11209
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Dupin's Indicatrix of a Torus
This Demonstration shows how Dupin's indicatrix changes at a variable point on a torus.
In the tangent plane at a point
of a surface
,
Dupin's indicatrix is given by the equation
,
where the
,
axes coincide with the principal directions at
and
,
are the principal curvatures of
at
.
• If
is an elliptical point, the indicatrix consists of two ellipses (one real and one imaginary).
• If
is a hyperbolic point, the indicatrix consists of two conjugate hyperbolas with asymptotes through the asymptotic directions at
.
• If
is a parabolic point, the indicatrix degenerates into a pair of parallel lines.
Contributed by:
Sonja Gorjanc
and
Desana Štambuk
THINGS TO TRY
Rotate and Zoom in 3D
Automatic Animation
SNAPSHOTS
RELATED LINKS
Torus
(
Wolfram
MathWorld
)
Dupin's Indicatrix
(
Wolfram
MathWorld
)
Gaussian Curvature
(
Wolfram
MathWorld
)
Principal Direction
(
Wolfram
MathWorld
)
Asymptotic Direction
(
Wolfram
MathWorld
)
Elliptic Point
(
Wolfram
MathWorld
)
Hyperbolic Point
(
Wolfram
MathWorld
)
Parabolic Point
(
Wolfram
MathWorld
)
PERMANENT CITATION
"
Dupin's Indicatrix of a Torus
" from
the Wolfram Demonstrations Project
http://demonstrations.wolfram.com/DupinsIndicatrixOfATorus/
Contributed by:
Sonja Gorjanc
and
Desana Štambuk
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Normal Curvature at a Regular Point of a Surface
Desana ?tambuk (University of Zagreb)
Geodesics and Conjugate Loci on a Torus
Matthew Cherrie and Thomas Waters
Unwrapping Involutes
Michael Rogers (Oxford College of Emory University)
Cone Geodesics
Antonin Slavik
Hyperboloid Geodesics
Antonin Slavik
Gauss Map and Curvature
Michael Rogers (Oxford College/Emory University)
Minimal and Maximal Surfaces Generated by the Holomorphic Function log(z)
Georgi Ganchev and Radostina Encheva
An Enneper-Weierstrass Minimal Surface
Michael Schreiber
Torus in Nil-Space
Benedek Schultz and János Pallagi
Boundary Value Problems for Cone Geodesics
Raja Kountanya
Related Topics
3D Graphics
Conic Sections
Curves
Differential Geometry
Surfaces
Browse all topics
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to
Mathematica Player 7EX
I already have
Mathematica Player
or
Mathematica 7+