Functions
double ANALYSIS_EXPORT	angle (Point3D p1, Point3D p2, Point3D p3, Point3D p4)
	Calculates the angle between two segments (in 2 dimension, z-values are ignored) More...

bool ANALYSIS_EXPORT	BarycentricToXY (double u, double v, double w, Point3D p1, Point3D p2, Point3D p3, Point3D result)

bool ANALYSIS_EXPORT	calcBarycentricCoordinates (double x, double y, Point3D p1, Point3D p2, Point3D p3, Point3D result)
	Calculates the barycentric coordinates of a point (x,y) with respect to p1, p2, p3 and stores the three barycentric coordinates in 'result'. More...

double ANALYSIS_EXPORT	calcBernsteinPoly (int n, int i, double t)
	Calculates the value of a Bernstein polynomial. More...

double ANALYSIS_EXPORT	calcCubicHermitePoly (int n, int i, double t)
	Calculates the value of a cubic Hermite polynomial. More...

double ANALYSIS_EXPORT	cFDerBernsteinPoly (int n, int i, double t)
	Calculates the first derivative of a Bernstein polynomial with respect to the parameter t. More...

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. More...

bool ANALYSIS_EXPORT	circumcenter (Point3D p1, Point3D p2, Point3D p3, Point3D result)
	Calculates the center of the circle passing through p1, p2 and p3. More...

double ANALYSIS_EXPORT	crossVec (Point3D first, Vector3D vec1, Point3D second, Vector3D vec2)
	Calculates the intersection of the two vectors vec1 and vec2, which start at first(vec1) and second(vec2) end. More...

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'. More...

double ANALYSIS_EXPORT	distPointFromLine (Point3D thepoint, Point3D p1, Point3D *p2)
	Calculates the (2 dimensional) distance from 'thepoint' to the line defined by p1 and p2. More...

int ANALYSIS_EXPORT	faculty (int n)
	Faculty function. More...

bool ANALYSIS_EXPORT	inCircle (Point3D testp, Point3D p1, Point3D p2, Point3D p3)
	Tests, whether 'testp' is inside the circle through 'p1', 'p2' and 'p3'. More...

bool ANALYSIS_EXPORT	inDiametral (Point3D p1, Point3D p2, Point3D *point)
	Tests, whether 'point' is inside the diametral circle through 'p1' and 'p2'. More...

double ANALYSIS_EXPORT	leftOf (Point3D thepoint, Point3D p1, Point3D *p2)
	Returns whether 'thepoint' is left or right of the line from 'p1' to 'p2'. More...

bool ANALYSIS_EXPORT	lineIntersection (Point3D p1, Point3D p2, Point3D p3, Point3D p4)
	Returns true, if line1 (p1 to p2) and line2 (p3 to p4) intersect. More...

bool ANALYSIS_EXPORT	lineIntersection (Point3D p1, Point3D p2, Point3D p3, Point3D p4, Point3D *intersection_point)
	Returns true, if line1 (p1 to p2) and line2 (p3 to p4) intersect. More...

int ANALYSIS_EXPORT	lower (int n, int i)
	Lower function. More...

double ANALYSIS_EXPORT	max (double x, double y)
	Returns the maximum of two doubles or the first argument if both are equal. More...

double ANALYSIS_EXPORT	min (double x, double y)
	Returns the minimum of two doubles or the first argument if both are equal. More...

void ANALYSIS_EXPORT	normalFromPoints (Point3D p1, Point3D p2, Point3D p3, Vector3D vec)
	Calculates the normal vector of the plane through the points p1, p2 and p3 and assigns the result to vec. More...

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'. More...

bool ANALYSIS_EXPORT	normalMinDistance (Vector3D tangent, Vector3D target, Vector3D *result)
	Calculates a Vector orthogonal to 'tangent' with length 1 and closest possible to result. More...

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'. More...

double ANALYSIS_EXPORT	planeTest (Point3D test, Point3D pt1, Point3D pt2, Point3D pt3)
	Tests, if 'test' is in the same plane as 'p1', 'p2' and 'p3' and returns the z-difference from the plane to 'test. More...

bool ANALYSIS_EXPORT	pointInsideTriangle (double x, double y, Point3D p1, Point3D p2, Point3D *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. More...

double ANALYSIS_EXPORT	power (double a, int b)
	Power function for integer coefficients. More...

double ANALYSIS_EXPORT	triArea (Point3D pa, Point3D pb, Point3D *pc)
	Returns the area of a triangle. More...

Function Documentation

◆ angle()

double ANALYSIS_EXPORT MathUtils::angle	(	Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3,
		Point3D *	p4
	)

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

◆ BarycentricToXY()

bool ANALYSIS_EXPORT MathUtils::BarycentricToXY	(	double	u,
		double	v,
		double	w,
		Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3,
		Point3D *	result
	)

◆ calcBarycentricCoordinates()

bool ANALYSIS_EXPORT MathUtils::calcBarycentricCoordinates	(	double	x,
		double	y,
		Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3,
		Point3D *	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

◆ calcBernsteinPoly()

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

Calculates the value of a Bernstein polynomial.

◆ calcCubicHermitePoly()

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

Calculates the value of a cubic Hermite polynomial.

◆ cFDerBernsteinPoly()

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

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

◆ cFDerCubicHermitePoly()

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

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

◆ circumcenter()

bool ANALYSIS_EXPORT MathUtils::circumcenter	(	Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3,
		Point3D *	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)

◆ crossVec()

double ANALYSIS_EXPORT MathUtils::crossVec	(	Point3D *	first,
		Vector3D *	vec1,
		Point3D *	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)

◆ derVec()

bool ANALYSIS_EXPORT 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'

◆ distPointFromLine()

double ANALYSIS_EXPORT MathUtils::distPointFromLine	(	Point3D *	thepoint,
		Point3D *	p1,
		Point3D *	p2
	)

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

◆ faculty()

int ANALYSIS_EXPORT MathUtils::faculty ( int n )

Faculty function.

◆ inCircle()

bool ANALYSIS_EXPORT MathUtils::inCircle	(	Point3D *	testp,
		Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3
	)

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

◆ inDiametral()

bool ANALYSIS_EXPORT MathUtils::inDiametral	(	Point3D *	p1,
		Point3D *	p2,
		Point3D *	point
	)

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

◆ leftOf()

double ANALYSIS_EXPORT MathUtils::leftOf	(	Point3D *	thepoint,
		Point3D *	p1,
		Point3D *	p2
	)

Returns whether 'thepoint' is left or right of the line from 'p1' to 'p2'.

Negativ values mean left and positiv values right. There may be numerical instabilities, so a threshold may be useful

◆ lineIntersection() [1/2]

bool ANALYSIS_EXPORT MathUtils::lineIntersection	(	Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3,
		Point3D *	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

◆ lineIntersection() [2/2]

bool ANALYSIS_EXPORT MathUtils::lineIntersection	(	Point3D *	p1,
		Point3D *	p2,
		Point3D *	p3,
		Point3D *	p4,
		Point3D *	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.

◆ lower()

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

Lower function.

◆ max()

double ANALYSIS_EXPORT MathUtils::max	(	double	x,
		double	y
	)

Returns the maximum of two doubles or the first argument if both are equal.

◆ min()

double ANALYSIS_EXPORT MathUtils::min	(	double	x,
		double	y
	)

Returns the minimum of two doubles or the first argument if both are equal.

◆ normalFromPoints()

void ANALYSIS_EXPORT MathUtils::normalFromPoints	(	Point3D *	p1,
		Point3D *	p2,
		Point3D *	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;

◆ normalLeft()

bool ANALYSIS_EXPORT 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.

◆ normalMinDistance()

bool ANALYSIS_EXPORT 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

◆ normalRight()

bool ANALYSIS_EXPORT 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

◆ planeTest()

double ANALYSIS_EXPORT MathUtils::planeTest	(	Point3D *	test,
		Point3D *	pt1,
		Point3D *	pt2,
		Point3D *	pt3
	)

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

◆ pointInsideTriangle()

bool ANALYSIS_EXPORT MathUtils::pointInsideTriangle	(	double	x,
		double	y,
		Point3D *	p1,
		Point3D *	p2,
		Point3D *	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

◆ power()

double ANALYSIS_EXPORT MathUtils::power	(	double	a,
		int	b
	)

Power function for integer coefficients.

◆ triArea()

double ANALYSIS_EXPORT MathUtils::triArea	(	Point3D *	pa,
		Point3D *	pb,
		Point3D *	pc
	)

Returns the area of a triangle.

If the points are ordered counterclockwise, the value will be positiv. If they are ordered clockwise, the value will be negativ

Functions