Circle and sphere blending with conformal geometric algebra
<|reference_start|>Circle and sphere blending with conformal geometric algebra: 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.<|reference_end|>
@article{doran2003circle,
    title={Circle and sphere blending with conformal geometric algebra},
    author={Chris Doran},
    journal={arXiv preprint arXiv:cs/0310017},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0310017},
    primaryClass={cs.CG cs.GR}
}