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Functions
MathUtils Namespace Reference

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

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 
)
inline

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

Definition at line 90 of file util.h.

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

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

Definition at line 96 of file util.h.

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