How can I prevent MATLAB from plotting an object and it's transformation? I am trying to rotate a surface and am using a transformation matrix to do it, but I don't want the surface to be plotted at any point, How can I stop it?
% Defines the input variables for the SC at the orbital point.
FoV = deg2rad(FoV);
dist = sqrt(xp^2 + yp^2 + zp^2);
xp = 168.820350140000;
yp = 22703.2636668300
zp = 40331.2908433900
% Generates a line from the orbit point to the centre of the Earth.
xl = linspace(0,xp);
yl = linspace(0,yp);
zl = linspace(0,zp);
% Plots the orbits, orbit point, and Earth object onto the same plot.
plot3(xl,yl,zl);
hold on
scatter3(xp,yp,zp,100,'x','blue')
% Creates a cone for the FoV of the SC that targets the Earth's centre.
[x,y,z] = cylinder([dist*tan(FoV) 0],100);
h = surface(y,dist*z,x);
t = hgtransform('Parent',ax);
set(h,'Parent',t);
x_temp = get(h,'xdata');y_temp = get(h,'ydata');z_temp = get(h,'zdata'); % Duplicates data.
% Determines the coordinate rotations needed to align the cone with the
% orbit point and transforms the cone using object R.
% This if loop calibrates the cone for the 4 quadrants of 2 tangents.
xa = atan(yp/xp);
za = atan(zp/sqrt(xp^2+yp^2));
if xp>0
xa = xa-pi/2;
else
xa = xa+pi/2;
end
R = makehgtform('zrotate',xa,'xrotate',za);
set(t,'Matrix',R);
% Performs the same numerical transformation of the duplicate data and
% creates a sew sets of coordinates that match the transformation.
for i = 1:101
new_first_row(i,:) = (R * [x_temp(1,i);y_temp(1,i);z_temp(1,i);1])';
new_second_row(i,:) = (R * [x_temp(2,i);y_temp(2,i);z_temp(2,i);1])';
end
xr = new_first_row(:,1)'; % Transformed x data.
xr(2,:) = new_second_row(:,1)';
yr = new_first_row(:,2)'; % Transformed y data.
yr(2,:) = new_second_row(:,2)';
zr = new_first_row(:,3)'; % Transformed z data.
zr(2,:) = new_second_row(:,3)';
I want xr, yr, and zr to be calculated, but don't want any plots to be created from this specific script. I later want to create a different plot using this data. If there are any other ways of doing this, please let me know.
As Ander Biguri already said, there are probably better ways than to cram a round peg into a square hole.
As to the question itself: figure visibility is controlled through figure('Visible', 'off'), where 'on' is obviously the default. Don't forget to close your figure though:
fig = figure('Visible', 'off'); % Create invisible figure with handle
h = surface(...); % Your plot
% (...) your other processing
close(fig); % Close figure to save RAM
Related
I have implemented the Hermite-Gaussian function in matlab for producing different modes. The light beam along z direction can be seen as a complex matrix in the plane.
The function for HG modes is as below.
%Hermite polynomial
function hk = HermitePoly(n)
if n==0
hk = 1;
elseif n==1
hk = [2 0];
else
hkm2 = zeros(1,n+1);
hkm2(n+1) = 1;
hkm1 = zeros(1,n+1);
hkm1(n) = 2;
for k=2:n
hk = zeros(1,n+1);
for e=n-k+1:2:n
hk(e) = 2*(hkm1(e+1) - (k-1)*hkm2(e));
end
hk(n+1) = -2*(k-1)*hkm2(n+1);
if k<n
hkm2 = hkm1;
hkm1 = hk;
end
end
end
% this is the function of HG modes in z position.
function [HGBeam,X,Y] = Hermite_Gaussian(N,hx,hy,w0,delta,lamda,z)
[X Y]=meshgrid((-N/2:N/2-1)*delta);
[theta,rad] = cart2pol(X,Y);
k=2*pi/lamda;
zr=pi*w0^2/lamda;
wz=w0*sqrt(1+(z/zr)^2);
qz=z+1i*zr;
q0=1i*zr;
if z==0
rz=Inf;
else
rz=z*(1+(zr/z)^2);
end
AmpLGB=sqrt(2/(2^(hx+hy)*pi*factorial(hx)*factorial(hy)*w0^2)).*(q0/qz).*(-conj(qz)/qz)^((hx+hy)/2).*exp(-(rad.*rad)/(wz)^2).*polyval(HermitePoly(hx),sqrt(2)*X/wz).*polyval(HermitePoly(hy),sqrt(2)*Y/wz);
PsLGB=exp(-1i*(k*(rad.*rad)/(2*rz)+k*z-(hx+hy+1)*atan(z/zr)));
HGBeam=AmpLGB.*PsLGB;
end
Now I plot one example for HG(2,0) as the following (example1):
clc
clear all;
close all;
lambda=809e-9; % optical wavelength
w0=0.025; %optical beam waist 15mm
k=2*pi/lambda; % optical wavenumber
Zr=pi*w0^2/lambda; % Rayleigh range
z0=0; % start position z=0; but careful 0*Inf is undefined, here 0*Inf=NAN
N=1024; % samples/side length at source plane
D1=0.25; % side length [m] at source plane
delta1=D1/N; % grid spacing [m]
x1=-D1/2:delta1:D1/2-delta1; % source plane x and y coordinates
y1=x1;
%% HG modes
HGx=2;
HGy=0;
HGintheory=Hermite_Gaussian(N,HGx,HGy,w0,delta1,lambda,z0);
h7=figure(7);
imagesc(x1,y1,abs(HGintheory).^2);
title(sprintf('z=%d; HG(%d,%d)',z0,HGx,HGy))
xlabel('x (m)'); ylabel('y (m)');
The plot of the light field will be as the following picture in the left side (its intensity):
We can use rot90() function to rotate matrix HGintheory (which is add one line code: HGintheory=rot90(HGintheory);) and then the field will rotate 90 degree (right side of the intensity plot).
Because I want to work with the light field. So the question is how can I rotate the complex matrix HGintheory in
arbitrary angle? For example 45 degree?
Does anyone knows how to rotate a complex matrix with big size? If something is wrong or unclear, please pointing out and Thank you in advance!
You can decompose your complex field into two real fields (amplitude and phase), rotate both with imrotate, and combine them afterwards pixel-wise
Hamp=abs(HGintheory);
Hphase=angle(HGintheory);
RotAngle=45;
HampRot=imrotate(Hamp,RotAngle,'bilinear','crop');
HphaseRot=imrotate(Hphase,RotAngle,'bilinear','crop');
HfullRot=HampRot.*exp(1i*HphaseRot);
figure(1);
imagesc(x1,y1,abs(HGintheory).^2);
figure(2);
imagesc(x1,y1,abs(HfullRot).^2);
You can rotate your initial meshgrid using:
[X,Y] = meshgrid(x1,y1)
xyc = [mean(x1), mean(y1)];
angel = 45;
R = [cosd(angel), -sind(angel); sind(angel), cosd(angel)];
XY = xyc' + R * ([X(:) Y(:)]-xyc)';
XR = reshape(XY(1,:),size(X));
YR = reshape(XY(2,:),size(Y));
and then use those transformed coordinates to plot:
imagesc(XR,YR,IntensityHGin);
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'm pretty new to different plots in Matlab and I'm trying to write a code that will show the flow field around a cylinder in Matlab. I'm at the very start and first of all I want to just make the circle in a rectangular domain (cylinder should not be right in the middle of the field).
So far, I have this set up but I want to know if it's possible to make the cylinder look more circular and less like an oval, especially because the domain is a rectangle and not a square. The points on the circle are correct but I want it to look better. Any tips on this? The code I have at the moment is:
U_i = 20; % Ambient velocity
a = 4; % cylinder radius
c = -a*5; % starting coordinate (x)
b = a*10; % ending coordinate (x)
d = -60; % starting coordinate (y)
e = 60; % ending coordinate (y)
n = a*50; % number of intervals (step size in grid)
[x,y] = meshgrid([c:(b-c)/n:b],[d:(e-d)/n:e]');
for i = 1:length(x)
for k = 1:length(x);
f = sqrt(x(i,k).^2 + y(i,k).^2);
if f < a
x(i,k) = 0;
y(i,k) = 0;
end
end
end
% Definition of polar variables
r = sqrt(x.^2+y.^2);
theta = atan2(y,x);
%% Creation of Streamline function
z = U_i.*r.*(1-a^2./r.^2).*sin(theta);%- G*log(r)/(2*pi);
%% Creation of Figure
m = 100;
s = ones(1,m+1)*a;
t = [0:2*pi/m:2*pi];
%% Streamline plot
contour(x,y,z,50);
hold on
polar(t,s,'-k');
% axis square
title('Stream Lines');
grid off
I have a surface map created from Northing (X), Easting (y), and Elevation (z) data. I would like to draw a circle around a specific point of a specific radius (say 400 m). The circle has to show up on the surface map. Below is my code for creating the surface map. Any help would be greatly appreciated.
% load the map data
x = elevgrid(:,4); % northing
y = elevgrid(:,5); % easting
z = elevgrid(:,3); % elevation
% Put data onto a grid
[qx,qy] = meshgrid(linspace(min(x),max(x)),linspace(min(y),max(y)));
F = TriScatteredInterp(x,y,z);
qz = F(qx,qy);
% plot in matrix form
surf(qx,qy,qz)
EDIT
Here is a link to a text file of sample data - format being longtitude, latitiude, elevation.
You should be able to do this with plot3 quite easily. See code below for a modified version of your posted code.
I'm not sure about how your sample data is represented (to avoid problems in the future, please try to brew your question down to just the bare essentials, with inputs included).
clear;clc
% create data
xy = -2.5 + 5*gallery('uniformdata',[200 2],0);
x = xy(:,1);
y = xy(:,2);
z = x.*exp(-x.^2-y.^2);
% Put data onto a grid
[qx,qy] = meshgrid(linspace(min(x),max(x)),linspace(min(y),max(y)));
F = scatteredInterpolant(x,y,z);
qz = F(qx,qy);
% plot in matrix form
mesh(qx,qy,qz)
% Plot circle
hold on
r = 0.6;
xp = 0.4;
yp = -1.2;
t = linspace(0,2*pi);
Xp = r*sin(t)+xp;
Yp = r*cos(t)+yp;
plot3(Xp,Yp,F(Xp,Yp))
hold off
BR Magnus