Circle and sphere blending with conformal geometric algebra
| dc.creator | Doran, Chris | |
| dc.date | 2003-10-09 | |
| dc.date.accessioned | 2026-07-07T03:20:25Z | |
| dc.date.available | 2026-07-07T03:20:25Z | |
| dc.description | 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. | |
| dc.description | 20 pages, 13 figures | |
| dc.identifier | https://arxiv.org/abs/cs/0310017 | |
| dc.identifier | http://arxiv.org/abs/cs/0310017 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/31823 | |
| dc.subject | Computational Geometry | |
| dc.subject | Graphics | |
| dc.subject | I.3.5 | |
| dc.title | Circle and sphere blending with conformal geometric algebra | |
| dc.type | text |