What's the relationship beween scatter markersize and its height and the length?

Here, I use scatter to label some points in the axes. So I need to know the height and the length of the scatter maker to avoid overlapping. But I only know the makersize. what's the relationship beween scatter makersize and its height and the length? As this picture shows:

[dpb]

From the doc for scatter

"sz — Marker area

36 (default) | numeric scalar | row or column vector | []

Marker area in points squared, specified in one of these forms:

• Numeric scalar — Plot all markers with equal size.
• Row or column vector — Use different sizes for each marker. Corresponding elements in x, y, and sz determine the location and area of each marker. The length of sz must equal the length of x and y.
• [] — Use the default area of 36 points squared.

The units for the marker area is points squared."

There's not a specific property for the actual marker dimensions in x/y coordinates other than by approximating the areas of the chosen marker styles in points by the appropriate conversion to data coordinates for the axis limits as set. For the default circle this is easy enough as the radius of the circle is ~sqrt(area) and equal both directions. What the correlation used internally inside the function for the more oddly-shaped markers isn't documented altho it appears by visual inspection using the approximation for all markers wouldn't be much in error altho visually the '>' appears to be somewhat larger and, for example, the 'h' a little small; the latter is probably owing to the shape than actual extent of points drawn.

[Image Analyst]

Personally I just do trial and error until I get a size I'm happy with.

[dpb]

"Personally I just do trial and error until I get a size I'm happy with."

Me too, for anything I've ever done but the OP is apparently trying to place points in near juxtaposition yet avoid collisions. Still the answer is to probably determine the spacing and size to use empirically via trial and error rather than trying to somehow compute a distance measure. Unless, of course, the scales change markedly and then a given offset doesn't produce the desired result. Probably expressing that empirical distance as fraction of the value would be more useful.

[Yuanjie Su]

Thanks for your answer. Today, I use plot instead of scatter and get some result.

First I set the axes unity property is point. Then I compute the markerwidth through axes.position, axes.XLim and s(the makerwith in x axes scale). Then I find maker 'o' and 'd' makerwidth is s in x axes scale.

handles=guihandles;
h1=plot(handles.axes1,0.5,0.5);
s = 0.4; %Marker width in units of X，axe1 units is point
axpos = get(handles.axes1,'Position');
xlim=get(handles.axes1,'XLim');
markerWidth = s/diff(xlim)*axpos(3); % Calculate Marker width in points
set(h1, 'Marker', 'square');
set(h1, 'MarkerSize', markerWidth);
hold on;
h2=plot(handles.axes1,0.5,0.5);
set(h2, 'Marker', 'o');
set(h2, 'MarkerSize', markerWidth);
h3=plot(handles.axes1,0.5,0.5);
set(h3, 'Marker', 'd');
set(h3, 'MarkerSize', markerWidth);

[Yuanjie Su]

The supplement for the last answer.

handles=guihandles;
h1=plot(handles.axes1,0.5,0.5);
s = 0.4; %Marker width in units of X，axe1 units is point
axpos = get(handles.axes1,'Position');
xlim=get(handles.axes1,'XLim');
markerWidth = s/diff(xlim)*axpos(3); % Calculate Marker width in points
set(h1, 'Marker', 'square');
set(h1, 'MarkerSize', 1.28*markerWidth);
hold on;
h2=plot(handles.axes1,0.5,0.5);
set(h2, 'Marker', 'o');
set(h2, 'MarkerSize', markerWidth);
h3=plot(handles.axes1,0.5,0.5);
set(h3, 'Marker', 'd');
set(h3, 'MarkerSize', markerWidth);
h4=plot(handles.axes1,0.565,0.5);
set(h4, 'Marker', '<');
set(h4, 'MarkerSize', markerWidth);
h5=plot(handles.axes1,0.435,0.5);
set(h5, 'Marker', '>');
set(h5, 'MarkerSize', markerWidth);
set(handles.axes1,'XLim',[-0.5,1.5]);