I would like to plot a 3D graph, y=100-x^2, cycle around the Y axis in 360 degrees. Eventually to become like a cone. Is that possible? I have an array x=1:1:100, and an array y, size(1 100).
I tried an Z array, z=1:1:100 as the 3th axis in the base of the cone. With plot3 I done the one graph of y=100-x^2. I would like to kinda animate it and have eventually a cone, or a surface cone.
Is this what you are looking for?
r = 1:1:100;
y = 100-r.^2;
theta = 0:pi/20:2*pi;
xx = bsxfun(#times,r',cos(theta));
zz = bsxfun(#times,r',sin(theta));
yy = repmat(y',1,length(theta));
surf(xx,yy,zz)
Source: Generating a 3D plot by revolution of a curve
Related
I have a function which takes a single variable:
function f = profile_func(x)
f = -1*(((sin(0.09*pi*x)).^6)./(2.^(2*((x-10)/80).^2)));
return
I can plot it to generate the following 2D profile:
x = linspace(0,100,1000)';
y = feval(profile_func,x);
plot(x,y,'r-','Linewidth',2);
Now, I would like revolve this profile to create a 3D surface, around the y axis. I know how to revolve it around the x axis using the cylinder function:
[X,Y,Z] = cylinder(y);
surf(X,Y,Z);
However, this is not what I want it to look like. I want to revolve it around the y axis instead so that it kind of resembles a rippling pond, I guess you could say.
Is there any MATLAB function that is like cylinder, but for the y axis?
I have a set of n=8000 cartesian coordinates X,Y and Z as vectors and also a vector V of same size which I want to use as values to create a heatmap on a sphere.
I saw this link (visualization of scattered data over a sphere surface MATLAB), but I don't understand how I convert this set of data into a meshgrid for plotting using surf.
Almost every example I saw uses meshgrids.
Right now, I am doing by plotting a sphere and then use scatter3 to plot my points as big balls and try to smooth them later. I looks like this:
I would like to get the figure as the plotting of the example in that link, where he uses:
k = 5;
n = 2^k-1;
[x,y,z] = sphere(n);
c = hadamard(2^k);
surf(x,y,z,c);
colormap([1 1 0; 0 1 1])
axis equal
EDIT:
(Sorry for taking so long to reply, the corona crises kept away from work)
What I am actually doing is:
for i=1:numel(pop0n)
ori(i,:)=ori(i,:)/norm(ori(i,:));
end
x = ori(:,1);
y = ori(:,2);
z = ori(:,3);
%// plot
m=100;
[aa,bb,cc] = sphere(m);
surf(aa,bb,cc,ones(m+1,m+1)*min(pop0n))
hold on
colormap jet;
scatter3(x,y,z,400,pop0n/norm(pop0n),'filled');
colorbar
shading interp
The array 'ori' is 8000x3, and contains the x, y and z coordinates of the points I want to plot and pop0n is a 8000 sized vector with the intensities of each coordinate.
My main question is how do I transform my x, y, z and pop0n, that are vectors, into 2D arrays (meshgrid) to use surf?
Because I cannot simply do surf(x,y,z,pop0n) if they are vectors.
Thanks in advance
As David suggested, griddata does the job.
What I did was:
for i=1:numel(pop0n)
ori(i,:)=ori(i,:)/norm(ori(i,:));
end
x = ori(:,1);
y = ori(:,2);
z = ori(:,3);
%// plot
m=100;
[aa,bb,cc] = sphere(m);
v = griddata(x,y,z,pop0n,aa,bb,cc,'nearest');
surf(aa,bb,cc,v)
colormap jet;
colorbar
shading interp
Getting right to the question: How can I make my plot go from looking like this:
to something like this:
where a right-handed Cartesian coordinate system (with axis labels at the end of the arrows, e.g., in this example the x-axis label is = $x_1^G$)
Some elaboration and prefacing: First, I am new to matlab and "matrix math". I tried searching on this site for questions similar to what I have posed above but did not see anything (but I may have missed), so hopefully this is not a duplicate.
Here is the code I have used to develop my rotated ellipsoid (since I'm new to matlab I would appreciate any comments on my code):
%Insert the components of the 3x3 matrix (i.e. the scalar values of the 2nd-rank symmetric tensor)
Pmatrix = [115.9547 12.03765 4.68235; 12.03765 116.3702 -2.47985; 4.68235 -2.47985 134.5488];
[R,D]=eig(Pmatrix); %find the eigenvectors (R) and eigenvalues (D) of the 2nd-rank tensor
[x, y, z] =sphere; %generate coordinates of a sphere, using the sphere command
%Stretch the coordinates of the sphere to form the tensor's representation ellipsoid, do this by multiplying the x, y, z coordinates by the square-roots of the eigenvalues
x1 = x*sqrt(D(1,1));
y1 = y*sqrt(D(2,2));
z1 = z*sqrt(D(3,3));
figure;
hmesh = mesh(x1,y1,z1);
set(hmesh,'FaceColor',[0.5,0.5,0.5],'FaceAlpha',0.5) %set color to gray, make mostly transparent
axis equal; %Make tick mark increments on all axes equal
xlabel('x');
ylabel('y');
zlabel('z');
theta1 = -asind(R(3,1)); %rotation around y-axis in degrees
psi1 = atan2d(R(3,2)/cos(theta1),R(3,3)/cos(theta1)); %rotation around x-axis in degrees
phi1 = atan2d(R(2,1)/cos(theta1),R(1,1)/cos(theta1)); %rotation around z-axis in degress
direction = [1 0 0]; %rotate the surface plot psi1 degrees around its x-axis
rotate(hmesh,direction,psi1)
direction = [0 1 0]; %rotate the surface plot theta1 degrees around its y-axis
rotate(hmesh,direction,theta1)
direction = [0 0 1]; %rotate the surface plot phi1 degrees around its z-axis
rotate(hmesh,direction,phi1)
view([-36 18]); %Change the camera viewpoint
To add to my question, I would like to add other (similar) items to my plot, so that the final product would look like this:
In the development of the image above, a set of axes collinear with the ellipsoid's eigenvectors are added (the red, green, blue arrows):
Then these axes are extended in the opposite direction, through the origin, where these portions of the axes are shown as a dashed lines:
Then, the angles between the global coordinate axes (black arrows) and the ellipsoid's axes (colored arrows) are notated as shown here:
To comment on this last addition, someone has built some matlab code with these features (see youtube video here). In the video's description it says the matlab code can be found here. Being new to matlab, I don't see where the code is, e.g., I don't see where on this page (screenshot below) the code is to build that matlab plot seen in the youtube video. If you can guide me on how to navigate that mathworks-fileexchage page that would be appreciated.
I have a rational polynomial function. I find zeros of numerator and denominator of it. Now I want to draw this function and I do it with meshgrid and mesh command in matlab. How can I draw a circle in this shape? I add my result figure at first and second figure is an image that I want to be like that( draw red circle).
Create x and y for your circle:
r = 1;
theta = 0:0.1:2*pi;
x = r*cos(theta);
y = r*sin(theta);
Get the value of your function at the x and y's and plot a line in 3D with the values:
z = f(x,y);
plot3(x,y,z);
The final result may have some artefacts where the line crosses in and out of the surface. If you are not so concerned about the accuracy in the plot add a very small value to z to "lift" it above the surface.
How can I plot a 3D nodes in a shape of truncated cone using matlab, and I want to connect each two nodes together with line.
Here is a truncated cone (based on http://msemac.redwoods.edu/~darnold/math50c/matlab/coordcyl/index.xhtml). I'm not sure if this is the type of mesh you are looking for.
r=linspace(1,2,25);
theta = linspace(0,2*pi,25);
[r,theta] = meshgrid(r,theta);
x = r.*cos(theta);
y = r.*sin(theta);
z = -r;
mesh(x,y,z)