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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.
The following code creates a 2D stacked histogram for two 2D distributions:
%%first dataset
x1 = 200 + 300.*rand(1000,1)'; %rand values between 0 and 200
y1 = 100 + 250.*rand(1000,1)'; %rand values between 100 and 500
%%secnd dataset
x2 = 100 + 200.*rand(1000,1)'; %rand values between 0 and 200
y2 = 200 + 400.*rand(1000,1)'; %rand values between 100 and 500
one = linspace(100,400,20);
two = linspace(100,500,20);
EDGES = {one, two}; %edges
[n1,c1] = hist3([x1' y1'],'Edges',EDGES);%first dataset
[n2,c2] = hist3([x2' y2'],'Edges',EDGES);%second dataset
figure('Color','w');
% plot the first data set
bh=bar3(n1);
% Loop through each row and shift bars upwards
for ii=1:length(bh)
zz = get(bh(ii),'Zdata');
kk = 1;
% Bars are defined by 6 faces(?), adding values from data2 will
% shift the bars upwards accordingly, I'm sure this could be made
% better!
for jj = 0:6:(6*length(bh)-6)
zz(jj+1:jj+6,:)=zz(jj+1:jj+6,:)+n2(kk,ii);
kk=kk+1;
end
%erase zero height bars
%# get the ZData matrix of the current group
Z = get(bh(ii), 'ZData');
%# row-indices of Z matrix. Columns correspond to each rectangular bar
rowsInd = reshape(1:size(Z,1), 6,[]);
%# find bars with zero height
barsIdx = all([Z(2:6:end,2:3) Z(3:6:end,2:3)]==0, 2);
%# replace their values with NaN for those bars
Z(rowsInd(:,barsIdx),:) = NaN;
%# update the ZData
set(bh(ii), 'ZData',Z)
end
% Set face colour to blue for data1
set(bh,'FaceColor',[0 0 1]);
% Apply hold so that data2 can be plotted
hold on;
% Plot data2
bh=bar3(n2);
%erase zero height bars
for ii=1:numel(bh)
%# get the ZData matrix of the current group
Z = get(bh(ii), 'ZData');
%# row-indices of Z matrix. Columns correspond to each rectangular bar
rowsInd = reshape(1:size(Z,1), 6,[]);
%# find bars with zero height
barsIdx = all([Z(2:6:end,2:3) Z(3:6:end,2:3)]==0, 2);
%# replace their values with NaN for those bars
Z(rowsInd(:,barsIdx),:) = NaN;
%# update the ZData
set(bh(ii), 'ZData',Z)
end
% Set face color to red
set(bh,'FaceColor',[1 0 0]);
%set ticks
set(gca,'XTick',1:6:numel(one),'XTickLabel',one(1:6:end))
set(gca,'YTick',1:6:numel(one),'YTickLabel',one(1:6:end))
view(20,40)
%labels
xlabel('x')
ylabel('y')
zlabel('z')
%set transparency
set(gcf,'renderer','opengl');
set(get(gca,'child'),'FaceAlpha',0.8);
set(get(gca,'child'),'EdgeAlpha',0.3);
A first issue is the transparency (but I think it is a problem of my matlab version 2014a, so I am not bothered by that). It just makes all blurry.
My question is how to add a mesh plot on the same picture. The code creating the meshes is the following:
%create surface I want to plot
[X,Y] = meshgrid(one,two);
inds1=find(X(:).*Y(:)<.3e5);%condition
inds2=find(X(:).*Y(:)>.3e5);
I=Y./X.^2;%first surface
I(inds1)=NaN;%second surface
figure('Color','w');hold on
mesh(X,Y,I,'FaceColor',[0 0 1],'EdgeColor','none')
I(:,:)=NaN;
I(inds1)=Y(inds1)./X(inds1);%second surface
mesh(X,Y,I,'FaceColor',[1 0 0],'EdgeColor','none')
alpha(.5)
grid on
view(20,40)
%labels
xlabel('x')
ylabel('y')
zlabel('z')
The domain of the histograms and the meshes are the same. So I just need to add an extra z-axis on the first figure.
I tried substituting figure('Color','w');hold on in the second code with AxesH = axes('NextPlot', 'add');, but I was really wrong about that:
That just overlayed the two figures..
I also tried something along the lines of:
%add axis
axesPosition = get(gca,'Position'); %# Get the current axes position
hNewAxes = axes('Position',axesPosition,... %# Place a new axes on top...
'Color','none',... %# ... with no background color
'ZLim',[0 400],... %# ... and a different scale
'ZAxisLocation','right',... %# ... located on the right
'XTick',[],... %# ... with no x tick marks
'YTick',[],... %# ... with no y tick marks
'Box','off');
but it is not feasible because the property ZAxisLocation does not exist.
Does anyone know how to add the z-axis?
Also, if you have other comments on how to ameliorate the code, they're welcome!
acknowledgements
2d stacked histogram:https://stackoverflow.com/a/17477348/3751931
erasing the zero values in the hist plot: https://stackoverflow.com/a/17477348/3751931
I now think that this is not yet possible (http://www.mathworks.com/matlabcentral/answers/95949-is-there-a-function-to-include-two-3-d-plots-with-different-z-axes-on-the-same-plot-area-similar-to).
So I just added a fake axis:
[X,Y] = meshgrid(one,two);
inds1=find(X(:).*Y(:)<.3e5);%condition
inds2=find(X(:).*Y(:)>.3e5);
s=Y./X.^2;%first surface
s(inds1)=NaN;%second surface
%mesh(X,Y,I,'FaceColor',[0 0 1],'EdgeColor','none')
mesh((X-min(min(X)))/max(max(X-min(min(X))))*20,(Y-min(min(Y)))/max(max(Y-min(min(Y))))*20,...
s/max(max(s))*max(max(n1))+max(max(n1)),'FaceColor','g','EdgeColor','none','facealpha',.5)
s(:,:)=NaN;
s(inds1)=Y(inds1)./X(inds1);%second surface
%mesh(X,Y,I,'FaceColor',[1 0 0],'EdgeColor','none')
mesh((X-min(min(X)))/max(max(X-min(min(X))))*20,(Y-min(min(Y)))/max(max(Y-min(min(Y))))*20,...
s/max(max(s))*max(max(n1))+max(max(n1)),'FaceColor','y','EdgeColor','none','facealpha',.5)
alpha(.5)
grid on
%add fake z axis
line([20 20],[1 1],[max(max(n1))-min(min(s)) 20],...
'color','g','linewidth',2)
% text(20*ones(1,5),zeros(1,5),linspace(max(max(n1))-min(min(I)),20,5),...
% num2str(linspace(0,max(max(I)),5)),'color','g')
z=linspace(max(max(n1))-min(min(s)),20,5);
txto=linspace(0,max(max(s)),5);
for ii=1:5
line([20 20.3],[1 1],[z(ii) z(ii)],'color','g')%ticks
text(20,0,z(ii),num2str(txto(ii)),'color','g')%ticklabel
end
text(19.8,1,21,'s','color','g')%label
Over all the code is quite ugly and needs a lot of tuning..
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.