| 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 | |