Contains various geometry utility functions. More...

#include <qgsgeometryutils.h>

Classes
struct	SelfIntersection

Public Types
enum	ComponentType { Vertex, Ring, Part }

Static Public Member Functions
static double	angleBetweenThreePoints (double x1, double y1, double x2, double y2, double x3, double y3)
	Calculates the angle between the lines AB and BC, where AB and BC described by points a, b and b, c. More...

static bool	angleOnCircle (double angle, double angle1, double angle2, double angle3)
	Returns true if an angle is between angle1 and angle3 on a circle described by angle1, angle2 and angle3. More...

static double	averageAngle (double x1, double y1, double x2, double y2, double x3, double y3)
	Calculates the average angle (in radians) between the two linear segments from (x1, y1) to (x2, y2) and (x2, y2) to (x3, y3). More...

static double	averageAngle (double a1, double a2)
	Averages two angles, correctly handling negative angles and ensuring the result is between 0 and 2 pi. More...

static double	ccwAngle (double dy, double dx)
	Returns the counter clockwise angle between a line with components dx, dy and the line with dx > 0 and dy = 0. More...

static bool	circleAngleBetween (double angle, double angle1, double angle2, bool clockwise)
	Returns true if, in a circle, angle is between angle1 and angle2. More...

static void	circleCenterRadius (const QgsPoint &pt1, const QgsPoint &pt2, const QgsPoint &pt3, double &radius, double &centerX, double &centerY)
	Returns radius and center of the circle through pt1, pt2, pt3. More...

static int	circleCircleInnerTangents (const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2, QgsPointXY &line1P1, QgsPointXY &line1P2, QgsPointXY &line2P1, QgsPointXY &line2P2)
	Calculates the inner tangent points for two circles, centered at center1 and center2 and with radii of radius1 and radius2 respectively. More...

static int	circleCircleIntersections (QgsPointXY center1, double radius1, QgsPointXY center2, double radius2, QgsPointXY &intersection1, QgsPointXY &intersection2)
	Calculates the intersections points between the circle with center center1 and radius radius1 and the circle with center center2 and radius radius2. More...

static int	circleCircleOuterTangents (const QgsPointXY &center1, double radius1, const QgsPointXY &center2, double radius2, QgsPointXY &line1P1, QgsPointXY &line1P2, QgsPointXY &line2P1, QgsPointXY &line2P2)
	Calculates the outer tangent points for two circles, centered at center1 and center2 and with radii of radius1 and radius2 respectively. More...

static bool	circleClockwise (double angle1, double angle2, double angle3)
	Returns true if the circle defined by three angles is ordered clockwise. More...

static double	circleLength (double x1, double y1, double x2, double y2, double x3, double y3)
	Length of a circular string segment defined by pt1, pt2, pt3. More...

static double	circleTangentDirection (const QgsPoint &tangentPoint, const QgsPoint &cp1, const QgsPoint &cp2, const QgsPoint &cp3)
	Calculates the direction angle of a circle tangent (clockwise from north in radians) More...

static QgsPoint	closestPoint (const QgsAbstractGeometry &geometry, const QgsPoint &point)
	Returns the nearest point on a segment of a geometry for the specified point. More...

template<class T >
static double	closestSegmentFromComponents (T &container, ComponentType ctype, const QgsPoint &pt, QgsPoint &segmentPt, QgsVertexId &vertexAfter, int *leftOf, double epsilon)

static QgsPoint	closestVertex (const QgsAbstractGeometry &geom, const QgsPoint &pt, QgsVertexId &id)
	Returns the closest vertex to a geometry for a specified point. More...

static void	coefficients (const QgsPoint &pt1, const QgsPoint &pt2, double &a, double &b, double &c)
	Returns the coefficients (a, b, c for equation "ax + by + c = 0") of a line defined by points pt1 and pt2. More...

static double	distanceToVertex (const QgsAbstractGeometry &geom, QgsVertexId id)
	Returns the distance along a geometry from its first vertex to the specified vertex. More...

static QVector< QgsLineString * >	extractLineStrings (const QgsAbstractGeometry *geom)
	Returns list of linestrings extracted from the passed geometry. More...

static double	gradient (const QgsPoint &pt1, const QgsPoint &pt2)
	Returns the gradient of a line defined by points pt1 and pt2. More...

static double	interpolateArcValue (double angle, double a1, double a2, double a3, double zm1, double zm2, double zm3)
	Interpolate a value at given angle on circular arc given values (zm1, zm2, zm3) at three different angles (a1, a2, a3). More...

static QgsPoint	interpolatePointOnArc (const QgsPoint &pt1, const QgsPoint &pt2, const QgsPoint &pt3, double distance)
	Interpolates a point on an arc defined by three points, pt1, pt2 and pt3. More...

static QgsPointXY	interpolatePointOnLine (double x1, double y1, double x2, double y2, double fraction)
	Interpolates the position of a point a fraction of the way along the line from (x1, y1) to (x2, y2). More...

static QgsPoint	interpolatePointOnLine (const QgsPoint &p1, const QgsPoint &p2, double fraction)
	Interpolates the position of a point a fraction of the way along the line from p1 to p2. More...

static QgsPointXY	interpolatePointOnLineByValue (double x1, double y1, double v1, double x2, double y2, double v2, double value)
	Interpolates the position of a point along the line from (x1, y1) to (x2, y2). More...

static int	leftOfLine (const double x, const double y, const double x1, const double y1, const double x2, const double y2)
	Returns a value < 0 if the point (x, y) is left of the line from (x1, y1) -> ( x2, y2). More...

static int	leftOfLine (const QgsPoint &point, const QgsPoint &p1, const QgsPoint &p2)
	Returns a value < 0 if the point point is left of the line from p1 -> p2. More...

static double	lineAngle (double x1, double y1, double x2, double y2)
	Calculates the direction of line joining two points in radians, clockwise from the north direction. More...

static bool	lineCircleIntersection (const QgsPointXY &center, double radius, const QgsPointXY &linePoint1, const QgsPointXY &linePoint2, QgsPointXY &intersection)
	Compute the intersection of a line and a circle. More...

static bool	lineIntersection (const QgsPoint &p1, QgsVector v1, const QgsPoint &p2, QgsVector v2, QgsPoint &intersection)
	Computes the intersection between two lines. More...

static double	linePerpendicularAngle (double x1, double y1, double x2, double y2)
	Calculates the perpendicular angle to a line joining two points. More...

static bool	linesIntersection3D (const QgsVector3D &La1, const QgsVector3D &La2, const QgsVector3D &Lb1, const QgsVector3D &Lb2, QgsVector3D &intersection)
	An algorithm to calculate an (approximate) intersection of two lines in 3D. More...

static QgsPoint	midpoint (const QgsPoint &pt1, const QgsPoint &pt2)
	Returns a middle point between points pt1 and pt2. More...

static double	normalizedAngle (double angle)
	Ensures that an angle is in the range 0 <= angle < 2 pi. More...

static QgsLineString	perpendicularSegment (const QgsPoint &p, const QgsPoint &s1, const QgsPoint &s2)
	Create a perpendicular line segment from p to segment [s1, s2]. More...

static QgsPoint	pointOnLineWithDistance (const QgsPoint &startPoint, const QgsPoint &directionPoint, double distance)
	Returns a point a specified distance toward a second point. More...

static void	pointOnLineWithDistance (double x1, double y1, double x2, double y2, double distance, double &x, double &y, double z1=nullptr, double z2=nullptr, double z=nullptr, double m1=nullptr, double m2=nullptr, double m=nullptr)
	Calculates the point a specified distance from (x1, y1) toward a second point (x2, y2). More...

static QgsPointSequence	pointsFromWKT (const QString &wktCoordinateList, bool is3D, bool isMeasure)
	Returns a list of points contained in a WKT string. More...

static QDomElement	pointsToGML2 (const QgsPointSequence &points, QDomDocument &doc, int precision, const QString &ns, QgsAbstractGeometry::AxisOrder axisOrder=QgsAbstractGeometry::AxisOrder::XY)
	Returns a gml::coordinates DOM element. More...

static QDomElement	pointsToGML3 (const QgsPointSequence &points, QDomDocument &doc, int precision, const QString &ns, bool is3D, QgsAbstractGeometry::AxisOrder axisOrder=QgsAbstractGeometry::AxisOrder::XY)
	Returns a gml::posList DOM element. More...

static QString	pointsToJSON (const QgsPointSequence &points, int precision)
	Returns a geoJSON coordinates string. More...

static void	pointsToWKB (QgsWkbPtr &wkb, const QgsPointSequence &points, bool is3D, bool isMeasure)
	Returns a LinearRing { uint32 numPoints; Point points[numPoints]; }. More...

static QString	pointsToWKT (const QgsPointSequence &points, int precision, bool is3D, bool isMeasure)
	Returns a WKT coordinate list. More...

static QgsPoint	projectPointOnSegment (const QgsPoint &p, const QgsPoint &s1, const QgsPoint &s2)
	Project the point on a segment. More...

static bool	segmentIntersection (const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &q1, const QgsPoint &q2, QgsPoint &intersectionPoint, bool &isIntersection, double tolerance=1e-8, bool acceptImproperIntersection=false)
	Compute the intersection between two segments. More...

static void	segmentizeArc (const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &p3, QgsPointSequence &points, double tolerance=M_PI_2/90, QgsAbstractGeometry::SegmentationToleranceType toleranceType=QgsAbstractGeometry::MaximumAngle, bool hasZ=false, bool hasM=false)
	Convert circular arc defined by p1, p2, p3 (p1/p3 being start resp. More...

static bool	segmentMidPoint (const QgsPoint &p1, const QgsPoint &p2, QgsPoint &result, double radius, const QgsPoint &mousePos)
	Calculates midpoint on circle passing through p1 and p2, closest to the given coordinate mousePos. More...

static QgsPoint	segmentMidPointFromCenter (const QgsPoint &p1, const QgsPoint &p2, const QgsPoint &center, bool useShortestArc=true)
	Calculates the midpoint on the circle passing through p1 and p2, with the specified center coordinate. More...

static int	segmentSide (const QgsPoint &pt1, const QgsPoint &pt3, const QgsPoint &pt2)
	For line defined by points pt1 and pt3, find out on which side of the line is point pt3. More...

static QVector< SelfIntersection >	selfIntersections (const QgsAbstractGeometry *geom, int part, int ring, double tolerance)
	Find self intersections in a polyline. More...

static bool	setZValueFromPoints (const QgsPointSequence &points, QgsPoint &point)
	A Z dimension is added to point if one of the point in the list points is in 3D. More...

static double	skewLinesDistance (const QgsVector3D &P1, const QgsVector3D &P12, const QgsVector3D &P2, const QgsVector3D &P22)
	An algorithm to calculate the shortest distance between two skew lines. More...

static bool	skewLinesProjection (const QgsVector3D &P1, const QgsVector3D &P12, const QgsVector3D &P2, const QgsVector3D &P22, QgsVector3D &X1, double epsilon=0.0001)
	A method to project one skew line onto another. More...

static double	sqrDistance2D (const QgsPoint &pt1, const QgsPoint &pt2)
	Returns the squared 2D distance between two points. More...

static double	sqrDistToLine (double ptX, double ptY, double x1, double y1, double x2, double y2, double &minDistX, double &minDistY, double epsilon)
	Returns the squared distance between a point and a line. More...

static double	sweepAngle (double centerX, double centerY, double x1, double y1, double x2, double y2, double x3, double y3)
	Calculates angle of a circular string part defined by pt1, pt2, pt3. More...

static bool	tangentPointAndCircle (const QgsPointXY &center, double radius, const QgsPointXY &p, QgsPointXY &pt1, QgsPointXY &pt2)
	Calculates the tangent points between the circle with the specified center and radius and the point p. More...

static bool	verticesAtDistance (const QgsAbstractGeometry &geometry, double distance, QgsVertexId &previousVertex, QgsVertexId &nextVertex)
	Retrieves the vertices which are before and after the interpolated point at a specified distance along a linestring (or polygon boundary). More...

static QStringList	wktGetChildBlocks (const QString &wkt, const QString &defaultType=QString())
	Parses a WKT string and returns of list of blocks contained in the WKT. More...

static QPair< QgsWkbTypes::Type, QString >	wktReadBlock (const QString &wkt)
	Parses a WKT block of the format "TYPE( contents )" and returns a pair of geometry type to contents ("Pair(wkbType, "contents")") More...

Detailed Description

Contains various geometry utility functions.

Since: QGIS 2.10

Definition at line 36 of file qgsgeometryutils.h.

Member Enumeration Documentation

◆ ComponentType

enum QgsGeometryUtils::ComponentType

Note: not available in Python bindings

Enumerator
Vertex
Ring
Part

Definition at line 672 of file qgsgeometryutils.h.

Member Function Documentation

◆ angleBetweenThreePoints()

double QgsGeometryUtils::angleBetweenThreePoints	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

Calculates the angle between the lines AB and BC, where AB and BC described by points a, b and b, c.

Parameters

x1	x-coordinate of point a
y1	y-coordinate of point a
x2	x-coordinate of point b
y2	y-coordinate of point b
x3	x-coordinate of point c
y3	y-coordinate of point c

Returns: angle between lines in radians. Returned value is undefined if two or more points are equal.

Definition at line 1389 of file qgsgeometryutils.cpp.

◆ angleOnCircle()

bool QgsGeometryUtils::angleOnCircle	(	double	angle,
		double	angle1,
		double	angle2,
		double	angle3
	)

static

Returns true if an angle is between angle1 and angle3 on a circle described by angle1, angle2 and angle3.

Definition at line 743 of file qgsgeometryutils.cpp.

◆ averageAngle() [1/2]

double QgsGeometryUtils::averageAngle	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

Calculates the average angle (in radians) between the two linear segments from (x1, y1) to (x2, y2) and (x2, y2) to (x3, y3).

Definition at line 1403 of file qgsgeometryutils.cpp.

◆ averageAngle() [2/2]

double QgsGeometryUtils::averageAngle	(	double	a1,
		double	a2
	)

static

Averages two angles, correctly handling negative angles and ensuring the result is between 0 and 2 pi.

Parameters

a1	first angle (in radians)
a2	second angle (in radians)

Returns: average angle (in radians)

Definition at line 1411 of file qgsgeometryutils.cpp.

◆ ccwAngle()

double QgsGeometryUtils::ccwAngle	(	double	dy,
		double	dx
	)

static

Returns the counter clockwise angle between a line with components dx, dy and the line with dx > 0 and dy = 0.

Definition at line 653 of file qgsgeometryutils.cpp.

◆ circleAngleBetween()

bool QgsGeometryUtils::circleAngleBetween	(	double	angle,
		double	angle1,
		double	angle2,
		bool	clockwise
	)

static

Returns true if, in a circle, angle is between angle1 and angle2.

Definition at line 717 of file qgsgeometryutils.cpp.

◆ circleCenterRadius()

void QgsGeometryUtils::circleCenterRadius	(	const QgsPoint &	pt1,
		const QgsPoint &	pt2,
		const QgsPoint &	pt3,
		double &	radius,
		double &	centerX,
		double &	centerY
	)

static

Returns radius and center of the circle through pt1, pt2, pt3.

Definition at line 667 of file qgsgeometryutils.cpp.

◆ circleCircleInnerTangents()

int QgsGeometryUtils::circleCircleInnerTangents	(	const QgsPointXY &	center1,
		double	radius1,
		const QgsPointXY &	center2,
		double	radius2,
		QgsPointXY &	line1P1,
		QgsPointXY &	line1P2,
		QgsPointXY &	line2P1,
		QgsPointXY &	line2P2
	)

static

Calculates the inner tangent points for two circles, centered at center1 and center2 and with radii of radius1 and radius2 respectively.

The inner tangent points correspond to the points at which the two lines which are drawn so that they are tangential to both circles and are crossing each other.

The first tangent line is described by the points stored in line1P1 and line1P2, and the second line is described by the points stored in line2P1 and line2P2.

Returns the number of tangents (either 0 or 2).

Since: QGIS 3.6

Definition at line 493 of file qgsgeometryutils.cpp.

◆ circleCircleIntersections()

int QgsGeometryUtils::circleCircleIntersections	(	QgsPointXY	center1,
		double	radius1,
		QgsPointXY	center2,
		double	radius2,
		QgsPointXY &	intersection1,
		QgsPointXY &	intersection2
	)

static

Calculates the intersections points between the circle with center center1 and radius radius1 and the circle with center center2 and radius radius2.

If found, the intersection points will be stored in intersection1 and intersection2.

Returns: number of intersection points found.

Since: QGIS 3.2

Definition at line 369 of file qgsgeometryutils.cpp.

◆ circleCircleOuterTangents()

int QgsGeometryUtils::circleCircleOuterTangents	(	const QgsPointXY &	center1,
		double	radius1,
		const QgsPointXY &	center2,
		double	radius2,
		QgsPointXY &	line1P1,
		QgsPointXY &	line1P2,
		QgsPointXY &	line2P1,
		QgsPointXY &	line2P2
	)

static

Calculates the outer tangent points for two circles, centered at center1 and center2 and with radii of radius1 and radius2 respectively.

The outer tangent points correspond to the points at which the two lines which are drawn so that they are tangential to both circles touch the circles.

The first tangent line is described by the points stored in line1P1 and line1P2, and the second line is described by the points stored in line2P1 and line2P2.

Returns the number of tangents (either 0 or 2).

Since: QGIS 3.2

Definition at line 457 of file qgsgeometryutils.cpp.

◆ circleClockwise()

bool QgsGeometryUtils::circleClockwise	(	double	angle1,
		double	angle2,
		double	angle3
	)

static

Returns true if the circle defined by three angles is ordered clockwise.

The angles are defined counter-clockwise from the origin, i.e. using Euclidean angles as opposed to geographic "North up" angles.

Definition at line 705 of file qgsgeometryutils.cpp.

◆ circleLength()

double QgsGeometryUtils::circleLength	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

Length of a circular string segment defined by pt1, pt2, pt3.

Definition at line 749 of file qgsgeometryutils.cpp.

◆ circleTangentDirection()

double QgsGeometryUtils::circleTangentDirection	(	const QgsPoint &	tangentPoint,
		const QgsPoint &	cp1,
		const QgsPoint &	cp2,
		const QgsPoint &	cp3
	)

static

Calculates the direction angle of a circle tangent (clockwise from north in radians)

Definition at line 847 of file qgsgeometryutils.cpp.

◆ closestPoint()

QgsPoint QgsGeometryUtils::closestPoint	(	const QgsAbstractGeometry &	geometry,
		const QgsPoint &	point
	)

static

Returns the nearest point on a segment of a geometry for the specified point.

The z and m values will be linearly interpolated between the two neighbouring vertices.

Definition at line 97 of file qgsgeometryutils.cpp.

◆ closestSegmentFromComponents()

template<class T >

static double QgsGeometryUtils::closestSegmentFromComponents	(	T &	container,
		ComponentType	ctype,
		const QgsPoint &	pt,
		QgsPoint &	segmentPt,
		QgsVertexId &	vertexAfter,
		int *	leftOf,
		double	epsilon
	)

inlinestatic

Note: not available in Python bindings

Definition at line 680 of file qgsgeometryutils.h.

◆ closestVertex()

QgsPoint QgsGeometryUtils::closestVertex	(	const QgsAbstractGeometry &	geom,
		const QgsPoint &	pt,
		QgsVertexId &	id
	)

static

Returns the closest vertex to a geometry for a specified point.

On error null point will be returned and "id" argument will be invalid.

Definition at line 66 of file qgsgeometryutils.cpp.

◆ coefficients()

void QgsGeometryUtils::coefficients	(	const QgsPoint &	pt1,
		const QgsPoint &	pt2,
		double &	a,
		double &	b,
		double &	c
	)

static

Returns the coefficients (a, b, c for equation "ax + by + c = 0") of a line defined by points pt1 and pt2.

Parameters

pt1	first point.
pt2	second point.
a	Output parameter, a coefficient of the equation.
b	Output parameter, b coefficient of the equation.
c	Output parameter, c coefficient of the equation.

Since: QGIS 3.0

Definition at line 1321 of file qgsgeometryutils.cpp.

◆ distanceToVertex()

double QgsGeometryUtils::distanceToVertex	(	const QgsAbstractGeometry &	geom,
		QgsVertexId	id
	)

static

Returns the distance along a geometry from its first vertex to the specified vertex.

Parameters

geom	geometry
id	vertex id to find distance to

Returns: distance to vertex (following geometry)

Since: QGIS 2.16

Definition at line 130 of file qgsgeometryutils.cpp.

◆ extractLineStrings()

QVector< QgsLineString * > QgsGeometryUtils::extractLineStrings ( const QgsAbstractGeometry * geom )

static

Returns list of linestrings extracted from the passed geometry.

The returned objects have to be deleted by the caller.

Definition at line 30 of file qgsgeometryutils.cpp.

◆ gradient()

double QgsGeometryUtils::gradient	(	const QgsPoint &	pt1,
		const QgsPoint &	pt2
	)

static

Returns the gradient of a line defined by points pt1 and pt2.

Parameters

pt1	first point.
pt2	second point.

Returns: The gradient of this linear entity, or infinity if vertical

Since: QGIS 3.0

Definition at line 1309 of file qgsgeometryutils.cpp.

◆ interpolateArcValue()

double QgsGeometryUtils::interpolateArcValue	(	double	angle,
		double	a1,
		double	a2,
		double	a3,
		double	zm1,
		double	zm2,
		double	zm3
	)

static

Interpolate a value at given angle on circular arc given values (zm1, zm2, zm3) at three different angles (a1, a2, a3).

Since: 3.0

Definition at line 1009 of file qgsgeometryutils.cpp.

◆ interpolatePointOnArc()

QgsPoint QgsGeometryUtils::interpolatePointOnArc	(	const QgsPoint &	pt1,
		const QgsPoint &	pt2,
		const QgsPoint &	pt3,
		double	distance
	)

static

Interpolates a point on an arc defined by three points, pt1, pt2 and pt3.

The arc will be interpolated by the specified distance from pt1.

Any z or m values present in the points will also be linearly interpolated in the output.

Since: QGIS 3.4

Definition at line 628 of file qgsgeometryutils.cpp.

◆ interpolatePointOnLine() [1/2]

QgsPointXY QgsGeometryUtils::interpolatePointOnLine	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	fraction
	)

static

Interpolates the position of a point a fraction of the way along the line from (x1, y1) to (x2, y2).

Usually the fraction should be between 0 and 1, where 0 represents the point at the start of the line (x1, y1) and 1 represents the end of the line (x2, y2). However, it is possible to use a fraction < 0 or > 1, in which case the returned point is extrapolated from the supplied line.

See also: interpolatePointOnLineByValue()

Since: QGIS 3.0.2

Definition at line 1293 of file qgsgeometryutils.cpp.

◆ interpolatePointOnLine() [2/2]

QgsPoint QgsGeometryUtils::interpolatePointOnLine	(	const QgsPoint &	p1,
		const QgsPoint &	p2,
		double	fraction
	)

static

Interpolates the position of a point a fraction of the way along the line from p1 to p2.

Usually the fraction should be between 0 and 1, where 0 represents the point at the start of the line (p1) and 1 represents the end of the line (p2). However, it is possible to use a fraction < 0 or > 1, in which case the returned point is extrapolated from the supplied line.

Any Z or M values present in the input points will also be interpolated and present in the returned point.

See also: interpolatePointOnLineByValue()

Since: QGIS 3.0.2

Definition at line 1283 of file qgsgeometryutils.cpp.

◆ interpolatePointOnLineByValue()

QgsPointXY QgsGeometryUtils::interpolatePointOnLineByValue	(	double	x1,
		double	y1,
		double	v1,
		double	x2,
		double	y2,
		double	v2,
		double	value
	)

static

Interpolates the position of a point along the line from (x1, y1) to (x2, y2).

The position is interpolated using a supplied target value and the value at the start of the line (v1) and end of the line (v2). The returned point will be linearly interpolated to match position corresponding to the target value.

See also: interpolatePointOnLine()

Since: QGIS 3.0.2

Definition at line 1300 of file qgsgeometryutils.cpp.

◆ leftOfLine() [1/2]

int QgsGeometryUtils::leftOfLine	(	const double	x,
		const double	y,
		const double	x1,
		const double	y1,
		const double	x2,
		const double	y2
	)

static

Returns a value < 0 if the point (x, y) is left of the line from (x1, y1) -> ( x2, y2).

A positive return value indicates the point is to the right of the line.

If the return value is 0, then the test was unsuccessful (e.g. due to testing a point exactly on the line, or exactly in line with the segment) and the result is undefined.

Definition at line 583 of file qgsgeometryutils.cpp.

◆ leftOfLine() [2/2]

int QgsGeometryUtils::leftOfLine	(	const QgsPoint &	point,
		const QgsPoint &	p1,
		const QgsPoint &	p2
	)

static

Returns a value < 0 if the point point is left of the line from p1 -> p2.

A positive return value indicates the point is to the right of the line.

If the return value is 0, then the test was unsuccessful (e.g. due to testing a point exactly on the line, or exactly in line with the segment) and the result is undefined.

Since: QGIS 3.6

Definition at line 578 of file qgsgeometryutils.cpp.

◆ lineAngle()

double QgsGeometryUtils::lineAngle	(	double	x1,
		double	y1,
		double	x2,
		double	y2
	)

static

Calculates the direction of line joining two points in radians, clockwise from the north direction.

Parameters

x1	x-coordinate of line start
y1	y-coordinate of line start
x2	x-coordinate of line end
y2	y-coordinate of line end

Returns: angle in radians. Returned value is undefined if start and end point are the same.

Definition at line 1382 of file qgsgeometryutils.cpp.

◆ lineCircleIntersection()

bool QgsGeometryUtils::lineCircleIntersection	(	const QgsPointXY &	center,
		double	radius,
		const QgsPointXY &	linePoint1,
		const QgsPointXY &	linePoint2,
		QgsPointXY &	intersection
	)

static

Compute the intersection of a line and a circle.

If the intersection has two solutions (points), the closest point to the initial intersection point is returned.

Parameters

center	the center of the circle
radius	the radius of the circle
linePoint1	a first point on the line
linePoint2	a second point on the line
intersection	the initial point and the returned intersection point

Returns: true if an intersection has been found

Definition at line 317 of file qgsgeometryutils.cpp.

◆ lineIntersection()

bool QgsGeometryUtils::lineIntersection	(	const QgsPoint &	p1,
		QgsVector	v1,
		const QgsPoint &	p2,
		QgsVector	v2,
		QgsPoint &	intersection
	)

static

Computes the intersection between two lines.

Z dimension is supported and is retrieved from the first 3D point amongst p1 and p2.

Parameters

p1	Point on the first line
v1	Direction vector of the first line
p2	Point on the second line
v2	Direction vector of the second line
intersection	Output parameter, the intersection point

Returns: Whether the lines intersect

Definition at line 238 of file qgsgeometryutils.cpp.

◆ linePerpendicularAngle()

double QgsGeometryUtils::linePerpendicularAngle	(	double	x1,
		double	y1,
		double	x2,
		double	y2
	)

static

Calculates the perpendicular angle to a line joining two points.

Returned angle is in radians, clockwise from the north direction.

Parameters

x1	x-coordinate of line start
y1	y-coordinate of line start
x2	x-coordinate of line end
y2	y-coordinate of line end

Returns: angle in radians. Returned value is undefined if start and end point are the same.

Definition at line 1396 of file qgsgeometryutils.cpp.

◆ linesIntersection3D()

bool QgsGeometryUtils::linesIntersection3D	(	const QgsVector3D &	La1,
		const QgsVector3D &	La2,
		const QgsVector3D &	Lb1,
		const QgsVector3D &	Lb2,
		QgsVector3D &	intersection
	)

static

An algorithm to calculate an (approximate) intersection of two lines in 3D.

Parameters

La1	is the first point on the first line,
La2	is the second point on the first line,
Lb1	is the first point on the second line,
Lb2	is the second point on the second line,
intersection	is the result intersection, of it can be found.

Returns: true if the intersection can be found, false - otherwise. example:
QgsGeometryUtils.linesIntersection3D(QgsVector3D(0,0,0), QgsVector3D(5,0,0), QgsVector3D(2,1,0), QgsVector3D(2,3,0))
# (True, PyQt5.QtGui.QgsVector3D(2.0, 0.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(0,0,0), QgsVector3D(5,0,0), QgsVector3D(2,1,0), QgsVector3D(2,0,0))
# (True, PyQt5.QtGui.QgsVector3D(2.0, 0.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(0,0,0), QgsVector3D(5,0,0), QgsVector3D(0,1,0), QgsVector3D(0,3,0))
# (True, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(0,0,0), QgsVector3D(5,0,0), QgsVector3D(0,1,0), QgsVector3D(0,0,0))
# (True, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(0,0,0), QgsVector3D(5,0,0), QgsVector3D(5,1,0), QgsVector3D(5,3,0))
# (False, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(0,0,0), QgsVector3D(5,0,0), QgsVector3D(5,1,0), QgsVector3D(5,0,0))
# (False, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(1,1,0), QgsVector3D(2,2,0), QgsVector3D(3,1,0), QgsVector3D(3,2,0))
# (True, PyQt5.QtGui.QgsVector3D(3.0, 3.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(1,1,0), QgsVector3D(2,2,0), QgsVector3D(3,2,0), QgsVector3D(3,1,0))
# (True, PyQt5.QtGui.QgsVector3D(3.0, 3.0, 0.0))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(5,5,5), QgsVector3D(0,0,0), QgsVector3D(0,5,5), QgsVector3D(5,0,0))
# (True, PyQt5.QtGui.QgsVector3D(2.5, 2.5, 2.5))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(2.5,2.5,2.5), QgsVector3D(0,5,0), QgsVector3D(2.5,2.5,2.5), QgsVector3D(5,0,0))
# (True, PyQt5.QtGui.QgsVector3D(2.5, 2.5, 2.5))
QgsGeometryUtils.linesIntersection3D(QgsVector3D(2.5,2.5,2.5), QgsVector3D(5,0,0), QgsVector3D(0,5,5), QgsVector3D(5,5,5))
# (True, PyQt5.QtGui.QgsVector3D(0.0, 5.0, 5.0))

Definition at line 1492 of file qgsgeometryutils.cpp.

◆ midpoint()

QgsPoint QgsGeometryUtils::midpoint	(	const QgsPoint &	pt1,
		const QgsPoint &	pt2
	)

static

Returns a middle point between points pt1 and pt2.

Z value is computed if one of this point have Z. M value is computed if one of this point have M.

Parameters

pt1	first point.
pt2	second point.

Returns

New point at middle between points pt1 and pt2.

Example:
p = QgsPoint( 4, 6 ) # 2D point
pr = midpoint ( p, QgsPoint( 2, 2 ) )
# pr is a 2D point: 'Point (3 4)'
pr = midpoint ( p, QgsPoint( QgsWkbTypes.PointZ, 2, 2, 2 ) )
# pr is a 3D point: 'PointZ (3 4 1)'
pr = midpoint ( p, QgsPoint( QgsWkbTypes.PointM, 2, 2, 0, 2 ) )
# pr is a 3D point: 'PointM (3 4 1)'
pr = midpoint ( p, QgsPoint( QgsWkbTypes.PointZM, 2, 2, 2, 2 ) )
# pr is a 3D point: 'PointZM (3 4 1 1)'

Since: QGIS 3.0

Definition at line 1258 of file qgsgeometryutils.cpp.

◆ normalizedAngle()

double QgsGeometryUtils::normalizedAngle ( double angle )

static

Ensures that an angle is in the range 0 <= angle < 2 pi.

Parameters

angle angle in radians

Returns: equivalent angle within the range [0, 2 pi)

Definition at line 1197 of file qgsgeometryutils.cpp.

◆ perpendicularSegment()

QgsLineString QgsGeometryUtils::perpendicularSegment	(	const QgsPoint &	p,
		const QgsPoint &	s1,
		const QgsPoint &	s2
	)

static

Create a perpendicular line segment from p to segment [s1, s2].

Parameters

p	The point
s1	The segment start point
s2	The segment end point

Returns: A line (segment) from p to perpendicular point on segment [s1, s2]

Definition at line 1344 of file qgsgeometryutils.cpp.

◆ pointOnLineWithDistance() [1/2]

QgsPoint QgsGeometryUtils::pointOnLineWithDistance	(	const QgsPoint &	startPoint,
		const QgsPoint &	directionPoint,
		double	distance
	)

static

Returns a point a specified distance toward a second point.

Definition at line 594 of file qgsgeometryutils.cpp.

◆ pointOnLineWithDistance() [2/2]

void QgsGeometryUtils::pointOnLineWithDistance	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	distance,
		double &	x,
		double &	y,
		double *	z1 = `nullptr`,
		double *	z2 = `nullptr`,
		double *	z = `nullptr`,
		double *	m1 = `nullptr`,
		double *	m2 = `nullptr`,
		double *	m = `nullptr`
	)

static

Calculates the point a specified distance from (x1, y1) toward a second point (x2, y2).

Optionally, interpolated z and m values can be obtained by specifying the z1, z2 and z arguments and/or the m1, m2, m arguments.

Note: Not available in Python bindings

Since: QGIS 3.4

Definition at line 601 of file qgsgeometryutils.cpp.

◆ pointsFromWKT()

QgsPointSequence QgsGeometryUtils::pointsFromWKT	(	const QString &	wktCoordinateList,
		bool	is3D,
		bool	isMeasure
	)

static

Returns a list of points contained in a WKT string.

Note: not available in Python bindings

Definition at line 1029 of file qgsgeometryutils.cpp.

◆ pointsToGML2()

QDomElement QgsGeometryUtils::pointsToGML2	(	const QgsPointSequence &	points,
		QDomDocument &	doc,
		int	precision,
		const QString &	ns,
		QgsAbstractGeometry::AxisOrder	axisOrder = `QgsAbstractGeometry::AxisOrder::XY`
	)

static

Returns a gml::coordinates DOM element.

Note: not available in Python bindings

Definition at line 1133 of file qgsgeometryutils.cpp.

◆ pointsToGML3()

QDomElement QgsGeometryUtils::pointsToGML3	(	const QgsPointSequence &	points,
		QDomDocument &	doc,
		int	precision,
		const QString &	ns,
		bool	is3D,
		QgsAbstractGeometry::AxisOrder	axisOrder = `QgsAbstractGeometry::AxisOrder::XY`
	)

static

Returns a gml::posList DOM element.

Note: not available in Python bindings

Definition at line 1160 of file qgsgeometryutils.cpp.

◆ pointsToJSON()

QString QgsGeometryUtils::pointsToJSON	(	const QgsPointSequence &	points,
		int	precision
	)

static

Returns a geoJSON coordinates string.

Note: not available in Python bindings

Definition at line 1182 of file qgsgeometryutils.cpp.

◆ pointsToWKB()

void QgsGeometryUtils::pointsToWKB	(	QgsWkbPtr &	wkb,
		const QgsPointSequence &	points,
		bool	is3D,
		bool	isMeasure
	)

static

Returns a LinearRing { uint32 numPoints; Point points[numPoints]; }.

Note: not available in Python bindings

Definition at line 1097 of file qgsgeometryutils.cpp.

◆ pointsToWKT()

QString QgsGeometryUtils::pointsToWKT	(	const QgsPointSequence &	points,
		int	precision,
		bool	is3D,
		bool	isMeasure
	)

static

Returns a WKT coordinate list.

Note: not available in Python bindings

Definition at line 1114 of file qgsgeometryutils.cpp.

◆ projectPointOnSegment()

static QgsPoint QgsGeometryUtils::projectPointOnSegment	(	const QgsPoint &	p,
		const QgsPoint &	s1,
		const QgsPoint &	s2
	)

inlinestatic

Project the point on a segment.

Parameters

p	The point
s1	The segment start point
s2	The segment end point

Returns: The projection of the point on the segment

Definition at line 235 of file qgsgeometryutils.h.

◆ segmentIntersection()

bool QgsGeometryUtils::segmentIntersection	(	const QgsPoint &	p1,
		const QgsPoint &	p2,
		const QgsPoint &	q1,
		const QgsPoint &	q2,
		QgsPoint &	intersectionPoint,
		bool &	isIntersection,
		double	tolerance = `1e-8`,
		bool	acceptImproperIntersection = `false`
	)

static

Compute the intersection between two segments.

Parameters

p1	First segment start point
p2	First segment end point
q1	Second segment start point
q2	Second segment end point
intersectionPoint	Output parameter, the intersection point
isIntersection	Output parameter, return true if an intersection is found
tolerance	The tolerance to use
acceptImproperIntersection	By default, this method returns true only if segments have proper intersection. If set true, returns also true if segments have improper intersection (end of one segment on other segment ; continuous segments).

Returns

Whether the segments intersect

Example:
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 1 ), QgsPoint( 1, 1 ), QgsPoint( 1, 0 ) )
ret[0], ret[1].asWkt(), ret[2]
# Whether the segments intersect, the intersection point, is intersect
# (False, 'Point (0 0)', False)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 5 ), QgsPoint( 1, 5 ) )
ret[0], ret[1].asWkt(), ret[2]
# (False, 'Point (0 5)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 5 ), QgsPoint( 1, 5 ), acceptImproperIntersection=True )
ret[0], ret[1].asWkt(), ret[2]
# (True, 'Point (0 5)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 2 ), QgsPoint( 1, 5 ) )
ret[0], ret[1].asWkt(), ret[2]
# (False, 'Point (0 2)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 2 ), QgsPoint( 1, 5 ), acceptImproperIntersection=True )
ret[0], ret[1].asWkt(), ret[2]
# (True, 'Point (0 2)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, -5 ), QgsPoint( 0, 5 ), QgsPoint( 2, 0 ), QgsPoint( -1, 0 ) )
ret[0], ret[1].asWkt(), ret[2]
# (True, 'Point (0 0)', True)

Definition at line 257 of file qgsgeometryutils.cpp.

◆ segmentizeArc()

void QgsGeometryUtils::segmentizeArc	(	const QgsPoint &	p1,
		const QgsPoint &	p2,
		const QgsPoint &	p3,
		QgsPointSequence &	points,
		double	tolerance = `M_PI_2 / 90`,
		QgsAbstractGeometry::SegmentationToleranceType	toleranceType = `QgsAbstractGeometry::MaximumAngle`,
		bool	hasZ = `false`,
		bool	hasM = `false`
	)

static

Convert circular arc defined by p1, p2, p3 (p1/p3 being start resp.

end point, p2 lies on the arc) into a sequence of points.

Since: 3.0

Definition at line 871 of file qgsgeometryutils.cpp.

◆ segmentMidPoint()

bool QgsGeometryUtils::segmentMidPoint	(	const QgsPoint &	p1,
		const QgsPoint &	p2,
		QgsPoint &	result,
		double	radius,
		const QgsPoint &	mousePos
	)

static

Calculates midpoint on circle passing through p1 and p2, closest to the given coordinate mousePos.

Z dimension is supported and is retrieved from the first 3D point amongst p1 and p2.

See also: segmentMidPointFromCenter()

Definition at line 791 of file qgsgeometryutils.cpp.

◆ segmentMidPointFromCenter()

QgsPoint QgsGeometryUtils::segmentMidPointFromCenter	(	const QgsPoint &	p1,
		const QgsPoint &	p2,
		const QgsPoint &	center,
		bool	useShortestArc = `true`
	)

static

Calculates the midpoint on the circle passing through p1 and p2, with the specified center coordinate.

If useShortestArc is true, then the midpoint returned will be that corresponding to the shorter arc from p1 to p2. If it is false, the longer arc from p1 to p2 will be used (i.e. winding the other way around the circle).

See also: segmentMidPoint()

Since: QGIS 3.2

Definition at line 838 of file qgsgeometryutils.cpp.

◆ segmentSide()

int QgsGeometryUtils::segmentSide	(	const QgsPoint &	pt1,
		const QgsPoint &	pt3,
		const QgsPoint &	pt2
	)

static

For line defined by points pt1 and pt3, find out on which side of the line is point pt3.

Returns -1 if pt3 on the left side, 1 if pt3 is on the right side or 0 if pt3 lies on the line.

Since: 3.0

Definition at line 988 of file qgsgeometryutils.cpp.

◆ selfIntersections()

QVector< QgsGeometryUtils::SelfIntersection > QgsGeometryUtils::selfIntersections	(	const QgsAbstractGeometry *	geom,
		int	part,
		int	ring,
		double	tolerance
	)

static

Find self intersections in a polyline.

Parameters

geom	The geometry to check
part	The part of the geometry to check
ring	The ring of the geometry part to check
tolerance	The tolerance to use

Returns: The list of self intersections

Note: not available in Python bindings

Since: QGIS 2.12

Definition at line 538 of file qgsgeometryutils.cpp.

◆ setZValueFromPoints()

bool QgsGeometryUtils::setZValueFromPoints	(	const QgsPointSequence &	points,
		QgsPoint &	point
	)

static

A Z dimension is added to point if one of the point in the list points is in 3D.

Moreover, the Z value of point is updated with.

Parameters

points	List of points in which a 3D point is searched.
point	The point to update with Z dimension and value.

Returns: true if the point is updated, false otherwise

Since: QGIS 3.0

Definition at line 1561 of file qgsgeometryutils.cpp.

◆ skewLinesDistance()

double QgsGeometryUtils::skewLinesDistance	(	const QgsVector3D &	P1,
		const QgsVector3D &	P12,
		const QgsVector3D &	P2,
		const QgsVector3D &	P22
	)

static

An algorithm to calculate the shortest distance between two skew lines.

Parameters

P1	is the first point of the first line,
P12	is the second point on the first line,
P2	is the first point on the second line,
P22	is the second point on the second line.

Returns: the shortest distance

Definition at line 1438 of file qgsgeometryutils.cpp.

◆ skewLinesProjection()

bool QgsGeometryUtils::skewLinesProjection	(	const QgsVector3D &	P1,
		const QgsVector3D &	P12,
		const QgsVector3D &	P2,
		const QgsVector3D &	P22,
		QgsVector3D &	X1,
		double	epsilon = `0.0001`
	)

static

A method to project one skew line onto another.

Parameters

P1	is a first point that belonds to first skew line,
P12	is the second point that belongs to first skew line,
P2	is the first point that belongs to second skew line,
P22	is the second point that belongs to second skew line,
X1	is the result projection point of line P2P22 onto line P1P12,
epsilon	the tolerance to use.

Returns: true if such point exists, false - otherwise.

Definition at line 1450 of file qgsgeometryutils.cpp.

◆ sqrDistance2D()

double QgsGeometryUtils::sqrDistance2D	(	const QgsPoint &	pt1,
		const QgsPoint &	pt2
	)

static

Returns the squared 2D distance between two points.

Definition at line 194 of file qgsgeometryutils.cpp.

◆ sqrDistToLine()

double QgsGeometryUtils::sqrDistToLine	(	double	ptX,
		double	ptY,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double &	minDistX,
		double &	minDistY,
		double	epsilon
	)

static

Returns the squared distance between a point and a line.

Definition at line 199 of file qgsgeometryutils.cpp.

◆ sweepAngle()

double QgsGeometryUtils::sweepAngle	(	double	centerX,
		double	centerY,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3
	)

static

Calculates angle of a circular string part defined by pt1, pt2, pt3.

Definition at line 761 of file qgsgeometryutils.cpp.

◆ tangentPointAndCircle()

bool QgsGeometryUtils::tangentPointAndCircle	(	const QgsPointXY &	center,
		double	radius,
		const QgsPointXY &	p,
		QgsPointXY &	pt1,
		QgsPointXY &	pt2
	)

static

Calculates the tangent points between the circle with the specified center and radius and the point p.

If found, the tangent points will be stored in pt1 and pt2.

Since: QGIS 3.2

Definition at line 433 of file qgsgeometryutils.cpp.

◆ verticesAtDistance()

bool QgsGeometryUtils::verticesAtDistance	(	const QgsAbstractGeometry &	geometry,
		double	distance,
		QgsVertexId &	previousVertex,
		QgsVertexId &	nextVertex
	)

static

Retrieves the vertices which are before and after the interpolated point at a specified distance along a linestring (or polygon boundary).

Parameters

geometry	line or polygon geometry
distance	distance to traverse along geometry
previousVertex	will be set to previous vertex ID
nextVertex	will be set to next vertex ID

Returns: true if vertices were successfully retrieved

Note: if the distance coincides exactly with a vertex, then both previousVertex and nextVertex will be set to this vertex

Since: QGIS 3.0

Definition at line 149 of file qgsgeometryutils.cpp.

◆ wktGetChildBlocks()

QStringList QgsGeometryUtils::wktGetChildBlocks	(	const QString &	wkt,
		const QString &	defaultType = `QString()`
	)

static

Parses a WKT string and returns of list of blocks contained in the WKT.

Parameters

wkt	WKT string in the format "TYPE1 (contents1), TYPE2 (TYPE3 (contents3), TYPE4 (contents4))"
defaultType	default geometry type for children

Returns: list of WKT child block strings, e.g., List("TYPE1 (contents1)", "TYPE2 (TYPE3 (contents3), TYPE4 (contents4))")

Note: not available in Python bindings

Definition at line 1222 of file qgsgeometryutils.cpp.

◆ wktReadBlock()

QPair< QgsWkbTypes::Type, QString > QgsGeometryUtils::wktReadBlock ( const QString & wkt )

static

Parses a WKT block of the format "TYPE( contents )" and returns a pair of geometry type to contents ("Pair(wkbType, "contents")")

Note: not available in Python bindings

Definition at line 1211 of file qgsgeometryutils.cpp.

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

/tmp/buildd/qgis-3.6.0+99unstable/src/core/geometry/qgsgeometryutils.h
/tmp/buildd/qgis-3.6.0+99unstable/src/core/geometry/qgsgeometryutils.cpp

Classes

Public Types

Static Public Member Functions

Detailed Description

Member Enumeration Documentation

◆ ComponentType

Member Function Documentation

◆ angleBetweenThreePoints()

◆ angleOnCircle()

◆ averageAngle() [1/2]

◆ averageAngle() [2/2]

◆ ccwAngle()

◆ circleAngleBetween()

◆ circleCenterRadius()

◆ circleCircleInnerTangents()

◆ circleCircleIntersections()

◆ circleCircleOuterTangents()

◆ circleClockwise()

◆ circleLength()

◆ circleTangentDirection()

◆ closestPoint()

◆ closestSegmentFromComponents()

◆ closestVertex()

◆ coefficients()

◆ distanceToVertex()

◆ extractLineStrings()

◆ gradient()

◆ interpolateArcValue()

◆ interpolatePointOnArc()

◆ interpolatePointOnLine() [1/2]

◆ interpolatePointOnLine() [2/2]

◆ interpolatePointOnLineByValue()

◆ leftOfLine() [1/2]

◆ leftOfLine() [2/2]

◆ lineAngle()

◆ lineCircleIntersection()

◆ lineIntersection()

◆ linePerpendicularAngle()

◆ linesIntersection3D()

◆ midpoint()

◆ normalizedAngle()

◆ perpendicularSegment()

◆ pointOnLineWithDistance() [1/2]

◆ pointOnLineWithDistance() [2/2]

◆ pointsFromWKT()

◆ pointsToGML2()

◆ pointsToGML3()

◆ pointsToJSON()

◆ pointsToWKB()

◆ pointsToWKT()

◆ projectPointOnSegment()

◆ segmentIntersection()

◆ segmentizeArc()

◆ segmentMidPoint()

◆ segmentMidPointFromCenter()

◆ segmentSide()

◆ selfIntersections()

◆ setZValueFromPoints()

◆ skewLinesDistance()

◆ skewLinesProjection()

◆ sqrDistance2D()

◆ sqrDistToLine()

◆ sweepAngle()

◆ tangentPointAndCircle()

◆ verticesAtDistance()

◆ wktGetChildBlocks()

◆ wktReadBlock()