Ratioquadrics: an alternative model for superquadrics

This paper presents a new family of 2D curves and its extension to 3D surfaces, respectively, calledrationconics andratioquadrics that have been designed as alternatives to the well-known superconics and superquadrics. This new model is intended as an improvement to the original one on three main points: first, it involves lower computation cost and provides better numerical robustness; second, it offers higher order continuities (C1/G2 orC2/G2 instead ofC0/G0); and third, it provides a greater variety of shapes for the resulting curves and surfaces. All these improvements are obtained by replacing the signed power function involved in the formulation of superconics and superquadrics by linear or quadratic rational polynomials.