Utility functions for working with angles. More...

#include <Angle.h>

Static Public Member Functions
static double	toDegrees (double radians)

static double	toRadians (double angleDegrees)

static double	angle (const geom::CoordinateXY &p0, const geom::CoordinateXY &p1)
	Returns the angle of the vector from p0 to p1, relative to the positive X-axis.

static double	angle (const geom::CoordinateXY &p)
	Returns the angle that the vector from (0,0) to p, relative to the positive X-axis.

static bool	isAcute (const geom::CoordinateXY &p0, const geom::CoordinateXY &p1, const geom::CoordinateXY &p2)

static bool	isObtuse (const geom::CoordinateXY &p0, const geom::CoordinateXY &p1, const geom::CoordinateXY &p2)

static double	angleBetween (const geom::CoordinateXY &tip1, const geom::CoordinateXY &tail, const geom::CoordinateXY &tip2)

static double	angleBetweenOriented (const geom::CoordinateXY &tip1, const geom::CoordinateXY &tail, const geom::CoordinateXY &tip2)

static double	bisector (const geom::CoordinateXY &tip1, const geom::CoordinateXY &tail, const geom::CoordinateXY &tip2)

static double	interiorAngle (const geom::CoordinateXY &p0, const geom::CoordinateXY &p1, const geom::CoordinateXY &p2)

static int	getTurn (double ang1, double ang2)
	Returns whether an angle must turn clockwise or counterclockwise to overlap another angle.

static double	normalize (double angle)
	Computes the normalized value of an angle, which is the equivalent angle in the range ( -Pi, Pi ].

static double	normalizePositive (double angle)
	Computes the normalized positive value of an angle, which is the equivalent angle in the range [ 0, 2*Pi ).

static bool	isWithinCCW (double angle, double from, double to)

static double	diff (double ang1, double ang2)

static void	sinCosSnap (const double ang, double &rSin, double &rCos)
	Computes both sin and cos of an angle, snapping near-zero values to zero.

static geom::CoordinateXY	project (const geom::CoordinateXY &p, double angle, double dist)

Static Public Attributes
static constexpr double	PI_TIMES_2 = 2.0 * MATH_PI

static constexpr double	PI_OVER_2 = MATH_PI / 2.0

static constexpr double	PI_OVER_4 = MATH_PI / 4.0

static const int	COUNTERCLOCKWISE = Orientation::COUNTERCLOCKWISE
	Constant representing counterclockwise orientation.

static const int	CLOCKWISE = Orientation::CLOCKWISE
	Constant representing clockwise orientation.

static const int	NONE = Orientation::COLLINEAR
	Constant representing no orientation.

Detailed Description

Utility functions for working with angles.

Unless otherwise noted, methods in this class express angles in radians.

Member Function Documentation

◆ angle() [1/2]

static double geos::algorithm::Angle::angle ( const geom::CoordinateXY & p )

static

Returns the angle that the vector from (0,0) to p, relative to the positive X-axis.

The angle is normalized to be in the range ( -Pi, Pi ].

Returns: the normalized angle (in radians) that p makes with the positive x-axis.

◆ angle() [2/2]

static double geos::algorithm::Angle::angle	(	const geom::CoordinateXY &	p0,
		const geom::CoordinateXY &	p1
	)

static

Returns the angle of the vector from p0 to p1, relative to the positive X-axis.

The angle is normalized to be in the range [ -Pi, Pi ].

Returns: the normalized angle (in radians) that p0-p1 makes with the positive x-axis.

◆ angleBetween()

static double geos::algorithm::Angle::angleBetween	(	const geom::CoordinateXY &	tip1,
		const geom::CoordinateXY &	tail,
		const geom::CoordinateXY &	tip2
	)

static

Returns the unoriented smallest angle between two vectors.

The computed angle will be in the range [0, Pi).

Parameters

tip1	the tip of one vector
tail	the tail of each vector
tip2	the tip of the other vector

Returns: the angle between tail-tip1 and tail-tip2

◆ angleBetweenOriented()

static double geos::algorithm::Angle::angleBetweenOriented	(	const geom::CoordinateXY &	tip1,
		const geom::CoordinateXY &	tail,
		const geom::CoordinateXY &	tip2
	)

static

Returns the oriented smallest angle between two vectors.

The computed angle will be in the range (-Pi, Pi]. A positive result corresponds to a counterclockwise rotation from v1 to v2; a negative result corresponds to a clockwise rotation.

Parameters

tip1	the tip of v1
tail	the tail of each vector
tip2	the tip of v2

Returns: the angle between v1 and v2, relative to v1

◆ bisector()

static double geos::algorithm::Angle::bisector	(	const geom::CoordinateXY &	tip1,
		const geom::CoordinateXY &	tail,
		const geom::CoordinateXY &	tip2
	)

static

Computes the angle of the unoriented bisector of the smallest angle between two vectors. The computed angle will be in the range (-Pi, Pi]. Collinear inputs are handled.

Parameters

tip1	the tip of v1
tail	the tail of each vector
tip2	the tip of v2

Returns: the angle of the bisector between v1 and v2

◆ diff()

static double geos::algorithm::Angle::diff	(	double	ang1,
		double	ang2
	)

static

Computes the unoriented smallest difference between two angles.

The angles are assumed to be normalized to the range [-Pi, Pi]. The result will be in the range [0, Pi].

Parameters

ang1	the angle of one vector (in [-Pi, Pi] )
ang2	the angle of the other vector (in range [-Pi, Pi] )

Returns: the angle (in radians) between the two vectors (in range [0, Pi] )

◆ getTurn()

static int geos::algorithm::Angle::getTurn	(	double	ang1,
		double	ang2
	)

static

Returns whether an angle must turn clockwise or counterclockwise to overlap another angle.

Parameters

ang1	an angle (in radians)
ang2	an angle (in radians)

Returns: whether a1 must turn CLOCKWISE, COUNTERCLOCKWISE or NONE to overlap a2.

◆ interiorAngle()

static double geos::algorithm::Angle::interiorAngle	(	const geom::CoordinateXY &	p0,
		const geom::CoordinateXY &	p1,
		const geom::CoordinateXY &	p2
	)

static

Computes the interior angle between two segments of a ring.

The ring is assumed to be oriented in a clockwise direction. The computed angle will be in the range [0, 2Pi]

Parameters

p0	a point of the ring
p1	the next point of the ring
p2	the next point of the ring

Returns: the interior angle based at p1

◆ isAcute()

static bool geos::algorithm::Angle::isAcute	(	const geom::CoordinateXY &	p0,
		const geom::CoordinateXY &	p1,
		const geom::CoordinateXY &	p2
	)

static

Tests whether the angle between p0-p1-p2 is acute.

An angle is acute if it is less than 90 degrees.

Note: this implementation is not precise (deterministic) for angles very close to 90 degrees.

Parameters

p0	an endpoint of the angle
p1	the base of the angle
p2	the other endpoint of the angle

◆ isObtuse()

static bool geos::algorithm::Angle::isObtuse	(	const geom::CoordinateXY &	p0,
		const geom::CoordinateXY &	p1,
		const geom::CoordinateXY &	p2
	)

static

Tests whether the angle between p0-p1-p2 is obtuse.

An angle is obtuse if it is greater than 90 degrees.

Note: this implementation is not precise (deterministic) for angles very close to 90 degrees.

Parameters

p0	an endpoint of the angle
p1	the base of the angle
p2	the other endpoint of the angle

◆ isWithinCCW()

static bool geos::algorithm::Angle::isWithinCCW	(	double	angle,
		double	from,
		double	to
	)

static

Returns true if angle x is within the counterclockwise arc from angle a to angle b

Parameters

angle	angle to test
from	starting angle of arc
to	ending angle of arc

Returns: true if angle is within [from, to]

◆ normalize()

static double geos::algorithm::Angle::normalize ( double angle )

static

Computes the normalized value of an angle, which is the equivalent angle in the range ( -Pi, Pi ].

Parameters

angle the angle to normalize

Returns: an equivalent angle in the range (-Pi, Pi]

◆ normalizePositive()

static double geos::algorithm::Angle::normalizePositive ( double angle )

static

Computes the normalized positive value of an angle, which is the equivalent angle in the range [ 0, 2*Pi ).

E.g.:

normalizePositive(0.0) = 0.0
normalizePositive(-PI) = PI
normalizePositive(-2PI) = 0.0
normalizePositive(-3PI) = PI
normalizePositive(-4PI) = 0
normalizePositive(PI) = PI
normalizePositive(2PI) = 0.0
normalizePositive(3PI) = PI
normalizePositive(4PI) = 0.0

Parameters

angle the angle to normalize, in radians

Returns: an equivalent positive angle

◆ project()

static geom::CoordinateXY geos::algorithm::Angle::project	(	const geom::CoordinateXY &	p,
		double	angle,
		double	dist
	)

static

Projects a point by a given angle and distance.

Parameters

p	the point to project
angle	the angle at which to project
dist	the distance to project

Returns: the projected point

◆ sinCosSnap()

static void geos::algorithm::Angle::sinCosSnap	(	const double	ang,
		double &	rSin,
		double &	rCos
	)

inlinestatic

Computes both sin and cos of an angle, snapping near-zero values to zero.

The angle does not need to be normalized. Unlike std::sin and std::cos, this method will snap near-zero values to zero for (e.g.) sin(pi) and cos(pi/2).

Parameters

ang	the input angle (in radians)
rSin	the result of sin(ang)
rCos	the result of cos(ang)

◆ toDegrees()

static double geos::algorithm::Angle::toDegrees ( double radians )

static

Converts from radians to degrees.

Parameters

radians an angle in radians

Returns: the angle in degrees

◆ toRadians()

static double geos::algorithm::Angle::toRadians ( double angleDegrees )

static

Converts from degrees to radians.

Parameters

angleDegrees an angle in degrees

Returns: the angle in radians

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

Angle.h

Static Public Member Functions

Static Public Attributes

Detailed Description

Member Function Documentation

◆ angle() [1/2]

◆ angle() [2/2]

◆ angleBetween()

◆ angleBetweenOriented()

◆ bisector()

◆ diff()

◆ getTurn()

◆ interiorAngle()

◆ isAcute()

◆ isObtuse()

◆ isWithinCCW()

◆ normalize()

◆ normalizePositive()

◆ project()

◆ sinCosSnap()

◆ toDegrees()

◆ toRadians()