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, J├╝rgen (2011). Perspectives on Projective Geometry - A Guided Tour Through Real and Complex Geometry, Springer, Berlin, ISBN: 978-3-642-17285-4