This paper addresses path generation for autonomous robots, industrial robots, and CNC machines by producing smooth, executable paths from discrete planning outputs such as waypoint sequences. The authors introduce directional mollification, a novel approach that overcomes the fundamental geometric constraint of standard mollification, where the smoothed path was confined within the convex hull of the original path. This method provides formal smoothness and curvature guarantees while enabling exact waypoint interpolation as required by mission specifications, offering advantages over traditional spline interpolation and optimization-based approaches for trajectory tracking controllers and nonholonomic systems.