Theorems · Definition · geometry

EuclideanGeometry.Sphere.secondInter

{V : Type u_1} →
  {P : Type u_2} →
    [inst : NormedAddCommGroup V] →
      [InnerProductSpace ℝ V] →
        [inst_2 : MetricSpace P] → [NormedAddTorsor V P] → EuclideanGeometry.Sphere P → P → V → P

The second intersection of a sphere with a line through a point on that sphere; that point if it is the only point of intersection of the line with the sphere. The intended use of this definition is when p ∈ s; the definition does not use s.radius, so in general it returns the second intersection with the sphere through p and with center s.center.

Defined in

Mathlib.Geometry.Euclidean.Sphere.SecondInter

Cited by

18 results in Mathlib

Foundations

Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupInnerProductSpaceMetricSpaceNormedAddTorsor