#include <hikogui/graphic_path/bezier_curve.hpp>

Data Structures
struct	sdf_distance_result

Public Types
enum class	Type : uint8_t { None , Linear , Quadratic , Cubic }

Public Member Functions
	bezier_curve (bezier_curve const &other) noexcept=default

	bezier_curve (bezier_curve &&other) noexcept=default

bezier_curve &	operator= (bezier_curve const &other) noexcept=default

bezier_curve &	operator= (bezier_curve &&other) noexcept=default

	bezier_curve (point2 const P1, point2 const P2) noexcept

	bezier_curve (point2 const P1, point2 const C1, point2 const P2) noexcept

	bezier_curve (point2 const P1, point2 const C1, point2 const C2, point2 const P2) noexcept

	bezier_curve (Type const type, point2 const P1, point2 const C1, point2 const C2, point2 const P2) noexcept

point2	pointAt (float const t) const noexcept

constexpr vector2	tangentAt (float const t) const noexcept

lean_vector< float >	solveXByY (float const y) const noexcept

hi_force_inline lean_vector< float >	solveTForNormalsIntersectingPoint (point2 P) const noexcept

sdf_distance_result	sdf_distance (point2 P) const noexcept
	Find the distance from the point to the curve.

std::pair< bezier_curve, bezier_curve >	cubicSplit (float const t) const noexcept

std::pair< bezier_curve, bezier_curve >	quadraticSplit (float const t) const noexcept

std::pair< bezier_curve, bezier_curve >	linearSplit (float const t) const noexcept

std::pair< bezier_curve, bezier_curve >	split (float const t) const noexcept

void	subdivideUntilFlat_impl (std::vector< bezier_curve > &r, float const minimumFlatness) const noexcept

std::vector< bezier_curve >	subdivideUntilFlat (float const tolerance) const noexcept

float	flatness () const noexcept

bezier_curve	toParallelLine (float const offset) const noexcept

Data Fields
Type	type

point2	P1
	First point.

point2	C1
	Control point.

point2	C2
	Control point.

point2	P2
	Last point.

Friends
bool	operator== (bezier_curve const &lhs, bezier_curve const &rhs) noexcept

bezier_curve	operator* (transformer2 auto const &lhs, bezier_curve const &rhs) noexcept

bezier_curve	operator~ (bezier_curve const &rhs) noexcept

Detailed Description

Bezier Curve A linear, quadratic or cubic bezier curve.

Constructor & Destructor Documentation

◆ bezier_curve() [1/4]

hi::v1::bezier_curve::bezier_curve	(	point2 const	P1,
		point2 const	P2 )

inlinenoexcept

Construct a linear bezier-curve.

◆ bezier_curve() [2/4]

hi::v1::bezier_curve::bezier_curve	(	point2 const	P1,
		point2 const	C1,
		point2 const	P2 )

inlinenoexcept

Construct a quadratic bezier-curve.

◆ bezier_curve() [3/4]

hi::v1::bezier_curve::bezier_curve	(	point2 const	P1,
		point2 const	C1,
		point2 const	C2,
		point2 const	P2 )

inlinenoexcept

Construct a cubic bezier-curve.

◆ bezier_curve() [4/4]

hi::v1::bezier_curve::bezier_curve	(	Type const	type,
		point2 const	P1,
		point2 const	C1,
		point2 const	C2,
		point2 const	P2 )

inlinenoexcept

Construct a bezier-curve of any type.

Member Function Documentation

◆ cubicSplit()

std::pair< bezier_curve, bezier_curve > hi::v1::bezier_curve::cubicSplit ( float const t ) const

inlinenoexcept

Split a cubic bezier-curve into two cubic bezier-curve.

Parameters

t	a relative distance between 0.0 (point P1) and 1.0 (point P2) where to split the curve.

Returns: two cubic bezier-curves.

◆ flatness()

float hi::v1::bezier_curve::flatness ( ) const

inlinenoexcept

Return the flatness of a curve.

Returns: 1.0 when completely flat, < 1.0 when curved.

◆ linearSplit()

std::pair< bezier_curve, bezier_curve > hi::v1::bezier_curve::linearSplit ( float const t ) const

inlinenoexcept

Split a linear bezier-curve into two linear bezier-curve.

Parameters

t	a relative distance between 0.0 (point P1) and 1.0 (point P2) where to split the curve.

Returns: two linear bezier-curves.

◆ pointAt()

point2 hi::v1::bezier_curve::pointAt ( float const t ) const

inlinenoexcept

Return a point on the bezier-curve. Values of t beyond 0.0 and 1.0 will find a point extrapolated beyond the bezier segment.

Parameters

t	a relative distance between 0.0 (point P1) and 1.0 (point P2).

Returns: the coordinates of the point on the curve.

◆ quadraticSplit()

std::pair< bezier_curve, bezier_curve > hi::v1::bezier_curve::quadraticSplit ( float const t ) const

inlinenoexcept

Split a quadratic bezier-curve into two quadratic bezier-curve.

Parameters

t	a relative distance between 0.0 (point P1) and 1.0 (point P2) where to split the curve.

Returns: two quadratic bezier-curves.

◆ sdf_distance()

sdf_distance_result hi::v1::bezier_curve::sdf_distance ( point2 P ) const

inlinenoexcept

Find the distance from the point to the curve.

If the distances are equal between two curves, take the one with a maximum orthognality. If the orthogonality >= then the point is inside that edge.

Parameters

P	The point from which to calculate the distance to this curve.

Returns: squared distance from curve, orthogonality.

◆ solveXByY()

lean_vector< float > hi::v1::bezier_curve::solveXByY ( float const y ) const

inlinenoexcept

Return the x values where the curve crosses the y-axis.

Parameters

y y-axis.

Returns: 0 to 3, or infinite number of x values.

◆ split()

std::pair< bezier_curve, bezier_curve > hi::v1::bezier_curve::split ( float const t ) const

inlinenoexcept

Split a bezier-curve into two bezier-curve of the same type.

Parameters

t	a relative distance between 0.0 (point P1) and 1.0 (point P2) where to split the curve.

Returns: two bezier-curves.

◆ subdivideUntilFlat()

std::vector< bezier_curve > hi::v1::bezier_curve::subdivideUntilFlat ( float const tolerance ) const

inlinenoexcept

Subdivide a bezier-curve until each are flat enough.

Parameters

tolerance maximum amount of curviness.

Returns: resulting list of curve segments.

◆ subdivideUntilFlat_impl()

void hi::v1::bezier_curve::subdivideUntilFlat_impl	(	std::vector< bezier_curve > &	r,
		float const	minimumFlatness ) const

inlinenoexcept

Subdivide a bezier-curve until each are flat enough.

Parameters

r	resulting list of linear segments.
minimumFlatness	minimum amount of flatness of the resulting curve segments.

◆ tangentAt()

constexpr vector2 hi::v1::bezier_curve::tangentAt ( float const t ) const

inlineconstexprnoexcept

Return a tangent on the bezier-curve. Values of t beyond 0.0 and 1.0 will find a point extrapolated beyond the bezier segment.

Parameters

t	a relative distance between 0.0 (point P1) and 1.0 (point P2).

Returns: the tangent-vector at point t on the curve

◆ toParallelLine()

bezier_curve hi::v1::bezier_curve::toParallelLine ( float const offset ) const

inlinenoexcept

Return a line-segment from a curve at a certain distance.

Parameters

offset positive means the parallel line will be on the starboard of the curve.

Returns: line segment offset from the curve.

Friends And Related Symbol Documentation

◆ operator~

bezier_curve operator~ ( bezier_curve const & rhs )

friend

Reverse direction of a curve.

Field Documentation

◆ C1

point2 hi::v1::bezier_curve::C1

Control point.

◆ C2

point2 hi::v1::bezier_curve::C2

Control point.

◆ P1

point2 hi::v1::bezier_curve::P1

First point.

◆ P2

point2 hi::v1::bezier_curve::P2

Last point.

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

hikogui/src/hikogui/graphic_path/bezier_curve.hpp

Data Structures

Public Types

Public Member Functions

Data Fields

Friends

Detailed Description

Constructor & Destructor Documentation

◆ bezier_curve() [1/4]

◆ bezier_curve() [2/4]

◆ bezier_curve() [3/4]

◆ bezier_curve() [4/4]

Member Function Documentation

◆ cubicSplit()

◆ flatness()

◆ linearSplit()

◆ pointAt()

◆ quadraticSplit()

◆ sdf_distance()

◆ solveXByY()

◆ split()

◆ subdivideUntilFlat()

◆ subdivideUntilFlat_impl()

◆ tangentAt()

◆ toParallelLine()

Friends And Related Symbol Documentation

◆ operator~

Field Documentation

◆ C1

◆ C2

◆ P1

◆ P2