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785c727 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | import OAI.Geometry.CylinderCovering.Angular.MarginsDefinitions
namespace OAI
noncomputable section
namespace CylinderCovering.Cubic
def speedSq (l r : ℝ) : ℝ := alpha l r ^ 2 + 2 * beta l r ^ 2
def areaTerm (eps l r : ℝ) : ℝ :=
(r - l) * cap eps l r ^ 2 / Real.sqrt (1 + eps ^ 2 * speedSq l r)
def areaDensity (q : ℝ) : ℝ := -(1 / 8 : ℝ) - q ^ 2 / 4 + 7 * q ^ 4 / 8
def areaSum (eps : ℝ) (N : ℕ) : ℝ :=
∑ j : Fin N, areaTerm eps (node N j) (node N (j + 1))
end CylinderCovering.Cubic
end
end OAI
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