Rational curves and isoparametric transformations

Curve approximation associated with the finite element method usually implies linear or parabolic approximating segments when the transformation of polygonal master-elements is involved. We consider the construction of transformations and of associated bases that result in general conic approximating curve segments, while still allowing us to do all the required calculations on the simpler straight-edged elements. We show that projective transformations can be used to produce conic parameterizations in a systematic way. Examples of transformations and of suitable bases are given for triangular elements with one conic and two straight edges.