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cead56f | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | 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
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