hi::v1::bezier_curve Struct Reference

#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.

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

• hikogui/src/hikogui/graphic_path/bezier_curve.hpp