Theorems · Theorem · geometry

Affine.Simplex.mongePoint_vsub_face_centroid_eq_weightedVSub_of_pointsWithCircumcenter

∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
  [inst_3 : NormedAddTorsor V P] {n : ℕ} (s : Affine.Simplex ℝ P (n + 2)) {i₁ i₂ : Fin (n + 3)},
  i₁ ≠ i₂ →
    s.mongePoint -ᵥ Finset.centroid ℝ {i₁, i₂}ᶜ s.points =
      (Finset.univ.weightedVSub s.pointsWithCircumcenter)
        (Affine.Simplex.mongePointVSubFaceCentroidWeightsWithCircumcenter i₁ i₂)

The Monge point of an (n+2)-simplex, minus the centroid of an n-dimensional face, in terms of pointsWithCircumcenter.

Defined in

Mathlib.Geometry.Euclidean.MongePoint

Cited by

1 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor