Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 RectifyingPlane

Source Notebook

Compute the rectifying plane of a space curve

Contributed by: Alfred Gray

ResourceFunction["RectifyingPlane"][c,t]

computes the rectifying plane of space curve c with parameter t.

Details and Options

The rectifying plane is spanned by the tangent and binormal vectors.
ResourceFunction["RectifyingPlane"] gives an InfinitePlane object.

Examples

Basic Examples (3) 

Define a helix curve:

In[1]:=
helix = Entity["SpaceCurve", "Helix"]["ParametricEquations"][1, 1][t];

Compute the rectifying plane:

In[2]:=
ResourceFunction["RectifyingPlane"][helix, t]
Out[2]=

Plot the different planes while traversing the helix:

In[3]:=
Manipulate[ With[{helix = Entity["SpaceCurve", "Helix"]["ParametricEquations"][1, 1][t]}, Show[ParametricPlot3D[helix, {t, 0, 3}], Graphics3D[{Opacity[.5], ResourceFunction["OsculatingPlane"][helix, t], ResourceFunction["RectifyingPlane"][helix, t], ResourceFunction["NormalPlane"][helix, t]} /. t -> tf], PlotRange -> {{-1, 1}, {0, 1}, {0, 3}}]], {{tf, 1}, 0, 3}]
Out[3]=

Publisher

Enrique Zeleny

Version History

  • 1.0.0 – 31 March 2020

Source Metadata

  • Citation:
    • Gray, A., Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.

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