QGIS API Documentation  3.10.0-A Coruña (6c816b4204)
QgsGeometryUtils Class Reference

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 json pointsToJson (const QgsPointSequence &points, int precision)
Returns coordinates as json object. 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< SelfIntersectionselfIntersections (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 double triangleArea (double aX, double aY, double bX, double bY, double cX, double cY)
Returns the area of the triangle denoted by the points (aX, aY), (bX, bY) and (cX, cY). 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 void weightedPointInTriangle (double aX, double aY, double bX, double bY, double cX, double cY, double weightB, double weightC, double &pointX, double &pointY)
Returns a weighted point inside the triangle denoted by the points (aX, aY), (bX, bY) and (cX, cY). 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 37 of file qgsgeometryutils.h.

## ◆ ComponentType

Note
not available in Python bindings
Enumerator
Vertex
Ring
Part

Definition at line 707 of file qgsgeometryutils.h.

## ◆ 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 1429 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 746 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 1443 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
Returns

Definition at line 1451 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 656 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 720 of file qgsgeometryutils.cpp.

 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 670 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 496 of file qgsgeometryutils.cpp.

## ◆ circleCircleIntersections()

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

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 372 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 460 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 708 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 752 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 850 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 98 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 715 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 67 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 1361 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 131 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 31 of file qgsgeometryutils.cpp.

 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 1349 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 1016 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 631 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.

interpolatePointOnLineByValue()
Since
QGIS 3.0.2

Definition at line 1333 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.

interpolatePointOnLineByValue()
Since
QGIS 3.0.2

Definition at line 1323 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.

interpolatePointOnLine()
Since
QGIS 3.0.2

Definition at line 1340 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 586 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 581 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 1422 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 318 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 239 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 1436 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:
# (True, PyQt5.QtGui.QgsVector3D(2.0, 0.0, 0.0))
# (True, PyQt5.QtGui.QgsVector3D(2.0, 0.0, 0.0))
# (True, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
# (True, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
# (False, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
# (False, PyQt5.QtGui.QgsVector3D(0.0, 0.0, 0.0))
# (True, PyQt5.QtGui.QgsVector3D(3.0, 3.0, 0.0))
# (True, PyQt5.QtGui.QgsVector3D(3.0, 3.0, 0.0))
# (True, PyQt5.QtGui.QgsVector3D(2.5, 2.5, 2.5))
# (True, PyQt5.QtGui.QgsVector3D(2.5, 2.5, 2.5))
# (True, PyQt5.QtGui.QgsVector3D(0.0, 5.0, 5.0))

Definition at line 1532 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 1298 of file qgsgeometryutils.cpp.

## ◆ normalizedAngle()

 double QgsGeometryUtils::normalizedAngle ( double angle )
static

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

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

Definition at line 1222 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 1384 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 597 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 604 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 1036 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 1140 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 1167 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 1189 of file qgsgeometryutils.cpp.

## ◆ pointsToJson()

 json QgsGeometryUtils::pointsToJson ( const QgsPointSequence & points, int precision )
static

Returns coordinates as json object.

Note
not available in Python bindings

Definition at line 1205 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 1104 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 1121 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 236 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

Definition at line 258 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 874 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.

segmentMidPointFromCenter()

Definition at line 794 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).

segmentMidPoint()
Since
QGIS 3.2

Definition at line 841 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 995 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 541 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 1625 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 1478 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 1490 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 195 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 200 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 764 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 436 of file qgsgeometryutils.cpp.

## ◆ triangleArea()

 double QgsGeometryUtils::triangleArea ( double aX, double aY, double bX, double bY, double cX, double cY )
static

Returns the area of the triangle denoted by the points (aX, aY), (bX, bY) and (cX, cY).

Since
QGIS 3.10

Definition at line 1601 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 150 of file qgsgeometryutils.cpp.

## ◆ weightedPointInTriangle()

 void QgsGeometryUtils::weightedPointInTriangle ( double aX, double aY, double bX, double bY, double cX, double cY, double weightB, double weightC, double & pointX, double & pointY )
static

Returns a weighted point inside the triangle denoted by the points (aX, aY), (bX, bY) and (cX, cY).

Parameters
 aX x-coordinate of first vertex in triangle aY y-coordinate of first vertex in triangle bX x-coordinate of second vertex in triangle bY y-coordinate of second vertex in triangle cX x-coordinate of third vertex in triangle cY y-coordinate of third vertex in triangle weightB weighting factor along axis A-B (between 0 and 1) weightC weighting factor along axis A-C (between 0 and 1) pointX x-coordinate of generated point pointY y-coordinate of generated point
Since
QGIS 3.10

Definition at line 1606 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 1262 of file qgsgeometryutils.cpp.