Today I read a paper titled “Circle and sphere blending with conformal geometric algebra”
The abstract is:
Blending schemes based on circles provide smooth `fair’ interpolations between series of points.
Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases.
An arbitrary level of G-continuity can be achieved by simple alterations to the underlying parameterisation.
Our method exploits the computational framework provided by conformal geometric algebra.
This employs a five-dimensional representation of points in space, in contrast to the four-dimensional representation typically used in projective geometry.
The advantage of the conformal scheme is that straight lines and circles are treated in a single, unified framework.
As a further illustration of the power of the conformal framework, the basic idea is extended to the case of sphere blending to interpolate over a surface..