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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 24 25 26 27 28 29 30 | import OAI.Geometry.CylinderCovering.Singular.EdgeOneCoverDefinitions
import OAI.Geometry.CylinderCovering.Rational.RealizationDefinitions
import OAI.Geometry.CylinderCovering.Convexity.GlobalDefinitions
namespace OAI
noncomputable section
open Set
namespace CylinderCovering.SingularEdgeOneCover
open RuledApproximation
def NormalizationStatement : Prop :=
tetrahedron =
(fun z : Space => z + vec3 0 0 (height / 2)) '' SlopeRational.referenceTetrahedron ∧
minimumShadowArea tetrahedron = height / 2 ∧
∀ (n m : ℕ) (C : Fin n → Cylinder) (D : Fin m → Cylinder) (B₁ B₂ : Cylinder),
familyArea C + familyArea D + B₁.area + B₂.area < height / 4 →
familyArea C + familyArea D + B₁.area + B₂.area <
minimumShadowArea tetrahedron / 2 ∧
relativeCost tetrahedron C + relativeCost tetrahedron D +
B₁.area / shadowArea tetrahedron B₁.axis +
B₂.area / shadowArea tetrahedron B₂.axis < 1 / 2
end CylinderCovering.SingularEdgeOneCover
end
end OAI
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