How to vary the color of a dynamic line?

Hello,

I am currently doing a program that can show the live trajectory of a car, based on recorded data of an RC car (here I created values in an Excel file). This trajectory is a line and its color is supposed to change with the velocity of the car (blue for the lowest speeds, red for the highest ones).

I have a "for" loop where the position of the car and of its trajectory is updated and I tried to include the change of color in the "set". In order to do that, I wrote an RGB code that varies with the speed vector "v".

The problem is that there is a change of the color of the whole trajectory, not just the last updated section.

Thank you in advance for your help.

(I have Matlab R2018b)

Answer 1

[Adam Danz]

There are a few ways around this (see this answer for demos). One way is to plot the line in segments such that each segment can be controlled individually and then, within a loop, make each segement visible. Some alternatives are to use patch() or fill() but then you're no longer working with lines.

See inline comments for details.

% Reshape lines to segments
% Assumes x and y are *column* vectors
% Example:  x = (1:.1:5)';  y = x.^2
xseg = [x(1:end-1),x(2:end)]; 
yseg = [y(1:end-1),y(2:end)]; 

% Plot all line segments (invisible for now unless you remove 'visible','off')
h = plot(xseg',yseg','-','LineWidth',4,'Visible','Off'); 
axis equal;
xlim([min(x) max(x)]);
ylim([min(y) max(y)]);
 
% Set all line segment colors (FOR DATA PROVIDED BY OP)
%     segColors = [v./max(v),zeros(size(v)),1-v./max(v)]; 
%     set(h, {'Color'}, mat2cell(segColors,ones(size(v)),3))

% Set all line segment colors (GENERAL SOLUTION)
segColors = jet(size(xseg,1)); % Choose a colormap
set(h, {'Color'}, mat2cell(segColors,ones(size(xseg,1),1),3))

% Make segements visible in loop
%     for n = 1:numel(t)-1
%         pause(.05)
%         set(h(n),'Visible', 'on')
%         drawnow(); 
%     end

% Or make it all visible at once
set(h, 'Visible', 'on')

Answer 2

[Jon]

I was just trying to code up an example, but when I finished I saw you already had an answer from Adam. My solultion used a similar approach to the answer just given by Adam.That is plot line segments and vary the color of each segment. In case it is useful I have put my code here, which might give you some alternatives for implementing the details:

% assign some parameters
numColors = 256; % resolution of color map
numPoints = 100; % number of points on trajectory
tFinal = 100; % final time

% assign color map

colorMap = jet(numColors)


% make up a trajectory and associated velocity value
% no physical meaning here, just to test the program
t = linspace(0,tFinal,numPoints);
x = 3*t.^2;
y = 5*t.^3;
d = sqrt(x.^2 + y.^2);
v = [0,diff(d)]/(tFinal/numPoints); % approximate velocity
vMax = max(v); % save maximum velocity for scaling colors

% plot the data with color change
% accomplish this by plotting individual segments of trajectory each with
% their own color according to the average velocity of the segment
figure % make a new figure
for k = 1:numPoints-1
    
    % calculate average velocity for this segment
    vAvg = (v(k) + v(k+1))/2;
    
    % look up color for current velocity
    idx = ceil(vAvg/vMax*numColors) % normalize by maximum velocity
    color = colorMap(idx,:);
    
    plot([x(k),x(k+1)],[y(k),y(k+1)],'-','Color',color)
    hold on % keep the previously plotted segments
end
hold off % back to normal
xlabel('X position')
ylabel('y position')

Answer 3

[Alexandre Piot]

Thank you very much Adam and Jon for your answers, it works perfectly!

I put the final code with the animation of the car below, I hope it will help other people (if you want to use it you have also to download the excel file attached in my first message).

clear, close, clc

%% Download and organize input data
% Raw input data
input_data = xlsread('input_values.xlsx');
t = input_data(:,1);
x = input_data(:,2);
y = input_data(:,3);
z = zeros(size(t));

% Matrix of the crossing points for the car (required for makehgtform)
pt = cat(2,x,y,z);

% Calculation of a speed vector
v = [sqrt(x(2)^2+y(2)^2)/t(2)];
for m = 2:numel(t)-1
    v = cat(1,v,(sqrt(x(m+1)^2+y(m+1)^2)-sqrt(x(m)^2+y(m)^2))/(t(m+1)-t(m)));
end

% Calculation of the angle (angle between the tangent and the y-axis)
alph = [acos(((x(2)-x(1))*0+(y(2)-y(1))*1)/(norm([x(2)-x(1) y(2)-y(1)])*norm([1 0])))];

for m = 2:numel(t)-1
    alph = cat(1,alph,acos(((x(m)-x(m-1))*0+(y(m)-y(m-1))*1)/(norm([x(m)-x(m-1) y(m)-y(m-1)])*norm([1 0]))));
end

% Geometry of the vehicle
wb = 4;
wt = 2.5;

%% Realization of the animation
% Reshape lines to segments
% Assumes x and y are column vectors
xseg = [x(1:end-1),x(2:end)]; 
yseg = [y(1:end-1),y(2:end)]; 
% Plot all line segments (invisible!)
h = plot(xseg',yseg','-','LineWidth',2,'Visible','Off'); 
axis equal;
xlim([min(x) max(x)]);
ylim([min(y) max(y)]);

%Initialize the rectangle position (the car)
xr = [x(1)-wt/2,x(1)-wt/2,x(1)+wt/2,x(1)+wt/2];
yr = [y(1)-wb/2,y(1)+wb/2,y(1)+wb/2,y(1)-wb/2];
r = hgtransform;
patch('XData',xr,'YData',yr,'FaceColor','black','Parent',r);
 
% Set all line segment colors
segColors = [v./max(v),zeros(size(v)),1-v./max(v)]; 
set(h, {'Color'}, mat2cell(segColors,ones(size(v)),3))
% Make segements visible in loop
for n = 1:numel(t)-1
    pause(t(n+1)-t(n))
    set(h(n),'Visible', 'on')
    r.Matrix = makehgtform('translate',pt(n+1,:),'zrotate',-alph(n));
    drawnow(); 
end

[Adam Danz]

Nice work! You can add a colorbar that defines the velocity by adding these 4 lines below.

colormap(sortrows(segColors,1))
cbh = colorbar();
caxis([min(v), max(v)])
ylabel(cbh, 'velocity (m/s)')  %or whatever the units are

[Alexandre Piot]

Thank you Adam that is a very good idea! I also changed the RGB code to have something fancier:

segColors = [sin((pi/2).*v./max(v)),sin(pi.*v./max(v)),sin((pi/2).*(1-v./max(v)))]; 

[Adam]

Beware though that plotting a line as segments tends to have an adverse affect on performance if you have too many segments. Ideally 1 graphics object containing your whole 'line' is far more performant than 1000 graphics objects making up a line. If it isn't a problem for your usage though then no need to worry about it, just something to be aware of if your data size gets bigger.

[Alexandre Piot]

The goal is too have a dynamic display of the trajectory while the information comes from the IMU on the RC car, that's why I need such a segmentation of the curve. I don't know if it's possible to have 1 graphic object which would dynamic and that would update in real time.