# Class: QgsGeometryUtils¶

class qgis.core.QgsGeometryUtils

Bases: `sip.wrapper`

Contains various geometry utility functions.

New in version 2.10:

Methods

 `angleBetweenThreePoints` Calculates the angle between the lines AB and BC, where AB and BC described by points a, b and b, c. `angleBisector` Returns the point (`pointX`, `pointY`) forming the bisector from segment (`aX` `aY`) (`bX` `bY`) and segment (`bX`, `bY`) (`dX`, `dY`). `angleOnCircle` Returns `True` if an angle is between angle1 and angle3 on a circle described by angle1, angle2 and angle3. `averageAngle` Calculates the average angle (in radians) between the two linear segments from (`x1`, `y1`) to (`x2`, `y2`) and (`x2`, `y2`) to (`x3`, `y3`). `bisector` Returns the point (`pointX`, `pointY`) forming the bisector from point (`aX`, `aY`) to the segment (`bX`, `bY`) (`cX`, `cY`). `ccwAngle` Returns the counter clockwise angle between a line with components dx, dy and the line with dx > 0 and dy = 0 `circleAngleBetween` Returns `True` if, in a circle, angle is between angle1 and angle2 `circleCenterRadius` Returns radius and center of the circle through pt1, pt2, pt3 `circleCircleInnerTangents` Calculates the inner tangent points for two circles, centered at a center1 and `center2` and with radii of `radius1` and `radius2` respectively. `circleCircleIntersections` Calculates the intersections points between the circle with center `center1` and radius `radius1` and the circle with center `center2` and radius `radius2`. `circleCircleOuterTangents` Calculates the outer tangent points for two circles, centered at `center1` and `center2` and with radii of `radius1` and `radius2` respectively. `circleClockwise` Returns `True` if the circle defined by three angles is ordered clockwise. `circleLength` Length of a circular string segment defined by pt1, pt2, pt3 `circleTangentDirection` Calculates the direction angle of a circle tangent (clockwise from north in radians) `closestPoint` Returns the nearest point on a segment of a `geometry` for the specified `point`. `closestSideOfRectangle` 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. `closestVertex` Returns the closest vertex to a geometry for a specified point. `coefficients` Returns the coefficients (a, b, c for equation "ax + by + c = 0") of a line defined by points `pt1` and `pt2`. `distanceToVertex` Returns the distance along a geometry from its first vertex to the specified vertex. `extractLineStrings` Returns list of linestrings extracted from the passed geometry. `gradient` Returns the gradient of a line defined by points `pt1` and `pt2`. `interpolateArcValue` Interpolate a value at given angle on circular arc given values (zm1, zm2, zm3) at three different angles (a1, a2, a3). `interpolatePointOnArc` Interpolates a point on an arc defined by three points, `pt1`, `pt2` and `pt3`. `interpolatePointOnLine` Interpolates the position of a point a `fraction` of the way along the line from (`x1`, `y1`) to (`x2`, `y2`). `interpolatePointOnLineByValue` Interpolates the position of a point along the line from (`x1`, `y1`) to (`x2`, `y2`). `leftOfLine` Returns a value < 0 if the point (`x`, `y`) is left of the line from (`x1`, `y1`) -> (`x2`, `y2`). `lineAngle` Calculates the direction of line joining two points in radians, clockwise from the north direction. `lineCircleIntersection` Compute the intersection of a line and a circle. `lineIntersection` Computes the intersection between two lines. `linePerpendicularAngle` Calculates the perpendicular angle to a line joining two points. `linesIntersection3D` An algorithm to calculate an (approximate) intersection of two lines in 3D. `midpoint` Returns a middle point between points pt1 and pt2. `normalizedAngle` Ensures that an angle is in the range 0 <= angle < 2 pi. `perpendicularOffsetPointAlongSegment` 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. `perpendicularSegment` Create a perpendicular line segment from p to segment [s1, s2] `pointContinuesArc` Returns `True` if point `b` is on the arc formed by points `a1`, `a2`, and `a3`, but not within that arc portion already described by `a1`, `a2` and `a3`. `pointOnLineWithDistance` Returns a point a specified `distance` toward a second point. `projectPointOnSegment` Project the point on a segment `segmentIntersection` Compute the intersection between two segments `segmentMidPoint` Calculates midpoint on circle passing through `p1` and `p2`, closest to the given coordinate `mousePos`. `segmentMidPointFromCenter` Calculates the midpoint on the circle passing through `p1` and `p2`, with the specified `center` coordinate. `segmentSide` For line defined by points pt1 and pt3, find out on which side of the line is point pt3. `segmentizeArc` Convert circular arc defined by p1, p2, p3 (p1/p3 being start resp. `setZValueFromPoints` A Z dimension is added to `point` if one of the point in the list `points` is in 3D. `skewLinesDistance` An algorithm to calculate the shortest distance between two skew lines. `skewLinesProjection` A method to project one skew line onto another. `sqrDistToLine` Returns the squared distance between a point and a line. `sqrDistance2D` Returns the squared 2D distance between two points. `sweepAngle` Calculates angle of a circular string part defined by pt1, pt2, pt3 `tangentPointAndCircle` Calculates the tangent points between the circle with the specified `center` and `radius` and the point `p`. `transferFirstMValueToPoint` A M dimension is added to `point` if one of the points in the list `points` contains an M value. `transferFirstZOrMValueToPoint` A Z or M dimension is added to `point` if one of the points in the list `points` contains Z or M value. `transferFirstZValueToPoint` A Z dimension is added to `point` if one of the point in the list `points` is in 3D. `triangleArea` Returns the area of the triangle denoted by the points (`aX`, `aY`), (`bX`, `bY`) and (`cX`, `cY`). `verticesAtDistance` Retrieves the vertices which are before and after the interpolated point at a specified distance along a linestring (or polygon boundary). `weightedPointInTriangle` Returns a weighted point inside the triangle denoted by the points (`aX`, `aY`), (`bX`, `bY`) and (`cX`, `cY`).
angleBetweenThreePoints(x1: float, y1: float, x2: float, y2: float, x3: float, y3: float) float

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

Parameters:
• x1 (float) – x-coordinate of point a

• y1 (float) – y-coordinate of point a

• x2 (float) – x-coordinate of point b

• y2 (float) – y-coordinate of point b

• x3 (float) – x-coordinate of point c

• y3 (float) – y-coordinate of point c

Return type:

float

Returns:

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

angleBisector(aX: float, aY: float, bX: float, bY: float, cX: float, cY: float, dX: float, dY: float) Tuple[bool, float, float, float]

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 (float) – x-coordinate of first vertex of the segment ab

• aY (float) – y-coordinate of first vertex of the segment ab

• bX (float) – x-coordinate of second vertex of the segment ab

• bY (float) – y-coordinate of second vertex of the segment ab

• cX (float) – x-coordinate of first vertex of the segment cd

• cY (float) – y-coordinate of first vertex of the segment cd

• dX (float) – x-coordinate of second vertex of the segment cd

• dY (float) – y-coordinate of second vertex of the segment cd

Return type:

Tuple[bool, float, float, float]

Returns:

• `True` if the bisector exists (A B and C D are not collinear)

• pointX: x-coordinate of generated point

• pointY: y-coordinate of generated point

• angle: angle of the bisector from pointX, pointY origin on [ab-cd]

New in version 3.18.

angleOnCircle(angle: float, angle1: float, angle2: float, angle3: float) bool

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

Parameters:
• angle (float) –

• angle1 (float) –

• angle2 (float) –

• angle3 (float) –

Return type:

bool

averageAngle(x1: float, y1: float, x2: float, y2: float, x3: float, y3: float) float

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

averageAngle(a1: float, a2: float) -> float 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)

• x1 (float) –

• y1 (float) –

• x2 (float) –

• y2 (float) –

• x3 (float) –

• y3 (float) –

Return type:

float

Returns:

bisector(aX: float, aY: float, bX: float, bY: float, cX: float, cY: float) Tuple[bool, float, float]

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 (float) – x-coordinate of first vertex in triangle

• aY (float) – y-coordinate of first vertex in triangle

• bX (float) – x-coordinate of second vertex in triangle

• bY (float) – y-coordinate of second vertex in triangle

• cX (float) – x-coordinate of third vertex in triangle

• cY (float) – y-coordinate of third vertex in triangle

Return type:

Tuple[bool, float, float]

Returns:

• `True` if the bisector exists (A B and C are not collinear)

• pointX: x-coordinate of generated point

• pointY: y-coordinate of generated point

New in version 3.18.

ccwAngle(dy: float, dx: float) float

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

Parameters:
• dy (float) –

• dx (float) –

Return type:

float

circleAngleBetween(angle: float, angle1: float, angle2: float, clockwise: bool) bool

Returns `True` if, in a circle, angle is between angle1 and angle2

Parameters:
• angle (float) –

• angle1 (float) –

• angle2 (float) –

• clockwise (bool) –

Return type:

bool

circleCenterRadius(pt1: QgsPoint, pt2: QgsPoint, pt3: QgsPoint) Tuple[float, float, float]

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

Parameters:
Return type:

Tuple[float, float, float]

circleCircleInnerTangents(center1: QgsPointXY, radius1: float, center2: QgsPointXY, radius2: float) Tuple[int, QgsPointXY, QgsPointXY, QgsPointXY, QgsPointXY]

Calculates the inner tangent points for two circles, centered at a 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).

New in version 3.6.

Parameters:
Return type:

Tuple[int, `QgsPointXY`, `QgsPointXY`, `QgsPointXY`, QgsPointXY]

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

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

Return type:

Tuple[int, `QgsPointXY`, QgsPointXY]

Returns:

number of intersection points found.

New in version 3.2.

Parameters:
circleCircleOuterTangents(center1: QgsPointXY, radius1: float, center2: QgsPointXY, radius2: float) Tuple[int, QgsPointXY, QgsPointXY, QgsPointXY, QgsPointXY]

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).

New in version 3.2.

Parameters:
Return type:

Tuple[int, `QgsPointXY`, `QgsPointXY`, `QgsPointXY`, QgsPointXY]

circleClockwise(angle1: float, angle2: float, angle3: float) bool

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.

Parameters:
• angle1 (float) –

• angle2 (float) –

• angle3 (float) –

Return type:

bool

circleLength(x1: float, y1: float, x2: float, y2: float, x3: float, y3: float) float

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

Parameters:
• x1 (float) –

• y1 (float) –

• x2 (float) –

• y2 (float) –

• x3 (float) –

• y3 (float) –

Return type:

float

circleTangentDirection(tangentPoint: QgsPoint, cp1: QgsPoint, cp2: QgsPoint, cp3: QgsPoint) float

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

Parameters:
Return type:

float

closestPoint(geometry: QgsAbstractGeometry, point: QgsPoint)

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.

Parameters:
Return type:

QgsPoint

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

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.

New in version 3.20.

Parameters:
• right (float) –

• bottom (float) –

• left (float) –

• top (float) –

• x (float) –

• y (float) –

Return type:

int

closestVertex(geom: QgsAbstractGeometry, pt: QgsPoint) Tuple[QgsPoint, QgsVertexId]

Returns the closest vertex to a geometry for a specified point. On error null point will be returned and “id” argument will be invalid.

Parameters:
Return type:

Tuple[`QgsPoint`, QgsVertexId]

coefficients(pt1: QgsPoint, pt2: QgsPoint) Tuple[float, float, float]

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

Parameters:
Return type:

Tuple[float, float, float]

Returns:

• a: Output parameter, a coefficient of the equation.

• b: Output parameter, b coefficient of the equation.

• c: Output parameter, c coefficient of the equation.

New in version 3.0.

distanceToVertex(geom: QgsAbstractGeometry, id: QgsVertexId) float

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

Parameters:
Return type:

float

Returns:

distance to vertex (following geometry)

New in version 2.16.

extractLineStrings(geom: QgsAbstractGeometry) List[QgsLineString]

Returns list of linestrings extracted from the passed geometry. The returned objects have to be deleted by the caller.

Parameters:

geom (QgsAbstractGeometry) –

Return type:

List[QgsLineString]

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

Parameters:
Return type:

float

Returns:

The gradient of this linear entity, or infinity if vertical

New in version 3.0.

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

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

New in version 3.0.

Parameters:
• angle (float) –

• a1 (float) –

• a2 (float) –

• a3 (float) –

• zm1 (float) –

• zm2 (float) –

• zm3 (float) –

Return type:

float

interpolatePointOnArc(pt1: QgsPoint, pt2: QgsPoint, pt3: QgsPoint, distance: float)

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.

New in version 3.4.

Parameters:
Return type:

QgsPoint

interpolatePointOnLine(x1: float, y1: float, x2: float, y2: float, fraction: float)

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.

New in version 3.0.2.

interpolatePointOnLine(p1: `QgsPoint`, p2: `QgsPoint`, fraction: float) -> QgsPoint 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.

New in version 3.0.2.

Parameters:
• x1 (float) –

• y1 (float) –

• x2 (float) –

• y2 (float) –

• fraction (float) –

Return type:

QgsPointXY

interpolatePointOnLineByValue(x1: float, y1: float, v1: float, x2: float, y2: float, v2: float, value: float)

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`.

New in version 3.0.2.

Parameters:
• x1 (float) –

• y1 (float) –

• v1 (float) –

• x2 (float) –

• y2 (float) –

• v2 (float) –

• value (float) –

Return type:

QgsPointXY

leftOfLine(x: float, y: float, x1: float, y1: float, x2: float, y2: float) int

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.

leftOfLine(point: `QgsPoint`, p1: `QgsPoint`, p2: `QgsPoint`) -> int 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.

New in version 3.6.

Parameters:
• x (float) –

• y (float) –

• x1 (float) –

• y1 (float) –

• x2 (float) –

• y2 (float) –

Return type:

int

lineAngle(x1: float, y1: float, x2: float, y2: float) float

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

Parameters:
• x1 (float) – x-coordinate of line start

• y1 (float) – y-coordinate of line start

• x2 (float) – x-coordinate of line end

• y2 (float) – y-coordinate of line end

Return type:

float

Returns:

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

lineCircleIntersection(center: QgsPointXY, radius: float, linePoint1: QgsPointXY, linePoint2: QgsPointXY, intersection: QgsPointXY) Tuple[bool, QgsPointXY]

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 (QgsPointXY) – the center of the circle

• linePoint1 (QgsPointXY) – a first point on the line

• linePoint2 (QgsPointXY) – a second point on the line

• intersection (QgsPointXY) – the initial point and the returned intersection point

Return type:

Tuple[bool, QgsPointXY]

Returns:

`True` if an intersection has been found

lineIntersection(p1: QgsPoint, v1: QgsVector, p2: QgsPoint, v2: QgsVector) Tuple[bool, QgsPoint]

Computes the intersection between two lines. Z dimension is supported and is retrieved from the first 3D point amongst `p1` and `p2`.

Parameters:
• p1 (QgsPoint) – Point on the first line

• v1 (QgsVector) – Direction vector of the first line

• p2 (QgsPoint) – Point on the second line

• v2 (QgsVector) – Direction vector of the second line

Return type:

Tuple[bool, QgsPoint]

Returns:

• Whether the lines intersect

• intersection: Output parameter, the intersection point

linePerpendicularAngle(x1: float, y1: float, x2: float, y2: float) float

Calculates the perpendicular angle to a line joining two points. Returned angle is in radians, clockwise from the north direction.

Parameters:
• x1 (float) – x-coordinate of line start

• y1 (float) – y-coordinate of line start

• x2 (float) – x-coordinate of line end

• y2 (float) – y-coordinate of line end

Return type:

float

Returns:

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

linesIntersection3D(La1: QgsVector3D, La2: QgsVector3D, Lb1: QgsVector3D, Lb2: QgsVector3D) Tuple[bool, QgsVector3D]

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

Parameters:
• La1 (QgsVector3D) – is the first point on the first line,

• La2 (QgsVector3D) – is the second point on the first line,

• Lb1 (QgsVector3D) – is the first point on the second line,

• Lb2 (QgsVector3D) – is the second point on the second line,

Return type:

Tuple[bool, QgsVector3D]

Returns:

• `True` if the intersection can be found, `False` - otherwise.

• intersection: is the result intersection, of it can be found.

## 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))
```
midpoint(pt1: QgsPoint, pt2: QgsPoint)

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:
Return type:

QgsPoint

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)'
```

New in version 3.0.

normalizedAngle(angle: float) float

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

Parameters:

angle (float) – angle in radians

Return type:

float

Returns:

equivalent angle within the range [0, 2 pi)

perpendicularOffsetPointAlongSegment(x1: float, y1: float, x2: float, y2: float, proportion: float, offset: float) Tuple[float, float]

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 (float) – x-coordinate of start of segment

• y1 (float) – y-coordinate of start of segment

• x2 (float) – x-coordinate of end of segment

• y2 (float) – y-coordinate of end of segment

• proportion (float) – proportion of the segment’s length at which to place the point (between 0.0 and 1.0)

• offset (float) – 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.

## 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)
```
rtype:

Tuple[float, float]

return:
• x: calculated point x-coordinate

• y: calculated point y-coordinate

New in version 3.20.

perpendicularSegment(p: QgsPoint, s1: QgsPoint, s2: QgsPoint)

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

Parameters:
Return type:

QgsLineString

Returns:

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

pointContinuesArc(a1: QgsPoint, a2: QgsPoint, a3: QgsPoint, b: QgsPoint, distanceTolerance: float, pointSpacingAngleTolerance: float) bool

Returns `True` if point `b` is on the arc formed by points `a1`, `a2`, and `a3`, but not within that arc portion already described by `a1`, `a2` and `a3`.

The `distanceTolerance` specifies the maximum deviation allowed between the original location of point b and where it would fall on the candidate arc.

This method only consider a segments as continuing an arc if the points are all regularly spaced on the candidate arc. The `pointSpacingAngleTolerance` parameter specifies the maximum angular deviation (in radians) allowed when testing for regular point spacing.

Note

The API is considered EXPERIMENTAL and can be changed without a notice

New in version 3.14.

Parameters:
Return type:

bool

pointOnLineWithDistance(startPoint: QgsPoint, directionPoint: QgsPoint, distance: float)

Returns a point a specified `distance` toward a second point.

Parameters:
Return type:

QgsPoint

projectPointOnSegment(p: QgsPoint, s1: QgsPoint, s2: QgsPoint)

Project the point on a segment

Parameters:
Return type:

QgsPoint

Returns:

The projection of the point on the segment

segmentIntersection(p1: QgsPoint, p2: QgsPoint, q1: QgsPoint, q2: QgsPoint, tolerance: float = 1e-08, acceptImproperIntersection: bool = False) Tuple[bool, QgsPoint, bool]

Compute the intersection between two segments

Parameters:
• p1 (QgsPoint) – First segment start point

• p2 (QgsPoint) – First segment end point

• q1 (QgsPoint) – Second segment start point

• q2 (QgsPoint) – Second segment end point

• tolerance (float = 1e-08) – The tolerance to use

• acceptImproperIntersection (bool = False) – 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).

Return type:

Tuple[bool, `QgsPoint`, bool]

Returns:

• Whether the segments intersect

• intersectionPoint: Output parameter, the intersection point

• isIntersection: Output parameter, return `True` if an intersection is found

## Example¶

```ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 1 ), QgsPoint( 1, 1 ), QgsPoint( 1, 0 ) )
ret[0], ret[1].asWkt(), ret[2]
# Whether the segments intersect, the intersection point, is intersect
# (False, 'Point (0 0)', False)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 5 ), QgsPoint( 1, 5 ) )
ret[0], ret[1].asWkt(), ret[2]
# (False, 'Point (0 5)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 5 ), QgsPoint( 1, 5 ), acceptImproperIntersection=True )
ret[0], ret[1].asWkt(), ret[2]
# (True, 'Point (0 5)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 2 ), QgsPoint( 1, 5 ) )
ret[0], ret[1].asWkt(), ret[2]
# (False, 'Point (0 2)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, 0 ), QgsPoint( 0, 5 ), QgsPoint( 0, 2 ), QgsPoint( 1, 5 ), acceptImproperIntersection=True )
ret[0], ret[1].asWkt(), ret[2]
# (True, 'Point (0 2)', True)
ret = QgsGeometryUtils.segmentIntersection( QgsPoint( 0, -5 ), QgsPoint( 0, 5 ), QgsPoint( 2, 0 ), QgsPoint( -1, 0 ) )
ret[0], ret[1].asWkt(), ret[2]
# (True, 'Point (0 0)', True)
```
segmentMidPoint(p1: QgsPoint, p2: QgsPoint, radius: float, mousePos: QgsPoint) Tuple[bool, QgsPoint]

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`.

Parameters:
Return type:

Tuple[bool, QgsPoint]

segmentMidPointFromCenter(p1: QgsPoint, p2: QgsPoint, center: QgsPoint, useShortestArc: bool = True)

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).

New in version 3.2.

Parameters:
Return type:

QgsPoint

segmentSide(pt1: QgsPoint, pt3: QgsPoint, pt2: QgsPoint) int

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.

New in version 3.0.

Parameters:
Return type:

int

segmentizeArc(p1: QgsPoint, p2: QgsPoint, p3: QgsPoint, tolerance: float = M_PI_2 / 90, toleranceType: QgsAbstractGeometry.SegmentationToleranceType = QgsAbstractGeometry.MaximumAngle, hasZ: bool = False, hasM: bool = False) List[QgsPoint]

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.

New in version 3.0.

Parameters:
• p1 (QgsPoint) –

• p2 (QgsPoint) –

• p3 (QgsPoint) –

• tolerance (float = M_PI_2/90) –

• toleranceType (QgsAbstractGeometry.SegmentationToleranceType = QgsAbstractGeometry.MaximumAngle) –

• hasZ (bool = False) –

• hasM (bool = False) –

Return type:

List[QgsPoint]

setZValueFromPoints(points: Iterable[QgsPoint], point: QgsPoint) bool

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 the first Z value found in list `points` even if `point` already contains a Z value.

Parameters:
• points (Iterable[QgsPoint]) – List of points in which a 3D point is searched.

• point (QgsPoint) – The point to update with Z dimension and value.

Return type:

bool

Returns:

`True` if the point is updated, `False` otherwise

Warning

This method does not copy the z value of the coordinate from the points whose z value is closest to the original x/y point, but only the first one found.

New in version 3.0.

Deprecated since version QGIS: 3.20 use transferFirstZValueToPoint( const `QgsPointSequence` &points, `QgsPoint` &point ) instead

skewLinesDistance(P1: QgsVector3D, P12: QgsVector3D, P2: QgsVector3D, P22: QgsVector3D) float

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

Parameters:
• P1 (QgsVector3D) – is the first point of the first line,

• P12 (QgsVector3D) – is the second point on the first line,

• P2 (QgsVector3D) – is the first point on the second line,

• P22 (QgsVector3D) – is the second point on the second line.

Return type:

float

Returns:

the shortest distance

skewLinesProjection(P1: QgsVector3D, P12: QgsVector3D, P2: QgsVector3D, P22: QgsVector3D, epsilon: float = 0.0001) Tuple[bool, QgsVector3D]

A method to project one skew line onto another.

Parameters:
• P1 (QgsVector3D) – is a first point that belonds to first skew line,

• P12 (QgsVector3D) – is the second point that belongs to first skew line,

• P2 (QgsVector3D) – is the first point that belongs to second skew line,

• P22 (QgsVector3D) – is the second point that belongs to second skew line,

• X1 – is the result projection point of line P2P22 onto line P1P12,

• epsilon (float = 0.0001) – the tolerance to use.

Return type:

Tuple[bool, QgsVector3D]

Returns:

`True` if such point exists, `False` - otherwise.

sqrDistToLine(ptX: float, ptY: float, x1: float, y1: float, x2: float, y2: float, epsilon: float) Tuple[float, float, float]

Returns the squared distance between a point and a line.

Parameters:
• ptX (float) –

• ptY (float) –

• x1 (float) –

• y1 (float) –

• x2 (float) –

• y2 (float) –

• epsilon (float) –

Return type:

Tuple[float, float, float]

sqrDistance2D(pt1: QgsPoint, pt2: QgsPoint) float

Returns the squared 2D distance between two points.

Parameters:
Return type:

float

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

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

Parameters:
• centerX (float) –

• centerY (float) –

• x1 (float) –

• y1 (float) –

• x2 (float) –

• y2 (float) –

• x3 (float) –

• y3 (float) –

Return type:

float

tangentPointAndCircle(center: QgsPointXY, radius: float, p: QgsPointXY) Tuple[bool, QgsPointXY, QgsPointXY]

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`.

New in version 3.2.

Parameters:
Return type:

Tuple[bool, `QgsPointXY`, QgsPointXY]

transferFirstMValueToPoint(points: Iterable[QgsPoint], point: QgsPoint) bool

A M dimension is added to `point` if one of the points in the list `points` contains an M value. Moreover, the M value of `point` is updated with the first M value found in list `points` even if `point` already contains a M value.

Parameters:
• points (Iterable[QgsPoint]) – List of points in which a M point is searched.

• point (QgsPoint) – The point to update with M dimension and value.

Return type:

bool

Returns:

`True` if the point is updated, `False` otherwise

Warning

This method does not copy the m value of the coordinate from the points whose m value is closest to the original x/y point, but only the first one found.

New in version 3.20.

transferFirstZOrMValueToPoint(points: Iterable[QgsPoint], point: QgsPoint) bool

A Z or M dimension is added to `point` if one of the points in the list `points` contains Z or M value.

This method is equivalent to successively calling Z and M but avoiding looping twice over the set of points.

Parameters:
• points (Iterable[QgsPoint]) – List of points in which a M point is searched.

• point (QgsPoint) – The point to update with Z or M dimension and value.

Returns:

`True` if the point is updated, `False` otherwise

Warning

This method does not copy the z or m value of the coordinate from the points whose z or m value is closest to the original x/y point, but only the first one found.

New in version 3.20.

transferFirstZOrMValueToPoint(geom: `QgsGeometry`, point: `QgsPoint`) -> bool A Z or M dimension is added to `point` if one of the points in the list `points` contains Z or M value.

This method is equivalent to successively calling Z and M but avoiding looping twice over the set of points.

Parameters:
• geom – geometry in which a M point is searched.

• point – The point to update with Z or M dimension and value.

Return type:

bool

Returns:

`True` if the point is updated, `False` otherwise

Warning

This method does not copy the z or m value of the coordinate from the points whose z or m value is closest to the original x/y point, but only the first one found.

New in version 3.20.

transferFirstZValueToPoint(points: Iterable[QgsPoint], point: QgsPoint) bool

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 the first Z value found in list `points` even if `point` already contains a Z value.

Parameters:
• points (Iterable[QgsPoint]) – List of points in which a 3D point is searched.

• point (QgsPoint) – The point to update with Z dimension and value.

Return type:

bool

Returns:

`True` if the point is updated, `False` otherwise

Warning

This method does not copy the z value of the coordinate from the points whose z value is closest to the original x/y point, but only the first one found.

New in version 3.20.

triangleArea(aX: float, aY: float, bX: float, bY: float, cX: float, cY: float) float

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

New in version 3.10.

Parameters:
• aX (float) –

• aY (float) –

• bX (float) –

• bY (float) –

• cX (float) –

• cY (float) –

Return type:

float

verticesAtDistance(geometry: QgsAbstractGeometry, distance: float) Tuple[bool, QgsVertexId, QgsVertexId]

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

Parameters:
• geometry (QgsAbstractGeometry) – line or polygon geometry

• distance (float) – distance to traverse along geometry

• previousVertex – will be set to previous vertex ID

Return type:

Tuple[bool, `QgsVertexId`, QgsVertexId]

Returns:

• `True` if vertices were successfully retrieved

• nextVertex: will be set to next vertex ID

Note

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

New in version 3.0.

weightedPointInTriangle(aX: float, aY: float, bX: float, bY: float, cX: float, cY: float, weightB: float, weightC: float) Tuple[float, float]

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

Parameters:
• aX (float) – x-coordinate of first vertex in triangle

• aY (float) – y-coordinate of first vertex in triangle

• bX (float) – x-coordinate of second vertex in triangle

• bY (float) – y-coordinate of second vertex in triangle

• cX (float) – x-coordinate of third vertex in triangle

• cY (float) – y-coordinate of third vertex in triangle

• weightB (float) – weighting factor along axis A-B (between 0 and 1)

• weightC (float) – weighting factor along axis A-C (between 0 and 1)

Return type:

Tuple[float, float]

Returns:

• pointX: x-coordinate of generated point

• pointY: y-coordinate of generated point

New in version 3.10.