I am using MATLAB to print my simulation results. The results concerns a UAV's trajectory and waypoints that the UAV has to visit. The UAV is supposed to be equipped with a camera, whose range view is 10x10. Right now, the diagram shows the UAV's trajectory as a line visiting the waypoints. Is it possible, to show the camera's footprint, instead of the actual trajectory? I would like it to plot the rectangular camera's view to show the exhaustive coverage of the area. There is the option to plot the points as square, or cross, or cyrcles, but is it possible to set the boundaries of those?
Thank you in advance
The problem with using the marker size to indicate the range view is that there is no direct relation between the data units of your waypoints and the marker size. In other words, a value of 10 for the marker size doesn't necessarily mean that a side of a square marker is going to be 10 data units long (as defined by the scaling and limits of the axes).
An alternative is to plot square patches at each of your waypoints where the patch is aligned with the trajectory of the UAV. Here's how you can do this:
% Generate some sample data:
N = 20; % Number of waypoints
x = cumsum(5.*rand(1, N)); % X coordinates of UAV
y = cumsum(5.*rand(1, N)); % Y coordinates of UAV
% Compute vectors parallel and perpendicular to the trajectory at each point:
v = [diff(x); diff(y); zeros(1, N-1)]; % Vectors (1 per column)
v = bsxfun(#rdivide, v, sqrt(sum(v.^2, 1))); % Normalize each column to a unit vector
v = v(:, [1 1:end]); % Replicate a vector for starting point
vCross = cross(v, [zeros(2, N); ones(1, N)]); % Perpendicular vector
% Generate patch coordinates:
R = 10; % Range view
xPatch = [x+(R/2).*(v(1, :)+vCross(1, :)); ...
x+(R/2).*(v(1, :)-vCross(1, :)); ...
x-(R/2).*(v(1, :)+vCross(1, :)); ...
x-(R/2).*(v(1, :)-vCross(1, :))];
yPatch = [y+(R/2).*(v(2, :)+vCross(2, :)); ...
y+(R/2).*(v(2, :)-vCross(2, :)); ...
y-(R/2).*(v(2, :)+vCross(2, :)); ...
y-(R/2).*(v(2, :)-vCross(2, :))];
% Plot the patches and trajectory:
patch(xPatch, yPatch, [0 0.3 0], 'FaceAlpha', 0.25, 'EdgeColor', 'none');
hold on;
plot(x, y, '-', 'Color', [0.8 0 0], 'Marker', '.', 'MarkerSize', 12);
axis equal;
And here's a sample plot:
As a first attempt you can specify marker shape as square and set constant marker size, e.g.
plot(x,y,'s','markersize',10)
Here x and y are the vectors, holding the UAV coordinates. The letter 's' sets marker shape as square, and size is set to 10.
In reality, UAV trajectory is defined in a 3d space, where varying height above the ground corresponds to varying footprint size and shape. Taking this into account would require a bit more effort.
Also this assumes that the points are spaced closely enough otherwise there would be empty areas between markers.
Related
I try to solve the following 2D elliptic PDE electrostatic problem by fixing the Parallel plate Capacitors code. But I have problem to plot the circle region. How can I plot a circle region rather than the square?
% I use following two lines to label the 50V and 100V squares
% (but it should be two circles)
V(pp1-r_circle_small:pp1+r_circle_small,pp1-r_circle_small:pp1+r_circle_small) = 50;
V(pp2-r_circle_big:pp2+r_circle_big,pp2-r_circle_big:pp2+r_circle_big) = 100;
% Contour Display for electric potential
figure(1)
contour_range_V = -101:0.5:101;
contour(x,y,V,contour_range_V,'linewidth',0.5);
axis([min(x) max(x) min(y) max(y)]);
colorbar('location','eastoutside','fontsize',10);
xlabel('x-axis in meters','fontsize',10);
ylabel('y-axis in meters','fontsize',10);
title('Electric Potential distribution, V(x,y) in volts','fontsize',14);
h1=gca;
set(h1,'fontsize',10);
fh1 = figure(1);
set(fh1, 'color', 'white')
% Contour Display for electric field
figure(2)
contour_range_E = -20:0.05:20;
contour(x,y,E,contour_range_E,'linewidth',0.5);
axis([min(x) max(x) min(y) max(y)]);
colorbar('location','eastoutside','fontsize',10);
xlabel('x-axis in meters','fontsize',10);
ylabel('y-axis in meters','fontsize',10);
title('Electric field distribution, E (x,y) in V/m','fontsize',14);
h2=gca;
set(h2,'fontsize',10);
fh2 = figure(2);
set(fh2, 'color', 'white')
You're creating a square due to the way you're indexing (see this post on indexing). You've specified the rows to run from pp1-r_circle_small to pp1+r_circle_small and similar for the columns. Given that Swiss cheese is not an option, you're creating a complete square.
From geometry we know that all points within distance sqrt((X-X0)^2 - (Y-Y0)^2) < R from the centre of the circle at (X0,Y0) with radius R are within the circle, and the rest outside. This means that you can simply build a mask:
% Set up your grid
Xsize = 30; % Your case: 1
Ysize = 30; % Your case: 1
step = 1; % Amount of gridpoints; use 0.001 or something
% Build indexing grid for circle search, adapt as necessary
X = 0:step:Xsize;
Y = 0:step:Ysize;
[XX,YY] = meshgrid(X, Y);
V = zeros(numel(X), numel(Y));
% Repeat the below for both circles
R = 10; % Radius of your circle; your case 0.1 and 0.15
X0 = 11; % X coordinate of the circle's origin; your case 0.3 and 0.7
Y0 = 15; % Y coordinate of the circle's origin; your case 0.3 and 0.7
% Logical check to see whether a point is inside or outside
mask = sqrt( (XX - X0).^2 + (YY - Y0).^2) < R;
V(mask) = 50; % Give your circle the desired value
imagesc(V) % Just to show you the result
axis equal % Use equal axis to have no image distortion
mask is a logical matrix containing 1 where points are within your circle and 0 where points are outside. You can then use this mask to logically index your potential grid V to set it to the desired value.
Note: This will, obviously, not create a perfect circle, given you cannot plot a perfect circle on a square grid. The finer the grid, the more circle-like your "circle" will be. This shows the result with step = 0.01
Note 2: You'll need to tweek your definition of X, Y, X0, Y0 and R to match your values.
Here are the coordinates that I am planning to plot, filename is Coords:
x y
0.0110 0.1105
-0.2730 0.2559
0.3610 0.1528
-0.0077 -0.2520
-0.2412 -0.1979
0.0444 -0.0526
0.0543 -0.0076
-0.1710 0.1170
0.12741 -0.0448
0.0949 -0.0811
Here is my code that plots the scatter graph first:
Hold on
%Plot Coordinate
For i=1:10
dot_size = 100;
scatter ( Coords(i,1) ,Coords(i,2), dot_size, 'filled', 'MarkerEdgeColor', 'k' );
end
%Draw line distance between each points
for i=1:10
for j=1:10
plot( [Coords(i,1) Coords(i,2)], [Coords(j,1) Coords(j,2)] );
end
end
Hold off
%Sets the size of the y and x axis
xlim( [ min( Coords(:,1)) max( Coords(:,1)) ] );
ylim( [ min( Coords(:,2)) max( Coords(:,2)) ] );
axis off;
Here is the result I get:
I don't know why the lines are being drawn everywhere. I also notice that even when plot(x,y) = 0, the line is still being drawn.
I also would like to change the thickness and opacity of the line depending on the distance between the two points: E.g. thicker and darker line for short distance between points. And thinner /lighter line if the distance between two points are long.
I want my plot to look something like this:
The reason your lines do not match the scattered points is the coordinates you give to plot; The coordinates are in wrong order and therefore they do not define the lines correctly.
I modified your code to correct this issue. I replaced plot with line, but you can also do the same with plot. In addition, I defined the anonymous functions f and g to define the color and thickness of each line based on distance of the two ends, d. You can modify these functionalities to get different graphical behaviors.
n = 10; % number of points
dot_size = 100;
Coords = rand(n, 2);
% maximum possible length in your coordination plane:
L = norm([max(Coords(:,1))-min(Coords(:,1)),max(Coords(:,2))-min(Coords(:,2))]);
% this function defines the line width:
f = #(x) L / (x + 0.1); % 0.1 avoids huge line widths in very small distances
% this function defines the color:
g = #(x) x * [1 1 1] / L;
figure
hold on
for ii = 1:n-1
for jj = ii+1:n
d = norm([Coords(ii,1)-Coords(jj,1), Coords(ii,2)-Coords(jj,2)]);
line([Coords(ii,1) Coords(jj,1)], [Coords(ii,2) Coords(jj,2)], ...
'LineWidth', f(d), 'Color', g(d));
end
end
scatter (Coords(:,1), Coords(:,2), dot_size, 'filled', 'MarkerEdgeColor', 'k');
axis tight
axis off
With this output:
Notes:
axis tight is a command that sets the limits to the tightest possible. It is equivalent to your xlim( [ min( Coords(:,1)) max( Coords(:,1)) ] ); and the next line.
In the for-loops you should try to avoid choosing one pair of points twice or same point as both sides of a line.
For scattering you do not need a loop. It could all be done at once.
I brought scatter after plotting the lines, so the circles are drawn on top.
There is also a specialized MATLAB function for generating plots like this: gplot.
data = [
0.0110 0.1105
-0.2730 0.2559
0.3610 0.1528
-0.0077 -0.2520
-0.2412 -0.1979
0.0444 -0.0526
0.0543 -0.0076
-0.1710 0.1170
0.12741 -0.0448
0.0949 -0.0811]; % Coordinates
adjM = squareform(pdist(data)); %
adjM (adjM > 0) = 1; % Form adjacency matrix based on Euclidean distances
figure; gplot(adjM, data, '-o') % Plot figure based on coordinates and adjacency matrix
Then, customize to your liking, e.g. if you want to change marker type, remove the axis, add labels etc.
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 am trying to sort random coordinates on a 2D cartesian grid using MATLAB into "bins" defined by a grid.
For example if I have a 2D domain with X ranging from [-1,1] and Y from [-1,1] and I generate some random coordinates within the domain, how can I "count" how many coordinates fall into each quadrant?
I realize that for and if statements can be used to determine the if each coordinate is within the quadrants, but I would like to scale this to much larger square grids that have more than just 4 quadrants.
Any concise and efficient approach would be appreciated!
Below is an example adapted from the code I mentioned.
The resulting binned points are be stored the variable subs; Each row contains 2d subscript indices of the bin to which a point was assigned.
% 2D points, both coordinates in the range [-1,1]
XY = rand(1000,2)*2 - 1;
% define equal-sized bins that divide the [-1,1] grid into 10x10 quadrants
mn = [-1 -1]; mx = [1 1]; % mn = min(XY); mx = max(XY);
N = 10;
edges = linspace(mn(1), mx(1), N+1);
% map points to bins
% We fix HISTC handling of last edge, so the intervals become:
% [-1, -0.8), [-0.8, -0.6), ..., [0.6, 0.8), [0.8, 1]
% (note the last interval is closed on the right side)
[~,subs] = histc(XY, edges, 1);
subs(subs==N+1) = N;
% 2D histogram of bins count
H = accumarray(subs, 1, [N N]);
% plot histogram
imagesc(H.'); axis image xy
set(gca, 'TickDir','out')
colormap gray; colorbar
xlabel('X'); ylabel('Y')
% show bin intervals
ticks = (0:N)+0.5;
labels = strtrim(cellstr(num2str(edges(:),'%g')));
set(gca, 'XTick',ticks, 'XTickLabel',labels, ...
'YTick',ticks, 'YTickLabel',labels)
% plot 2D points on top, correctly scaled from [-1,1] to [0,N]+0.5
XY2 = bsxfun(#rdivide, bsxfun(#minus, XY, mn), mx-mn) * N + 0.5;
line(XY2(:,1), XY2(:,2), 'LineStyle','none', 'Marker','.', 'Color','r')
I need to plot a list of 3d lines in matlab. What is the quickest way to do that?
I am currently doing something like
%edges is a MX2 matrix, holding the list of edges
%points are the vertices' coordinates
hold on; %so all the lines will be saved
for i=1:size(edges,1)
a=edges(i,1); %get first point's index
b=edges(i,2); %get second point's index
p=[points(:,a) points(:,b)]; %construct a 3X2 matrix out of the 2 points
plot3(p(1,:),p(2,:),p(3,:)); %plot a line
end
But this is not only slow during the actual loop, but also at the end, the resulting plot is very slow and irresponsive when I try to, for instance, rotate it using the drag & rotate tool.
I know the same plot using opengl etc would run much faster...
You can use the LINE low-level function, using NaN to plot as separate segments:
%# sample graph vertices and edges (similar to your data)
[adj,XYZ] = bucky;
[r c] = find(adj);
edges = [r c]; %# M-by-2 matrix holding the vertex indices
points = XYZ'; %# 3-by-N matrix of points X/Y/Z coordinates
%# build a list of separated lines
e = edges';
e(end+1,:) = 1;
e = e(:);
p = points(:,e);
p(:,3:3:end) = NaN;
figure
h = line(p(1,:), p(2,:), p(3,:));
view(3)
This is very efficient as it creates a single line object. Now you can customize the line, but it is restricted to have one color for the entire thing:
set(h, 'Color',[.4 .4 1], 'Marker','.', 'MarkerSize',10, ...
'MarkerFaceColor','g', 'MarkerEdgeColor','g')
According to the comments, if you want to have each edge in your graph in a specified color, consider the following code instead. It involves using the SURFACE function:
p = p'; %'# transpose the above p for convenience
clr = (1:size(p,1))'; %'# for each edge, color index in current colormap
figure
surface(p(:,[1 1]), p(:,[2 2]), p(:,[3 3]), [clr clr], ...
'EdgeColor','flat', 'FaceColor','none')
colormap( hsv(numel(clr)) ) %# specify your colormap here
view(3)
I think you can do something like this (caution - brain compiled code...)
figure;
patch('faces', edges, 'vertices', points, 'edgecolor', 'b');
axis equal;
Where edges should be an Nx2 matrix of indices and points should be an Mx3 matrix of coordinates (the transpose of your points array).
From my experience, calling patch directly can be significantly faster than repeated calls to plot.
To give some idea, the times to generate 1000 randomly generated line segments, using my (admittedly old!) MATLAB 7.1 are as follows:
Calling patch: 0.03 seconds.
Calling plot: 0.5 seconds.
EDIT: One way to get the edge colour behaving as you want (specifying a single colour per edge) is to introduce duplicate vertices as follows:
This works-around the issue that the edge colour can only be specified indirectly via vertex colour data. If we were to rely only on the vertex colours then all edges sharing a common vertex might end up with the colour assigned to that vertex - check out the 'flat 'edgecolour description here.
%% a "star" shape, so that we can really see what's going on
%% with the edge colours!!
pp = [0,0,0; 1,-1,0; 1,1,0; -1,1,0; -1,-1,0];
ee = [1,2; 1,3; 1,4; 1,5];
%% important - only 1 colour known per edge, not per vertex!!
cc = (1:size(ee,1))';
%% setup a new set of vertices/edges/colours with duplicate vertices
%% so that each edge gets it's correct colour
nnum = 0;
pnew = zeros(2 * size(ee, 1), 3); %% new vertices
enew = zeros(1 * size(ee, 1), 2); %% new edge indices
cnew = zeros(2 * size(ee, 1), 1); %% new edge colours - via vertices
for j = 1 : size(ee, 1)
n1 = ee(j, 1); %% old edge indices
n2 = ee(j, 2);
enew(j, 1) = nnum + 1; %% new edge indicies into pnew
enew(j, 2) = nnum + 2;
pnew(nnum + 1, :) = pp(n1, :); %% create duplicate vertices
pnew(nnum + 2, :) = pp(n2, :);
cnew(nnum + 1) = cc(j); %% map single edge colour onto both vertices
cnew(nnum + 2) = cc(j);
nnum = nnum + 2;
end
%% Draw the set efficiently via patch
tic
figure;
hold on;
patch('faces', enew, 'vertices', pnew, 'facevertexcdata', cnew, ...
'edgecolor', 'flat', 'facecolor', 'none');
plot(pnew(:,1), pnew(:,2), 'b.');
axis equal;
toc
It would be nicer if MATLAB allowed you to directly specify the edge colour data - but it doesn't seem to support that...
Hope this helps.