Theorems · Theorem · geometry

signedDist_apply

∀ {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] (v : V) (p : P),
  (signedDist v) p =
    ((innerSL ℝ) (NormedSpace.normalize v)).toContinuousAffineMap.comp
      (ContinuousAffineMap.id ℝ P -ᵥ ContinuousAffineMap.const ℝ P p)

Defined in

Mathlib.Geometry.Euclidean.SignedDist

Cited by

0 results in Mathlib

Foundations

Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor