Efficient algorithm to fulfil a set of coordinate constraints

Question

I have a set of labelled points and a set of distance constraints between pairs of points, consisting of a lower and upper distance bound. There is definitely an arrangement of the points in 3D space that fulfils all distance constraints.

I wish to generate arrangements of the points where all constraints are fulfilled. Any approach is allowed as long as each arrangement is independently generated from the others.

What algorithm is most suitable? Mainly in terms of efficiency.

As an extension, how would I incorporate constraints on the angle defined by three points? And on the dihedral angle defined by four points (the dihedral angle between points ABCD is the angle between the plane defined by ABC and the plane defined by BCD)?