| import OAI.Geometry.ProjectionVolume.PolytopeCauchy | |
| namespace OAI | |
| universe uι | |
| open scoped RealInnerProductSpace | |
| namespace Paper092 | |
| theorem polytope_brightness {d : ℕ} (_hd : 2 ≤ d) {ι : Type uι} [Fintype ι] | |
| (P : HPolytope d ι) (u : Euclidean d) : | |
| brightness P.body u = (1 / 2 : ℝ) * ∑ i, P.faceArea i * |⟪P.normal i, u⟫| := by | |
| simpa only [real_inner_comm, div_eq_mul_inv, one_mul, mul_comm] using P.brightness_eq_sum u | |
| theorem polytope_projectionBody {d : ℕ} (_hd : 2 ≤ d) {ι : Type uι} [Fintype ι] | |
| (P : HPolytope d ι) : projectionBody P.body = P.facetZonotope := | |
| P.projectionBody_eq_facetZonotope | |
| end Paper092 | |
| end OAI | |