I have a matrix a=360x360x2048
now I want to plot them in 3d
My attempt
x = 1:size(a,2);
y = 1:size(a,1);
z = 1:size(a,3);
How to plot this in 3d
Now I want to 3d plot this
now I want to plot them all
Instead of using imagesc() which only works in 2D, you could try to use scatter() and its 3D extension scatter3().
nslices = 100;
nelems = 360;
A = rand(nelems, nelems, nslices); % your matrix
% Marker settings for scatter plot
mrkrSize = 10;
mrkr = '.';
figure
hold on
view(3)
for i = 1:nslices
% Get the i-th matrix
Aslice = A(:, :, i);
idx = find(Aslice);
[x, y] = ind2sub(size(Aslice), idx);
z = i.*ones(size(x));
scatter3(x, y, z, mrkrSize, Aslice(idx), 'Marker', mrkr);
end
Using Slices of a Matrix to Create 3D Plot
Given that I saw the question before the multiple edits. Using the slice() function may help to plot the 3D matrix as slices in a 3D plot. The slice() function takes three additional inputs along with the matrix/volume to be plotted. The following three inputs dictate the method used to slice the matrix. In this example, slicing was done so that you can have a set of xy-planes that are stacked along the z-axis.
%Generating a random test array%
X_Dimension = 360; Y_Dimension = 360; Z_Dimension = 5;
Volume = rand(X_Dimension,Y_Dimension,Z_Dimension);
%Configuring the slicing method%
X_Slice = [];
Y_Slice = [];
Z_Slice = 1:size(Volume,3);
%Plotting slices of array%
Slices = slice(Volume,X_Slice,Y_Slice,Z_Slice);
xlabel("x"); ylabel("y"); zlabel("z");
%Removing edge lines%
for Slice = 1: length(Slices)
Slices(Slice).EdgeAlpha = 0;
end
%Angle of 3D plot and colorbar%
Angle = 72; Elevation = 10;
view(Angle, Elevation);
colorbar
Ran using MATLAB R2019b
Related
I made two 3D plots on the same axis. now I desire to give them different colors for easy identification. How do I do this coloring? The MATLAB code is shown below.
tic
Nx = 50;
Ny = 50;
x = linspace(0,1,Nx);
y = linspace(0,0.5,Ny);
[X,Y] = meshgrid(x,y);
[M,N] = size(X);
for m=1:M
for n=1:N
%get x,y coordinate
x_mn = X(m,n);
y_mn = Y(m,n);
%%% X=D2 and Y=D1
%Check if x_mn and y_mn satisfy requirement
if(x_mn >= y_mn)
%evaluate function 1
Z(m,n) = (x_mn^2 - 2*x_mn*y_mn + y_mn^2);
Z_1(m,n) = (x_mn^2);
elseif(x_mn < y_mn)
%evaluate function 2
Z(m,n) = 0;
Z_1(m,n) = (x_mn^2);
%% Z(m,n) = 2*(2*x_mn*y_mn + y_mn - y_mn^2 - 2*x_mn);
else
Z(m,n) = 0;
end
end
end
%Plot the surface
figure
surf(X,Y,Z) %first plot
surfc(X,Y,Z)
hold on
surf(X,Y,Z_1) %second plot
xlabel('Dm');
ylabel('D');
zlabel('pR');
grid on
shading interp
toc
disp('DONE!')
How can I create two differently colored surfaces?
figure
surf(X,Y,Z) %first plot
surfc(X,Y,Z)
hold on
surf(X,Y,Z_1)
Your surfc() call actually overwrites your surf() call, is this intended?
As to your colour: the documentation is a marvellous thing:
surfc(X,Y,Z,C) additionally specifies the surface color.
In other words: just specify the colour as you want it. C needs to be a matrix of size(Z) with the desired colours, i.e. set all of them equal to create an monocoloured surface:
x = 1:100;
y = 1:100;
z = rand(100);
figure;
surfc(x,y,z,ones(size(z)))
hold on
surfc(x,y,z+6,ones(size(z))+4)
Results in (MATLAB R2007b, but the syntax is the same nowadays)
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 have created some MatLab code that plots a plane wave using two different expressions that give the same plane wave. The first expression is in Cartesian coordinates and works fine. However, the second expression is in polar coordinates and when I calculate the plane wave in this case, the plot is distorted. Both plots should look the same. So what am I doing wrong in transforming to/from polar coordinates?
function Plot_Plane_wave()
clc
clear all
close all
%% Step 0. Input paramaters and derived parameters.
alpha = 0*pi/4; % angle of incidence
k = 1; % wavenumber
wavelength = 2*pi/k; % wavelength
%% Step 1. Define various equivalent versions of the incident wave.
f_u_inc_1 = #(alpha,x,y) exp(1i*k*(x*cos(alpha)+y*sin(alpha)));
f_u_inc_2 = #(alpha,r,theta) exp(1i*k*r*cos(theta-alpha));
%% Step 2. Evaluate the incident wave on a grid.
% Grid for field
gridMax = 10;
gridN = 2^3;
g1 = linspace(-gridMax, gridMax, gridN);
g2 = g1;
[x,y] = meshgrid(g1, g2);
[theta,r] = cart2pol(x,y);
u_inc_1 = f_u_inc_1(alpha,x,y);
u_inc_2 = 0*x;
for ir=1:gridN
rVal = r(ir);
for itheta=1:gridN
thetaVal = theta(itheta);
u_inc_2(ir,itheta) = f_u_inc_2(alpha,rVal,thetaVal);
end
end
%% Step 3. Plot the incident wave.
figure(1);
subplot(2,2,1)
imagesc(g1(1,:), g1(1,:), real(u_inc_1));
hGCA = gca; set(hGCA, 'YDir', 'normal');
subplot(2,2,2)
imagesc(g1(1,:), g1(1,:), real(u_inc_2));
hGCA = gca; set(hGCA, 'YDir', 'normal');
end
Your mistake is that your loop is only going through the first gridN values of r and theta. Instead you want to step through the indices of ix and iy and pull out the rVal and thetaVal of the matrices r and theta.
You can change your loop to
for ix=1:gridN
for iy=1:gridN
rVal = r(ix,iy); % Was equivalent to r(ix) outside inner loop
thetaVal = theta(ix,iy); % Was equivalent to theta(iy)
u_inc_2(ix,iy) = f_u_inc_2(alpha,rVal,thetaVal);
end
end
which gives the expected graphs.
Alternatively you can simplify your code by feeding matrices in to your inline functions. To do this you would have to use an elementwise product .* instead of a matrix multiplication * in f_u_inc_2:
alpha = 0*pi/4;
k = 1;
wavelength = 2*pi/k;
f_1 = #(alpha,x,y) exp(1i*k*(x*cos(alpha)+y*sin(alpha)));
f_2 = #(alpha,r,theta) exp(1i*k*r.*cos(theta-alpha));
% Change v
f_old = #(alpha,r,theta) exp(1i*k*r *cos(theta-alpha));
gridMax = 10;
gridN = 2^3;
[x,y] = meshgrid(linspace(-gridMax, gridMax, gridN));
[theta,r] = cart2pol(x,y);
subplot(1,3,1)
contourf(x,y,real(f_1(alpha,x,y)));
title 'Cartesian'
subplot(1,3,2)
contourf(x,y,real(f_2(alpha,r,theta)));
title 'Polar'
subplot(1,3,3)
contourf(x,y,real(f_old(alpha,r,theta)));
title 'Wrong'
I need to create a surface generate by rotation on y axis of shape formed by two curves. I already have the equation for this two curves. Here is the shape
I already create the surface but for simetric cone formed by one of this curve, here is my script:
h=20;
rw=1;
hw=5;
L=25;
r=linspace(rw,L,50);
theta=linspace(0,2*pi,25);
[r,theta] = meshgrid(r,theta);
xx=r.*cos(theta);
yy=r.*sin(theta);
z=sqrt(log(r/rw)*(h^2-hw^2)/log(L/rw)+hw^2); %Fuction of curve
surf(xx,yy,z)
Here is my result
In the other curve is the same fuction (z) but change r,h,L
Thanks for your help,
you should use parameter grids instead of scalars:
% parameters
h=[20 25];
rw=1;
hw=5;
L=[25 30];
nr = 50;
nt = 25;
theta=linspace(0,2*pi,nt);
rmax = linspace(L(1),L(2),floor((nt+1)/2));
% generating **grids** for all parameters
l = [linspace(L(1),L(2),floor((nt+1)/2)) linspace(L(2),L(1),floor((nt)/2))];
hh = [linspace(h(1),h(2),floor((nt+1)/2)) linspace(h(2),h(1),floor((nt)/2))];
[~,thetaGrid] = meshgrid(1:nr,theta);
[~,lGrid] = meshgrid(1:nr,l);
[~,hGrid] = meshgrid(1:nr,hh);
rGrid = zeros(size(thetaGrid));
for ii = 1:floor((nt+1)/2)
rGrid(ii,:) = linspace(rw,rmax(ii),nr);
end
rGrid(ceil((nt+1)/2):end,:) = rGrid(floor((nt+1)/2):-1:1,:);
% set coordinate grids
xx=rGrid.*cos(thetaGrid);
yy=rGrid.*sin(thetaGrid);
z=sqrt(log(rGrid./rw).*(hGrid.^2-hw^2)./log(lGrid./rw)+hw.^2); %Fuction of curve
% plot
surf(xx,yy,z)
Question: is it possible to illustrate an image on non-uniform axis?
Details:
I need to illustrate a multidimensional timeseries as an image. But the time grid of this timeseries is very non-uniform. Here is an example:
m = 10;
n = 3;
t = sort(rand(m, 1)); % non-uniform time
values = randn(m, n); % some random values
The figure, plot(t, values); handles it well.
But imagesc() converts t into uniform time between t(1) and t(end) according to documentation:
imagesc(x,y,C) displays C as an image and specifies the bounds of the
x- and y-axis with vectors x and y.
Therefore, the command:
figure, imagesc(t, 1 : n, values'); colorbar;
illustrates the image on uniform time grid.
Edit: It's possible to re-sample the timeseries with higher uniform resolution. But my timeseries is already very large.
There is pcolor function in MATLAB. This function does exactly what you're asking.
m = 10;
n = 3;
t = sort(rand(m, 1)); % non-uniform time
values = randn(m, n); % some random values
figure
plot(t, values);
figure
pcolor(t, 1 : n, values');
colorbar;
try uimagesc from the file exchange.
Solution
Try using surface for non-uniform spacing.
First, create a 3D xyz surface of the same size as your input data:
m = 10;
n = 3;
t = sort(rand(m, 1)); % non-uniform time
values = randn(m, n); % some random values
x = repmat(t,1,n);
y = repmat(1:n,m,1);
z = zeros(size(y));
Then, colormap your values. There is a nice tool posted to the mathworks file exchange, real2rgb, that can do this for you:
cdata = real2rgb(values); % Where size(cdata) = [m n 3]
Lastly, plot the surface. You can even get fancy and set the transparency.
surface(x,y,z,cdata,'EdgeColor','none','FaceColor','texturemap',...
'CDataMapping','direct');
alpha(0.3)