, 10, y, 'filled')
Now let's rotate the points (specified by the values of x and y) around (0, 0) at a 45° angle:
P = [x(:) * sqrt(2), y(:) * 100] * [1, 1; -1, 1] / sqrt(2);
and then plot them on top of the scatter plot:
hold on
axis square
plot(P(:, 1), P(:, 2))
Note the additional things have been done here for visualization purposes:
The final x-coordinates have been stretched (by sqrt(2)) to the appropriate length.
The final y-coordinates have been magnified (by 100) so that the rotated plot stands out.
The axes have been squared to avoid distortion.
This is what you should get:
It seems like you are interested in 3D plotting.
If I understand your question correctly, you have a 2D curve represented as [x(t), y(t)].
Additionally, you have some value m(t) for each point.
Thus we are looking at the plot of a 3D curve [x(t) y(t) m(t)].
you can easily achieve this using
plot3( x, y, m ); % assuming x,y, and m are sorted w.r.t t
alternatively, you can use the 3D version of scatter
scatter3( x, y, m );
pick your choice.
Nice plot BTW.
Good luck with your thesis.
I am working in MATLAB and I'm stuck on a very simple problem: I've got an object defined by its position (x,y) and theta (an angle, in degrees). I would like to plot the point and add an arrow, starting from the point and pointing toward the direction defined by the angle. It actually doesn't even have to be an arrow, anything graphically showing the value of the angle will do!
Here's a picture showing the kind of thing I'm trying to draw:
removed dead ImageShack link
The quiver() plotting function plots arrows like this. Take your theta value and convert it to (x,y) cartesian coordinates representing the vector you want to plot as an arrow and use those as the (u,v) parameters to quiver().
theta = pi/9;
r = 3; % magnitude (length) of arrow to plot
x = 4; y = 5;
u = r * cos(theta); % convert polar (theta,r) to cartesian
v = r * sin(theta);
h = quiver(x,y,u,v);
set(gca, 'XLim', [1 10], 'YLim', [1 10]);
Take a look through online the Matlab documentation to see other plot types; there's a lot, including several radial plots. They're in the MATLAB > Functions > Graphics > Specialized Plotting section. Do "doc quiver" at the command line and browse around.
If you want to try and make something that looks like the image you linked to, here's some code to help you do it (NOTE: you would first have to download the submission arrow.m by Erik Johnson on the MathWorks File Exchange, which I always like to use for generating arrows of any shape and size):
x = 1; % X coordinate of arrow start
y = 2; % Y coordinate of arrow start
theta = pi/4; % Angle of arrow, from x-axis
L = 2; % Length of arrow
xEnd = x+L*cos(theta); % X coordinate of arrow end
yEnd = y+L*sin(theta); % Y coordinate of arrow end
points = linspace(0, theta); % 100 points from 0 to theta
xCurve = x+(L/2).*cos(points); % X coordinates of curve
yCurve = y+(L/2).*sin(points); % Y coordinates of curve
plot(x+[-L L], [y y], '--k'); % Plot dashed line
hold on; % Add subsequent plots to the current axes
axis([x+[-L L] y+[-L L]]); % Set axis limits
axis equal; % Make tick increments of each axis equal
arrow([x y], [xEnd yEnd]); % Plot arrow
plot(xCurve, yCurve, '-k'); % Plot curve
plot(x, y, 'o', 'MarkerEdgeColor', 'k', 'MarkerFaceColor', 'w'); % Plot point
And here's what it would look like:
You can then add text to the plot (for the angle and the coordinate values) using the text function.
Here's a partial answer, I expect you can figure out the rest. I fired up the Figures editor and opened the plot tools. I dragged an arrow from the palette onto my figure. Then I generated an m-file. This included the line:
annotation(figure1,'arrow',[0.1489 0.2945],[0.5793 0.6481]);
So, the first pair of coordinates is the start of the arrow. You're going to have to figure out the pointy end (second pair of coordinates) using a little bit of trigonometry. You might even be able to get the little arc if you do some more fiddling around with plot tools.
Let us know if the trig defeats you. Oh, and I forgot to plot the point, but I guess you can figure that out ?