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Cone Conversion Math

The task is to convert the physical parameters (Top Diameter, Bottom Diameter, Height) into the values required for the flat design (Large Radius (R), Small Radius (r), and Subtended Angle).

Key Formulas​

Let:

  • a = Top Diameter
  • b = Bottom Diameter
  • h = Vertical Height

The core formulas for calculating the frustum are:

  • Small Radius (r): r = √(b²/4 + (bh/(a-b))²)
  • Large Radius (R): R = √(a²/4 + (ah/(a-b))²)
  • Subtended Angle (θ): θ = πa/R (in radians)

These values (R, r, and angle) can then be used for further calculations or in other design software.

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