Find the shortest OPEN path connecting a set of 2D points (special case)
Your paths are varieties of what are often called angle-restricted paths in the literature, and exploring the literature may help with your
particular situation:


Fekete, Woeginger, 1997, "Angle-Restricted Tours in the plane."
Dumitrescu, Pach, Tóth, 2009, "Drawing Hamiltonian cycles with no large angles." 
Bárány, Pór, and Valtr, 2009, "Paths with No Small Angles"


The general angle-restricted TSP (Traveling Salesman Path) problem is NP-hard, as
established in the 1997 paper, "The Angular-Metric Traveling Salesman Problem."