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Compute the perpendicular surface of a curve
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. |
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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Perpendicular surface for the spherical spiral:
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