  A path or a polygonal domain is C-oriented if the orientations of its edges
belong to a set of C given orientations; this is a generalization of the
notable rectilinear case (C = 2). We study exact and approximation algorithms
for minimum-link C-oriented paths and paths with unrestricted orientations,
both in C-oriented and in general domains. Our two main algorithms are as
follows:
  A subquadratic-time algorithm with a non-trivial approximation guarantee for
general (unrestricted-orientation) minimum-link paths in general domains.
  An algorithm to find a minimum-link C-oriented path in a C-oriented domain.
Our algorithm is simpler and more time-space efficient than the prior
algorithm.
  We also obtain several related results:
  - 3SUM-hardness of determining the link distance with unrestricted
orientations (even in a rectilinear domain).
  - An optimal algorithm for finding a minimum-link rectilinear path in a
rectilinear domain. The algorithm and its analysis are simpler than the
existing ones.
  - An extension of our methods to find a C-oriented minimum-link path in a
general (not necessarily C-oriented) domain.
  - A more efficient algorithm to compute a 2-approximate C-oriented
minimum-link path.
  - A notion of "robust" paths. We show how minimum-link C-oriented paths
approximate the robust paths with unrestricted orientations to within an
additive error of 1.
