On the Characterization Diagrams of Planar Cubic Hybrid Hyperbolic Polynomial Curve

In this paper,we propose the geometric characterization diagrams of planar cubic H-curves based on the conditions of singularities for planar cubic H-curves presented by Reference(Wang G Z,Yang Q M.Planar cubic hybrid hyperbolic polynomial curve and its shape classification.Progress In Natural Science,2004,14(1):41-46) Since inflection points and singularities(loops or cusps) of curves are affinely invariant,we find out the geometrically intuitive relationship of these different geometric characterization diagrams in a common 3-dimension characterization space.This approach completes the theory of detecting singularities of H-curves in the point of elevating geometric characterization diagrams dimension.