Theorems · Definition · geometry

signedDist

{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 → P →ᵃ[ℝ] P →ᴬ[ℝ] ℝ

The signed distance between two points p and q, in the direction of a reference vector v. It is the size of q - p in the direction of v. In the degenerate case v = 0, it returns 0. TODO: once we have a topology on P →ᴬ[ℝ] ℝ, the type should be P →ᴬ[ℝ] P →ᴬ[ℝ] ℝ.

Defined in

Mathlib.Geometry.Euclidean.SignedDist

Cited by

42 results in Mathlib

Foundations

Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor