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.
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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 |
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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 |
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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 |
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Perspective Transformations on a Line |
| PR-Tf1 |
Vanishing Point of P1, P2, P3 (= Harmonic Conj.)
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| 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 |
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Perspectivity in a Triangle |
| TR-Tf1 |
Trilinear Polar |
| TR-Tf2 |
Trilinear Pole |
| TR-Tf3 |
Perspective Conjugate (= Isoconjugate)
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| TR-Tf4 |
Triangular Perspective Center
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Only the underlined items are currently accessible. The remaining items are intended to be introduced in due course.
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