## Abstract

A circular biarc can be defined by using two points K and L with their (oriented) tangents g
_{K} and g
_{L} as input. It is well-known that one can determine a one parametric set of circular arc pairs k,ℓ such that k starts at K with tangent g
_{K}, ℓ ends at L with tangent g
_{L} and k and ℓ meet with a common tangent in an intermediate point P. In this paper we investigate a similar construction where we replace the circle biarcs by pairs of conic arcs. It turns out that in this case we can prescribe a conic k
_{0} with a point K on it, another conic ℓ
_{0} with a point L on it, and moreover an intermediate point P to obtain a unique pair k,ℓ of conics such that k osculates k
_{0} in K, ℓ osculates ℓ
_{0} in L and k and ℓ osculate each other in P. This also confirms a result of H. Pottmann from 1991. We use our method to solve an interpolation task of Hermite type whose input consists of a series of points with their curvature circles and another series of intermediate points. The output is a GC
^{2} spline curve with conic arc segments.

Original language | English |
---|---|

Article number | 101904 |

Journal | Computer Aided Geometric Design |

Volume | 81 |

DOIs | |

Publication status | Published - Aug 2020 |

## Keywords

- Biarcs
- Conic arcs
- GC -spline
- Hermite interpolation
- Osculation
- Projective map

## ASJC Scopus subject areas

- Aerospace Engineering
- Automotive Engineering
- Modelling and Simulation
- Computer Graphics and Computer-Aided Design