The above double integral is the generalized distance functional between two polymer conformation. formula_13 is a spatial parameter and formula_14 is pseudo-time. This means that formula_15 is the polymer/string conformation at time formula_16 and is parameterized along the string length by formula_17. Similarly formula_18 is the trajectory of an infinitesimal segment of the string during transformation of the entire string from conformation formula_19 to conformation formula_20. The term with cofactor formula_21 is a Lagrange multiplier and its role is to ensure that the length of the polymer remains the same during the transformation. If two discrete polymers are inextensible, then the minimal-distance transformation between them no longer involves purely straight-line motion, even on a Euclidean metric. There is a potential application of such generalized distance to the problem of protein folding.