Triangulation with constrained edge lengths

I am using triangulation for a Monte Carlo simulation of a physical surface. The triangulation represents a tethered sphere network. In this simulation, I need the length of the tethers, represented by the edges, to be within a certain range of length. How can I triangulate a surface, such that the the edge have lengths between a minimum and maximum length?

[Matt J]

Shouldn't the physical equations take care of that? Aren't you randomly generating the points according to a distribution that controls the distance between spheres?

[T Abraham]

@Matt J the length constraints are there for self-avoiding such that it is impossible for the spheres to overlap with each other during the course of the simulation. I don't understand what you mean by the physical equations taking care of that...

[Matt J]

Well what data are you currently generating with the Monte Carlo simulation? And with what kind of random distribution?

[T Abraham]

@Matt J the data is the dynamics of the physical surface so basically the trajectories of vertices/spheres.

What do you mean by distribution? I use a Metropolis criterion, so I guess Boltzmann distribution.