
This application allows the user to explore planar curves:
 Specification by
 parametric formula (x(t), y(t))
 from curvature function k(t)
 Optional display of
 parallel curve
 evolute curve
 Display of curvature graph



This application allows the user to explore space curves:
 Specification by parametric formula (x(t), y(t), z(t))
 Menu of builtin examples.
 Optional display of evolute curve.
 Display of curvature and torsion graphs
 Animated display of Frenet frame and osculating circle.



This application allows the user to explore surface patches in R3:
 Specification by parametric formula (x(u,v), y(u,v), z(u,v))
 A menu containing many builtin examples.
 Interactive specification of definition rectangle.
 Display of Gaussian curvature and mean curvature graphs
 Draggable tangent plane and optional second order approximation.
 Sophisticated interactive 3D viewer with customized shading options



A jReality application realizing
different interactive visualizations in geometric knot theory.
 load, edit and save knots
 explore the crossing map of a given knot
 analyze the set of trisecants of a given knot and find quadrisecants
 create images of textured knots
Most program options are available via the context menu of corresponding
components and their toolbars and sliders. Rotate displayed objects using
the left mouse button. For further information see the application's Help
menu.
This lab was implemented by Martin Sommer as part of his Diploma Thesis
"Visualization in Geometric Knot Theory  Understanding the mathematical
structure of trisecants" using the jReality library.



This application allows to explore polygonal tractrix curves.
For more information see the online help of the application.
Ulrich Pinkall



Markus Schmies



Markus Schmies



Markus Schmies



Markus Schmies



Markus Schmies



Markus Schmies



Markus Schmies



Markus Schmies



This lab generates the triangulation of any number of points. You may
change the number of points. When you drag the points around the
triangulation will be adjusted interactively.
Press 'e' to encompass and <CTRL><Left Mouse Button>.
Lab author: Markus Schmies



Ulrich Pinkall



A KSurface is a surface of constant negative Gaussian curvature. The planar
strip may be edited on the left. On the right you may investigate the surface
and its Gauss map. The Gauss map may be seen as the evolution of massive
balls on the sphere connected by rubber bands.
There is a small mpeg (2MiB) video or animated gif (11MiB).
More ...
For the theoretical background consult
Designing Cylinders with Constant Negative Curvature.
Ulrich Pinkall



A KSurface is a surface of constant negative Gaussian curvature. The initial Gauss
map may be edited on the left. On the right hand side you may investigate the surface
and its Gauss map. The Gauss map may be seen as the evolution of massive
balls on the sphere connected by rubber bands.
More ...
For the theoretical background consult
Designing Cylinders with Constant Negative Curvature.
Ulrich Pinkall



In this lab you may investigate surfaces of
constant negative Gaussian curvature (Ksurfaces).
Double click on the surface allows you
to change the curvature and the length of the surface.
The initial curve may be
changed (at the bottom when the lab comes up).
Just drag the yellow
points of the initial curve. Double click on the initial curve to add more
control points and change the interpolation parameters.
Double click on the
initial curve to open a panel that allows to change the number of control points and
subdivision parameters.
More ...
.
The labs front end uses ViewerVR from our jReality project. You may wish to have a
look at the
ViewerVR User Manual.
For the theoretical background consult
Designing Cylinders with Constant Negative Curvature.
Ulrich Pinkall
