Lines Classification in the Conformal Space R^(n+1,1)

Lilian Aveneau (1) , Angel F. Tenorio (2)

1 XLIM-SIC - SIC
2 UPO - Universidad Pablo de Olavide [Sevilla]

Lines classification is the central tool for visibility calculation in dimension $n\ge 2$. It has been previously expressed in Grassmann Algebra, allowing to work with any couple of 2-vectors, which may represent two real lines or not. This article discusses about the nature of lines in the conformal model, searching if such a classification is still valid in R^(n+1,1). First, it shows that the projective classification can be expressed in terms of a {meet} operator. Then, given two real lines, the classification still works in the conformal model, but also allowing us to propound some techniques to identify lines and circles among general 3-vectors.

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]

Lilian Aveneau, Angel F. Tenorio. Lines Classification in the Conformal Space R^(n+1,1). AGACSE 2012, Jul 2012, La Rochelle, France. ⟨hal-00865114⟩