QGIS API Documentation  2.2.0-Valmiera
MathUtils Namespace Reference

## Functions

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'.
bool ANALYSIS_EXPORT BarycentricToXY (double u, double v, double w, Point3D *p1, Point3D *p2, Point3D *p3, Point3D *result)
double ANALYSIS_EXPORT calcBernsteinPoly (int n, int i, double t)
calculates the value of a Bernstein 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 calcCubicHermitePoly (int n, int i, double t)
calculates the value of a cubic Hermite polynomial
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 (Point3D *p1, Point3D *p2, Point3D *p3, Point3D *result)
Calculates the center of the circle passing through p1, p2 and p3.
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.
int ANALYSIS_EXPORT faculty (int n)
faculty function
bool ANALYSIS_EXPORT inCircle (Point3D *testp, Point3D *p1, Point3D *p2, Point3D *p3)
Tests, whether 'testp' is inside the circle through 'p1', 'p2' and 'p3'.
bool ANALYSIS_EXPORT inDiametral (Point3D *p1, Point3D *p2, Point3D *point)
Tests, whether 'point' is inside the diametral circle through 'p1' and 'p2'.
double ANALYSIS_EXPORT leftOf (Point3D *thepoint, Point3D *p1, Point3D *p2)
Returns whether 'thepoint' is left or right of the line from 'p1' to 'p2'.
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.
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.
int ANALYSIS_EXPORT lower (int n, int i)
lower function
double ANALYSIS_EXPORT max (double x, double y)
returns the maximum of two doubles or the first argument if both are equal
double ANALYSIS_EXPORT min (double x, double y)
returns the minimum of two doubles or the first argument if both are equal
double ANALYSIS_EXPORT power (double a, int b)
power function for integer coefficients
double ANALYSIS_EXPORT triArea (Point3D *pa, Point3D *pb, Point3D *pc)
returns the area of a triangle.
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'.
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.
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'.
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'.
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.
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.
bool ANALYSIS_EXPORT normalMinDistance (Vector3D *tangent, Vector3D *target, Vector3D *result)
Calculates a Vector orthogonal to 'tangent' with length 1 and closest possible to result.
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.
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)

## Function Documentation

 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)

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

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

calculates the value of a Bernstein polynomial

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

calculates the value of a cubic Hermite polynomial

 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

 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

 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)

 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)

 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'

 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.

 int ANALYSIS_EXPORT MathUtils::faculty ( int n )

faculty function

 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'.

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

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

 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

 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

 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.

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

lower function

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

 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.

 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

 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

 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.

 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

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

power function for integer coefficients

 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