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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
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