A rational quartic Bézier representation for conics Original Research Article

This paper presents a special representation for conic sections in the form of a rational quartic Bézier curve which has the same weight for all control points but the middle one. This representation allows a conic section to be joined with other conics in the same form or other integral B-spline curves in a way that the joined curve still possesses C1 continuity in the homogeneous space, which is not possible if rational quadratic representation is adopted. This also allows the creation of skinned surfaces from section curves containing conic sections to possess better parametrization and curvature property.