How to render a structured mesh in Octave - matlab

Question

I would like to recreate this sort of "cubic" surface rendering in GNU Octave:
[From AEG Mesher documentation]
How can I achieve this, given a list of coordinates which represent a surface or volume in a structured grid?

Answer 1

Obviously there's probably much more elaborate frameworks out there, but just to demonstrate the concept: the idea that you can only work with triangular patches is incorrect. You can specify your own patches as elaborately as you want.
In the following example, I create a simple function which draws a 3D cube 'patch', to be treated as a 'pixel' element in a structured 'mesh'.
function drawpatchpixel( x, y, z, c )
Vertices = [ 0, 0, 0
0, 1, 0
1, 1, 0
1, 0, 0
0, 0, 1
0, 1, 1
1, 1, 1
1, 0, 1 ];
Faces = [ 1, 2, 3, 4 # front
2, 6, 7, 3 # top
5, 6, 7, 8 # back
1, 5, 8, 4 # bottom
1, 2, 6, 5 # left
4, 3, 7, 8 ]; # right
patch( 'Faces', Faces, 'Vertices', Vertices + [x, y, z], 'facecolor', c )
endfunction
Then I simply draw the pixels in the preferred colour:
Pixels = { 0, 0, 0, 'r'; # base
1, 0, 0, 'r';
2, 0, 0, 'r';
3, 0, 0, 'r';
4, 0, 0, 'r';
4, 1, 0, 'r';
4, 2, 0, 'r';
4, 3, 0, 'r';
4, 4, 0, 'r';
3, 4, 0, 'r';
2, 4, 0, 'r';
1, 4, 0, 'r';
0, 4, 0, 'r';
0, 3, 0, 'r';
0, 2, 0, 'r';
0, 1, 0, 'r';
0, 0, 1, [0.5, 0.5, 0.5]; # pillars
0, 0, 2, [0.5, 0.5, 0.5];
0, 0, 3, [0.5, 0.5, 0.5];
0, 0, 4, [0.5, 0.5, 0.5];
4, 0, 1, [0.5, 0.5, 0.5];
4, 0, 2, [0.5, 0.5, 0.5];
4, 0, 3, [0.5, 0.5, 0.5];
4, 0, 4, [0.5, 0.5, 0.5];
4, 4, 1, [0.5, 0.5, 0.5];
4, 4, 2, [0.5, 0.5, 0.5];
4, 4, 3, [0.5, 0.5, 0.5];
4, 4, 4, [0.5, 0.5, 0.5];
0, 4, 1, [0.5, 0.5, 0.5];
0, 4, 2, [0.5, 0.5, 0.5];
0, 4, 3, [0.5, 0.5, 0.5];
0, 4, 4, [0.5, 0.5, 0.5];
0, 1, 4, 'g'; # roof
0, 2, 4, 'g';
0, 3, 4, 'g';
4, 1, 4, 'g';
4, 2, 4, 'g';
4, 3, 4, 'g';
1, 0, 4, 'g';
2, 0, 4, 'g';
3, 0, 4, 'g';
1, 4, 4, 'g';
2, 4, 4, 'g';
3, 4, 4, 'g';
};
NPixels = size( Pixels, 1 );
for i = 1 : NPixels
drawpatchpixel( Pixels{i, :} )
endfor
axis equal
view( 30, 30 )
xlabel( 'x'); ylabel('y'), zlabel('z');
camlight
Result: