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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 31 32 33 | import OAI.Geometry.CylinderCovering.Footprints.ShapesDefinitions
namespace OAI
noncomputable section
namespace CylinderCovering.Footprints
def radialReflection : (ℝ × ℝ) →ₗ[ℝ] (ℝ × ℝ) where
toFun p := (-p.1, p.2)
map_add' p q := by ext <;> simp [add_comm]
map_smul' a p := by ext <;> simp
def positiveAbsoluteVertices (m M d A B : ℝ) : Fin 4 → ℝ × ℝ :=
trapezoidVertices m (M + A * d) d 0 B
def negativeAbsoluteVertices (m d A B : ℝ) : Fin 4 → ℝ × ℝ :=
radialReflection ∘ trapezoidVertices (-m) (A * d) d 0 B
def AbsolutePolygonStatement : Prop :=
∀ m M d A B : ℝ, 0 ≤ M → 0 < d → 0 < A → 0 < B →
absoluteFootprint m M d A B =
convexHull ℝ (Set.range (positiveAbsoluteVertices m M d A B)) ∪
convexHull ℝ (Set.range (negativeAbsoluteVertices m d A B)) ∧
Function.Injective (positiveAbsoluteVertices m M d A B) ∧
Function.Injective (negativeAbsoluteVertices m d A B)
end CylinderCovering.Footprints
end
end OAI
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