QGIS API Documentation 3.39.0-Master (d0dedde5474)
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QgsGeometryUtilsBase Class Reference

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 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 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 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 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 30 of file qgsgeometryutils_base.h.

## ◆ 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 387 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 692 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 166 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
Returns

Definition at line 409 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 401 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 685 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 728 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 114 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 140 of file qgsgeometryutils_base.cpp.

 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 172 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 128 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 210 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:

1. Point is closest to top side of rectangle
2. Point is located on the top-right diagonal of rectangle, equally close to the top and right sides
3. Point is closest to right side of rectangle
4. Point is located on the bottom-right diagonal of rectangle, equally close to the bottom and right sides
5. Point is closest to bottom side of rectangle
6. Point is located on the bottom-left diagonal of rectangle, equally close to the bottom and left sides
7. Point is closest to left side of rectangle
8. 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 288 of file qgsgeometryutils_base.cpp.

## ◆ distance2D()

 static 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 58 of file qgsgeometryutils_base.h.

## ◆ distance3D()

 static 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 48 of file qgsgeometryutils_base.h.

## ◆ fuzzyDistanceEqual()

template<typename T , typename... Args>
 static 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.
fuzzyEqual
Since
QGIS 3.36

Definition at line 542 of file qgsgeometryutils_base.h.

## ◆ fuzzyEqual()

template<typename T , typename... Args>
 static 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.
fuzzyDistanceEqual
Since
QGIS 3.36

Definition at line 506 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 254 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 59 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 380 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 490 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 394 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

# (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))
static Q_DECL_DEPRECATED 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.
Class for storage of 3D vectors similar to QVector3D, with the difference that it uses double precisi...
Definition qgsvector3d.h:31

Definition at line 576 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
Returns
equivalent angle within the range [0, 2 pi)

Definition at line 273 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 365 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
# (6.0, 3.0)
# Offset point at center of segment by 2 units to the left
# (6.0, 7.0)
static Q_DECL_DEPRECATED 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,...
Since
QGIS 3.20

Definition at line 97 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 650 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 70 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 680 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 703 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 512 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 436 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 448 of file qgsgeometryutils_base.cpp.

## ◆ sqrDistance2D()

 static 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 53 of file qgsgeometryutils_base.h.

## ◆ sqrDistance3D()

 static 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 40 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 20 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 224 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 645 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 661 of file qgsgeometryutils_base.cpp.

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