Geometry classes and functions. More...

Classes
struct	gf::Circ< T >
	Utility class for manipulating circles. More...

struct	gf::Penetration
	Data about the collision between two objects. More...

class	gf::Bresenham
	State for the Bresenham's line algorithm. More...

struct	gf::Segment< T >
	A segment with two points. More...

class	gf::PointSequence
	A sequence of points. More...

class	gf::Polygon
	A convex polygon. More...

class	gf::Polyline
	A polyline. More...

struct	gf::Rect< T >
	Utility class for manipulating 2D axis aligned rectangles. More...

struct	gf::Rotation
	A rotation. More...

struct	gf::Translation
	A translation. More...

struct	gf::Transform
	A simple transformation (rotation then translation) More...

class	gf::EdgeRef< T >
	A reference to an edge (two points) More...

class	gf::TriangleRef< T >
	A reference to a triangle (three points) More...

Typedefs
using	gf::CircF = Circ< float >
	A `float` circle. More...

using	gf::CircD = Circ< double >
	A `double` circle. More...

using	gf::CircI = Circ< int >
	A `int` circle. More...

using	gf::CircU = Circ< unsigned >
	A `unsigned` circle. More...

using	gf::CircZ = Circ< std::size_t >
	A `std::size_t` circle. More...

using	gf::SegmentF = Segment< float >
	A segment with float vectors. More...

using	gf::SegmentD = Segment< double >
	A segment with double vectors. More...

using	gf::SegmentI = Segment< int >
	A segment with int vectors. More...

using	gf::RectF = Rect< float >
	A `float` rectangle. More...

using	gf::RectD = Rect< double >
	A `double` rectangle. More...

using	gf::RectI = Rect< int >
	A `int` rectangle. More...

using	gf::RectU = Rect< unsigned >
	A `unsigned` rectangle. More...

using	gf::RectZ = Rect< std::size_t >
	A `std::size_t` rectangle. More...

Enumerations
enum	gf::Direction : int8_t { gf::Direction::Center = -1, gf::Direction::Up = 0, gf::Direction::Right = 1, gf::Direction::Down = 2, gf::Direction::Left = 3 }
	Main four directions. More...

enum	gf::Orientation : int8_t { gf::Orientation::Center = -1, gf::Orientation::North = 0, gf::Orientation::NorthEast = 1, gf::Orientation::East = 2, gf::Orientation::SouthEast = 3, gf::Orientation::South = 4, gf::Orientation::SouthWest = 5, gf::Orientation::West = 6, gf::Orientation::NorthWest = 7 }
	Cardinal and ordinal orientation. More...

enum	gf::Winding { gf::Winding::Clockwise, gf::Winding::Counterclockwise }
	The direction of a polygon's rotation. More...

Functions
GF_CORE_API Vector2f	gf::unit (Direction direction)
	Get a unit vector from a direction. More...

GF_CORE_API Vector2i	gf::displacement (Direction direction)
	Get a vector from a direction. More...

GF_CORE_API float	gf::angle (Direction direction)
	Get an angle from a direction. More...

GF_CORE_API Direction	gf::opposite (Direction direction)
	Get the opposite direction. More...

GF_CORE_API Direction	gf::orthogonalCW (Direction direction)
	Get the orthogonal direction clockwise. More...

GF_CORE_API Direction	gf::orthogonalCCW (Direction direction)
	Get the orthogonal direction counter-clockwise. More...

GF_CORE_API Direction	gf::nextCW (Direction direction)
	Get the next direction clockwise. More...

GF_CORE_API Direction	gf::nextCCW (Direction direction)
	Get the next direction counter-clockwise. More...

GF_CORE_API std::vector< Vector2i >	gf::generateLine (Vector2i p0, Vector2i p1)
	Generate a line between two positions. More...

GF_CORE_API Polygon	gf::convexHull (Span< const Vector2f > points)
	Compute the convex hull of a set of points. More...

GF_CORE_API std::vector< Vector2f >	gf::simplifyPoints (Span< const Vector2f > points, float distance=Epsilon)
	Simplify a sequence of points. More...

GF_CORE_API std::vector< Polyline >	gf::buildLines (Span< const SegmentI > segments)
	Build a set of lines from a set of segments. More...

GF_CORE_API Vector2f	gf::unit (Orientation orientation)
	Get a unit vector from an orientation. More...

GF_CORE_API Vector2i	gf::displacement (Orientation orientation)
	Get a vector from an orientation. More...

GF_CORE_API float	gf::angle (Orientation orientation)
	Get an angle from a orientation. More...

GF_CORE_API Orientation	gf::orientation (float angle)
	Get an orientation from an angle. More...

GF_CORE_API Orientation	gf::opposite (Orientation orientation)
	Get the opposite orientation. More...

GF_CORE_API Orientation	gf::orthogonalCW (Orientation orientation)
	Get the orthogonal orientation clockwise. More...

GF_CORE_API Orientation	gf::orthogonalCCW (Orientation orientation)
	Get the orthogonal orientation counter-clockwise. More...

GF_CORE_API Orientation	gf::nextCW (Orientation orientation)
	Get the next orientation clockwise. More...

GF_CORE_API Orientation	gf::nextCCW (Orientation orientation)
	Get the next orientation counter-clockwise. More...

template<typename T >
constexpr Rect< T >	gf::computeBoxQuarter (const Rect< T > &other, Quarter quarter)
	Divide a rectangle in quarters. More...

constexpr Vector2f	gf::transform (const Matrix3f &mat, Vector2f point)
	Apply an affine transformation to a 2D point. More...

GF_CORE_API RectF	gf::transform (const Matrix3f &mat, const RectF &rect)
	Apply an affine transformaton to a rectangle. More...

constexpr Matrix3f	gf::identityTransform ()
	Identity transform. More...

Matrix3f	gf::translation (Vector2f offset)
	Get a translation matrix. More...

GF_CORE_API void	gf::translate (Matrix3f &mat, Vector2f offset)
	Combine the current transform with a translation. More...

Matrix3f	gf::rotation (float angle)
	Get a rotation matrix. More...

Matrix3f	gf::rotation (float angle, Vector2f center)
	Get a rotation matrix. More...

GF_CORE_API void	gf::rotate (Matrix3f &mat, float angle)
	Combine the current transform with a rotation. More...

GF_CORE_API void	gf::rotate (Matrix3f &mat, float angle, Vector2f center)
	Combine the current transform with a rotation. More...

Matrix3f	gf::scaling (Vector2f factor)
	Get a scaling matrix. More...

Matrix3f	gf::scaling (Vector2f factor, Vector2f center)
	Get a scaling matrix. More...

GF_CORE_API void	gf::scale (Matrix3f &mat, Vector2f factor)
	Combine the current transform with a scaling. More...

GF_CORE_API void	gf::scale (Matrix3f &mat, Vector2f factor, Vector2f center)
	Combine the current transform with a scaling. More...

GF_CORE_API std::vector< TriangleRef< const Vector2f > >	gf::triangulation (Span< const Vector2f > points)
	Compute a Delaunay triangulation of a set of points. More...

Detailed Description

Geometry classes and functions.

Typedef Documentation

◆ CircD

using gf::CircD = typedef Circ<double>

A double circle.

See also: gf::Circ

◆ CircF

using gf::CircF = typedef Circ<float>

A float circle.

See also: gf::Circ

◆ CircI

using gf::CircI = typedef Circ<int>

A int circle.

See also: gf::Circ

◆ CircU

using gf::CircU = typedef Circ<unsigned>

A unsigned circle.

See also: gf::Circ

◆ CircZ

using gf::CircZ = typedef Circ<std::size_t>

A std::size_t circle.

See also: gf::Circ

◆ RectD

using gf::RectD = typedef Rect<double>

A double rectangle.

See also: gf::Rect

◆ RectF

using gf::RectF = typedef Rect<float>

A float rectangle.

See also: gf::Rect

◆ RectI

using gf::RectI = typedef Rect<int>

A int rectangle.

See also: gf::Rect

◆ RectU

using gf::RectU = typedef Rect<unsigned>

A unsigned rectangle.

See also: gf::Rect

◆ RectZ

using gf::RectZ = typedef Rect<std::size_t>

A std::size_t rectangle.

See also: gf::Rect

◆ SegmentD

using gf::SegmentD = typedef Segment<double>

A segment with double vectors.

See also: gf::Segment

◆ SegmentF

using gf::SegmentF = typedef Segment<float>

A segment with float vectors.

See also: gf::Segment

◆ SegmentI

using gf::SegmentI = typedef Segment<int>

A segment with int vectors.

See also: gf::Segment

Enumeration Type Documentation

◆ Direction

enum gf::Direction : int8_t

strong

Main four directions.

gf::Direction represents one of the four main directions. A special value is added to represent the center, it indicates no direction.

See also: gf::Orientation

Enumerator
Center	The center, indicates no direction.
Up	The up direction.
Right	The right direction.
Down	The down direction.
Left	The left direction.

◆ Orientation

enum gf::Orientation : int8_t

strong

Cardinal and ordinal orientation.

gf::Orientation represents one the four cardinal orientations and the four ordinal (or intercardinal) orientations. A special value is added to represent the center, it indicates no orientation.

See also: gf::Direction

Enumerator
Center	The center, indicates no orientation.
North	The north orientation.
NorthEast	The north-east orientation.
East	The east orientation.
SouthEast	The south-east orientation.
South	The south orientation.
SouthWest	The south-west orientation.
West	The west orientation.
NorthWest	The north-west orientation.

◆ Winding

enum gf::Winding

strong

The direction of a polygon's rotation.

Enumerator
Clockwise	Same direction as a clock's hands.
Counterclockwise	Opposite direction of a clock's hands.

Function Documentation

◆ angle() [1/2]

GF_CORE_API float gf::angle ( Direction direction )

Get an angle from a direction.

Up is at angle 0 and angle grows clockwise.

Parameters

direction The direction

Returns: an angle (in radians) representing the direction

◆ angle() [2/2]

GF_CORE_API float gf::angle ( Orientation orientation )

Get an angle from a orientation.

East is at angle 0 and angle grows clockwise.

Parameters

orientation The orientation

Returns: An angle (in radians) representing the orientation

See also: gf::orientation()

◆ buildLines()

GF_CORE_API std::vector<Polyline> gf::buildLines ( Span< const SegmentI > segments )

Build a set of lines from a set of segments.

Parameters

segments A set of segments

Returns: An array of polylines representing the lines

◆ computeBoxQuarter()

template<typename T >

constexpr Rect<T> gf::computeBoxQuarter	(	const Rect< T > &	other,
		Quarter	quarter
	)

Divide a rectangle in quarters.

Parameters

other	The rectangle to divide
quarter	The quarter to compute

◆ convexHull()

GF_CORE_API Polygon gf::convexHull ( Span< const Vector2f > points )

Compute the convex hull of a set of points.

This function uses the Quickhull algorithm.

Complexity: \( O(n \log n)\) on average, \( O(n^2) \) on worst case

Parameters

points The set of points

Returns: A (convex) polygon that contains the points

◆ displacement() [1/2]

GF_CORE_API Vector2i gf::displacement ( Direction direction )

Get a vector from a direction.

The vector has its coordinates at -1, 0 or 1 depending on the direction. It can be used to represent the displacement on a grid in the given direction.

Parameters

direction The direction

Returns: A vector representing the direction

◆ displacement() [2/2]

GF_CORE_API Vector2i gf::displacement ( Orientation orientation )

Get a vector from an orientation.

The vector has its coordinates at -1, 0 or 1 depending on the orientation. It can be used to represent the displacement on a grid in the given orientation.

Parameters

orientation The orientation

Returns: A vector representing the orientation

◆ generateLine()

GF_CORE_API std::vector<Vector2i> gf::generateLine	(	Vector2i	p0,
		Vector2i	p1
	)

Generate a line between two positions.

This function uses Bresenham's line algorithm.

Parameters

p0	The first point of the line
p1	The last point of the line

Returns: A series of point beginning at the first point and ending just before the last point

See also: gf::Bresenham

◆ identityTransform()

constexpr Matrix3f gf::identityTransform ( )

Identity transform.

Returns: The identity matrix

◆ nextCCW() [1/2]

GF_CORE_API Direction gf::nextCCW ( Direction direction )

Get the next direction counter-clockwise.

Parameters

direction The direction

Returns: The next direction counter-clockwise

◆ nextCCW() [2/2]

GF_CORE_API Orientation gf::nextCCW ( Orientation orientation )

Get the next orientation counter-clockwise.

Parameters

orientation The orientation

Returns: The next orientation counter-clockwise

◆ nextCW() [1/2]

GF_CORE_API Direction gf::nextCW ( Direction direction )

Get the next direction clockwise.

Parameters

direction The direction

Returns: The next direction clockwise

◆ nextCW() [2/2]

GF_CORE_API Orientation gf::nextCW ( Orientation orientation )

Get the next orientation clockwise.

Parameters

orientation The orientation

Returns: The next orientation clockwise

◆ opposite() [1/2]

GF_CORE_API Direction gf::opposite ( Direction direction )

Get the opposite direction.

Parameters

direction The direction

Returns: The opposite direction

◆ opposite() [2/2]

GF_CORE_API Orientation gf::opposite ( Orientation orientation )

Get the opposite orientation.

Parameters

orientation The orientation

Returns: The opposite orientation

◆ orientation()

GF_CORE_API Orientation gf::orientation ( float angle )

Get an orientation from an angle.

East is at angle 0 and angle grows clockwise.

Parameters

angle The angle

Returns: An orientation for the angle

See also: gf::angle()

◆ orthogonalCCW() [1/2]

GF_CORE_API Direction gf::orthogonalCCW ( Direction direction )

Get the orthogonal direction counter-clockwise.

Parameters

direction The direction

Returns: The orthogonal direction counter-clockwise

◆ orthogonalCCW() [2/2]

GF_CORE_API Orientation gf::orthogonalCCW ( Orientation orientation )

Get the orthogonal orientation counter-clockwise.

Parameters

orientation The orientation

Returns: The orthogonal orientation counter-clockwise

◆ orthogonalCW() [1/2]

GF_CORE_API Direction gf::orthogonalCW ( Direction direction )

Get the orthogonal direction clockwise.

Parameters

direction The direction

Returns: The orthogonal direction clockwise

◆ orthogonalCW() [2/2]

GF_CORE_API Orientation gf::orthogonalCW ( Orientation orientation )

Get the orthogonal orientation clockwise.

Parameters

orientation The orientation

Returns: The orthogonal orientation clockwise

◆ rotate() [1/2]

GF_CORE_API void gf::rotate	(	Matrix3f &	mat,
		float	angle
	)

Combine the current transform with a rotation.

Parameters

mat	The current transform
angle	The angle of the rotation (in radians)

◆ rotate() [2/2]

GF_CORE_API void gf::rotate	(	Matrix3f &	mat,
		float	angle,
		Vector2f	center
	)

Combine the current transform with a rotation.

Parameters

mat	The current transform
angle	The angle of the rotation (in radians)
center	The center of the rotation

◆ rotation() [1/2]

Matrix3f gf::rotation ( float angle )

inline

Get a rotation matrix.

Parameters

angle The angle of the rotation (in radians)

Returns: A rotation of angle radians

◆ rotation() [2/2]

Matrix3f gf::rotation	(	float	angle,
		Vector2f	center
	)

inline

Get a rotation matrix.

Parameters

angle	The angle of the rotation (in radians)
center	The center of the rotation

Returns: A rotation of angle radians of origin center

◆ scale() [1/2]

GF_CORE_API void gf::scale	(	Matrix3f &	mat,
		Vector2f	factor
	)

Combine the current transform with a scaling.

Parameters

mat	The current transform
factor	The scaling factor

◆ scale() [2/2]

GF_CORE_API void gf::scale	(	Matrix3f &	mat,
		Vector2f	factor,
		Vector2f	center
	)

Combine the current transform with a scaling.

Parameters

mat	The current transform
factor	The scaling factor
center	The center of the scaling

◆ scaling() [1/2]

Matrix3f gf::scaling ( Vector2f factor )

inline

Get a scaling matrix.

Parameters

factor The scaling factor

Returns: A scaling by factor

◆ scaling() [2/2]

Matrix3f gf::scaling	(	Vector2f	factor,
		Vector2f	center
	)

inline

Get a scaling matrix.

Parameters

factor	The scaling factor
center	The center of the scaling

Returns: A scaling by factor of origin center

◆ simplifyPoints()

GF_CORE_API std::vector<Vector2f> gf::simplifyPoints	(	Span< const Vector2f >	points,
		float	distance = `Epsilon`
	)

Simplify a sequence of points.

This function uses the Douglas–Peucker algorithm.

Parameters

points	The sequence of points
distance	The maximum authorized distance between the original points and the simplified points

Returns: A new simplified sequence of points

◆ transform() [1/2]

constexpr Vector2f gf::transform	(	const Matrix3f &	mat,
		Vector2f	point
	)

Apply an affine transformation to a 2D point.

Parameters

mat	The transformation matrix
point	The point to transform

Returns: The transformed point

◆ transform() [2/2]

GF_CORE_API RectF gf::transform	(	const Matrix3f &	mat,
		const RectF &	rect
	)

Apply an affine transformaton to a rectangle.

The resulting rectangle is axis-aligned

Parameters

mat	The transformation matrix
rect	The rectangle to transform

Returns: The transformed rectangle

◆ translate()

GF_CORE_API void gf::translate	(	Matrix3f &	mat,
		Vector2f	offset
	)

Combine the current transform with a translation.

Parameters

mat	The current transform
offset	The offset of the translation

◆ translation()

Matrix3f gf::translation ( Vector2f offset )

inline

Get a translation matrix.

Parameters

offset The offset of the translation

Returns: A translation by offset

◆ triangulation()

GF_CORE_API std::vector<TriangleRef<const Vector2f> > gf::triangulation ( Span< const Vector2f > points )

Compute a Delaunay triangulation of a set of points.

Parameters

points The set of points

Returns: A set of triangles refering to the original points

◆ unit() [1/2]

GF_CORE_API Vector2f gf::unit ( Direction direction )

Get a unit vector from a direction.

Parameters

direction The direction

Returns: A unit vector representing the direction

◆ unit() [2/2]

GF_CORE_API Vector2f gf::unit ( Orientation orientation )

Get a unit vector from an orientation.

Parameters

orientation The orientation

Returns: A unit vector representing the orientation

Classes

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ CircD

◆ CircF

◆ CircI

◆ CircU

◆ CircZ

◆ RectD

◆ RectF

◆ RectI

◆ RectU

◆ RectZ

◆ SegmentD

◆ SegmentF

◆ SegmentI

Enumeration Type Documentation

◆ Direction

◆ Orientation

◆ Winding

Function Documentation

◆ angle() [1/2]

◆ angle() [2/2]

◆ buildLines()

◆ computeBoxQuarter()

◆ convexHull()

◆ displacement() [1/2]

◆ displacement() [2/2]

◆ generateLine()

◆ identityTransform()

◆ nextCCW() [1/2]

◆ nextCCW() [2/2]

◆ nextCW() [1/2]

◆ nextCW() [2/2]

◆ opposite() [1/2]

◆ opposite() [2/2]

◆ orientation()

◆ orthogonalCCW() [1/2]

◆ orthogonalCCW() [2/2]

◆ orthogonalCW() [1/2]

◆ orthogonalCW() [2/2]

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ rotation() [1/2]

◆ rotation() [2/2]

◆ scale() [1/2]

◆ scale() [2/2]

◆ scaling() [1/2]

◆ scaling() [2/2]

◆ simplifyPoints()

◆ transform() [1/2]

◆ transform() [2/2]

◆ translate()

◆ translation()

◆ triangulation()

◆ unit() [1/2]

◆ unit() [2/2]