Rational bi‐cubic G2 splines for design with basic shapes

The paper develops a rational bi‐cubic G² (curvature continuous) analogue of the non‐uniform polynomial C² cubic B‐spline paradigm. These rational splines can exactly reproduce parts of multiple basic shapes, such as cyclides and quadrics, in one by default smoothly‐connected structure. The versatility of this new tool for processing exact geometry is illustrated by conceptual design from basic shapes.