in reply to Data visualisation.
There are two possibilities: the set is known to be mappable or it is not.
Start with point A. Place it in a predefined position in your space. The space will need to be extensible in all directions (or there must be a procedure to move all existing points to make room for a new one).
Point B is then placed 633 units from A in a predefined direction.
There are now at most 2 points where C can go (257 from A and 390 from B). Choose one of these by a predetermined process.
The same process for C will apply to all subsequent points. This is where the question of known mappability comes in. If a set is known to be mappable but a point appears to be unmappable, use a least squares algorithm to find the most appropriate place for it. If the set might not be mappable, halt and report the problem.
This is my first pass approach to the algorithm. I'll continue to think about it & may respond further.
Regards,
John Davies