Free-form splines combining NURBS and basic shapes
We show how to automatically join, into one unified spline surface, C-2 tensor-product bi-cubic NURBS and G(2) bi-cubic rational splines. The G(2) splines are capable of exactly representing basic shapes such as (pieces of) quadrics and surfaces of revolution, including tori and cyclides. The main challenge is to transition between the differing forms of continuity. We transform the G(2) splines to splines that are C-2 in homogeneous space. This yields Hermite data for a transitional strip of tensor-product splines of degree (6,5) that guarantees overall curvature continuity. We also explain the simpler G(1) to C-1 transition. Key to the constructions is the C-2 parameterization of circles in homogeneous space. Crown Copyright (c) 2012 Published by Elsevier Inc. All rights reserved.
rational spline quadrics cyclides curvature continuity conics geometric continuity homogeneous c-2 parametrization geometric design