# matlab: scatter plots with high number of datapoints

I'm trying to plot scatter, something like:

```scatter(coor(:, 2), coor(:, 3), 1, coor(:, 4));
```

The problem is, that I have quite big number of coordinates to plot (~100 000). Its taking long time to plot it, and when I try to export figure to tiff - then matlab is dead for goooood few minutes... Any solution to improve plotting, or at least tiff export?

EDIT: Forgot to mention, 3rd coordinate (coor(:, 4)) is a color code.

So, when I'm using scatter (as above), I have something like on the image below, and thats exactly how I want to see it (just its super slow and I can't export that):

When I do:

plot3(coor(:, 2), coor(:, 3), coor(:, 4), '.')

effect is not as cool any more (note: images are not from the same coordinates...) :

You can use plot, but then all points have the same color. However, you can divide the set in different subsets and plot them each with their own color:

```N = 100000;
x = rand(N,1);
y = rand(N,1);
C = sin(2*x)+y;

cdivs = 10;
[~, edges] = hist(C,cdivs-1);
edges = [-Inf edges Inf]; % to include all points
[Nk, bink] = histc(C,edges);

figure;
hold on;
cmap = jet(cdivs);
for ii=1:cdivs
idx = bink==ii;
plot(x(idx),y(idx),'.','MarkerSize',4,'Color',cmap(ii,:));
end

colormap(cmap)
caxis([min(C) max(C)])
colorbar
```

which responds already a lot better than scatter(x,y,1,C) which gives about the same plot, but with higher color resolution (which is adjustable in my code above).

My experience is that the most efficient plotting command in matlab is Patch, and I have used it to emulate the functionality of scatter or scatter3 with much higher efficiency.

If you have a list of points, use each point to define a square patch (or octagons, or whatever) of reasonable edge length for your particular data, then plot the collection of patches with a single call to patch. After the graphic object is created, you can update its color data to individually color the squares.

You can use the same concept in 3D by building cubes or 3D crosses from your data set.

This snippet creates 1e5 randomly placed squares, with random colors in this case and runs in a little under a second on my four year old laptop. A similar call to scatter takes 40 seconds, and returns an unwieldy figure that is hard to manipulate.

```tic
P=rand(1e5,2);
Edge=.01;
X=[P(:,1)'; P(:,1)'+Edge; P(:,1)'+Edge; P(:,1)'];
Y=[P(:,2)'; P(:,2)'; P(:,2)'+Edge; P(:,2)'+Edge];
figure;
h=patch(X,Y,'r');
set(h,'facevertexcdata',rand(size(X,2),3),'facecolor','flat','edgecolor','none')
drawnow
toc
```

Yes, use plot3

```plot3(coor(:, 2), coor(:, 3), coor(:, 4), '.')
```

This will do the same as a 3d scatter plot (the points will be small dots, you can also use 'o' or 'x' if you want)

If you have too many points it might make sense to thin down the data.

Basically you could do two approaches:

1. simple - just select - say 10% of the points randomly.

2. discard points that would not be visible, obviously those outside your range, but also if you have that many quite a few overlap - say a point should be 3px in diameter - so a point would cover say 9px. On my machine a plot like you posted would be - say 400x400px so at most ceil(400*400/9) < 20 000 data points would be visible.

you could also try to separate the plot into smaller chunks - like plot 1000 points, issue a drawnow then the next 1000 till you are done. So you don't have to wait in front of a blank screen.