Converting Frenet TNB Coordinates to Cylindrical Coordinates

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SUMMARY

The discussion focuses on converting Frenet TNB coordinates to cylindrical coordinates (RTZ) for a circular helix. The user defines the tangent (t), binormal (b), and normal (n) vectors in relation to the cylinder's axis, with the tangent oriented at an angle A. The proposed conversion equations are R = -n, T = t cos(A) - b sin(A), and Z = T sin(A) + b cos(A). The user seeks validation of these equations for accurate representation in cylindrical coordinate system.

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  • Understanding of Frenet-Serret formulas
  • Knowledge of cylindrical coordinate systems (RTZ)
  • Familiarity with vector calculus
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Mathematicians, physicists, and engineers working on 3D modeling, computer graphics, or robotics who need to convert between coordinate systems for accurate representation of curves and surfaces.

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Hi all,

I have a circular helix with any point on the helix defined using the Frenet tnb triad.
t- tangent, b- binormal and n-normal acting towards the axis of the host circular cylinder.

The tangent of the helix t is oriented at angle A with respect to the base of the cylinder.

Now I want to convert the tnb coord system to the cylindrical coordinate system, RTZ. I need it because the cylinder has to be defined in terms of RTZ.

I came up with this:
R = -n
T = t cos(A) - b sin(A)
Z = T sin(A) + b cos(A)

Is this correct? (T is implicit in RTZ for representing a helix in cylindrical CSYS). I am confused. Any help would be appreciated. Thanks

-C
 
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