How to make color plots in 3D?

I am using isosurface to create 3D plots, but the colors aren't what I want. I have two examples with 2D plots with nice colormap and 3D plots using isosurface. I would like to reprduce the colors from 2D plot to my 3D plot if that's possible:

2D plot:

Nx = 256; 
Ny = 256; 
Lx = 128;  
Ly = 128;  
%coord mapping
xi  = (0:Nx-1)/Nx*2*pi;
xi_x =  2*pi/Lx;
x =  xi/xi_x;
yi  = (0:Ny-1)/Ny*2*pi;
yi_y =  2*pi/Ly;
y = yi/yi_y;

A = 2*pi / Lx;
B = 2*pi / Ly;
x0 = 64; 
y0 = 64;
rx0 = 20;
ry0 =  20;

p = 3;
b = 0.015;
c = 12; 
d = 1;
a = 4;

[X2,Y2] = meshgrid(x,y);

theta2 = atan2(Y2 -y0,  X2-x0) - (pi/c);
p02 =  ((X2-x0) .* (X2-x0)) /(rx0 * rx0) + ((Y2-y0) .* (Y2-y0))/(ry0 * ry0);
n2 =d + a * exp((-1. * p02 .* (1 - b * cos(c * theta2))).^p) ;

%plot
figure
pcolor(X2,Y2,n2); colorbar; colormap('inferno'); shading flat; axis tight;
grid on;

The same example for 3D:

Nx = 256; 
Ny = 256; 
Nz = 256;
Lx = 128;  
Ly = 128;  
Lz = 128;
%coord mapping
xi  = (0:Nx-1)/Nx*2*pi;
xi_x =  2*pi/Lx;
x =  xi/xi_x;
yi  = (0:Ny-1)/Ny*2*pi;
yi_y =  2*pi/Ly;
y = yi/yi_y;
zi  = (0:Nz-1)/Nz*2*pi;
zi_z =  2*pi/Lz;
z = zi/zi_z;

A = 2*pi / Lx;
B = 2*pi / Ly;
x0 = 64; 
y0 = 64;
z0 = 64; 
rx0 = 20;
ry0 =  20;
rz0 =  20;
p = 3;
b = 0.015;
c = 12; 
d = 1;
a = 4;

[X,Y,Z] = meshgrid(x,y,z);
theta = atan2(Y -y0,  X-x0) - (pi/c);
p0 =  ((X-x0) .* (X-x0)) /(rx0 * rx0) + ((Y-y0) .* (Y-y0))/(ry0 * ry0) + ((Z-z0) .* (Z-z0))/(rz0 * rz0);
n =d + a * exp((-1. * p0 .* (1 - b * cos(c * theta))).^p) ;
%plotting
figure
isosurface(X,Y,Z,n);
colorbar;
shading flat;
grid on;
xlabel('x'); ylabel('y'); zlabel('z'); 

[Adam Danz]

I edited your quesiton to run the code using the Run feature (green triangle > in edit mode). See the Rich Text Editor tools for help.

[Adam Danz]

1. For starters, you'll need to set the same custom colormap - colormap('inferno') (pretty neat, by the way).
2. See this example in the isosurface documentation that shows how to control surface color by using patch along with the isosurface outputs. https://www.mathworks.com/help/matlab/ref/isosurface.html#mw_0340c7e3-87a1-489e-99ec-454313c25169
3. Investigate the n variable to make sure it's doing what you want it to do.

See also the clim function which may be helpful to scale the colors.

[Jamie Al]

Thanks! This colormap 'inferno' is from someone else who converted from Python and it's very useful. I can make 2D slices and use this colormap, but I was thinking maybe 3D countor plots are better here.

Answer 1

[Walter Roberson]

If you

help isosurface

then currently Example 1 shows taking the output of isosurface() and passing it to patch() and then modifying the patch properties such as setting the face color.

  Example 1:
       [x y z v] = flow;
       p = patch(isosurface(x, y, z, v, -3));
       isonormals(x,y,z,v, p)
       p.FaceColor = 'red';
       p.EdgeColor = 'none';
       daspect([1 1 1])
       view(3)
       camlight; lighting phong
 

[Jamie Al]

Thanks, but I was wondering if I can do something like 3D contour plots using MATLAB. I can take 2D slices and use the MATLAB contoru function like:

for i = 140
figure(22)
contour3(X(:,:,i), Y(:,:,i), n(:,:,i));
end

But is there a way to make 3D contour plots in MATLAB similar to these?

[Walter Roberson]

Loop isosurface() calls, each with a different iso level. For example,

N = 10;  %number of surfaces
cmap = parula(N);
[minn, maxn] = bounds(n, 'all');
L = linspace(minn, maxn, N);
for K = 1 : N
   p = patch(isosurface(X, Y, n, L(K)));
   p.FaceColor = cmap(K,:);
   p.EdgeColor = 'none';
   p.FaceAlpha = 0.6;
end
view(3)