How to define a plane by matrices instead of a function?

I want to define the following plane which runs through 3 points, by matrices.

So I can use the slice function.

slice(X,Y,Z,V,xslice,yslice,zslice) draws slices for the volumetric data V. Specify X,Y, and Z as the coordinate data. Specify xslice, yslice, and zslice as the slice locations using one of these forms:

• To draw one or more slice planes that are orthogonal to a particular axis, specify the slice arguments as a scalar or vector.
• To draw a single slice along a surface, specify all the slice arguments as matrices that define a surface.

I don't know how to define a surface as a matrices.

If you runs this code you will get the function for the plane. Yf.

How to descripe a plane by matrices instead of a function?

A = [104,122,111];
B = [253,122,153];
C = [104,124,111];
 
normal = cross(A-B, A-C)
 
   syms X Y Z
            P = [X,Y,Z];
            realdot = @(u, v) u*transpose(v);
            plane_function=realdot(P-A,normal);
            yf=solve(plane_function,Y)
            Yf = matlabFunction(yf) %the PLANE
            S = syms;
            cellfun(@clear, S);

Answer 1

[Matt J]

For example,

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';

[Matt J]

OP's comment moved here:

Thank you, that is exactly what I mean!

However, my 3D image is a .tif image. Which gives the following error:

 V = single(squeeze(I));
Error using single
Conversion to single from Tiff is not possible.

Is there another way to use the code?

[Matt J]

You must read in all the .tif slices (as grayscale) and organize them as an MxNxP 3D array.