# How to make the marker size in a scatter plot 'to scale' with the axes?

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AS on 28 Dec 2016
Answered: Will Reeves on 14 Mar 2022
I am using 3D scatter command using the following syntax: scatter3(X,Y,Z,S). The marker size is variable in my case where S is a vector. But the marker size is not in scale with the plot axes. How to make the marker size proportional to the axes units?
Ahmet Cecen on 28 Dec 2016
Can you take a screenshot with something like snipping tool and use annotation (as simple as paint or powerpoint) to show what you currently have and what you want to see?

Walter Roberson on 29 Dec 2016
"The units for the marker area is points squared."
That is the same "points" as specifying 'points' for axes Units property
If you want to make something proportional, then
ax = gca;
old_units = get(ax, 'Units');
set(ax, 'Units', 'points');
pos_points = get(ax, 'Position');
set(ax, 'Units', old_units);
narrower_part_points = min(pos_points(3:4));
Now create something proportional to narrower_part_points. But remember that the size for scatter()'s purpose is area, which is points square. So for example something rand with diameter 1/20th of the width should be expressed as pi * narrower_part_points.^2 / 4
the division by 4 is the change between pi*r^2 and pi*(d/2)^2

KSSV on 29 Dec 2016
x = rand(10,1) ; % some random x
y = rand(10,1) ; % some random y
sizes = randsample(1:100,10) ; % random sizes for 1o points, which lie between 1 to 100
scatter(x,y,sizes,sizes,'filled') ; % scatter plot with varying sizes and sizes as color on them
You can extend it to 3D case.
AS on 29 Dec 2016
Sizes are different for markers but the size is not in the same scale as that of the axes.
KSSV on 29 Dec 2016
you fix the sizes depending on your scale.

Will Reeves on 14 Mar 2022
I'd like this functionality too, but I would like the simplicity of being able to pick an "absolute size" drawn in one (or more) of the axis units. For instance I currently use the "viscircles" function, found in the image processing tool box, to achieve this. However, it's really really slow if you want to visualise thousands of cirlces of say 20 micron radius on a plot. It also doesn't offer the "filled" functionality of the scatter plot.