Projective plane axioms and geometric checks (coincidence, Pappus, Desargues). More...
#include <array>#include <cassert>
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Namespaces | |
| namespace | fun |
Functions | |
| template<class Point , class Line > | |
| auto | fun::check_axiom (const Point &pt_p, const Point &pt_q, const Line &ln_l) -> bool |
| Check Projective plane Axiom. | |
| template<class Point , class Line = typename Point::Dual> | |
| constexpr auto | fun::coincident (const Point &pt_p, const Point &pt_q, const Point &pt_r) -> bool |
| Coincident. | |
| template<class Point , class Line = typename Point::Dual> | |
| constexpr auto | fun::check_pappus (const std::array< Point, 3 > &coline1, const std::array< Point, 3 > &coline2) -> bool |
| Check Pappus Theorem. | |
| template<class Point , class Line = typename Point::Dual> | |
| constexpr auto | fun::tri_dual (const std::array< Point, 3 > &triangle) -> std::array< Line, 3 > |
| Dual of triangle. | |
| template<class Point , class Line = typename Point::Dual> | |
| constexpr auto | fun::persp (const std::array< Point, 3 > &tri1, const std::array< Point, 3 > &tri2) -> bool |
| return whether two triangles are perspective | |
| template<class Point , class Line = typename Point::Dual> | |
| constexpr auto | fun::check_desargue (const std::array< Point, 3 > &tri1, const std::array< Point, 3 > &tri2) -> bool |
| Check Desargue's Theorem. | |
| template<typename Value , class Point , class Line > | |
| auto | fun::check_axiom2 (const Point &pt_p, const Point &pt_q, const Line &ln_l, const Value &a, const Value &b) -> bool |
| Check Axiom 2 for extended projective plane properties. | |
| template<typename Value , class Point , class Line = typename Point::Dual> | |
| constexpr auto | fun::harm_conj (const Point &pt_a, const Point &pt_b, const Point &pt_c) -> Point |
| Harmonic conjugate. | |
| template<typename Value , class Point , class Line > | |
| constexpr auto | fun::involution (const Point &origin, const Line &mirror, const Point &pt_p) -> Point |
| Involution on a point. | |
Detailed Description
Projective plane axioms and geometric checks (coincidence, Pappus, Desargues).
