You want to set the positions of the labels considering 2 criteria:
- The text areas do not overlap
- The labels appear next to the data points, such that it is clear to which point they belong to
The problem is not trivial, because the 2nd criterion cannot be defined easily in mathematical terms. It is a complicated optimization problem which must take into account the visual reception system of humen. In addition the solution will depend on the medium the diagram is displayed on: You can simply and intuitively rotate it in 3D on the screen to "look behind the labels": Users are used to change their 3D position to look behind obstacles. But this fails, when the diagram is printed on paper.
Do you simply want to visualize the results of some computations or is you goal writing a PhD about optimal label placement in scientific publications?
I'd decide for short labels and a legend. Even then an overlap can and will happen if the view angle is fixed, but it will be much faster to control this manually.
