# Computations on conics

### Description

Solve some conic related problems (intersection of conics with lines and conics, arc length of an ellipse, polar lines, etc.).

### Details

Package: | RConics |

Type: | Package |

Version: | 1.0 |

Date: | 2014-02-21 |

License: | GPL 2 |

### Note

Some of the functions are based on the *projective* geometry.
In projective geometry parallel lines meet at an infinite point and all infinite points are incident to a line at infinity. Points and lines of a projective plane are represented by *homogeneous* coordinates, that means by 3D vectors: *(x, y, z)* for the points and *(a, b, c)* such that *ax + by + c = 0* for the lines. The Euclidian points correspond to *(x, y, 1)*, the infinite points to *(x, y, 0)*, the Euclidian lines to *(a, b, c)* with *a \neq 0* or *b \neq 0*, the line at infinity to *(0, 0, 1)*.

**Advice**: to plot conics use the package `conics`

from Bernard Desgraupes.

This work was funded by the Swiss National Science Foundation within the ENSEMBLE project (grant no. CRSI_132249).

### Author(s)

Emanuel Huber

Maintainer: Emanuel Huber <emanuel.huber@unibas.ch>

### References

Richter-Gebert, Jürgen (2011). *Perspectives on Projective Geometry - A Guided Tour Through Real and Complex Geometry*, Springer, Berlin, ISBN: 978-3-642-17285-4