Functions
double ANALYSIS_EXPORT	angle (QgsPoint p1, QgsPoint p2, QgsPoint p3, QgsPoint p4)
	Calculates the angle between two segments (in 2 dimension, z-values are ignored).
bool ANALYSIS_EXPORT	BarycentricToXY (double u, double v, double w, QgsPoint p1, QgsPoint p2, QgsPoint p3, QgsPoint result)
bool ANALYSIS_EXPORT	calcBarycentricCoordinates (double x, double y, QgsPoint p1, QgsPoint p2, QgsPoint p3, QgsPoint result)
	Calculates the barycentric coordinates of a point (x,y) with respect to p1, p2, p3 and stores the three barycentric coordinates in 'result'. Thus the u-coordinate is stored in result::x, the v-coordinate in result::y and the w-coordinate in result::z. Attention: p1, p2 and p3 have to be ordered counterclockwise.
double ANALYSIS_EXPORT	calcBernsteinPoly (int n, int i, double t)
	Calculates the value of a Bernstein polynomial.
double ANALYSIS_EXPORT	calcCubicHermitePoly (int n, int i, double t)
	Calculates the value of a cubic Hermite polynomial.
double ANALYSIS_EXPORT	cFDerBernsteinPoly (int n, int i, double t)
	Calculates the first derivative of a Bernstein polynomial with respect to the parameter t.
double ANALYSIS_EXPORT	cFDerCubicHermitePoly (int n, int i, double t)
	Calculates the first derivative of a cubic Hermite polynomial with respect to the parameter t.
bool ANALYSIS_EXPORT	circumcenter (QgsPoint p1, QgsPoint p2, QgsPoint p3, QgsPoint result)
	Calculates the center of the circle passing through p1, p2 and p3. Returns `true` in case of success and `false` otherwise (e.g. all three points on a line).
double ANALYSIS_EXPORT	crossVec (QgsPoint first, Vector3D vec1, QgsPoint second, Vector3D vec2)
	Calculates the intersection of the two vectors vec1 and vec2, which start at first(vec1) and second(vec2) end. The return value is t2(multiplication of v2 with t2 and adding to 'second' results the intersection point).
bool ANALYSIS_EXPORT	derVec (const Vector3D v1, const Vector3D v2, Vector3D *result, double x, double y)
	Calculates the z-component of a vector with coordinates 'x' and 'y'which is in the same tangent plane as the tangent vectors 'v1' and 'v2'. The result is assigned to 'result'.
double ANALYSIS_EXPORT	distPointFromLine (QgsPoint thepoint, QgsPoint p1, QgsPoint *p2)
	Calculates the (2 dimensional) distance from 'thepoint' to the line defined by p1 and p2.
int ANALYSIS_EXPORT	faculty (int n)
	Faculty function.
bool ANALYSIS_EXPORT	inCircle (QgsPoint testp, QgsPoint p1, QgsPoint p2, QgsPoint p3)
	Tests, whether 'testp' is inside the circle through 'p1', 'p2' and 'p3'.
bool ANALYSIS_EXPORT	inDiametral (QgsPoint p1, QgsPoint p2, QgsPoint *point)
	Tests, whether 'point' is inside the diametral circle through 'p1' and 'p2'.
double ANALYSIS_EXPORT	leftOf (const QgsPoint &thepoint, const QgsPoint p1, const QgsPoint p2)
	Returns whether 'thepoint' is left or right of the line from 'p1' to 'p2'. Negative values mean left and positive values right. There may be numerical instabilities, so a threshold may be useful.
bool ANALYSIS_EXPORT	lineIntersection (QgsPoint p1, QgsPoint p2, QgsPoint p3, QgsPoint p4)
	Returns `true`, if line1 (p1 to p2) and line2 (p3 to p4) intersect. If the lines have an endpoint in common, `false` is returned.
bool ANALYSIS_EXPORT	lineIntersection (QgsPoint p1, QgsPoint p2, QgsPoint p3, QgsPoint p4, QgsPoint *intersection_point)
	Returns `true`, if line1 (p1 to p2) and line2 (p3 to p4) intersect. If the lines have an endpoint in common, `false` is returned. The intersecting point is stored in 'intersection_point.
int ANALYSIS_EXPORT	lower (int n, int i)
	Lower function.
void ANALYSIS_EXPORT	normalFromPoints (QgsPoint p1, QgsPoint p2, QgsPoint p3, Vector3D vec)
	Calculates the normal vector of the plane through the points p1, p2 and p3 and assigns the result to vec. If the points are ordered counterclockwise, the normal will have a positive z-coordinate;.
bool ANALYSIS_EXPORT	normalLeft (Vector3D v1, Vector3D result, double length)
	Assigns the vector 'result', which is normal to the vector 'v1', on the left side of v1 and has length 'length'. This method works only with two dimensions.
bool ANALYSIS_EXPORT	normalMinDistance (Vector3D tangent, Vector3D target, Vector3D *result)
	Calculates a Vector orthogonal to 'tangent' with length 1 and closest possible to result. Returns `true` in case of success and `false` otherwise.
bool ANALYSIS_EXPORT	normalRight (Vector3D v1, Vector3D result, double length)
	Assigns the vector 'result', which is normal to the vector 'v1', on the right side of v1 and has length 'length'. The calculation is only in two dimensions.
double ANALYSIS_EXPORT	planeTest (QgsPoint test, QgsPoint pt1, QgsPoint pt2, QgsPoint pt3)
	Tests, if 'test' is in the same plane as 'p1', 'p2' and 'p3' and returns the z-difference from the plane to 'test.
bool ANALYSIS_EXPORT	pointInsideTriangle (double x, double y, QgsPoint p1, QgsPoint p2, QgsPoint *p3)
	Returns `true`, if the point with coordinates x and y is inside (or at the edge) of the triangle p1,p2,p3 and `false`, if it is outside. p1, p2 and p3 have to be ordered counterclockwise.
double ANALYSIS_EXPORT	triArea (QgsPoint pa, QgsPoint pb, QgsPoint *pc)
	Returns the area of a triangle. If the points are ordered counterclockwise, the value will be positive. If they are ordered clockwise, the value will be negative.

Function Documentation

◆ angle()

double MathUtils::angle	(	QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		QgsPoint *	p4 )

Calculates the angle between two segments (in 2 dimension, z-values are ignored).

Definition at line 747 of file MathUtils.cpp.

◆ BarycentricToXY()

bool MathUtils::BarycentricToXY	(	double	u,
		double	v,
		double	w,
		QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		QgsPoint *	result )

Definition at line 56 of file MathUtils.cpp.

◆ calcBarycentricCoordinates()

bool MathUtils::calcBarycentricCoordinates	(	double	x,
		double	y,
		QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		QgsPoint *	result )

Calculates the barycentric coordinates of a point (x,y) with respect to p1, p2, p3 and stores the three barycentric coordinates in 'result'. Thus the u-coordinate is stored in result::x, the v-coordinate in result::y and the w-coordinate in result::z. Attention: p1, p2 and p3 have to be ordered counterclockwise.

Definition at line 28 of file MathUtils.cpp.

◆ calcBernsteinPoly()

double MathUtils::calcBernsteinPoly	(	int	n,
		int	i,
		double	t )

Calculates the value of a Bernstein polynomial.

Definition at line 121 of file MathUtils.cpp.

◆ calcCubicHermitePoly()

double MathUtils::calcCubicHermitePoly	(	int	n,
		int	i,
		double	t )

Calculates the value of a cubic Hermite polynomial.

Definition at line 390 of file MathUtils.cpp.

◆ cFDerBernsteinPoly()

double MathUtils::cFDerBernsteinPoly	(	int	n,
		int	i,
		double	t )

Calculates the first derivative of a Bernstein polynomial with respect to the parameter t.

Definition at line 131 of file MathUtils.cpp.

◆ cFDerCubicHermitePoly()

double MathUtils::cFDerCubicHermitePoly	(	int	n,
		int	i,
		double	t )

Calculates the first derivative of a cubic Hermite polynomial with respect to the parameter t.

Definition at line 423 of file MathUtils.cpp.

◆ circumcenter()

bool MathUtils::circumcenter	(	QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		QgsPoint *	result )

Calculates the center of the circle passing through p1, p2 and p3. Returns true in case of success and false otherwise (e.g. all three points on a line).

Definition at line 136 of file MathUtils.cpp.

◆ crossVec()

double MathUtils::crossVec	(	QgsPoint *	first,
		Vector3D *	vec1,
		QgsPoint *	second,
		Vector3D *	vec2 )

Calculates the intersection of the two vectors vec1 and vec2, which start at first(vec1) and second(vec2) end. The return value is t2(multiplication of v2 with t2 and adding to 'second' results the intersection point).

Definition at line 604 of file MathUtils.cpp.

◆ derVec()

bool MathUtils::derVec	(	const Vector3D *	v1,
		const Vector3D *	v2,
		Vector3D *	result,
		double	x,
		double	y )

Calculates the z-component of a vector with coordinates 'x' and 'y'which is in the same tangent plane as the tangent vectors 'v1' and 'v2'. The result is assigned to 'result'.

Definition at line 462 of file MathUtils.cpp.

◆ distPointFromLine()

double MathUtils::distPointFromLine	(	QgsPoint *	thepoint,
		QgsPoint *	p1,
		QgsPoint *	p2 )

Calculates the (2 dimensional) distance from 'thepoint' to the line defined by p1 and p2.

Definition at line 179 of file MathUtils.cpp.

◆ faculty()

int MathUtils::faculty ( int n )

Faculty function.

Definition at line 199 of file MathUtils.cpp.

◆ inCircle()

bool MathUtils::inCircle	(	QgsPoint *	testp,
		QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3 )

Tests, whether 'testp' is inside the circle through 'p1', 'p2' and 'p3'.

Definition at line 204 of file MathUtils.cpp.

◆ inDiametral()

bool MathUtils::inDiametral	(	QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	point )

Tests, whether 'point' is inside the diametral circle through 'p1' and 'p2'.

Definition at line 244 of file MathUtils.cpp.

◆ leftOf()

double MathUtils::leftOf	(	const QgsPoint &	thepoint,
		const QgsPoint *	p1,
		const QgsPoint *	p2 )

Returns whether 'thepoint' is left or right of the line from 'p1' to 'p2'. Negative values mean left and positive values right. There may be numerical instabilities, so a threshold may be useful.

Definition at line 249 of file MathUtils.cpp.

◆ lineIntersection() [1/2]

bool MathUtils::lineIntersection	(	QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		QgsPoint *	p4 )

Returns true, if line1 (p1 to p2) and line2 (p3 to p4) intersect. If the lines have an endpoint in common, false is returned.

Definition at line 268 of file MathUtils.cpp.

◆ lineIntersection() [2/2]

bool MathUtils::lineIntersection	(	QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		QgsPoint *	p4,
		QgsPoint *	intersection_point )

Returns true, if line1 (p1 to p2) and line2 (p3 to p4) intersect. If the lines have an endpoint in common, false is returned. The intersecting point is stored in 'intersection_point.

Definition at line 311 of file MathUtils.cpp.

◆ lower()

int MathUtils::lower	(	int	n,
		int	i )

Lower function.

Definition at line 364 of file MathUtils.cpp.

◆ normalFromPoints()

void MathUtils::normalFromPoints	(	QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3,
		Vector3D *	vec )

Calculates the normal vector of the plane through the points p1, p2 and p3 and assigns the result to vec. If the points are ordered counterclockwise, the normal will have a positive z-coordinate;.

Definition at line 587 of file MathUtils.cpp.

◆ normalLeft()

bool MathUtils::normalLeft	(	Vector3D *	v1,
		Vector3D *	result,
		double	length )

Assigns the vector 'result', which is normal to the vector 'v1', on the left side of v1 and has length 'length'. This method works only with two dimensions.

Definition at line 477 of file MathUtils.cpp.

◆ normalMinDistance()

bool MathUtils::normalMinDistance	(	Vector3D *	tangent,
		Vector3D *	target,
		Vector3D *	result )

Calculates a Vector orthogonal to 'tangent' with length 1 and closest possible to result. Returns true in case of success and false otherwise.

Definition at line 651 of file MathUtils.cpp.

◆ normalRight()

bool MathUtils::normalRight	(	Vector3D *	v1,
		Vector3D *	result,
		double	length )

Assigns the vector 'result', which is normal to the vector 'v1', on the right side of v1 and has length 'length'. The calculation is only in two dimensions.

Definition at line 532 of file MathUtils.cpp.

◆ planeTest()

double MathUtils::planeTest	(	QgsPoint *	test,
		QgsPoint *	pt1,
		QgsPoint *	pt2,
		QgsPoint *	pt3 )

Tests, if 'test' is in the same plane as 'p1', 'p2' and 'p3' and returns the z-difference from the plane to 'test.

Definition at line 728 of file MathUtils.cpp.

◆ pointInsideTriangle()

bool MathUtils::pointInsideTriangle	(	double	x,
		double	y,
		QgsPoint *	p1,
		QgsPoint *	p2,
		QgsPoint *	p3 )

Returns true, if the point with coordinates x and y is inside (or at the edge) of the triangle p1,p2,p3 and false, if it is outside. p1, p2 and p3 have to be ordered counterclockwise.

Definition at line 633 of file MathUtils.cpp.

◆ triArea()

double MathUtils::triArea	(	QgsPoint *	pa,
		QgsPoint *	pb,
		QgsPoint *	pc )

Returns the area of a triangle. If the points are ordered counterclockwise, the value will be positive. If they are ordered clockwise, the value will be negative.

Definition at line 376 of file MathUtils.cpp.

Functions