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*I'll attempt an independent 'square-to-round' thread as well in the near future after I'm more confident about some of the geometry/area data.
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The transition from square to round is defined by the
superellipse equation with 1<
n<2. Just run the subset (not quite square to not round) solving for area backward for each % reduction in area at subsequent longitudinal stations.
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The area inside the superellipse can be expressed in terms of the gamma function, Γ(x), as:
\mathrm{Area} = 4 a b \frac{\left(\Gamma \left(1+\tfrac{1}{n}\right)\right)^2}{\Gamma \left(1+\tfrac{2}{n}\right)} .
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