Numerical Shape Interrogation of Planar Generalized Cubic Curves

The authors in Gabrielides and Sapidis (2020) presented a shape analysis of planar as well as of spatial Generalized Cubic Curves (GCC). The present paper, focusing on planar GCCs, complements (Gabrielides and Sapidis, 2020) with vital new results, offering necessary and sufficient conditions to directly identify the cases where a GCC is convex, non-convex or irregular, and/or if it presents a loop. These conditions lead to a simple and efficient algorithm, fully detailed in this paper, performing comprehensive shape interrogation of a GCC.