Convenience functions for geometry utils. More...

#include <qgsgeometryutils_base.h>

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.
static bool	angleBisector (double aX, double aY, double bX, double bY, double cX, double cY, double dX, double dY, double &pointX, double &pointY, double &angle)
	Returns the point (pointX, pointY) forming the bisector from segment (aX aY) (bX bY) and segment (bX, bY) (dX, dY).
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.
static double	averageAngle (double a1, double a2)
	Averages two angles, correctly handling negative angles and ensuring the result is between 0 and 2 pi.
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).
static double	azimuth (double x1, double y1, double x2, double y2)
	Calculates Cartesian azimuth between points (x1, y1) and (x2, y2) (clockwise in degree, starting from north).
static bool	bisector (double aX, double aY, double bX, double bY, double cX, double cY, double &pointX, double &pointY)
	Returns the point (pointX, pointY) forming the bisector from point (aX, aY) to the segment (bX, bY) (cX, cY).
static double	calculateArcLength (double centerX, double centerY, double radius, double x1, double y1, double x2, double y2, double x3, double y3, int fromVertex, int toVertex)
	Calculates the precise arc length between two vertices on a circular arc.
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.
static bool	circleAngleBetween (double angle, double angle1, double angle2, bool clockwise)
	Returns `true` if, in a circle, angle is between angle1 and angle2.
static void	circleCenterRadius (double x1, double y1, double x2, double y2, double x3, double y3, double &radius, double &centerX, double &centerY)
	Returns radius and center of the circle through (x1 y1), (x2 y2), (x3 y3).
static bool	circleClockwise (double angle1, double angle2, double angle3)
	Returns `true` if the circle defined by three angles is ordered clockwise.
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.
static int	closestSideOfRectangle (double right, double bottom, double left, double top, double x, double y)
	Returns a number representing the closest side of a rectangle defined by /a right, bottom, left, top to the point at (x, y), where the point may be in the interior of the rectangle or outside it.
static bool	createChamfer (const double segment1StartX, const double segment1StartY, const double segment1EndX, const double segment1EndY, const double segment2StartX, const double segment2StartY, const double segment2EndX, const double segment2EndY, const double distance1, const double distance2, double &chamferStartX, double &chamferStartY, double &chamferEndX, double &chamferEndY, double trim1StartX=nullptr, double trim1StartY=nullptr, double trim1EndX=nullptr, double trim1EndY=nullptr, double trim2StartX=nullptr, double trim2StartY=nullptr, double trim2EndX=nullptr, double trim2EndY=nullptr, const double epsilon=1e-8)
	Creates a chamfer (angled corner) between two line segments.
static bool	createFillet (const double segment1StartX, const double segment1StartY, const double segment1EndX, const double segment1EndY, const double segment2StartX, const double segment2StartY, const double segment2EndX, const double segment2EndY, const double radius, double filletPointsX, double filletPointsY, double trim1StartX=nullptr, double trim1StartY=nullptr, double trim1EndX=nullptr, double trim1EndY=nullptr, double trim2StartX=nullptr, double trim2StartY=nullptr, double trim2EndX=nullptr, double trim2EndY=nullptr, const double epsilon=1e-8)
	Creates a fillet (rounded corner) between two line segments.
static double	distance2D (double x1, double y1, double x2, double y2)
	Returns the 2D distance between (x1, y1) and (x2, y2).
static double	distance3D (double x1, double y1, double z1, double x2, double y2, double z2)
	Returns the 3D distance between (x1, y1, z1) and (x2, y2, z2).
template<typename T, typename... Args>
static bool	fuzzyDistanceEqual (T epsilon, const Args &... args) noexcept
	Compare equality between multiple pairs of values with a specified epsilon.
template<typename T, typename... Args>
static bool	fuzzyEqual (T epsilon, const Args &... args) noexcept
	Performs fuzzy comparison between pairs of values within a specified epsilon.
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).
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).
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.
static bool	lineIntersection (double p1x, double p1y, QgsVector v1, double p2x, double p2y, QgsVector v2, double &intersectionX, double &intersectionY)
	Computes the intersection between two lines.
static double	linePerpendicularAngle (double x1, double y1, double x2, double y2)
	Calculates the perpendicular angle to a line joining two points.
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.
static double	maxFilletRadius (const double segment1StartX, const double segment1StartY, const double segment1EndX, const double segment1EndY, const double segment2StartX, const double segment2StartY, const double segment2EndX, const double segment2EndY, double epsilon=1e-8)
	Calculates the maximum allowed fillet radius for the given segment configuration.
static double	normalizedAngle (double angle)
	Ensures that an angle is in the range 0 <= angle < 2 pi.
static void	perpendicularCenterSegment (double centerPointX, double centerPointY, double segmentPoint1x, double segmentPoint1y, double segmentPoint2x, double segmentPoint2y, double &perpendicularSegmentPoint1x, double &perpendicularSegmentPoint1y, double &perpendicularSegmentPoint2x, double &perpendicularSegmentPoint2y, double segmentLength=0)
	Create a perpendicular line segment to a given segment [segmentPoint1,segmentPoint2] with its center at centerPoint.
static void	perpendicularOffsetPointAlongSegment (double x1, double y1, double x2, double y2, double proportion, double offset, double x, double y)
	Calculates a point a certain proportion of the way along the segment from (x1, y1) to (x2, y2), offset from the segment by the specified offset amount.
static double	pointFractionAlongLine (double x1, double y1, double x2, double y2, double px, double py)
	Given the line (x1, y1) to (x2, y2) and a point (px, py) returns the fraction of the line length at which the point lies.
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).
static bool	points3DAreCollinear (double x1, double y1, double z1, double x2, double y2, double z2, double x3, double y3, double z3, double epsilon)
	Given the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) returns `true` if these points can be considered collinear with a specified tolerance epsilon.
static bool	pointsAreCollinear (double x1, double y1, double x2, double y2, double x3, double y3, double epsilon)
	Given the points (x1, y1), (x2, y2) and (x3, y3) returns `true` if these points can be considered collinear with a specified tolerance epsilon.
static void	project (double aX, double aY, double aZ, double distance, double azimuth, double inclination, double &resultX, double &resultY, double &resultZ)
	Returns coordinates of a point which corresponds to this point projected by a specified distance with specified angles (azimuth and inclination), using Cartesian mathematics.
static bool	segmentIntersection (double p1x, double p1y, double p2x, double p2y, double q1x, double q1y, double q2x, double q2y, double &intersectionPointX, double &intersectionPointY, bool &isIntersection, double tolerance=1e-8, bool acceptImproperIntersection=false)
	Compute the intersection between two segments.
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.
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.
static double	sqrDistance2D (double x1, double y1, double x2, double y2)
	Returns the squared 2D distance between (x1, y1) and (x2, y2).
static double	sqrDistance3D (double x1, double y1, double z1, double x2, double y2, double z2)
	Returns the squared 3D distance between (x1, y1, z1) and (x2, y2, z2).
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.
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.
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).
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).

Detailed Description

Convenience functions for geometry utils.

Since: QGIS 3.34

Definition at line 31 of file qgsgeometryutils_base.h.

Member Function Documentation

◆ angleBetweenThreePoints()

double QgsGeometryUtilsBase::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 457 of file qgsgeometryutils_base.cpp.

◆ angleBisector()

bool QgsGeometryUtilsBase::angleBisector	(	double	aX,
		double	aY,
		double	bX,
		double	bY,
		double	cX,
		double	cY,
		double	dX,
		double	dY,
		double &	pointX,
		double &	pointY,
		double &	angle )

static

Returns the point (pointX, pointY) forming the bisector from segment (aX aY) (bX bY) and segment (bX, bY) (dX, dY).

The bisector segment of AB-CD is (point, projection of point by angle)

Parameters

aX	x-coordinate of first vertex of the segment ab
aY	y-coordinate of first vertex of the segment ab
bX	x-coordinate of second vertex of the segment ab
bY	y-coordinate of second vertex of the segment ab
cX	x-coordinate of first vertex of the segment cd
cY	y-coordinate of first vertex of the segment cd
dX	x-coordinate of second vertex of the segment cd
dY	y-coordinate of second vertex of the segment cd
pointX	x-coordinate of generated point
pointY	y-coordinate of generated point
angle	angle of the bisector from pointX, pointY origin on [ab-cd]

Returns: true if the bisector exists (A B and C D are not collinear)

Since: QGIS 3.18

Definition at line 773 of file qgsgeometryutils_base.cpp.

◆ angleOnCircle()

bool QgsGeometryUtilsBase::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 168 of file qgsgeometryutils_base.cpp.

◆ averageAngle() [1/2]

double QgsGeometryUtilsBase::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 479 of file qgsgeometryutils_base.cpp.

◆ averageAngle() [2/2]

double QgsGeometryUtilsBase::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 471 of file qgsgeometryutils_base.cpp.

◆ azimuth()

double QgsGeometryUtilsBase::azimuth	(	double	x1,
		double	y1,
		double	x2,
		double	y2 )

static

Calculates Cartesian azimuth between points (x1, y1) and (x2, y2) (clockwise in degree, starting from north).

Parameters

x1	x-coordinate of the start point
y1	y-coordinate of the start point
x2	x-coordinate of the end point
y2	y-coordinate of the end point

Since: QGIS 3.34

Definition at line 766 of file qgsgeometryutils_base.cpp.

◆ bisector()

bool QgsGeometryUtilsBase::bisector	(	double	aX,
		double	aY,
		double	bX,
		double	bY,
		double	cX,
		double	cY,
		double &	pointX,
		double &	pointY )

static

Returns the point (pointX, pointY) forming the bisector from point (aX, aY) to the segment (bX, bY) (cX, cY).

The bisector segment of ABC is (A-point)

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
pointX	x-coordinate of generated point
pointY	y-coordinate of generated point

Returns: true if the bisector exists (A B and C are not collinear)

Since: QGIS 3.18

Definition at line 809 of file qgsgeometryutils_base.cpp.

◆ calculateArcLength()

double QgsGeometryUtilsBase::calculateArcLength	(	double	centerX,
		double	centerY,
		double	radius,
		double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3,
		int	fromVertex,
		int	toVertex )

static

Calculates the precise arc length between two vertices on a circular arc.

This method calculates the exact distance along the arc between any two vertices on a circle defined by three points. The arc follows the geometric path of the circle.

Parameters

centerX	X coordinate of the circle center
centerY	Y coordinate of the circle center
radius	radius of the circle
x1	X coordinate of the first point defining the arc
y1	Y coordinate of the first point defining the arc
x2	X coordinate of the second point defining the arc
y2	Y coordinate of the second point defining the arc
x3	X coordinate of the third point defining the arc
y3	Y coordinate of the third point defining the arc
fromVertex	vertex index to start from (0, 1, or 2)
toVertex	vertex index to end at (0, 1, or 2)

Returns: precise arc length between the vertices, or 0 if vertices are the same

Since: QGIS 4.00

Definition at line 226 of file qgsgeometryutils_base.cpp.

◆ ccwAngle()

double QgsGeometryUtilsBase::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 116 of file qgsgeometryutils_base.cpp.

◆ circleAngleBetween()

bool QgsGeometryUtilsBase::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 142 of file qgsgeometryutils_base.cpp.

◆ circleCenterRadius()

void QgsGeometryUtilsBase::circleCenterRadius	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3,
		double &	radius,
		double &	centerX,
		double &	centerY )

static

Returns radius and center of the circle through (x1 y1), (x2 y2), (x3 y3).

Definition at line 174 of file qgsgeometryutils_base.cpp.

◆ circleClockwise()

bool QgsGeometryUtilsBase::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 130 of file qgsgeometryutils_base.cpp.

◆ circleLength()

double QgsGeometryUtilsBase::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 212 of file qgsgeometryutils_base.cpp.

◆ closestSideOfRectangle()

int QgsGeometryUtilsBase::closestSideOfRectangle	(	double	right,
		double	bottom,
		double	left,
		double	top,
		double	x,
		double	y )

static

Returns a number representing the closest side of a rectangle defined by /a right, bottom, left, top to the point at (x, y), where the point may be in the interior of the rectangle or outside it.

The returned value may be:

Point is closest to top side of rectangle
Point is located on the top-right diagonal of rectangle, equally close to the top and right sides
Point is closest to right side of rectangle
Point is located on the bottom-right diagonal of rectangle, equally close to the bottom and right sides
Point is closest to bottom side of rectangle
Point is located on the bottom-left diagonal of rectangle, equally close to the bottom and left sides
Point is closest to left side of rectangle
Point is located on the top-left diagonal of rectangle, equally close to the top and left sides

Note: This method effectively partitions the space outside of the rectangle into Voronoi cells, so a point to the top left of the rectangle may be assigned to the left or top sides based on its position relative to the diagonal line extended from the rectangle's top-left corner.

Since: QGIS 3.20

Definition at line 358 of file qgsgeometryutils_base.cpp.

◆ createChamfer()

bool QgsGeometryUtilsBase::createChamfer	(	const double	segment1StartX,
		const double	segment1StartY,
		const double	segment1EndX,
		const double	segment1EndY,
		const double	segment2StartX,
		const double	segment2StartY,
		const double	segment2EndX,
		const double	segment2EndY,
		const double	distance1,
		const double	distance2,
		double &	chamferStartX,
		double &	chamferStartY,
		double &	chamferEndX,
		double &	chamferEndY,
		double *	trim1StartX = nullptr,
		double *	trim1StartY = nullptr,
		double *	trim1EndX = nullptr,
		double *	trim1EndY = nullptr,
		double *	trim2StartX = nullptr,
		double *	trim2StartY = nullptr,
		double *	trim2EndX = nullptr,
		double *	trim2EndY = nullptr,
		const double	epsilon = 1e-8 )

static

Creates a chamfer (angled corner) between two line segments.

This method generates a straight-line chamfer connecting two line segments at their intersection point. The chamfer distances can be specified independently for each segment, allowing for both symmetric and asymmetric chamfers.

Parameters

segment1StartX	x-coordinate of first segment start point
segment1StartY	y-coordinate of first segment start point
segment1EndX	x-coordinate of first segment end point
segment1EndY	y-coordinate of first segment end point
segment2StartX	x-coordinate of second segment start point
segment2StartY	y-coordinate of second segment start point
segment2EndX	x-coordinate of second segment end point
segment2EndY	y-coordinate of second segment end point
distance1	chamfer distance along first segment
distance2	chamfer distance along second segment (if < 0, uses distance1)
chamferStartX	output x-coordinate of chamfer start point
chamferStartY	output y-coordinate of chamfer start point
chamferEndX	output x-coordinate of chamfer end point
chamferEndY	output y-coordinate of chamfer end point
trim1StartX	optional output x-coordinate of trimmed first segment start
trim1StartY	optional output y-coordinate of trimmed first segment start
trim1EndX	optional output x-coordinate of trimmed first segment end
trim1EndY	optional output y-coordinate of trimmed first segment end
trim2StartX	optional output x-coordinate of trimmed second segment start
trim2StartY	optional output y-coordinate of trimmed second segment start
trim2EndX	optional output x-coordinate of trimmed second segment end
trim2EndY	optional output y-coordinate of trimmed second segment end
epsilon	tolerance for numerical comparisons and intersection detection

Returns: true if chamfer was successfully created

Note: Not available in Python bindings

Since: QGIS 4.0

Definition at line 1074 of file qgsgeometryutils_base.cpp.

◆ createFillet()

bool QgsGeometryUtilsBase::createFillet	(	const double	segment1StartX,
		const double	segment1StartY,
		const double	segment1EndX,
		const double	segment1EndY,
		const double	segment2StartX,
		const double	segment2StartY,
		const double	segment2EndX,
		const double	segment2EndY,
		const double	radius,
		double *	filletPointsX,
		double *	filletPointsY,
		double *	trim1StartX = nullptr,
		double *	trim1StartY = nullptr,
		double *	trim1EndX = nullptr,
		double *	trim1EndY = nullptr,
		double *	trim2StartX = nullptr,
		double *	trim2StartY = nullptr,
		double *	trim2EndX = nullptr,
		double *	trim2EndY = nullptr,
		const double	epsilon = 1e-8 )

static

Creates a fillet (rounded corner) between two line segments.

This method generates a circular arc connecting two line segments at their intersection point. The fillet returns exactly 3 points defining a CircularString: start point, middle point, and end point of the arc.

Parameters

segment1StartX	x-coordinate of first segment start point
segment1StartY	y-coordinate of first segment start point
segment1EndX	x-coordinate of first segment end point
segment1EndY	y-coordinate of first segment end point
segment2StartX	x-coordinate of second segment start point
segment2StartY	y-coordinate of second segment start point
segment2EndX	x-coordinate of second segment end point
segment2EndY	y-coordinate of second segment end point
radius	radius of the fillet arc
filletPointsX	output array of x-coordinates for 3 fillet points (start, middle, end)
filletPointsY	output array of y-coordinates for 3 fillet points (start, middle, end)
trim1StartX	optional output x-coordinate of trimmed first segment start
trim1StartY	optional output y-coordinate of trimmed first segment start
trim1EndX	optional output x-coordinate of trimmed first segment end
trim1EndY	optional output y-coordinate of trimmed first segment end
trim2StartX	optional output x-coordinate of trimmed second segment start
trim2StartY	optional output y-coordinate of trimmed second segment start
trim2EndX	optional output x-coordinate of trimmed second segment end
trim2EndY	optional output y-coordinate of trimmed second segment end
epsilon	tolerance for numerical comparisons and intersection detection

Returns: true if fillet was successfully created

Note: The caller must ensure that filletPointsX and filletPointsY arrays are large enough to hold exactly 3 points defining the CircularString arc.; Not available in Python bindings

Since: QGIS 4.0

Definition at line 906 of file qgsgeometryutils_base.cpp.

◆ distance2D()

double QgsGeometryUtilsBase::distance2D	(	double	x1,
		double	y1,
		double	x2,
		double	y2 )

inlinestatic

Returns the 2D distance between (x1, y1) and (x2, y2).

Definition at line 59 of file qgsgeometryutils_base.h.

◆ distance3D()

double QgsGeometryUtilsBase::distance3D	(	double	x1,
		double	y1,
		double	z1,
		double	x2,
		double	y2,
		double	z2 )

inlinestatic

Returns the 3D distance between (x1, y1, z1) and (x2, y2, z2).

Warning: No check is done if z contains NaN value. This is the caller's responsibility.

Since: QGIS 3.36

Definition at line 49 of file qgsgeometryutils_base.h.

◆ fuzzyDistanceEqual()

template<typename T, typename... Args>

bool QgsGeometryUtilsBase::fuzzyDistanceEqual	(	T	epsilon,
		const Args &...	args )

inlinestaticnoexcept

Compare equality between multiple pairs of values with a specified epsilon.

Traditionally, the comparison is done by examining the specific values (such as x and y) that define the location of points. It focuses on the numerical differences or relationships between these values. On the other hand, comparing distances between points considers the actual spatial separation or length between the points, regardless of their coordinate values. This comparison involves measuring the distance between two points using formulas like the distance formula. Here, it's the "distance comparison" (fuzzyDistanceEqual).

Template Parameters

T	Floating-point type (double or float) for the values to be compared.
Args	Type of arguments for the values to be compared.

Parameters

epsilon	The range within which the differences are checked.
args	Variadic list of values to be compared in pairs. The number of arguments must be greater than or equal to 4. It must follow the pattern: x1, y1, x2, y2, or x1, y1, z1, x2, y2, z2, ...

Returns: true if the squares of differences between pairs of values sum up to less than epsilon squared, false otherwise.

See also: fuzzyEqual

Since: QGIS 3.36

Definition at line 576 of file qgsgeometryutils_base.h.

◆ fuzzyEqual()

template<typename T, typename... Args>

bool QgsGeometryUtilsBase::fuzzyEqual	(	T	epsilon,
		const Args &...	args )

inlinestaticnoexcept

Performs fuzzy comparison between pairs of values within a specified epsilon.

This function compares a variable number of pairs of values to check if their differences fall within a specified epsilon range using qgsNumberNear. It returns true if all the differences are within the given epsilon range; otherwise, it returns false.

Template Parameters

T	Floating-point type (double or float) for the values to be compared.
Args	Type of arguments for the values to be compared.

Parameters

epsilon	The range within which the differences are checked.
args	Variadic list of values to be compared in pairs. The number of arguments must be greater than 0 and even. It must follow the pattern: x1, y1, x2, y2, or x1, y1, z1, x2, y2, z2, ...

Returns: true if all the differences between pairs of values are within epsilon, false otherwise.

See also: fuzzyDistanceEqual

Since: QGIS 3.36

Definition at line 540 of file qgsgeometryutils_base.h.

◆ interpolateArcValue()

double QgsGeometryUtilsBase::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).

Definition at line 324 of file qgsgeometryutils_base.cpp.

◆ leftOfLine()

int QgsGeometryUtilsBase::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 61 of file qgsgeometryutils_base.cpp.

◆ lineAngle()

double QgsGeometryUtilsBase::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 450 of file qgsgeometryutils_base.cpp.

◆ lineIntersection()

bool QgsGeometryUtilsBase::lineIntersection	(	double	p1x,
		double	p1y,
		QgsVector	v1,
		double	p2x,
		double	p2y,
		QgsVector	v2,
		double &	intersectionX,
		double &	intersectionY )

static

Computes the intersection between two lines.

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

Parameters

p1x	x-coordinate of point on the first line
p1y	y-coordinate of point on the first line
v1	Direction vector of the first line
p2x	x-coordinate of second point on the first line
p2y	y-coordinate of second point on the first line
v2	Direction vector of the second line
intersectionX	x-coordinate of the intersection point
intersectionY	y-coordinate of the intersection point

Returns: Whether the lines intersect

Definition at line 560 of file qgsgeometryutils_base.cpp.

◆ linePerpendicularAngle()

double QgsGeometryUtilsBase::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 464 of file qgsgeometryutils_base.cpp.

◆ linesIntersection3D()

bool QgsGeometryUtilsBase::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 646 of file qgsgeometryutils_base.cpp.

◆ maxFilletRadius()

double QgsGeometryUtilsBase::maxFilletRadius	(	const double	segment1StartX,
		const double	segment1StartY,
		const double	segment1EndX,
		const double	segment1EndY,
		const double	segment2StartX,
		const double	segment2StartY,
		const double	segment2EndX,
		const double	segment2EndY,
		double	epsilon = 1e-8 )

static

Calculates the maximum allowed fillet radius for the given segment configuration.

Parameters

segment1StartX	x-coordinate of first segment start point
segment1StartY	y-coordinate of first segment start point
segment1EndX	x-coordinate of first segment end point
segment1EndY	y-coordinate of first segment end point
segment2StartX	x-coordinate of second segment start point
segment2StartY	y-coordinate of second segment start point
segment2EndX	x-coordinate of second segment end point
segment2EndY	y-coordinate of second segment end point
epsilon	tolerance for intersection and angle calculations

Returns: Maximum fillet radius that can be applied, or -1.0 if no fillet is possible

Since: QGIS 4.0

Definition at line 823 of file qgsgeometryutils_base.cpp.

◆ normalizedAngle()

double QgsGeometryUtilsBase::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 343 of file qgsgeometryutils_base.cpp.

◆ perpendicularCenterSegment()

void QgsGeometryUtilsBase::perpendicularCenterSegment	(	double	centerPointX,
		double	centerPointY,
		double	segmentPoint1x,
		double	segmentPoint1y,
		double	segmentPoint2x,
		double	segmentPoint2y,
		double &	perpendicularSegmentPoint1x,
		double &	perpendicularSegmentPoint1y,
		double &	perpendicularSegmentPoint2x,
		double &	perpendicularSegmentPoint2y,
		double	segmentLength = 0 )

static

Create a perpendicular line segment to a given segment [segmentPoint1,segmentPoint2] with its center at centerPoint.

May be used to split geometries. Unless segmentLength is specified the new centered perpendicular line segment will have double the length of the input segment.

The result is a line (segment) centered in point p and perpendicular to segment [segmentPoint1, segmentPoint2].

Parameters

centerPointX	x-coordinate of the point where the center of the perpendicular should be located
centerPointY	y-coordinate of the point where the center of the perpendicular should be located
segmentPoint1x	x-coordinate of segmentPoint1, the segment's start point
segmentPoint1y	y-coordinate of segmentPoint1, the segment's start point
segmentPoint2x	x-coordinate of segmentPoint2, the segment's end point
segmentPoint2y	y-coordinate of segmentPoint2, the segment's end point
perpendicularSegmentPoint1x	x-coordinate of the perpendicularCenterSegment's start point
perpendicularSegmentPoint1y	y-coordinate of the perpendicularCenterSegment's start point
perpendicularSegmentPoint2x	x-coordinate of the perpendicularCenterSegment's end point
perpendicularSegmentPoint2y	y-coordinate of the perpendicularCenterSegment's end point
segmentLength	(optional) Trims to given length. A segmentLength value of 0 refers to the default length which is double the length of the input segment. Set to 1 for a normalized length.

Since: QGIS 3.24

Definition at line 435 of file qgsgeometryutils_base.cpp.

◆ perpendicularOffsetPointAlongSegment()

void QgsGeometryUtilsBase::perpendicularOffsetPointAlongSegment	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	proportion,
		double	offset,
		double *	x,
		double *	y )

static

Calculates a point a certain proportion of the way along the segment from (x1, y1) to (x2, y2), offset from the segment by the specified offset amount.

Parameters

x1	x-coordinate of start of segment
y1	y-coordinate of start of segment
x2	x-coordinate of end of segment
y2	y-coordinate of end of segment
proportion	proportion of the segment's length at which to place the point (between 0.0 and 1.0)
offset	perpendicular offset from segment to apply to point. A negative offset shifts the point to the left of the segment, while a positive offset will shift it to the right of the segment.
x	calculated point x-coordinate
y	calculated point y-coordinate

Example

# Offset point at center of segment by 2 units to the right
x, y = QgsGeometryUtils.perpendicularOffsetPointAlongSegment( 1, 5, 11, 5, 0.5, 2 )
# (6.0, 3.0)
 
# Offset point at center of segment by 2 units to the left
x, y = QgsGeometryUtils.perpendicularOffsetPointAlongSegment( 1, 5, 11, 5, 0.5, -2 )
# (6.0, 7.0)

Since: QGIS 3.20

Definition at line 99 of file qgsgeometryutils_base.cpp.

◆ pointFractionAlongLine()

double QgsGeometryUtilsBase::pointFractionAlongLine	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	px,
		double	py )

static

Given the line (x1, y1) to (x2, y2) and a point (px, py) returns the fraction of the line length at which the point lies.

Warning: this method requires that the point definitely lies on the line!

Since: QGIS 3.32

Definition at line 720 of file qgsgeometryutils_base.cpp.

◆ pointOnLineWithDistance()

void QgsGeometryUtilsBase::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 72 of file qgsgeometryutils_base.cpp.

◆ points3DAreCollinear()

bool QgsGeometryUtilsBase::points3DAreCollinear	(	double	x1,
		double	y1,
		double	z1,
		double	x2,
		double	y2,
		double	z2,
		double	x3,
		double	y3,
		double	z3,
		double	epsilon )

static

Given the points (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) returns true if these points can be considered collinear with a specified tolerance epsilon.

Since: QGIS 4.0

Definition at line 755 of file qgsgeometryutils_base.cpp.

◆ pointsAreCollinear()

bool QgsGeometryUtilsBase::pointsAreCollinear	(	double	x1,
		double	y1,
		double	x2,
		double	y2,
		double	x3,
		double	y3,
		double	epsilon )

static

Given the points (x1, y1), (x2, y2) and (x3, y3) returns true if these points can be considered collinear with a specified tolerance epsilon.

Since: QGIS 3.32

Definition at line 750 of file qgsgeometryutils_base.cpp.

◆ project()

void QgsGeometryUtilsBase::project	(	double	aX,
		double	aY,
		double	aZ,
		double	distance,
		double	azimuth,
		double	inclination,
		double &	resultX,
		double &	resultY,
		double &	resultZ )

static

Returns coordinates of a point which corresponds to this point projected by a specified distance with specified angles (azimuth and inclination), using Cartesian mathematics.

M value is preserved. resultX, resultY, resultZ are coordinates of the point projected. If a 2D point is projected a 3D point will be returned except if inclination is 90. A 3D point is always returned if a 3D point is projected.

Parameters

aX	x-coordinate of the point to project
aY	y-coordinate of the point to project
aZ	z-coordinate of the point to project
distance	distance to project
azimuth	angle to project in X Y, clockwise in degrees starting from north
inclination	angle to project in Z (3D). If the point is 2D, the Z value is assumed to be 0.
resultX	Output parameter, x-coordinates of the point projected.
resultY	Output parameter, y-coordinates of the point projected.
resultZ	Output parameter, z-coordinates of the point projected.

Since: QGIS 3.34

Definition at line 784 of file qgsgeometryutils_base.cpp.

◆ segmentIntersection()

bool QgsGeometryUtilsBase::segmentIntersection	(	double	p1x,
		double	p1y,
		double	p2x,
		double	p2y,
		double	q1x,
		double	q1y,
		double	q2x,
		double	q2y,
		double &	intersectionPointX,
		double &	intersectionPointY,
		bool &	isIntersection,
		double	tolerance = 1e-8,
		bool	acceptImproperIntersection = false )

static

Compute the intersection between two segments.

Parameters

p1x	x-coordinate of the first segment start point
p1y	y-coordinate of the first segment start point
p2x	x-coordinate of the first segment end point
p2y	y-coordinate of the first segment end point
q1x	x-coordinate of the second segment start point
q1y	y-coordinate of the second segment start point
q2x	x-coordinate of the second segment end point
q2y	y-coordinate of the second segment end point
intersectionPointX	Output parameter, x-coordinate of the intersection point
intersectionPointY	Output parameter, y-coordinate of 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 582 of file qgsgeometryutils_base.cpp.

◆ skewLinesDistance()

double QgsGeometryUtilsBase::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 506 of file qgsgeometryutils_base.cpp.

◆ skewLinesProjection()

bool QgsGeometryUtilsBase::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 518 of file qgsgeometryutils_base.cpp.

◆ sqrDistance2D()

double QgsGeometryUtilsBase::sqrDistance2D	(	double	x1,
		double	y1,
		double	x2,
		double	y2 )

inlinestatic

Returns the squared 2D distance between (x1, y1) and (x2, y2).

Definition at line 54 of file qgsgeometryutils_base.h.

◆ sqrDistance3D()

double QgsGeometryUtilsBase::sqrDistance3D	(	double	x1,
		double	y1,
		double	z1,
		double	x2,
		double	y2,
		double	z2 )

inlinestatic

Returns the squared 3D distance between (x1, y1, z1) and (x2, y2, z2).

Warning: No check is done if z contains NaN value. This is the caller's responsibility.

Since: QGIS 3.36

Definition at line 41 of file qgsgeometryutils_base.h.

◆ sqrDistToLine()

double QgsGeometryUtilsBase::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 22 of file qgsgeometryutils_base.cpp.

◆ sweepAngle()

double QgsGeometryUtilsBase::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 294 of file qgsgeometryutils_base.cpp.

◆ triangleArea()

double QgsGeometryUtilsBase::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 715 of file qgsgeometryutils_base.cpp.

◆ weightedPointInTriangle()

void QgsGeometryUtilsBase::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 731 of file qgsgeometryutils_base.cpp.

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

/build/qgis-3.99.0+git20251210+2fe06baccd8+99sid/src/core/geometry/qgsgeometryutils_base.h
/build/qgis-3.99.0+git20251210+2fe06baccd8+99sid/src/core/geometry/qgsgeometryutils_base.cpp

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ angleBetweenThreePoints()

◆ angleBisector()

◆ angleOnCircle()

◆ averageAngle() [1/2]

◆ averageAngle() [2/2]

◆ azimuth()

◆ bisector()

◆ calculateArcLength()

◆ ccwAngle()

◆ circleAngleBetween()

◆ circleCenterRadius()

◆ circleClockwise()

◆ circleLength()

◆ closestSideOfRectangle()

◆ createChamfer()

◆ createFillet()

◆ distance2D()

◆ distance3D()

◆ fuzzyDistanceEqual()

◆ fuzzyEqual()

◆ interpolateArcValue()

◆ leftOfLine()

◆ lineAngle()

◆ lineIntersection()

◆ linePerpendicularAngle()

◆ linesIntersection3D()

Example

◆ maxFilletRadius()

◆ normalizedAngle()

◆ perpendicularCenterSegment()

◆ perpendicularOffsetPointAlongSegment()

Example

◆ pointFractionAlongLine()

◆ pointOnLineWithDistance()

◆ points3DAreCollinear()

◆ pointsAreCollinear()

◆ project()

◆ segmentIntersection()

◆ skewLinesDistance()

◆ skewLinesProjection()

◆ sqrDistance2D()

◆ sqrDistance3D()

◆ sqrDistToLine()

◆ sweepAngle()

◆ triangleArea()

◆ weightedPointInTriangle()