  Generalizing the well-known relations on characteristic functions on a plane
to the case of a one-dimensional regular surface (curve) with compact support,
we establish implicit equations for these functions. Introducing an
approximation, we solve the combinatorial problems and reduce these equations
to a set of linear equations for a finite number of unknown functions. Imposing
natural conditions, we obtain a closed system of linear equations which can be
solved for a given surface. Its solutions can be used to calculate the
distribution of hitting probabilities for a regular surface with compact
support.
  In order to verify the accuracy of the approximate distribution of hitting
probabilities, numerical analysis is being made for a chosen surface.
