%0 Generic %1 doran2003circle %A Doran, Chris %D 2003 %K geometricalgebra %T Circle and sphere blending with conformal geometric algebra %U http://arxiv.org/abs/cs/0310017 %X 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.

@misc{doran2003circle, abstract = {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.}, added-at = {2015-06-24T23:05:45.000+0200}, author = {Doran, Chris}, biburl = {https://www.bibsonomy.org/bibtex/2ced794d3267d397f2a87fd20a5e954ae/wolftype}, description = {[cs/0310017] Circle and sphere blending with conformal geometric algebra}, interhash = {d0a974649032d69a5891093e41773482}, intrahash = {ced794d3267d397f2a87fd20a5e954ae}, keywords = {geometricalgebra}, note = {cite arxiv:cs/0310017Comment: 20 pages, 13 figures}, timestamp = {2015-06-24T23:05:45.000+0200}, title = {Circle and sphere blending with conformal geometric algebra}, url = {http://arxiv.org/abs/cs/0310017}, year = 2003 }