Graph different 2D ellipses in 3D axes at different heights in MATLAB - matlab

I want to graph different ellipses at different heights (z-coordinates).
My idea was to write the following code:
z=0:1/64:3/8;
t=linspace(-pi,pi,25);
[t,z]=meshgrid(t,z);
x=cos(-t);
y=cos(-t-4*pi*z);
I would like MATLAB to read my code like:
"Find x and y, and plot at the corresponding height (z). By doing so, join the points such that you'll form an ellipse at constant z".
I'm not sure what kind of function I could use here to do this and was hoping for someone to tell me if there exists such a function that will do the job or something similar.
In case you're wondering, I want to graph the polarization of light given two counterpropagating beams.
EDIT: While this is similar to the question draw ellipse and ellipsoid in MATLAB, that question doesn't address plotting 2D ellipses in 3D axes, which is what I am trying to do.

This can be solved by removing the meshgrid, and just using a plain old for-loop.
t = linspace(-pi,pi,25);
z = 0:1/64:3/8
f = figure;
hold on;
for i = 1:length(z)
x=cos(-t); y=cos(-t-4*pi*z(i));
plot3(x,y,z(i)*ones(length(z),1));
end
The problem in the original code is that you're trying build the ellipses all at once, but each ellipse only depends on a single z value, not the entire array of z values.
When I run this code, it produces the following plot:

Related

Using streamslice/quiver and inpolygon crop

Suppose we have quiver field i.e. we have a meshgrid and then we assign a vector to each point. Is it possible to plot only the quiver field within some polygon?
So in the figure below, we want everything outside the triangle to be cropped out.
Ideally the code will also be helpful for the next step of having multiple such polygons and cropping out everything on their complement.
Some approaches:
A direct way is to figure out the meshgrid for the particular polygon and then assign a vector to each point. But that will take a lot of time to figure out as polygons get more complicated. In other words, the regular meshgrid is the square polygon, so we must modify the meshgrid matrix depending on our polygon. A friend informed me of a mesh generator matlab code.
Use inpolygon. The input of inpolygon are points in (x,y). But in our case we only have the vector field assigned to a meshgrid. One idea is to solve the ode system to obtain concrete solution pairs (x,y) to plug into the polygon. But solving them takes a lot longer and the pictures are not as nice.
Here's some sample code which I think will generate the kind of plot you want. It uses inpolygon to "filter" out the points inside the polygon. The vector field is still evaluated at the original meshgrid points. It easily extends to multiple polygons too.
clear
clc
x = linspace(0, 1, 21);
[X,Y] = meshgrid(x,x);
U = -Y; %some velocity field
V = X;
hold off
quiver(X,Y,U,V); %quiver on all points
polygon = [0.2,0.2;
0.7,0.5;
0.5,0.8]; %polygon vertices
ind = inpolygon(X,Y,polygon(:,1),polygon(:,2)); %get indices of points inside polygon
hold on
quiver(X(ind),Y(ind),U(ind),V(ind)); %quiver of points inside polygon

Making an accurate colorbar for a simple plot

I am trying to make a simple plot (for this example doing a plot of y=x^2 will suffice) where I want to set the colors of the points based on their magnitude given some colormap.
Following along my simple example say I had:
x = 1:10;
y = x.^2;
Use gscatter(x,y,jet(10)); legend hide; colorbar which produces a plot with the points colored but the colorbar does not agree with the colored values. (Can't post picture as this is my first post). Using a caxis([1,100]) command gives the right range but the colors are still off.
So I have two questions:
(1) How can I fix the colors to fit to a colorbar given a range? In my real data, I am looking at values that range from -50 to 50 in some instances and have many more data points.
(2) I want to create a different plot with the same points (but on different axes) and I want the colors of each point on this new plot to have the same colors as their counterparts in the previous plot. How can I, programmatically, extract the color from each point so I can plot it on two different sets of axes?
I would just move the points into a matrix and do an imagesc() command but they aren't spaced as integers or equally so simple scaling wouldn't work either.
Thanks for any help!
Regarding you first question, you need to interpolate the y values into a linear index to the colormap. Something like:
x = 1:10;
y = x.^4;
csize = 128;
cmap = jet(csize);
ind = interp1(linspace(min(y),max(y),csize),1:csize,y,'nearest');
scatter(x,y,14,cmap(ind,:),'filled')
colorbar
caxis([min(y) max(y)])
Using interp1 in this case is an overkill; you could calculate it directly. However, I think in this way it is clearer.
I think it also answers your 2nd question, since you have the index of the color of each data point, so you can use it again in the same way.

matlab - plot inequality in 3d with surf

I want to plot an inequality in 3d using surf. My condition is
0<=x<=1
0<=y<=1
0<=z<=x/(1+y)
I can create a surface plot using the following commands
[x y]=meshgrid(0:0.01:1);
z=x./(1+y);
surf(x,y,z);
This plot gives me regions where z=x/(1+y) but I am interested in regions where 0<=z<=x/(1+y) over all values of x and y. However, I am unable to plot/color the region explicitly. Can you please help.
A similar question has been asked but there was no acceptable answer and my question is also different.
Using isosurface you can show the boundary. There are two options, first create the points
[X,Y,Z]=meshgrid(0:.01:1);
then plot the boundaries in the z-direction (i.e. Z=0 and Z=X./(1+Y))
isosurface(X,Y,Z,Z.*(X./(1+Y)-Z),0)
or plot all the boundaries (including X=0, X=1, Y=0 and Y=1)
isosurface(X,Y,Z,Z.*(X./(1+Y)-Z).*X.*(X-1).*Y.*(Y-1),0)
All you have to do is come up with a function that is constant on any boundary, its value inside or outside is irrelevant as long as it is not zero.

MATLAB: Plotting Contours at Specfic Points (x,y)

I'm currently producing a contour plot using
contour(x,y,z)
However, I would like to specify some additional contour lines to the ones provided.
I understand that I can use contour(x,y,z,v) where v is some vector containing values of the contour levels I would like but I don't really want to use this since I don't know exactly the levels.
Instead is it possible to plot the contour that goes through a specific point (x,y)?
Thanks.
You can overplot a second contour with a single, specific value for the contour, optionally specifying parameters like line width to make it obvious:
contour(x,y,z)
hold on
lev = z(n,m); % find the value you want in z
contour(x,y,z,lev,'Linewidth',2);

mathcad / matlab 3D plot of transfer function

I have a problem plotting a 3D plot of my transfer function. In matlab I have tryed this:
[T,w] = meshgrid(1:1:32,1:1:100);
sys2=20*log((1-w.*(T./2)./w.*T).*(((2.56.*(w.^2)+1.6.*w+1)./(0.0008.*(w.^6)+0.0124.* (w.^5)+0.173.*(w.^4)+(w.^3)))./1+(((2.56.*(w.^2)+1.6.*w+1)./(0.0008.*(w.^6)+0.0124.*(w.^5)+0.173.*(w.^4)+(w.^3))))));
surf(T,w,sys2);
But I get this error:
??? Error using ==> surf at 78
X, Y, Z, and C cannot be complex.
What could be wrong please?
Or can anyone tell me how to plot this in Mathcad?
Thank you.
You can't plot a complex number versus two independent variables -- you would need four axes.
What you can do is:
Use two separate figures (or two subplots in the same figure) to plot real part and imaginary part. In Matlab,
surf(T,w,real(sys2));
figure %// create new figure for the other graph
surf(T,w,imag(sys2));
Alternatively, plot absolute value and phase:
surf(T,w,abs(sys2));
figure %// create new figure for the other graph
surf(T,w,angle(sys2));
A more exotic possibility is to use z axis for absolute value and colour for phase, in the same graph:
surf(T,w,abs(sys2),angle(sys2)); %// fourth argument of surf specifies colour