proj_plane.hpp File Reference

#include <array>
#include <cassert>
#include <tuple>
#include "proj_plane_concepts.h"

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Classes
class	fun::Involution< Point, Line >
class	fun::involution_generic< Point, Line >
	Generic involution class for projective planes. More...

Namespaces
namespace	fun

Typedefs
template<typename Point >
using	fun::Triple = std::array< Point, 3 >
	Type alias for an array of three points (a triangle)

Functions
template<typename Point , typename Line > requires ProjectivePlane<Point, Line>
constexpr auto	fun::incident (const Point &pt_p, const Line &ln_l) -> bool
	The code snippet is defining a function named incident that checks if a point pt_p is incident to a line ln_l in a projective plane. The function uses the dot method of the Point class and compares it to zero to determine if the point is incident to the line. The function returns a boolean value indicating whether the point is incident to the line or not.
template<typename Line , typename... Args> requires (ProjectivePlanePrim<Line, Args> && ...)
constexpr auto	fun::coincident (const Line &ln_l, const Args &... pt_r) -> bool
	Coincident.
template<ProjectivePlanePrim2 Point>
constexpr auto	fun::tri_dual (const Triple< Point > &triangle)
	Compute the dual triangle (sides as points).
template<ProjectivePlanePrim2 Point, typename Fn >
constexpr auto	fun::tri_func (Fn &&func, const Triple< Point > &triangle)
	Apply a binary function to all pairs of triangle vertices.
template<ProjectivePlanePrim2 Point>
constexpr auto	fun::persp (const Triple< Point > &tri1, const Triple< Point > &tri2) -> bool
	return whether two triangles are perspective
template<ProjectivePlane2 Point>
constexpr auto	fun::harm_conj (const Point &A, const Point &B, const Point &C) -> Point
	Compute the harmonic conjugate of three collinear points.
template<ProjectivePlaneGeneric2 _Point>
constexpr auto	fun::harm_conj (const _Point &A, const _Point &B, const _Point &C) -> _Point
	Compute the harmonic conjugate (generic version).
template<ProjectivePlane2 Point>
constexpr auto	fun::is_harmonic (const Point &A, const Point &B, const Point &C, const Point &D) -> bool
	Check if four points form a harmonic range.
template<ProjectivePlanePrim2 Point>
void	fun::check_pappus (const Triple< Point > &coline1, const Triple< Point > &coline2)
	Check Pappus Theorem for two sets of collinear points.
template<ProjectivePlanePrim2 Point>
void	fun::check_desargue (const Triple< Point > &tri1, const Triple< Point > &tri2)
	Check Desargues' theorem for two triangles.

Detailed Description

This is a C++ Library header.