A new implicit representation of a planar rational curve with high order singularity Original Research Article

This paper presents a new representation for the implicit equation of a planar rational curve with high order singularity by using moving curves technique. The new representation is the determinant of a matrix which is less than one half the size of the conventional expression based on the Bezoutʹs resultant. An efficient algorithm to compute the new representation is derived, and comparisons for the computational costs between various resultant based methods are made. The results show that the implicit representation developed in this paper is not only more compact but also much more efficient to compute the implicit equation of the rational curve than previous methods.