Affine.Simplex.signedInfDist_affineCombination
∀ {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} [inst_4 : NeZero n] (s : Affine.Simplex ℝ P n) (i : Fin (n + 1))
{w : Fin (n + 1) → ℝ},
∑ i, w i = 1 →
(s.signedInfDist i) ((Finset.affineCombination ℝ Finset.univ s.points) w) =
w i * ‖s.points i -ᵥ ↑((s.faceOpposite i).orthogonalProjectionSpan (s.points i))‖- Defined in
- Mathlib.Geometry.Euclidean.SignedDist
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites36
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Norm.normstatement and proof · cited by 5,413
- Finset.sumstatement and proof · cited by 5,195
- Set.rangestatement · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- Finset.univstatement and proof · cited by 3,473
- add_zeroproof · cited by 2,707
- Finset.sum_congrproof · cited by 2,323
- HVAdd.hVAddproof · cited by 1,820
Cited by4
Results whose statement or proof uses this declaration.
- Affine.Simplex.ExcenterExists.sign_touchpointWeightsproof · cited by 4
- Affine.Simplex.ExcenterExists.sign_signedInfDist_excenterproof · cited by 2
- Affine.Simplex.ExcenterExists.signedInfDist_excenter_eq_mul_sum_invproof · cited by 1