Enumeration of points, lines, planes, etc.

Packing Lines, Planes, etc.: Packings in Grassmannian Spaces

Clifford algebra of points, lines and planes

The Clifford algebra for the group of rigid body motions is described. Linear elements, that is points, lines and planes are identified as homogeneous elements in the algebra. In each case the action of the group of rigid motions on the linear elements is found. The relationships between these linear elements are found in terms of operations in the algebra. That is, incidence relations, the con...

Manifolds Obtained by Soldering Together Points, Lines, Etc

where Rij is the Ricci curvature tensor of the metric and R is its scalar curvature. This equation tells us how the metric tensor gij (i.e. the field mediating the gravitation) is obeying to constraints imposed by the energy-momentum tensor Tij , which encodes informations about the distribution of energy and momentum in spacetime. For simplicity we will assume in the following that Tij = 0, i....

3D Motion from structures of points, lines and planes

In this article we propose a method for estimating the camera motion from a video-sequence acquired in the presence of general 3D structures. Solutions to this problem are commonly based on the tracking of point-like features, as they usually back-project onto viewpoint-invariant 3D features. In order to improve the robustness, the accuracy and the generality of the approach, we are interested ...

Cross Ratios of Points and Lines in Moufang Planes

In this paper, first we extend the known definition of cross-ratio of collinear points to whole Moufang plane. Later we introduce the cross-ratios for lines and the known results about the cross-ratios of points which are adapted to crossratios of lines without using the principle of duality. Finally, we give a theorem which describes the relation between the cross-ratios of points and lines. M...