Differential Geometry and Geometric Structures
Main Page | Staff | Hans Havlicek | Visualisation | Elliptic Linear Congruence

Students' Work: Elliptic Linear Congruence

Illustration

An elliptic linear congruence is a particular set of lines which sends precisely one line through each point of the three-dimensional real projective space. It is also called a regular spread. Our example admits - from a Euclidean point of view - a rotational symmetry.
This set of lines can be split into reguli lying on a family of hyperbolic paraboloids which share two generators, one of them being at infinity.
The image depicts some of these paraboloids and the reguli on them.

Created by Katharina Schneider (2010) using POV-Ray - The Persistance of Vision Raytracer.

Change Image


first previous 44/249 next last

Archimedean Solids
Cockles
Confocal Quadrics
Dupin Cyclides
Elliptic Linear Congruence
Geodesics on a Cone
Helices on a Helicoid
Hyperosculating Spheres
Impossible Objects
Klein Bottle
Knots
Menger Sponge
Möbius Tetrahedra
Pascal's Pyramid
Pipe Surfaces
Planar Sections of a Torus
Platonic Solids
Prince Rupert's Cube
Saddle Surfaces
Schwarz Lanterns
Snails
Spherical Loxodromes
Stationary Points
Striction Curves

Quick Links


Sitemap

External Links


POV-Ray

Copyright © 1996-2016 by Differential Geometry and Geometric Structures. All rights reserved.
Last modified on February 18th, 2016.