Perspective Fields

The hidden structure in Triangle Geometry

 

For pragmatic reasons, the description of the Perspective Fields has been placed under Triangle Geometry, as this is the area in which the subject matter finds its most extensive application. Nevertheless, the underlying theory is equally applicable to all other branches of n‑Geometry (Quadri‑, Penta‑, Hexa‑Geometry, etc.).

Definitions

A Perspective Field is a structured configuration of points and lines organized by perspectival relations, typically arising from a fixed center or axis of perspectivity.

A Perspective Row is a sequence of aligned points determined by a perspectival structure.

  Perspective Fields (PF)
PF-1 Notes on Perspective Fields
PF-2 Examples of Perspective Fields
PF-3 Presentation on Perspective Fields
PF-4 Some nice pictures
   
  Coordinate Transformations
PF-Tf1 Barycentric to Perspective Coordinates
PF-Tf2 Barycentric to Cartesian Coordinates
PF-Tf3 Perspective to Barycentric Coordinates
PF-Tf4 Perspective to Cartesian Coordinates
PF-Tf5 Cartesian to Barycentric Coordinates
PF-Tf6 Cartesian to Perspective Coordinates
   
   
   
   
   
   
  Perspective Rows (PR)
PR-1 Notes on Perspective Scales
PR-2 Notes on Perspective Rows
PR-3 The Harmonic Conjugate
PR-4 Examples of Perspective Rows
   
  Perspective Transformations on a Line
PR-Tf1

Vanishing Point of P1, P2, P3 (= Harmonic Conj.)

PR-Tf2 Perspective Midpoint of P1 and P2
PR-Tf3 Perspective Reflection of P1 in P2
PR-Tf4 Perspective Complement of P1 wrt P2
PR-Tf5 Perspective AntiComplement of P1 wrt P2
PR-Tf6 Corresponding point of two PR’s
   
  Perspectivity in a Triangle
TR-Tf1 Trilinear Polar
TR-Tf2 Trilinear Pole
TR-Tf3

Perspective Conjugate (= Isoconjugate)

TR-Tf4

Triangular Perspective Center


Only the underlined items are currently accessible. The remaining items are intended to be introduced in due course.

 




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