Rational Parametrizations of Edge and Corner Blends for Isogeometric Analysis

Abstract

Rational variable radius rolling ball blends between pairs of natural quadrics can be constructed from rational curves in their bisector surface in $\mathbb{R}^{3,1}$. For certain configurations of natural quadrics, these curves can be constructed by taking hyperplane sections, or by constructing Bézier curves in the bisector surface. When blending a configuration of edges and corners in a composite corner, we need to ensure that adjacent corner and edge blends are joined with at least G ¹ continuity. In this paper we show, using an example corner, how such a rational composite blend can be constructed, guided by the placement of control spheres specifying the blending radius at certain key points. The construction is watertight, i.e., the boundary curves of the blend lies on the original surfaces, thus it is well-suited for applications in Isogeometric Analysis where this is a requirement.