Perspective-Euclidean plane class. More...

#include <persp_plane.hpp>

Inheritance diagram for fun::persp_euclid_plane< Point, Line >:

Collaboration diagram for fun::persp_euclid_plane< Point, Line >:

Public Member Functions
constexpr	persp_euclid_plane (Point I_re, Point I_im, Line l_inf)
	Construct a new persp euclid plane object.

constexpr auto	l_inf () const -> const Line &

constexpr auto	perp (const Line &v) const -> Point
	Compute the pole of a line.

constexpr auto	is_parallel (const Line &ln_l, const Line &ln_m) const -> bool
	Check if two lines are parallel.

constexpr auto	midpoint (const Point &pt_a, const Point &pt_b) const -> Point
	Compute the midpoint of two points.

constexpr auto	tri_midpoint (const Triple< Point > &triangle) const
	Compute the midpoints of all three sides of a triangle.

constexpr auto	omega (const Point &x) const -> K
	Compute the omega value for a point.

constexpr auto	omega (const Line &x) const -> K
	Compute the omega value for a line.

template<ProjectivePlane2 _Point>
constexpr auto	measure (const _Point &a1, const _Point &a2) const
	Compute the cross-ratio measure between two elements.

Detailed Description

template<typename Point, typename Line = typename Point::Dual>
requires ProjectivePlanePrim<Point, Line>
class fun::persp_euclid_plane< Point, Line >

Perspective-Euclidean plane class.

A Cayley-Klein plane that combines projective geometry with Euclidean metrics.

Template Parameters

Point	The point type
Line	The line type (dual of point)

Constructor & Destructor Documentation

◆ persp_euclid_plane()

template<typename Point , typename Line = typename Point::Dual>

constexpr fun::persp_euclid_plane< Point, Line >::persp_euclid_plane	(	Point	I_re,
		Point	I_im,
		Line	l_inf
	)

inlineconstexpr

Construct a new persp euclid plane object.

Member Function Documentation

◆ is_parallel()

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::is_parallel	(	const Line &	ln_l,
		const Line &	ln_m
	)		const -> bool

inlineconstexpr

Check if two lines are parallel.

Parameters

[in]	ln_l	First line
[in]	ln_m	Second line

Returns: true if lines are parallel, false otherwise

◆ l_inf()

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::l_inf ( ) const -> const Line&

inlineconstexpr

◆ measure()

template<typename Point , typename Line = typename Point::Dual>

template<ProjectivePlane2 _Point>

constexpr auto fun::persp_euclid_plane< Point, Line >::measure	(	const _Point &	a1,
		const _Point &	a2
	)		const

inlineconstexpr

Compute the cross-ratio measure between two elements.

Returns the ratio of omega values for measuring projective relationships.

\[ \mu(a_1, a_2) = \frac{\omega(a_1 \times a_2)}{\omega(a_1)\omega(a_2)} \]

Parameters

[in]	a1	First point or line
[in]	a2	Second point or line

Returns: auto The measure value

◆ midpoint()

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::midpoint	(	const Point &	pt_a,
		const Point &	pt_b
	)		const -> Point

inlineconstexpr

Compute the midpoint of two points.

\[ M = \operatorname{parametrize}(\alpha,\; a,\; \beta,\; b) \]

where \(\alpha = a \cdot l_\infty\), \(\beta = b \cdot l_\infty\).

Parameters

[in]	pt_a	First point
[in]	pt_b	Second point

Returns: Point The midpoint

◆ omega() [1/2]

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::omega ( const Line & x ) const -> K

inlineconstexpr

Compute the omega value for a line.

The omega function measures how far a line is from the ideal points.

\[ \omega(l) = (l \cdot I_{\mathrm{re}})^2 + (l \cdot I_{\mathrm{im}})^2 \]

Parameters

[in] x A line

Returns: K The omega value

◆ omega() [2/2]

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::omega ( const Point & x ) const -> K

inlineconstexpr

Compute the omega value for a point.

The omega function measures how far a point is from the line at infinity.

\[ \omega(p) = (p \cdot l_\infty)^2 \]

Parameters

[in] x A point

Returns: K The omega value

◆ perp()

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::perp ( const Line & v ) const -> Point

inlineconstexpr

Compute the pole of a line.

\[ v^\perp = \alpha I_{\mathrm{re}} + \beta I_{\mathrm{im}} \]

where \(\alpha = v \cdot I_{\mathrm{re}}\) and \(\beta = v \cdot I_{\mathrm{im}}\).

Parameters

[in] v A line

Returns: Point The pole (polar) of the line

◆ tri_midpoint()

template<typename Point , typename Line = typename Point::Dual>

constexpr auto fun::persp_euclid_plane< Point, Line >::tri_midpoint ( const Triple< Point > & triangle ) const

inlineconstexpr

Compute the midpoints of all three sides of a triangle.

Parameters

[in] triangle Array of three points

Returns: Triple<Point> Array of three midpoints

The documentation for this class was generated from the following file:

projgeom/persp_plane.hpp

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ persp_euclid_plane()

Member Function Documentation

◆ is_parallel()

◆ l_inf()

◆ measure()

◆ midpoint()

◆ omega() [1/2]

◆ omega() [2/2]

◆ perp()

◆ tri_midpoint()