Computer Aided Geometric Design - Special issue: Topics in CAGD
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Multiple-knot and rational cubic beta-splines
ACM Transactions on Graphics (TOG)
Circle and sphere as rational splines
Neural, Parallel & Scientific Computations - computer aided geometric design
Bezier and B-Spline Techniques
Bezier and B-Spline Techniques
Rational Beta-Splines for Representing Curves and Surfaces
IEEE Computer Graphics and Applications
Beta Continuity and Its Application to Rational Beta-splines
Beta Continuity and Its Application to Rational Beta-splines
Graphical Models
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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.