We call an embedding of a weighted graph G on a surface S isometric, if edges 
of G are mapped to geodesic arcs on S so that arc lengths are equal to 
corresponding edge weights. The metric conditions of an embedding correspond 
to systems of nonlinear differential and algebraic equations, describing a net of 
intersecting geodesic arcs on the surface. 

As a real-world application (and as the actual incentive for this work), consider 
fitting snow tire chains to a car tire. The chain segments under tension follow 
geodesic curves along the convex hull of the tire surface. A tension chain will 
pull out all possible slack, thus enforcing a minimum distance condition between 
a set of vertices.

We present algorithms that either find a feasible embedding or, since there may 
be no solution fulfilling all constraints, an embedding that at least approximately 
fulfills all distance conditions.

IMFM and Univerza v Ljubljani, 
Fakulteta za matematiko in fiziko
Jadranska 21 (the new building)