Cracked-glass–like plot in Matlab - matlab

I would like make a plot that looks like this:
Namely a scatter plot with series of replicates connected via lines to the centroid.
I am not sure whether I saw it somewhere or whether I am simply getting glyphplot confused. I do not know what it is called, so Google has failed me —"cracked glass plot" is what I would personally call it.
In Matlab there is no native one line way to show a scatterplot with both x and y errorbars —yet Excel can. This makes me think there is a better way, such as this cracked glass plot.
Does it exist or do I need to write it myself?

I don't know of any native function to do this, but you can quite easily make use of line to plot something to fit your purposes, e.g.
function scatterPlotToCentroid(scatterPoints)
numScatters = size(scatterPoints,2);
scatterX = scatterPoints(1,:);
scatterY = scatterPoints(2,:);
centroid = mean(scatterPoints,2);
c1 = centroid(1);
c2 = centroid(2);
X = [repmat(c1,1,numScatters); scatterX];
Y = [repmat(c2,1,numScatters); scatterY];
hold on
line(X,Y,'Color','k');
scatter(scatterX, scatterY, 'r*');
end
Example call
% example: scatter sample (two groups)
numPoints = 10;
scatterDiff = 5;
scatterPointsA = 4+scatterDiff*(rand(2,numPoints)-0.5);
scatterPointsB = 8+scatterDiff*(rand(2,numPoints)-0.5);
% for each scatter sample group, plot scatter points
% and lines to centroid
hold on, box on
scatterPlotToCentroid(scatterPointsA)
scatterPlotToCentroid(scatterPointsB)
axis([0 12 0 12])
Example plot
Below follows the initial version of this answer, that left out the "centroid" part of the question (missed...), and instead generated random scatters around a given center-point; drawing lines from the latter to these scatter points.
function scatterPlotAt(centerPoint, numScatters, maxScatterSideLength)
c1 = centerPoint(1);
c2 = centerPoint(2);
scatterX = c1-maxScatterSideLength + ...
randi(2*maxScatterSideLength,1,numScatters);
scatterY = c2-maxScatterSideLength + ...
randi(2*maxScatterSideLength,1,numScatters);
X = [repmat(c1,1,numScatters); scatterX];
Y = [repmat(c2,1,numScatters); scatterY];
hold on
line(X,Y,'Color','k');
scatter(scatterX, scatterY, 'r*');
end
Example call
hold on, box on
scatterPlotAt([4; 4], 6, 3)
scatterPlotAt([8; 8], 6, 3)
axis([0 12 0 12])
Example result

Related

Plotting circles with complex numbers in MATLAB

I want to make a figure in MATLAB as described in the following image
What I did is the following:
x = [1 2 3];
y = [2 2 4];
radius = [1 1.2 2.2];
theta = [-pi 0 pi];
figure;
scatter(x,y,radius)
How do I add an angle theta to the plot to represent a complex number z = radius.*exp(1j*theta) at every spacial coordinates?
Technically speaking, those are only circles if x and y axes are scaled equally. That is because scatter always plots circles, independently of the scales (and they remain circles if you zoom in nonuniformly. + you have the problem with the line, which should indicate the angle...
You can solve both issues by drawing the circles:
function plotCirc(x,y,r,theta)
% calculate "points" where you want to draw approximate a circle
ang = 0:0.01:2*pi+.01;
xp = r*cos(ang);
yp = r*sin(ang);
% calculate start and end point to indicate the angle (starting at math=0, i.e. right, horizontal)
xt = x + [0 r*sin(theta)];
yt = y + [0 r*cos(theta)];
% plot with color: b-blue
plot(x+xp,y+yp,'b', xt,yt,'b');
end
having this little function, you can call it to draw as many circles as you want
x = [1 2 3];
y = [2 2 4];
radius = [1 1.2 2.2];
theta = [-pi 0 pi];
figure
hold on
for i = 1:length(x)
plotCirc(x(i),y(i),radius(i),theta(i))
end
I went back over scatter again, and it looks like you can't get that directly from the function. Hopefully there's a clean built-in way to do this, and someone else will chime in with it, but as a backup plan, you can just add the lines yourself.
You'd want a number of lines that's the same as the length of your coordinate set, from the center point to the edge at the target angle, and fortunately 'line' does multiple lines if you feed it a matrix.
You could just tack this on to the end of your code to get the angled line:
x_lines = [x; x + radius.*cos(theta)];
y_lines = [y; y + radius.*sin(theta)];
line(x_lines, y_lines, 'Color', 'b')
I had to assign the color specifically, since otherwise 'line' makes each new line cycle through the default colors, but that also means you could easily change the line color to stand out more. There's also no center dot, but that'd just be a second scatter plot with tiny radius. Should plot most of what you're looking for, at least.
(My version of Matlab is old enough that scatter behaves differently, so I can only check the line part, but they have the right length and location.)
Edit: Other answer makes a good point on whether scatter is appropriate here. Probably better to draw the circle too.

Generate trajectories for 3 agents/robots with same tangent in specific point - MATLAB

I want to simulate the movements of 3 robots/agents in space and I would like to generate 3 different trajectories which have one constraint: in a certain time T the all the trajectories must have the same tangent.
I want something like in the following picture:
I need to do it through MATLAB and/or SIMULINK.
Thanks a lot for your help.
I do not know if this is enough for what I need or not but I probably figured out something.
What I did is to fit a polynomial to some points and constraining the derivative of the polynomial in a certain point to be equal to 0.
I used the following function:
http://www.mathworks.com/matlabcentral/fileexchange/54207-polyfix-x-y-n-xfix-yfix-xder-dydx-
It is pretty easy, but it saved me some work.
And, if you try the following:
% point you want your functions to pass
p1 = [1 1];
p2 = [1 3];
% First function
x1 = linspace(0,4);
y1 = linspace(0,4);
p = polyfix(x1,y1,degreePoly,p1(1),p1(2),[1],[0]);
% p = [-0.0767 0.8290 -1.4277 1.6755];
figure
plot(x1,polyval(p,x1))
xlim([0 3])
ylim([0 3])
grid on
hold on
% Second function
x2 = linspace(0,4);
y2 = linspace(0,4);
p = polyfix(x2,y2,degreePoly,[1],[3],[1],[0])
% p = [0.4984 -2.7132 3.9312 1.2836];
plot(x2,polyval(p,x2))
xlim([0 3])
ylim([0 3])
grid on
If you don't have the polyfix function and you don't want to download it you can try the same code commenting the polyfix lines:
p = polyfix(x1,y1,degreePoly,p1(1),p1(2),[1],[0]);
p = polyfix(x2,y2,degreePoly,p2(1),p2(1),[1],[0]);
And uncommenting the lines:
% p = [-0.0767 0.8290 -1.4277 1.6755];
% p = [0.4984 -2.7132 3.9312 1.2836];
You will get this:
Now I will use this polynomial as a position (x,y) over time of my robots and I think I should be done. The x of the polynomial will be also the time, in this way I am sure that the robots will arrive in the 0-derivative point at the same time.
What do you think? Does it make sense?
Thanks again.
To have tangents same all the time, curves (or trajectories) needs to be always parallel. Generate trajectory for one object and keep other objects at fixed distance apart and following master trajectory.
In image provides if we take time next to three dots trajectories will not be same (or parallel) as objects moved in different directions. So i guess you've to keep then always parallel

Matlab plot of several digital signals

I'm trying to find a way to nicely plot my measurement data of digital signals.
So I have my data available as csv and mat file, exported from an Agilent Oscilloscope. The reason I'm not just taking a screen shot of the Oscilloscope screen is that I need to be more flexible (make several plots with one set of data, only showing some of the lines). Also I need to be able to change the plot in a month or two so my only option is creating a plot from the data with a computer.
What I'm trying to achieve is something similar to this picture:
The only thing missing on that pic is a yaxis with 0 and 1 lines.
My first try was to make a similar plot with Matlab. Here's what I got:
What's definitely missing is that the signal names are right next to the actual line and also 0 and 1 ticks on the y-axis.
I'm not even sure if Matlab is the right tool for this and I hope you guys can give me some hints/a solution on how to make my plots :-)
Here's my Matlab code:
clear;
close all;
clc;
MD.RAW = load('Daten/UVLOT1 debounced 0.mat'); % get MeasurementData
MD.N(1) = {'INIT\_DONE'};
MD.N(2) = {'CONF\_DONE'};
MD.N(3) = {'NSDN'};
MD.N(4) = {'NRST'};
MD.N(5) = {'1V2GD'};
MD.N(6) = {'2V5GD'};
MD.N(7) = {'3V3GD'};
MD.N(8) = {'5VGD'};
MD.N(9) = {'NERR'};
MD.N(10) = {'PGD'};
MD.N(11) = {'FGD'};
MD.N(12) = {'IGAGD'};
MD.N(13) = {'GT1'};
MD.N(14) = {'NERRA'};
MD.N(15) = {'GT1D'};
MD.N(16) = {'GB1D'};
% concat vectors into one matrix
MD.D = [MD.RAW.Trace_D0, MD.RAW.Trace_D1(:,2), MD.RAW.Trace_D2(:,2), MD.RAW.Trace_D3(:,2), ...
MD.RAW.Trace_D4(:,2), MD.RAW.Trace_D5(:,2), MD.RAW.Trace_D6(:,2), MD.RAW.Trace_D7(:,2), ...
MD.RAW.Trace_D8(:,2), MD.RAW.Trace_D9(:,2), MD.RAW.Trace_D10(:,2), MD.RAW.Trace_D11(:,2), ...
MD.RAW.Trace_D12(:,2), MD.RAW.Trace_D13(:,2), MD.RAW.Trace_D14(:,2), MD.RAW.Trace_D15(:,2)];
cm = hsv(size(MD.D,2)); % make colormap for plot
figure;
hold on;
% change timebase to ns
MD.D(:,1) = MD.D(:,1) * 1e9;
% plot lines
for i=2:1:size(MD.D,2)
plot(MD.D(:,1), MD.D(:,i)+(i-2)*1.5, 'color', cm(i-1,:));
end
hold off;
legend(MD.N, 'Location', 'EastOutside');
xlabel('Zeit [ns]'); % x axis label
title('Messwerte'); % title
set(gca, 'ytick', []); % hide y axis
Thank you guys for your help!
Dan
EDIT:
Here's a pic what I basically want. I added the signal names via text now the only thing that's missing are the 0, 1 ticks. They are correct for the init done signal. Now I just need them repeated instead of the other numbers on the y axis (sorry, kinda hard to explain :-)
So as written in my comment to the question. For appending Names to each signal I would recommend searching the documentation of how to append text to graph. There you get many different ways how to do it. You can change the position (above, below) and the exact point of data. As an example you could use:
text(x_data, y_data, Var_Name,'VerticalAlignment','top');
Here (x_data, y_data) is the data point where you want to append the text and Var_Name is the name you want to append.
For the second question of how to get a y-data which contains 0 and 1 values for each signal. I would do it by creating your signal the way, that your first signal has values of 0 and 1. The next signal is drawn about 2 higher. Thus it changes from 2 to 3 and so on. That way when you turn on y-axis (grid on) you get values at each integer (obviously you can change that to other values if you prefer less distance between 2 signals). Then you can relabel the y-axis using the documentation of axes (check the last part, because the documentation is quite long) and the set() function:
set(gca, 'YTick',0:1:last_entry, 'YTickLabel',new_y_label(0:1:last_entry))
Here last_entry is 2*No_Signals-1 and new_y_label is an array which is constructed of 0,1,0,1,0,....
For viewing y axis, you can turn the grid('on') option. However, you cannot chage the way the legends appear unless you resize it in the matlab figure. If you really want you can insert separate textboxes below each of the signal plots by using the insert ->Textbox option and then change the property (linestyle) of the textbox to none to get the exact same plot as above.
This is the end result and all my code, in case anybody else wants to use the good old ctrl-v ;-)
Code:
clear;
close all;
clc;
MD.RAW = load('Daten/UVLOT1 debounced 0.mat'); % get MeasurementData
MD.N(1) = {'INIT\_DONE'};
MD.N(2) = {'CONF\_DONE'};
MD.N(3) = {'NSDN'};
MD.N(4) = {'NRST'};
MD.N(5) = {'1V2GD'};
MD.N(6) = {'2V5GD'};
MD.N(7) = {'3V3GD'};
MD.N(8) = {'5VGD'};
MD.N(9) = {'NERR'};
MD.N(10) = {'PGD'};
MD.N(11) = {'FGD'};
MD.N(12) = {'IGAGD'};
MD.N(13) = {'GT1'};
MD.N(14) = {'NERRA'};
MD.N(15) = {'GT1D'};
MD.N(16) = {'GB1D'};
% concat vectors into one matrix
MD.D = [MD.RAW.Trace_D0, MD.RAW.Trace_D1(:,2), MD.RAW.Trace_D2(:,2), MD.RAW.Trace_D3(:,2), ...
MD.RAW.Trace_D4(:,2), MD.RAW.Trace_D5(:,2), MD.RAW.Trace_D6(:,2), MD.RAW.Trace_D7(:,2), ...
MD.RAW.Trace_D8(:,2), MD.RAW.Trace_D9(:,2), MD.RAW.Trace_D10(:,2), MD.RAW.Trace_D11(:,2), ...
MD.RAW.Trace_D12(:,2), MD.RAW.Trace_D13(:,2), MD.RAW.Trace_D14(:,2), MD.RAW.Trace_D15(:,2)];
cm = hsv(size(MD.D,2)); % make colormap for plot
figure;
hold on;
% change timebase to ns
MD.D(:,1) = MD.D(:,1) * 1e9;
% plot lines
for i=2:1:size(MD.D,2)
plot(MD.D(:,1), MD.D(:,i)+(i-2)*2, 'color', cm(i-1,:));
text(MD.D(2,1), (i-2)*2+.5, MD.N(i-1));
end
hold off;
%legend(MD.N, 'Location', 'EastOutside');
xlabel('Zeit [ns]'); % x axis label
title('Messwerte'); % title
% make y axis and grid the way I want it
set(gca, 'ytick', 0:size(MD.D,2)*2-3);
grid off;
set(gca,'ygrid','on');
set(gca, 'YTickLabel', {'0'; '1'});
ylim([-1,(size(MD.D,2)-1)*2]);

draw a line of best fit through data with shaded region for error

I have the following data:
dat = [9.3,0.6,0.4,0.7;...
3.2,1.2,0.7,1.9;...
3.9,1.8,0.7,1.9;...
1.0,7.4,5.6,10.7;...
4.7,1.0,0.5,1.3;...
2.2,2.6,1.2,2.7;...
7.2,1.0,0.5,1.1;...
1.0,4.8,7.5,10.3;...
2.7,1.8,1.7,4.0;...
8.2,0.8,0.4,0.9;...
1.0,4.9,5.7,8.2;...
12.9,1.3,0.6,1.6;...
7.7,0.8,0.5,1.3;...
5.8,0.9,0.6,1.9;...
1.1,4.5,6.2,12.1;...
1.1,4.5,2.8,4.8;...
16.4,0.3,0.3,0.5;...
10.4,0.6,0.3,0.7;...
2.2,3.1,2.2,4.6];
where the first column shows the observed values the second column shows the modeled values and the third and fourth columns show the min and max respectively.
I can plot the relationship between observed and modeled by
scatter(d(:,1),d(:,2))
Next, I would like to draw a smooth line through these points to show the relationship. How can this be done? Obviously a simple straight line would not be much use here.
Secondly, I would like to use the min and max (3rd and 4th columns respectively) to draw a shaded region around the modeled values in order to show the associated error.
I would eventually like to have something that looks like
http://www.giss.nasa.gov/research/briefs/rosenzweig_03/figure2.gif
Something like this?
%// Rename and sort your data
[x,I] = sort(dat(:,1));
y = dat(I,2);
mins = dat(I,3);
maxs = dat(I,4);
%// Assume a model of the form y = A + B/x. Solve for A and B
%// using least squares
P = [ones(size(x)) 1./x] \ y;
%// Initialize figure
figure(1), clf, hold on
set(1, 'Renderer', 'OpenGl');
%// Plot "shaded" areas
fill([x; flipud(x)], [mins; flipud(maxs)], 'y',...
'FaceAlpha', 0.2,...
'EdgeColor', 'r');
%// Plot data and fit
legendEntry(1) = plot(x, P(1) + P(2)./x, 'b',...
'LineWidth', 2);
legendEntry(2) = plot(dat(:,1), dat(:,2), 'r.',...
'Markersize', 15);

How to make a MATLAB plot interactive?

I'm trying to create a simple interface for plotting quadratic Lagrange polynomials. For this, you need just 3 points (with each their own x,y,z coordinates), which are then interpolated using the quadratic Lagrange polynomials.
It's easy to make a static version, or even one that lets the user input the 3 points before plotting the curve. But it should also be possible for the user to drag an existing point in the plot window to another position, and then re-plot the curve automatically using the new position of this point!
So in short, the user should be able to drag these black dots to another location. After that (or while dragging), the curve should be updated.
function Interact()
% Interactive stuff here
figure();
hold on;
axis([0 7 0 5])
DrawLagrange([1,1; 3,4; 6,2])
function DrawLagrange(P)
plot(P(:,1), P(:,2), 'ko--', 'MarkerSize', 10, 'MarkerFaceColor', 'k')
t = 0:.1:2;
Lagrange = [.5*t.^2 - 1.5*t + 1; -t.^2 + 2*t; .5*t.^2 - .5*t];
CurveX = P(1,1)*Lagrange(1,:) + P(2,1)*Lagrange(2,:) + P(3,1)*Lagrange(3,:);
CurveY = P(1,2)*Lagrange(1,:) + P(2,2)*Lagrange(2,:) + P(3,2)*Lagrange(3,:);
plot(CurveX, CurveY);
I think I either have to use functions like WindowButtonDownFcn, WindowButtonUpFcn and WindowButtonMotionFcn, or the ImPoint from the Image Processing Toolbox. But how?
[Edit]
It should also work in 3D, since I'd like to generalize this concept to tensor product surfaces.
Ok, I searched for some more information on the ImPoint option from the Image Processing Toolbox, and wrote this script.
Since ImPoint only works for a 2D setting (and I'd like to generalize this to 3D to be able to work with surfaces instead of curves), it is not really an acceptable answer! But somebody might benefit from it, or get an idea how to do this in 3D.
% -------------------------------------------------
% This file needs the Image Processing Toolbox!
% -------------------------------------------------
function Interact(Pos)
% This part is executed when you run it for the first time.
% In that case, the number of input arguments (nargin) == 0.
if nargin == 0
close all;
clear all;
clc;
figure();
hold on;
axis([0 7 0 5])
% I do not know how to do this without global variables?
global P0 P1 P2
% GCA = Get handle for Current Axis
P0 = ImPoint(gca,1,1);
setString(P0,'P0');
P1 = ImPoint(gca,2,4);
setString(P1,'P1');
P2 = ImPoint(gca,6,2);
setString(P2,'P2');
% Call subfunction
DrawLagrange(P0,P1,P2)
% Add callback to each point
addNewPositionCallback(P0,#Interact);
addNewPositionCallback(P1,#Interact);
addNewPositionCallback(P2,#Interact);
else
% If there _is_ some input argument, it has to be the updated
% position of a moved point.
global H1 H2 P0 P1 P2
% Display X and Y coordinates of moved point
Pos
% Important: remove old plots! Otherwise the graph will get messy.
delete(H1)
delete(H2)
DrawLagrange(P0,P1,P2)
end
function DrawLagrange(P0,P1,P2)
P = zeros(3,2);
% Get X and Y coordinates for the 3 points.
P(1,:) = getPosition(P0);
P(2,:) = getPosition(P1);
P(3,:) = getPosition(P2);
global H1 H2
H1 = plot(P(:,1), P(:,2), 'ko--', 'MarkerSize', 12);
t = 0:.1:2;
Lagrange = [.5*t.^2 - 1.5*t + 1; -t.^2 + 2*t; .5*t.^2 - .5*t];
CurveX = P(1,1)*Lagrange(1,:) + P(2,1)*Lagrange(2,:) + P(3,1)*Lagrange(3,:);
CurveY = P(1,2)*Lagrange(1,:) + P(2,2)*Lagrange(2,:) + P(3,2)*Lagrange(3,:);
H2 = plot(CurveX, CurveY);
I added some comments for clarity.
[Edit] In the preview the syntax highlighting doesn't look very good! Should I define the language to be highlighted somewhere?
A better solution (one that does not need any additional toolboxes) is to use events. First step:
H = figure('NumberTitle', 'off');
set(H, 'Renderer', 'OpenGL');
set(H, 'WindowButtonDownFcn', #MouseClick);
set(H, 'WindowButtonMotionFcn', #MouseMove);
set(H, 'WindowScrollWheelFcn', #MouseScroll);
set(H, 'KeyPressFcn', #KeyPress )
The next step is to define the functions like MouseClick, this is the place where you implement how to react to events (e.g. mouse buttons being clicked, keys being pressed).
In the meantime I implemented an interactive B-spline environment in MATLAB, the source code (along with a concise manual) can be downloaded from https://github.com/pjbarendrecht/BsplineLab.
Great question! I've had this problem too and wondered how to solve it before, but never looked into it. My first thought was to use ginput and then minimize the distance to the line and find the closest point. I thought that was a bit of a hack so I looked around. Seems like that's the only reasonable answer out there and was confirmed here with this code as an example.
%minimum absolute differences kick in again
xx = 1:10; %xdata
yy = exp(xx);
plot(xx,yy);
[xm ym] = ginput(1); %xmouse, ymouse
%Engine
[~, xidx] = min(abs(xx-xm)); %closest index
[~, yidx] = min(abs(yy-ym));
x_closest = xx(xidx) %extract
y_closest = yy(yidx)
Not sure how it scales to 3D, but I thought this would be a good start.