How to plot a function on a user defined plane when using spherical coordinate system by specifying elevation and azimuth values at a given radial distance?

Hi,

I want to plot a surface plot on plane defined by, (say: theta = 45 degree, phi = 25 degree, radial distance = 1 m).

Suppose I am using mesh grid to define X,Y,Z cordinates for a cartesian coordinate system.

Currently if I want to plot my function (f) on x-y plane at z = 10, I can use surf(x, y, f(:, :, 100))

Then by using coordinate transformation I define r,theta, and phi.

How do I plot the surface plot on (theta = 45 degree, phi = 25 degree, r = 1 m)

MATLAB CODE:

x = linspace(0,10,100)
y = linspace(0,10,100)
z = linspace(0,10,100)
[X,Y,Z] = meshgrid(x,y,z);      % Defining mesh grid
r = sqrt(X.^2+Y.^2+Z.^2);       % Define r vector
tht = acos(Z./r);                % Define theta
phi = atan(y./x);                % Define phi

Thank You.

Biplob Biswas

PhD Research Scholar

[Matt J]

How do I plot the surface plot on (theta = 45 degree, phi = 25 degree, r = 1 m)

The three spherical coordinates theta, phi, and r are not enough to specify a grid of sample points in an oblique plane. You must also define coordinate axes vectors b1 and b2 within the plane.

Answer 1

[Matt J]

See slice.

[Biplob]

I will try slice function. I already knew about this function.

Thanks Matt.

Answer 2

[Matt J]

The three spherical coordinates theta, phi, and r are not enough to define the sampling of a plane. You must also define coordinate axes vectors b1 and b2 within the plane.

And one way of doing so is by using this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-for-fitting-conics-and-quadrics

with particular attention to the Examples section Post-Sampling a Plane Fit.

[x0,y0,z0] = sph2cart(theta,phi,r);

plane = planarFit.groundtruth([],[x0,y0,z0],r);

b0=[1,0,0]; 
b1=cross([0,1,0],plane.normal); %Make one sampling direction parallel to x-z plane
b2=[];                         %Make the other direction orthogonal to b1

t=linspace(___); 

xyz=plane.sample(b0,b1,b2,2*t,t); %grid points in the plane

and then evaluate your function at those points.

F=arrayfun(f,xyz{:});  %function samples in plane

[Biplob]

Thanks Matt.

Understanding this code is a bit tough for me. But I will try to trobleshoot this code.

Using slice may be a easier option.

Let me try. I will revert back to you if I dont understand something.

[Biplob]

I have come acorss another answer given by you in some other thread in the forum.

The code is as follows:

MATLAB CODE:

A = [104,122,111];

B = [253,122,153];

C = [104,124,111];

normal=normalize( cross(A-B,A-C),'norm'); %calculate plane parameters

P=dot(A,normal);

load mri %set up some volume data

[X,Y,Z]=meshgrid(1:128,1:128,(1:27)-110);

V = single(squeeze(D));

[x,y]=meshgrid(linspace(1,128,512)); %compute sample locations in plane

z=(normal(1)*x+normal(2)*y-P)./normal(3);

h=slice(X,Y,Z,V,x,y,z,'cubic'); %plot

colormap(gray(256));

h.LineStyle='none';

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

In this above code, what do the A,B, and C variable represent? Why are we taking the cross product of A-B and A-C? Does it helps in finding the normal vector? Also why do we need the dot product of A and normal vector? Can you please explain the theoretical background behind it.

Also in the above code; V = single(squeeze(D)); Does it represent the function value? Why do we need to squeeze it?

[Matt J]

I do not remember the thread you extracted this from, and you haven't referenced a link to it. However, my impression is that A,B,C are three points lying in a plane of interest. Note that 3 points are needed to specify a plane. From these 3 points, the code determines the equation for the plane, which is of the form,

n1*x+n2*y+n3*z=P

Here [n1,n2,n3] is the normal to the plane. From the plane's equation, you can then solve for z as a function of x and y, provided that n3~=0:

z=(P-(n1*x+n2*y))/n3

[Biplob]

Thanks Matt. I understood your point.

Also I have successfully used the slice function mentioned by you to plot my function on a desired plane.

Thank a lot for you help.

Biplob.