Theorems · Theorem · geometry

Affine.Simplex.affineCombination_eq_touchpoint_iff

∀ {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} {signs : Finset (Fin (n + 1))}
  {i : Fin (n + 1)} {w : Fin (n + 1) → ℝ},
  ∑ j, w j = 1 →
    ((Finset.affineCombination ℝ Finset.univ s.points) w = s.touchpoint signs i ↔ w = s.touchpointWeights signs i)

Defined in

Mathlib.Geometry.Euclidean.Incenter

Cited by

3 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsorNeZero