Function Repository Resource:

# PerpendicularSurface

Compute the perpendicular surface of a curve

Contributed by: Wolfram Staff (original content by Alfred Gray)
 ResourceFunction["PerpendicularSurface"][c,t,{u,v},φ] computes the perpendicular surface with respect to variables u and v, making an angle ϕ with the normal surface of the curve parameterized by t.

## Details and Options

For any space curve α, there are other surfaces which lie between the normal surface and the binormal surface of the form , where , are the normal and binormal vector fields to α and sp[0,α] the normal surface of α and sp[π,α] the binormal surface.
The perpendicular surface is effectively a ruled surface.

## Examples

### Basic Examples (2)

Viviani's curve:

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Plot it:

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Compute the perpendicular surface for Viviani's curve:

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Plot both, varying the angle φ:

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The normal and binormal surfaces are special cases. Define Viviani's curve and compute its perpendicular surface:

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Compute the normal surface:

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Compute the binormal surface:

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Plots of normal and binormal surfaces:

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Combining the previous surfaces and Viviani's curve with an intermediate surface:

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### Neat Examples (1)

Perpendicular surface for the spherical spiral:

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Enrique Zeleny

## Version History

• 1.0.0 – 17 September 2020