11552
EXPLORE
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
3D Extrusion Using the Frenet-Serret System
This Demonstration illustrates the conversion of a parametrized three-dimensional space curve into a three-dimensional surface.
This can be done by using the built-in Mathematica command
FrenetSerretSystem
to extract the normal and binormal unit vectors
and
of the space curve.
The one-variable parametric equation of the space curve
can be combined with the polar equation of the cross section
.
The result is the two-variable parametric equation of a surface:
.
In this Demonstration, a parametric space curve
is defined, with the parameters
determining the shape of the curve.
Contributed by:
Erik Mahieu
THINGS TO TRY
Rotate and Zoom in 3D
Slider Zoom
Gamepad Controls
Automatic Animation
SNAPSHOTS
RELATED LINKS
Fundamental Theorem of Space Curves
(
Wolfram
MathWorld
)
Frenet Formulas
(
Wolfram
MathWorld
)
Normal Vector
(
Wolfram
MathWorld
)
Binormal Vector
(
Wolfram
MathWorld
)
PERMANENT CITATION
Erik Mahieu
"
3D Extrusion Using the Frenet-Serret System
"
http://demonstrations.wolfram.com/3DExtrusionUsingTheFrenetSerretSystem/
Wolfram Demonstrations Project
Published: October 24, 2017
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
Tracing a Cyclogon: Roulette of a Polygon Rolling along a Line
Erik Mahieu
Tracing a Peritrochoid
Erik Mahieu
Doyle Spirals and Möbius Transformations
Dieter Steemann
Steiner Surfaces
Enrique Zeleny
3D Object Designer Using Splines
Erik Mahieu
Lemniscate Linkage
Ed Pegg Jr
Newton Polygon and Branching of Algebraic Curves
Andrzej Kozlowski
Powered Clique Polyhedra
Ed Pegg Jr
The Klein Configuration
Ed Pegg Jr
Blooms from the Campanus Sphere
Izidor Hafner
Related Topics
3D Graphics
Algebraic Geometry
Curves
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+