plot the function which is dependent on x, y and z with x, y and z on three axis.

D_value = 0.1;
L_value = 0.1;
B_value = 0.1;

x = 0:0.01:L_value/D_value;
y = 0:0.01:B_value/D_value;
z = 0:0.01:0.25;
[Y, X, Z] = meshgrid(y, x, z);

Ra_value = 80;
xi = 0.3;
R_value = Ra_value*xi;


A1_1_1 = -8.2516;
A1_1_2 = -1.7735;
A1_2_1 = -1.0336;
A1_2_2 =  0.6812;
A2_1_1 = -0.5388;
A2_1_2 = -0.8701;
A2_2_1 = -0.0329;


Phi_z = @(x,y,z)  A1_1_1.*pi.*cos(pi.*Z) + 2.*A2_1_1.*pi.*cos(2.*pi.*Z) + A1_1_2.*pi.*cos((pi.*D_value.*Y)./B_value).*cos(pi.*Z) + 2.*A2_1_2.*pi.*cos((pi.*D_value.*Y)./B_value).*cos(2.*pi.*Z) + A1_2_1.*pi.*cos((pi.*D_value.*X)./L_value).*cos(pi.*Z) + 2.*A2_2_1.*pi.*cos((pi.*D_value.*X)./L_value).*cos(2.*pi.*Z) + A1_2_2.*pi.*cos((pi.*D_value.*Y)./B_value).*cos((pi.*D_value.*X)./L_value).*cos(pi.*Z);
xlabel('x');
ylabel('y');
zlabel('z');

plot the function Phi_z.

Answer 1

[Torsten]

You can plot the function on slices (i.e. 2d-objects (e.g. planes)) through the volume of interest.

Of course a full plot over a 3d-volume is not possible because we cannot see in 4d.

D_value = 0.1;
L_value = 0.1;
B_value = 0.1;

x = 0:0.01:L_value/D_value;
y = 0:0.01:B_value/D_value;
z = 0:0.01:0.25;
[X,Y,Z] = meshgrid(x,y,z);

Ra_value = 80;
xi = 0.3;
R_value = Ra_value*xi;


A1_1_1 = -8.2516;
A1_1_2 = -1.7735;
A1_2_1 = -1.0336;
A1_2_2 =  0.6812;
A2_1_1 = -0.5388;
A2_1_2 = -0.8701;
A2_2_1 = -0.0329;


Phi_z = @(X,Y,Z)  A1_1_1.*pi.*cos(pi.*Z) + 2.*A2_1_1.*pi.*cos(2.*pi.*Z) +...
                  A1_1_2.*pi.*cos((pi.*D_value.*Y)./B_value).*cos(pi.*Z) +...
                  2.*A2_1_2.*pi.*cos((pi.*D_value.*Y)./B_value).*cos(2.*pi.*Z) +...
                  A1_2_1.*pi.*cos((pi.*D_value.*X)./L_value).*cos(pi.*Z) +...
                  2.*A2_2_1.*pi.*cos((pi.*D_value.*X)./L_value).*cos(2.*pi.*Z) +...
                  A1_2_2.*pi.*cos((pi.*D_value.*Y)./B_value).*cos((pi.*D_value.*X)./...
                  L_value).*cos(pi.*Z);
slice(X,Y,Z,Phi_z(X,Y,Z),(x(1)+x(end))/2,[],[])
xlabel('x');
ylabel('y');
zlabel('z');
colorbar

Answer 2

[Fangjun Jiang]

You are asking for the impossible, the visualization of the 4th dimension.

1. I thought it was impossible in three dimentional world.
2. There migth be some methods to "help" the visualization. https://en.wikipedia.org/wiki/Four-dimensional_space
3. I can't think of any built-in method in MATLAB that can help. Maybe, you could plot a dot at each and every point of the whole (x,y,z) grid. Set the color of the dot according to the value of Phi_z. Could that be regarded as the visualization of the 4th dimension? Not sure what is the visual effect though.