| import Mathlib | |
| namespace OAI | |
| noncomputable section | |
| open scoped InnerProductSpace | |
| namespace CylinderNormalFrame | |
| abbrev Space := EuclideanSpace ℝ (Fin 3) | |
| abbrev BarycentricSpace := EuclideanSpace ℝ (Fin 4) | |
| def normal (i : Fin 4) : Space := | |
| (1 / Real.sqrt 3) • ![(!₂[0, Real.sqrt 2, -1] : Space), | |
| !₂[0, -Real.sqrt 2, -1], | |
| !₂[Real.sqrt 2, 0, 1], | |
| !₂[-Real.sqrt 2, 0, 1]] i | |
| def frameCost (u : Space) : ℝ := | |
| Real.sqrt 3 / 2 * ∑ i : Fin 4, |inner ℝ u (normal i)| | |
| def barycentricCost (u : BarycentricSpace) : ℝ := | |
| (1 / 2 : ℝ) * ∑ i : Fin 4, |u i| | |
| def edgeDirection : Space := !₂[1, 0, 0] | |
| def barycentricEdge : BarycentricSpace := | |
| !₂[1 / Real.sqrt 2, -(1 / Real.sqrt 2), 0, 0] | |
| end CylinderNormalFrame | |
| end | |
| end OAI | |