Rational G2 splines

We develop a class of rational, G2-connected splines of degree 3 that allow modeling multiple basic shapes, such as segments of conics and circle arcs in particular, in one structure.
► This can be used, for example, to have portions of a control polygon exactly reproduce segments of the shapes while other portions blend between these primary shapes. We also show how to reparameterize the splines to obtain parametrically C2 transitions.

Rational G2 splines can reproduce segments of conics and automatically blend them with user-modified portions.Figure optionsDownload as PowerPoint slideHighlights
► We develop a class of rational, G2-connected splines of degree 3.
► These allow modeling multiple basic shapes, eg conic segments, and blend automatically between them, in one structure.
► We show how to reparameterize the splines parametrically C2 if wanted.