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.
Related
I'm trying to fill an area between two curves with respect to a function which depends on the values of the curves.
Here is the code of what I've managed to do so far
i=50;
cc = #(xx,x,y) 1./(1+(exp(-xx)/(exp(-x)-exp(-y))));
n_vec = 2:0.1:10;
x_vec = linspace(2,10,length(n_vec));
y_vec = abs(sin(n_vec));
N=[n_vec,fliplr(n_vec)];
X=[x_vec,fliplr(y_vec)];
figure(1)
subplot(2,1,1)
hold on
plot(n_vec,x_vec,n_vec,y_vec)
hp = patch(N,X,'b')
plot([n_vec(i) n_vec(i)],[x_vec(i),y_vec(i)],'linewidth',5)
xlabel('n'); ylabel('x')
subplot(2,1,2)
xx = linspace(y_vec(i),x_vec(i),100);
plot(xx,cc(xx,y_vec(i),x_vec(i)))
xlabel('x'); ylabel('c(x)')
This code produces the following graph
The color code which I've added represent the color coding that each line (along the y axis at a point on the x axis) from the area between the two curves should be.
Overall, the entire area should be filled with a gradient color which depends on the values of the curves.
I've assisted the following previous questions but could not resolve a solution
MATLAB fill area between lines
Patch circle by a color gradient
Filling between two curves, according to a colormap given by a function MATLAB
NOTE: there is no importance to the functional form of the curves, I would prefer an answer which refers to two general arrays which consist the curves.
The surf plot method
The same as the scatter plot method, i.e. generate a point grid.
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px = linspace(min(n_vec), max(n_vec), resolution(1));
py = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px, py);
Generate a logical array indicating whether the points are inside the polygon, but no need to extract the points:
in = inpolygon(px, py, N, X);
Generate Z. The value of Z indicates the color to use for the surface plot. Hence, it is generated using the your function cc.
pz = 1./(1+(exp(-py_)/(exp(-y_vec(i))-exp(-x_vec(i)))));
pz = repmat(pz',1,resolution(2));
Set Z values for points outside the area of interest to NaN so MATLAB won't plot them.
pz(~in) = nan;
Generate a bounded colourmap (delete if you want to use full colour range)
% generate colormap
c = jet(100);
[s,l] = bounds(pz,'all');
s = round(s*100);
l = round(l*100);
if s ~= 0
c(1:s,:) = [];
end
if l ~= 100
c(l:100,:) = [];
end
Finally, plot.
figure;
colormap(jet)
surf(px,py,pz,'edgecolor','none');
view(2) % x-y view
Feel free to turn the image arround to see how it looks like in the Z-dimention - beautiful :)
Full code to test:
i=50;
cc = #(xx,x,y) 1./(1+(exp(-xx)/(exp(-x)-exp(-y))));
n_vec = 2:0.1:10;
x_vec = linspace(2,10,length(n_vec));
y_vec = abs(sin(n_vec));
% generate grid
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px_ = linspace(min(n_vec), max(n_vec), resolution(1));
py_ = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px_, py_);
% extract points
in = inpolygon(px, py, N, X);
% generate z
pz = 1./(1+(exp(-py_)/(exp(-y_vec(i))-exp(-x_vec(i)))));
pz = repmat(pz',1,resolution(2));
pz(~in) = nan;
% generate colormap
c = jet(100);
[s,l] = bounds(pz,'all');
s = round(s*100);
l = round(l*100);
if s ~= 0
c(1:s,:) = [];
end
if l ~= 100
c(l:100,:) = [];
end
% plot
figure;
colormap(c)
surf(px,py,pz,'edgecolor','none');
view(2)
You can use imagesc and meshgrids. See comments in the code to understand what's going on.
Downsample your data
% your initial upper and lower boundaries
n_vec_long = linspace(2,10,1000000);
f_ub_vec_long = linspace(2, 10, length(n_vec_long));
f_lb_vec_long = abs(sin(n_vec_long));
% downsample
n_vec = linspace(n_vec_long(1), n_vec_long(end), 1000); % for example, only 1000 points
% get upper and lower boundary values for n_vec
f_ub_vec = interp1(n_vec_long, f_ub_vec_long, n_vec);
f_lb_vec = interp1(n_vec_long, f_lb_vec_long, n_vec);
% x_vec for the color function
x_vec = 0:0.01:10;
Plot the data
% create a 2D matrix with N and X position
[N, X] = meshgrid(n_vec, x_vec);
% evaluate the upper and lower boundary functions at n_vec
% can be any function at n you want (not tested for crossing boundaries though...)
f_ub_vec = linspace(2, 10, length(n_vec));
f_lb_vec = abs(sin(n_vec));
% make these row vectors into matrices, to create a boolean mask
F_UB = repmat(f_ub_vec, [size(N, 1) 1]);
F_LB = repmat(f_lb_vec, [size(N, 1) 1]);
% create a mask based on the upper and lower boundary functions
mask = true(size(N));
mask(X > F_UB | X < F_LB) = false;
% create data matrix
Z = NaN(size(N));
% create function that evaluates the color profile for each defined value
% in the vectors with the lower and upper bounds
zc = #(X, ub, lb) 1 ./ (1 + (exp(-X) ./ (exp(-ub) - exp(-lb))));
CData = zc(X, f_lb_vec, f_ub_vec); % create the c(x) at all X
% put the CData in Z, but only between the lower and upper bound.
Z(mask) = CData(mask);
% normalize Z along 1st dim
Z = normalize(Z, 1, 'range'); % get all values between 0 and 1 for colorbar
% draw a figure!
figure(1); clf;
ax = axes; % create some axes
sc = imagesc(ax, n_vec, x_vec, Z); % plot the data
ax.YDir = 'normal' % set the YDir to normal again, imagesc reverses it by default;
xlabel('n')
ylabel('x')
This already looks kinda like what you want, but let's get rid of the blue area outside the boundaries. This can be done by creating an 'alpha mask', i.e. set the alpha value for all pixels outside the previously defined mask to 0:
figure(2); clf;
ax = axes; % create some axes
hold on;
sc = imagesc(ax, n_vec, x_vec, Z); % plot the data
ax.YDir = 'normal' % set the YDir to normal again, imagesc reverses it by default;
% set a colormap
colormap(flip(hsv(100)))
% set alpha for points outside mask
Calpha = ones(size(N));
Calpha(~mask) = 0;
sc.AlphaData = Calpha;
% plot the other lines
plot(n_vec, f_ub_vec, 'k', n_vec, f_lb_vec, 'k' ,'linewidth', 1)
% set axis limits
xlim([min(n_vec), max(n_vec)])
ylim([min(x_vec), max(x_vec)])
there is no importance to the functional form of the curves, I would prefer an answer which refers to two general arrays which consist the curves.
It is difficult to achieve this using patch.
However, you may use scatter plots to "fill" the area with coloured dots. Alternatively, and probably better, use surf plot and generate z coordinates using your cc function (See my seperate solution).
The scatter plot method
First, make a grid of points (resolution 500*500) inside the rectangular space bounding the two curves.
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px = linspace(min(n_vec), max(n_vec), resolution(1));
py = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px, py);
figure;
scatter(px(:), py(:), 1, 'r');
The not-interesting figure of the point grid:
Next, extract the points inside the polygon defined by the two curves.
in = inpolygon(px, py, N, X);
px = px(in);
py = py(in);
hold on;
scatter(px, py, 1, 'k');
Black points are inside the area:
Finally, create color and plot the nice looking gradient colour figure.
% create color for the points
cid = 1./(1+(exp(-py)/(exp(-y_vec(i))-exp(-x_vec(i)))));
c = jet(101);
c = c(round(cid*100)+1,:); % +1 to avoid zero indexing
% plot
figure;
scatter(px,py,16,c,'filled','s'); % use size 16, filled square markers.
Note that you may need a fairly dense grid of points to make sure the white background won't show up. You may also change the point size to a bigger value (won't impact performance).
Of cause, you may use patch to replace scatter but you will need to work out the vertices and face ids, then you may patch each faces separately with patch('Faces',F,'Vertices',V). Using patch this way may impact performance.
Complete code to test:
i=50;
cc = #(xx,x,y) 1./(1+(exp(-xx)/(exp(-x)-exp(-y))));
n_vec = 2:0.1:10;
x_vec = linspace(2,10,length(n_vec));
y_vec = abs(sin(n_vec));
% generate point grid
y = [x_vec(:); y_vec(:)];
resolution = [500,500];
px_ = linspace(min(n_vec), max(n_vec), resolution(1));
py_ = linspace(min(y), max(y), resolution(2));
[px, py] = meshgrid(px_, py_);
% extract points
in = inpolygon(px, py, N, X);
px = px(in);
py = py(in);
% generate color
cid = 1./(1+(exp(-py)/(exp(-y_vec(i))-exp(-x_vec(i)))));
c = jet(101);
c = c(round(cid*100)+1,:); % +1 to avoid zero indexing
% plot
figure;
scatter(px,py,16,c,'filled','s');
I want the color of each arrow in a quiver3 plot from MATLAB to correspond to the magnitude of each arrow. Is there any way to do that?
I saw a few examples online that are able to do this for the 2D quiver, however none of them work for the 3D variant, quiver3.
I have the following plot and want to replace the blue arrows with a color corresponding to their magnitude.
In the old graphics system (R2014a and earlier) this is not possible using the built-in quiver object. You can easily get all of the plot objects that are used to compose the quiver plot
q = quiver(1:5, 1:5, 1:5, 1:5);
handles = findall(q, 'type', 'line');
But the tails are all represented by one plot object, and the arrow heads are represented by another. As such, you can't alter the color of each head/tail individually.
set(handles(1), 'Color', 'r')
set(handles(2), 'Color', 'g')
However, with the introduction of HG2 (R2014b and later), you can actually get access to two (undocumented) LineStrip objects (matlab.graphics.primitive.world.LineStrip) (one represents the heads and one represents the tails). These are accessible via the hidden properties Tail and Head.
q = quiver(1, 1, 1, 1);
headLineStrip = q.Head;
tailLineStrip = q.Tail;
You can then alter the color properties of these objects to make each arrow a different color.
The Basic Idea
To do this, I first compute the magnitude of all quiver arrows (this works for both quiver and quiver3)
mags = sqrt(sum(cat(2, q.UData(:), q.VData(:), ...
reshape(q.WData, numel(q.UData), [])).^2, 2));
Then I use the current colormap to map each magnitude to an RGB value. The shortest arrow is assigned the lowest color on the colormap and the longest arrow is assigned the highest color on the colormap. histcounts works great for assigning each magnitude an index which can be passed to ind2rgb along with the colormap itself. We have to multiply by 255 because we need the color to be RGB as an 8-bit integer.
% Get the current colormap
currentColormap = colormap(gca);
% Now determine the color to make each arrow using a colormap
[~, ~, ind] = histcounts(mags, size(currentColormap, 1));
% Now map this to a colormap
cmap = uint8(ind2rgb(ind(:), currentColormap) * 255);
The LineStrip ColorData property (when specified as truecolor) also needs to have an alpha channel (which we will set to 255 meaning opaque).
cmap(:,:,4) = 255;
At this point we can then set the ColorBinding property to interpolated rather than object (to decouple it from the quiver object) and set the ColorData property of both q.Head and q.Tail to the colors we created above giving each arrow it's own color.
Full Solution
NOTE: This solution works for both quiver and quiver3 and the code does not have to be adapted at all.
%// Create a quiver3 as we normally would (could also be 2D quiver)
x = 1:10;
y = 1:10;
[X,Y] = meshgrid(x, y);
Z = zeros(size(X));
U = zeros(size(X));
V = zeros(size(X));
W = sqrt(X.^2 + Y.^2);
q = quiver3(X, Y, Z, U, V, W);
%// Compute the magnitude of the vectors
mags = sqrt(sum(cat(2, q.UData(:), q.VData(:), ...
reshape(q.WData, numel(q.UData), [])).^2, 2));
%// Get the current colormap
currentColormap = colormap(gca);
%// Now determine the color to make each arrow using a colormap
[~, ~, ind] = histcounts(mags, size(currentColormap, 1));
%// Now map this to a colormap to get RGB
cmap = uint8(ind2rgb(ind(:), currentColormap) * 255);
cmap(:,:,4) = 255;
cmap = permute(repmat(cmap, [1 3 1]), [2 1 3]);
%// We repeat each color 3 times (using 1:3 below) because each arrow has 3 vertices
set(q.Head, ...
'ColorBinding', 'interpolated', ...
'ColorData', reshape(cmap(1:3,:,:), [], 4).'); %'
%// We repeat each color 2 times (using 1:2 below) because each tail has 2 vertices
set(q.Tail, ...
'ColorBinding', 'interpolated', ...
'ColorData', reshape(cmap(1:2,:,:), [], 4).');
And applied to a 2D quiver object
If you don't necessarily want to scale the arrows to the entire range of the colormap you could use the following call to histcounts (instead of the line above) to map the magnitudes using the color limits of the axes.
clims = num2cell(get(gca, 'clim'));
[~, ~, ind] = histcounts(mags, linspace(clims{:}, size(currentColormap, 1)));
If your using a post r2014b version you can use undocumented features to change the colour of each line and head:
figure
[x,y] = meshgrid(-2:.5:2,-1:.5:1);
z = x .* exp(-x.^2 - y.^2);
[u,v,w] = surfnorm(x,y,z);
h=quiver3(x,y,z,u,v,w);
s = size(x);
nPoints = s(1)*s(2);
% create a colour map
cmap = parula(nPoints);
% x2 because each point has 2 points, a start and an end.
cd = uint8(repmat([255 0 0 255]', 1, nPoints*2));
count = 0;
% we need to assign a colour per point
for ii=1:nPoints
% and we need to assign a colour to the start and end of the
% line.
for jj=1:2
count = count + 1;
cd(1:3,count) = uint8(255*cmap(ii,:)');
end
end
% set the colour binding method and the colour data of the tail
set(h.Tail, 'ColorBinding','interpolated', 'ColorData',cd)
% create a color matrix for the heads
cd = uint8(repmat([255 0 0 255]', 1, nPoints*3));
count = 0;
% we need to assign a colour per point
for ii=1:nPoints
% and we need to assign a colour to the all the points
% at the head of the arrow
for jj=1:3
count = count + 1;
cd(1:3,count) = uint8(255*cmap(ii,:)');
end
end
% set the colour binding method and the colour data of the head
set(h.Head, 'ColorBinding','interpolated', 'ColorData',cd)
Note: I've not done anything clever with the magnitude and simply change the colour of each quiver based on the order in the original matrix - but you should be able to get the idea on how to use this "feature"
Note that if you are using Suevers solution and have NaNs in your data you should include this line before calling histcounts:
mags(isnan(mags)) = [];
Otherwise you will get an error about wrong input size because matlab does not create vertices for NaNs in your U/V/W data.
I want the color of each arrow in a quiver3 plot from MATLAB to correspond to the magnitude of each arrow. Is there any way to do that?
I saw a few examples online that are able to do this for the 2D quiver, however none of them work for the 3D variant, quiver3.
I have the following plot and want to replace the blue arrows with a color corresponding to their magnitude.
In the old graphics system (R2014a and earlier) this is not possible using the built-in quiver object. You can easily get all of the plot objects that are used to compose the quiver plot
q = quiver(1:5, 1:5, 1:5, 1:5);
handles = findall(q, 'type', 'line');
But the tails are all represented by one plot object, and the arrow heads are represented by another. As such, you can't alter the color of each head/tail individually.
set(handles(1), 'Color', 'r')
set(handles(2), 'Color', 'g')
However, with the introduction of HG2 (R2014b and later), you can actually get access to two (undocumented) LineStrip objects (matlab.graphics.primitive.world.LineStrip) (one represents the heads and one represents the tails). These are accessible via the hidden properties Tail and Head.
q = quiver(1, 1, 1, 1);
headLineStrip = q.Head;
tailLineStrip = q.Tail;
You can then alter the color properties of these objects to make each arrow a different color.
The Basic Idea
To do this, I first compute the magnitude of all quiver arrows (this works for both quiver and quiver3)
mags = sqrt(sum(cat(2, q.UData(:), q.VData(:), ...
reshape(q.WData, numel(q.UData), [])).^2, 2));
Then I use the current colormap to map each magnitude to an RGB value. The shortest arrow is assigned the lowest color on the colormap and the longest arrow is assigned the highest color on the colormap. histcounts works great for assigning each magnitude an index which can be passed to ind2rgb along with the colormap itself. We have to multiply by 255 because we need the color to be RGB as an 8-bit integer.
% Get the current colormap
currentColormap = colormap(gca);
% Now determine the color to make each arrow using a colormap
[~, ~, ind] = histcounts(mags, size(currentColormap, 1));
% Now map this to a colormap
cmap = uint8(ind2rgb(ind(:), currentColormap) * 255);
The LineStrip ColorData property (when specified as truecolor) also needs to have an alpha channel (which we will set to 255 meaning opaque).
cmap(:,:,4) = 255;
At this point we can then set the ColorBinding property to interpolated rather than object (to decouple it from the quiver object) and set the ColorData property of both q.Head and q.Tail to the colors we created above giving each arrow it's own color.
Full Solution
NOTE: This solution works for both quiver and quiver3 and the code does not have to be adapted at all.
%// Create a quiver3 as we normally would (could also be 2D quiver)
x = 1:10;
y = 1:10;
[X,Y] = meshgrid(x, y);
Z = zeros(size(X));
U = zeros(size(X));
V = zeros(size(X));
W = sqrt(X.^2 + Y.^2);
q = quiver3(X, Y, Z, U, V, W);
%// Compute the magnitude of the vectors
mags = sqrt(sum(cat(2, q.UData(:), q.VData(:), ...
reshape(q.WData, numel(q.UData), [])).^2, 2));
%// Get the current colormap
currentColormap = colormap(gca);
%// Now determine the color to make each arrow using a colormap
[~, ~, ind] = histcounts(mags, size(currentColormap, 1));
%// Now map this to a colormap to get RGB
cmap = uint8(ind2rgb(ind(:), currentColormap) * 255);
cmap(:,:,4) = 255;
cmap = permute(repmat(cmap, [1 3 1]), [2 1 3]);
%// We repeat each color 3 times (using 1:3 below) because each arrow has 3 vertices
set(q.Head, ...
'ColorBinding', 'interpolated', ...
'ColorData', reshape(cmap(1:3,:,:), [], 4).'); %'
%// We repeat each color 2 times (using 1:2 below) because each tail has 2 vertices
set(q.Tail, ...
'ColorBinding', 'interpolated', ...
'ColorData', reshape(cmap(1:2,:,:), [], 4).');
And applied to a 2D quiver object
If you don't necessarily want to scale the arrows to the entire range of the colormap you could use the following call to histcounts (instead of the line above) to map the magnitudes using the color limits of the axes.
clims = num2cell(get(gca, 'clim'));
[~, ~, ind] = histcounts(mags, linspace(clims{:}, size(currentColormap, 1)));
If your using a post r2014b version you can use undocumented features to change the colour of each line and head:
figure
[x,y] = meshgrid(-2:.5:2,-1:.5:1);
z = x .* exp(-x.^2 - y.^2);
[u,v,w] = surfnorm(x,y,z);
h=quiver3(x,y,z,u,v,w);
s = size(x);
nPoints = s(1)*s(2);
% create a colour map
cmap = parula(nPoints);
% x2 because each point has 2 points, a start and an end.
cd = uint8(repmat([255 0 0 255]', 1, nPoints*2));
count = 0;
% we need to assign a colour per point
for ii=1:nPoints
% and we need to assign a colour to the start and end of the
% line.
for jj=1:2
count = count + 1;
cd(1:3,count) = uint8(255*cmap(ii,:)');
end
end
% set the colour binding method and the colour data of the tail
set(h.Tail, 'ColorBinding','interpolated', 'ColorData',cd)
% create a color matrix for the heads
cd = uint8(repmat([255 0 0 255]', 1, nPoints*3));
count = 0;
% we need to assign a colour per point
for ii=1:nPoints
% and we need to assign a colour to the all the points
% at the head of the arrow
for jj=1:3
count = count + 1;
cd(1:3,count) = uint8(255*cmap(ii,:)');
end
end
% set the colour binding method and the colour data of the head
set(h.Head, 'ColorBinding','interpolated', 'ColorData',cd)
Note: I've not done anything clever with the magnitude and simply change the colour of each quiver based on the order in the original matrix - but you should be able to get the idea on how to use this "feature"
Note that if you are using Suevers solution and have NaNs in your data you should include this line before calling histcounts:
mags(isnan(mags)) = [];
Otherwise you will get an error about wrong input size because matlab does not create vertices for NaNs in your U/V/W data.
I have an arbitrary shape, of which the exterior boundary has been traced in MATLAB using bwboundaries. Using regionprops, I can calculate the total area enclosed by this shape.
However, I want to know the area for only the parts of the shape that fall within a circle of known radius R centered at coordinates [x1, y1]. What is the best way to accomplish this?
There are a few ways to approach this. One way you could alter the mask before performing bwboundaries (or regionprops) so that it only includes pixels which are within the given circle.
This example assumes that you already have a logical matrix M that you pass to bwboundaries.
function [A, boundaries] = traceWithinCircle(M, x1, y1, R);
%// Get pixel centers
[x,y] = meshgrid(1:size(M, 1), 1:size(M, 2));
%// Compute their distance from x1, y1
distances = sqrt(sum(bsxfun(#minus, [x(:), y(:)], [x1, y1]).^2, 2));
%// Determine which are inside of the circle with radius R
isInside = distances <= R;
%// Set the values outside of this circle in M to zero
%// This will ensure that they are not detected in bwboundaries
M(~isInside) = 0;
%// Now perform bwboundaries on things that are
%// inside the circle AND were 1 in M
boundaries = bwboundaries(M);
%// You can, however, get the area by simply counting the number of 1s in M
A = sum(M(:));
%// Of if you really want to use regionprops on M
%// props = regionprops(M);
%// otherArea = sum([props.Area]);
end
And as an example
%// Load some example data
data = load('mri');
M = data.D(:,:,12) > 60;
%// Trace the boundaries using the method described above
B = traceWithinCircle(M, 70, 90, 50);
%// Display the results
figure;
hax = axes();
him = imagesc(M, 'Parent', hax);
hold(hax, 'on');
colormap gray
axis(hax, 'image');
%// Plot the reference circle
t = linspace(0, 2*pi, 100);
plot(x1 + cos(t)*R, y1 + sin(t)*R);
%// Plot the segmented boundaries
B = bwboundaries(M);
for k = 1:numel(B)
plot(B{k}(:,2), B{k}(:,1), 'r');
end
I want the color of each arrow in a quiver3 plot from MATLAB to correspond to the magnitude of each arrow. Is there any way to do that?
I saw a few examples online that are able to do this for the 2D quiver, however none of them work for the 3D variant, quiver3.
I have the following plot and want to replace the blue arrows with a color corresponding to their magnitude.
In the old graphics system (R2014a and earlier) this is not possible using the built-in quiver object. You can easily get all of the plot objects that are used to compose the quiver plot
q = quiver(1:5, 1:5, 1:5, 1:5);
handles = findall(q, 'type', 'line');
But the tails are all represented by one plot object, and the arrow heads are represented by another. As such, you can't alter the color of each head/tail individually.
set(handles(1), 'Color', 'r')
set(handles(2), 'Color', 'g')
However, with the introduction of HG2 (R2014b and later), you can actually get access to two (undocumented) LineStrip objects (matlab.graphics.primitive.world.LineStrip) (one represents the heads and one represents the tails). These are accessible via the hidden properties Tail and Head.
q = quiver(1, 1, 1, 1);
headLineStrip = q.Head;
tailLineStrip = q.Tail;
You can then alter the color properties of these objects to make each arrow a different color.
The Basic Idea
To do this, I first compute the magnitude of all quiver arrows (this works for both quiver and quiver3)
mags = sqrt(sum(cat(2, q.UData(:), q.VData(:), ...
reshape(q.WData, numel(q.UData), [])).^2, 2));
Then I use the current colormap to map each magnitude to an RGB value. The shortest arrow is assigned the lowest color on the colormap and the longest arrow is assigned the highest color on the colormap. histcounts works great for assigning each magnitude an index which can be passed to ind2rgb along with the colormap itself. We have to multiply by 255 because we need the color to be RGB as an 8-bit integer.
% Get the current colormap
currentColormap = colormap(gca);
% Now determine the color to make each arrow using a colormap
[~, ~, ind] = histcounts(mags, size(currentColormap, 1));
% Now map this to a colormap
cmap = uint8(ind2rgb(ind(:), currentColormap) * 255);
The LineStrip ColorData property (when specified as truecolor) also needs to have an alpha channel (which we will set to 255 meaning opaque).
cmap(:,:,4) = 255;
At this point we can then set the ColorBinding property to interpolated rather than object (to decouple it from the quiver object) and set the ColorData property of both q.Head and q.Tail to the colors we created above giving each arrow it's own color.
Full Solution
NOTE: This solution works for both quiver and quiver3 and the code does not have to be adapted at all.
%// Create a quiver3 as we normally would (could also be 2D quiver)
x = 1:10;
y = 1:10;
[X,Y] = meshgrid(x, y);
Z = zeros(size(X));
U = zeros(size(X));
V = zeros(size(X));
W = sqrt(X.^2 + Y.^2);
q = quiver3(X, Y, Z, U, V, W);
%// Compute the magnitude of the vectors
mags = sqrt(sum(cat(2, q.UData(:), q.VData(:), ...
reshape(q.WData, numel(q.UData), [])).^2, 2));
%// Get the current colormap
currentColormap = colormap(gca);
%// Now determine the color to make each arrow using a colormap
[~, ~, ind] = histcounts(mags, size(currentColormap, 1));
%// Now map this to a colormap to get RGB
cmap = uint8(ind2rgb(ind(:), currentColormap) * 255);
cmap(:,:,4) = 255;
cmap = permute(repmat(cmap, [1 3 1]), [2 1 3]);
%// We repeat each color 3 times (using 1:3 below) because each arrow has 3 vertices
set(q.Head, ...
'ColorBinding', 'interpolated', ...
'ColorData', reshape(cmap(1:3,:,:), [], 4).'); %'
%// We repeat each color 2 times (using 1:2 below) because each tail has 2 vertices
set(q.Tail, ...
'ColorBinding', 'interpolated', ...
'ColorData', reshape(cmap(1:2,:,:), [], 4).');
And applied to a 2D quiver object
If you don't necessarily want to scale the arrows to the entire range of the colormap you could use the following call to histcounts (instead of the line above) to map the magnitudes using the color limits of the axes.
clims = num2cell(get(gca, 'clim'));
[~, ~, ind] = histcounts(mags, linspace(clims{:}, size(currentColormap, 1)));
If your using a post r2014b version you can use undocumented features to change the colour of each line and head:
figure
[x,y] = meshgrid(-2:.5:2,-1:.5:1);
z = x .* exp(-x.^2 - y.^2);
[u,v,w] = surfnorm(x,y,z);
h=quiver3(x,y,z,u,v,w);
s = size(x);
nPoints = s(1)*s(2);
% create a colour map
cmap = parula(nPoints);
% x2 because each point has 2 points, a start and an end.
cd = uint8(repmat([255 0 0 255]', 1, nPoints*2));
count = 0;
% we need to assign a colour per point
for ii=1:nPoints
% and we need to assign a colour to the start and end of the
% line.
for jj=1:2
count = count + 1;
cd(1:3,count) = uint8(255*cmap(ii,:)');
end
end
% set the colour binding method and the colour data of the tail
set(h.Tail, 'ColorBinding','interpolated', 'ColorData',cd)
% create a color matrix for the heads
cd = uint8(repmat([255 0 0 255]', 1, nPoints*3));
count = 0;
% we need to assign a colour per point
for ii=1:nPoints
% and we need to assign a colour to the all the points
% at the head of the arrow
for jj=1:3
count = count + 1;
cd(1:3,count) = uint8(255*cmap(ii,:)');
end
end
% set the colour binding method and the colour data of the head
set(h.Head, 'ColorBinding','interpolated', 'ColorData',cd)
Note: I've not done anything clever with the magnitude and simply change the colour of each quiver based on the order in the original matrix - but you should be able to get the idea on how to use this "feature"
Note that if you are using Suevers solution and have NaNs in your data you should include this line before calling histcounts:
mags(isnan(mags)) = [];
Otherwise you will get an error about wrong input size because matlab does not create vertices for NaNs in your U/V/W data.