How to colour a 3D image with a continuous spectrum of colours

I have a 3D image. I would like to shade it in a continuous colour. I.e. where the colour of the image is conditional on its location in 3D space. How can I do this for for my image? For example:

EG: http://4g-portal.com/wp-content/uploads/2013/03/Matlab.png EG2: http://www.math.utah.edu/lab/ms/matlab/gif/surface.png

My code to generate the image is below.

thanks

%%first download these two files:
%www.mathworks.co.uk/matlabcentral/fileexchange/30923-fast-stl-import-function
%www.cs.technion.ac.il/~gershon/EscherForReal/PenroseTriangleStl1.zip

myStr = 'D:\PenroseTriangle.stl';
[vertices, norms] = import_stl_fast(myStr,2);
n = length(vertices)/3;
X = reshape(vertices(:,1),3,n);
Y = reshape(vertices(:,2),3,n);
Z = reshape(vertices(:,3),3,n);
C = zeros(3,n);

%%Render
figure;
set(gcf, 'Color', 'white');
as = 0.95;
strt=1;
stop=6000;
patch(X(:,strt:stop),Y(:,strt:stop),Z(:,strt:stop),C(:,strt:stop),...
    'FaceColor',       [0 0 1], ...
    'EdgeColor',       'none',        ...
    'FaceLighting',    'phong',     ...
    'AmbientStrength', as);
strt=6001;
stop=6299;
patch(X(:,strt:stop),Y(:,strt:stop),Z(:,strt:stop),C(:,strt:stop),...
    'FaceColor',       [0 1 0], ...
    'EdgeColor',       'none',        ...
    'FaceLighting',    'phong',     ...
    'AmbientStrength', as);
strt=6300;
stop=6719;
patch(X(:,strt:stop),Y(:,strt:stop),Z(:,strt:stop),C(:,strt:stop),...
    'FaceColor',       [1 0 0], ...
    'EdgeColor',       'none',        ...
    'FaceLighting',    'phong',     ...
    'AmbientStrength', as);
view([-135 35]);
axis('image');
axis('off');
% colormap('hsv');
% shading('interp');
camlight('headlight');
material('shiny');

Answer 1

[Jason Nicholson]

The patch command's fourth argument, C, is the color of the that patch. Your C matrix is C=0. That is the problem. Instead use a function that defines the color matrix C. Matlab will scale C matrix to the default color values.

Try this:

% Euclidean distance in 3d 
C = sqrt(X.^2 + Y.^2 + Z.^2);

Here is what it does to your code:

%%first download these two files:
%www.mathworks.co.uk/matlabcentral/fileexchange/30923-fast-stl-import-function
%www.cs.technion.ac.il/~gershon/EscherForReal/PenroseTriangleStl1.zip
myStr = 'PenroseTriangle.stl';
[vertices, norms] = import_stl_fast(myStr,2);
n = length(vertices)/3;
X = reshape(vertices(:,1),3,n);
Y = reshape(vertices(:,2),3,n);
Z = reshape(vertices(:,3),3,n);
C = sqrt(X.^2 + Y.^2 + Z.^2);
%%Render
figure;
set(gcf, 'Color', 'white');
as = 0.95;
strt=1;
stop=6000;
patch(X(:,strt:stop),Y(:,strt:stop),Z(:,strt:stop),C(:,strt:stop),...
  'FaceColor',       'interp', ...
  'EdgeColor',       'none',        ...
  'FaceLighting',    'phong',     ...
  'AmbientStrength', as);
strt=6001;
stop=6299;
patch(X(:,strt:stop),Y(:,strt:stop),Z(:,strt:stop),C(:,strt:stop),...
  'FaceColor',      'interp', ...
  'EdgeColor',       'none',        ...
  'FaceLighting',    'phong',     ...
  'AmbientStrength', as);
strt=6300;
stop=6719;
patch(X(:,strt:stop),Y(:,strt:stop),Z(:,strt:stop),C(:,strt:stop),...
  'FaceColor',       'interp', ...
  'EdgeColor',       'none',        ...
  'FaceLighting',    'phong',     ...
  'AmbientStrength', as);
view([-135 35]);
axis('image');
axis('off');
colormap('hsv');
camlight('headlight');
material('shiny');

[Jason Nicholson]

If this answers your question, please mark this as the correct answer. It helps my reputation points on MATLAB answers.

[Cedric Wannaz]

About 1/3 people never come back to accept answers ;-/

..but hey, I'm voting for your answer!

[Image Analyst]

That would be about 2/3. See http://www.mathworks.com/matlabcentral/trendy/plots/795. I'll also vote for Jason. A good answer such as this deserves a vote. "none" can both Accept and Vote, which will give 4 points.

[Cedric Wannaz]

Interesting .. yet I meant something else with my 1/3 (which can be wrong): of the questions that I answered, 1/3 have my answer accepted, 1/3 have another answer accepted, and for the rest the OP never came back or said thank you but didn't click on accept.

[Image Analyst]

OK - that sounds about right/typical (for everyone except Greg of course!) And too bad Walter (our most prolific contributor to date) seems to have fallen off the planet. Wonder what happened to him. One time before he left for about 3 months before coming back so maybe he'll return some day.

[Cedric Wannaz]

Yes I was wondering as well. Hopefully he is just on a sunny island and was wise enough not to take his keyboard! Speaking of ratio, I built the code attached lately, just for fun (well, I was waiting at a bus stop, so .. "for more fun than just waiting").