A question about drawing a surface plot in MATLAB - matlab

Question

I wrote a matlab code for topology optimization. The code showing the results in a surface plot is:(a very simple example)
XYZG=[2.5 0 0;2.5 0 2.5;2.5 0 5;0 -2.5 0;0 -2.5 2.5;0 -2.5 5;-2.5 0 0;-2.5 0 2.5;-2.5 0 5];
ELNOD=[1 4 5 2;2 5 6 3;4 7 8 5;5 8 9 6];
nelement=4;
Dens=[0 1 1 0];
for element=1:nelement
for i=1:4
X(i)=XYZG(ELNOD(element,i),1);
Y(i)=XYZG(ELNOD(element,i),2);
Z(i)=XYZG(ELNOD(element,i),3);
end
XX=[X(1) X(2);X(4) X(3)];
YY=[Y(1) Y(2);Y(4) Y(3)];
ZZ=[Z(1) Z(2);Z(4) Z(3)];
tick=-Dens(element)*[1 1;1 1];
figure(1)
hold on
surf(XX,YY,ZZ,tick);
colormap gray;
end
This code is too slow. If I have for example 10,000 elements it takes a long time for drawing plot.
So I would appreciate any help on how to make this faster.

Answer 1

1] Minor improvement:
The code you gave as a sample can be simplified to avoid temporary assignment. Consider the following:
%% Sample data
XYZG=[2.5 0 0;2.5 0 2.5;2.5 0 5;0 -2.5 0;0 -2.5 2.5;0 -2.5 5;-2.5 0 0;-2.5 0 2.5;-2.5 0 5];
ELNOD=[1 4 5 2;2 5 6 3;4 7 8 5;5 8 9 6];
nelement=4;
Dens=[0 1 1 0];
%% pre-initialisation just to set the size (size=[2,2])
XX = zeros(2) ;
YY = XX ;
ZZ = XX ;
figure(1)
hold on
colormap gray;
for element=1:nelement
% Base vector combining (unused now)
% idx=1:4;
% X = XYZG( ELNOD(element,idx),1 ).';
% Y = XYZG( ELNOD(element,idx),2 ).';
% Z = XYZG( ELNOD(element,idx),3 ).';
% The block above is commented because we do not need these intermediate
% vectors to build the base matrices XX, YY and ZZ.
% This can be done directly using linear indexing:
idxOrder = [1 4 2 3] ;
XX(1:4) = XYZG( ELNOD(element,idxOrder) , 1 ) ;
YY(1:4) = XYZG( ELNOD(element,idxOrder) , 2 ) ;
ZZ(1:4) = XYZG( ELNOD(element,idxOrder) , 3 ) ;
tick=-Dens(element)*[1 1;1 1];
surf(XX,YY,ZZ,tick) ;
end
This should run marginally faster. Thanks to the avoidance of a few temporary arrays. We are now building each patch coordinates more directly. Also the function calls which only need to be used once have been taken out of the loop (something to generally look for if your loop is taking too long).
Now this is not going to be satisfying anyway. The real bottleneck in your structure is not so much the calculations/indexing in each loop iteration, it is the growing number of graphic handles that the system has to maintain. Every iteration of your loop create a surface object. These objects require memory to keep their coordinates, but also to maintain the large number of internal properties. Once you multiply these objects, your system will start to slow down. Some systems may not even be able to create 10,000 surface graphic objects on the same figure, and if they can it's going to be sluggishly painful (you know these situations where you click on the screen and wait ~25s to notice any reaction ...).
2] Major improvement:
One way to limit the number of graphic object would be to combine all of these cordinates in order to create a single graphic object. Of course we'd then have to color each face according to your rule.
Fortunately, I noticed that your base coordinates are actually organised perfectly to inject directly as a patch in Matlab. SO no need to demultiplex/remultiplex the data in and out, we can directly create and color a global patch:
% create a Black and White colormap
cmap = [1 1 1;
0 0 0] ;
figure
% generate a patch with all the 'faces','vertices' and 'color' data :-)
hp = patch('Faces',ELNOD, 'Vertices',XYZG, 'FaceVertexCData',Dens(:) ) ;
% last refinement to have the same appearance than in former code
shading flat
colormap(cmap)
hp.EdgeColor = 'k' ; % <= this needs to be executed AFTER "shading flat"
Voila !! No need any loop or any calculations. You already had all the data needed in the first place ;-)
I'd encourage you to read the documentation for patch, especially the way to use the property FaceVertexCData