Function Repository Resource:

# SphericalCurve

Get curves defined over a sphere

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["SphericalCurve"][{par1,par2,…},"type"] gives the parametrization of a curve of the given type on a sphere, with parameters pari.

## Details and Options

A spherical curve is a curve traced on a sphere.
Types of curves are "Clelia", "HyperbolicTangentSpiral", "SatelliteCurve", "SeiffertsSphericalSpiral", "SphereRhumbLine", "SphericalCardioid", "SphericalCycloid", "SphericalEllipse", "SphericalHelix", "SphericalHelix", "SphericalLissajous", "SphericalLoxodrome", "SphericalLoxodromeUnitSpeed", "SphericalNephroid", "SphericalPendulum", "SphericalSinusoid", "SphericalTrochoid", "SpheroCylindricalCurve", "SpinningTop" and "TennisBallSeam".

## Examples

### Basic Examples (2)

Get the expression for a hyperbolic tangent spiral on a sphere:

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Plot it:

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### Scope (13)

A sphero-cylindrical curve is the intersections between a sphere and a cylinder of revolution:

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Seiffert's spherical spiral:

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The Clelia:

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Spherical cycloid:

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Spherical trochoid:

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Spherical sinusoid:

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Spherical ellipses:

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Spherical helix:

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Spherical cardioid:

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Satellite curve (Clelias and the spherical helices are special cases):

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Spherical pendulum:

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Plot the curve:

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Stationary precession of a spinning top:

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Spherical rhumb line:

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Spherical loxodrome:

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Comparing with the unit–speed spherical loxodrome:

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### Properties and Relations (3)

Compute quantities like ArcLength:

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Compute the curvature:

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The torsion:

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### Applications (4)

The spherical nephroid:

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The Frenet–Serret system of the curve:

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Plot the Frenet–Serret system:

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The seam line of a tennis ball:

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Spherical Lissajous:

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Distinct types of surfaces (like ruled surfaces) can be constructed from curves (used in fields like architecture):

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Meridians and loxodrome:

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### Possible Issues (1)

For some values of parameters, can be nonreal:

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Enrique Zeleny

## Version History

• 1.0.0 – 17 September 2020