  We study the properties of least time trajectories for particles moving on a
two dimensional surface which consists of piecewise homogeneous regions. The
particles are assumed to move with different constant speeds on different
regions and on the boundary between regions. The speed of the particle is
assumed to be highest when it moves along the edges formed by the boundary of
two regions. We get an analogous behavior to Snell's Law of light refraction,
but in a more generalized form. The model could be used for studying properties
of animal and insect trails which tend to form predominantly along edges. The
model predicts three types of behavior for the trajectories near a corner
forming edge: fully edge following, partial edge following and complete
avoidance of the edge, which are indeed observed in natural ant trails.
