Generalized conic curves and their applications in curve approximation

Abstract

The appriximation properties of generalized conic curves are studied in this paper. A generalized conic curve is defined as one of the following curves or their affine and translation equivalent curves: (i) conic curves, including parabolas, hyperbolas and ellipses; (ii) generalized monomial curves, including curves of the form x=yγ, γ∈R, γ≠0,1, in the x−y Cartesian coordinate system; (iii) exponential spiral curves of the form ρ(ϑ)=Aeγϑ, A>0, γ≠0, in the ρ-ϑ polar coordinate system.