MathUtils.h File Reference

Set of functions supporting mathematic operations. More...

#include <algorithm>
#include <cmath>
#include <iostream>
#include "BoundingBox.h"

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Functions
double	det2 (double a1, double b1, double c1, double d1)
	Calculates the determinant of the given 2x2 matrix. More...
double	det3 (double matrix[3][3])
	Calculates the determinant of the given 3x3 matrix. More...
void	eig3 (double matrix[3][3], double lambda, double(&result)[3])
	Calculates eigenvector of the given 3x3 matrix for the given eigenvalue. More...
void	cubicEq (double au, double bu, double cu, double du, double(&result)[3])
	Calculates the solution of a cubic equation ( ). More...
template<typename T >
void	averageD (std::vector< T > &points, double(&v1)[3], double(&averageD))
	Calculates the average coefficient d for the plane ( ) given by normal vector and interpolated through the given points. More...
template<typename T >
void	planeFromPoints (std::vector< T > &points, std::vector< int > &indexes, double(&v1)[3], double &averageD)
	Interpolates the plane through the given points. More...
template<typename T >
void	planeFromPoints (std::vector< T > &points, double(&v1)[3], double(&v2)[3], double(&v3)[3], double &averageD)
	Interpolates the plane through the given points. More...
double	angleBetweenPlanes (double a1, double b1, double c1, double a2, double b2, double c2)
	Calculates the angle between two planes ( ). More...
double	angleBetweenPlanes (double n1[3], double n2[3])
	Calculates the angle between two planes given by normal vectors. More...
double	dot (double ax, double ay, double az, double bx, double by, double bz)
	Calculates the dot product of two vectors. More...
void	cross (double(&a)[3], double(&b)[3], double(&result)[3])
	Calculates the cross product of two vectors. More...
void	normalize (double(&vec)[3])
	Normalizes the given vector. More...
template<typename T >
void	rotatePointsToLocal (std::vector< T > &points, double(&locx)[3], double(&locy)[3])
	Rotates points in the local coordinate system (z = 0). More...
template<typename T >
void	rotatePoint (T &pt, double(&v1)[3], double(&v2)[3], double(&v3)[3])
	Rotates point in the local coordinate system given by its base vectors. More...
template<typename T >
void	rotatePoints (std::vector< T > &points, double(&v1)[3], double(&v2)[3], double(&v3)[3])
	Rotates points in the local coordinate system given by its base vectors. More...
template<typename T >
void	moveCSorigin (std::vector< T > &points, T O)
	Recalculates the coordinates of the points when the new origin of the coordinate system is set. More...
template<typename T >
void	moveBackCSorigin (std::vector< T > &points, T O)
	Recalculates the coordinates of the points when the origin of the coordinate system is reset from the given O to (0, 0, 0). More...
template<typename T >
void	giveLocalCS (std::vector< T > &points, double(&locx)[3], double(&locy)[3], double(&locz)[3])
	Calculates local coordinate system of the plane defined by the given points. More...
void	giveLtoGVectorsFromLocalCS (double(&locx)[3], double(&locy)[3], double(&locz)[3], double(&l2g1)[3], double(&l2g2)[3], double(&l2g3)[3])
	Calculates the global-to-local (G2L) transformation vectors to local-to-global (L2G) transformation vectors. More...
template<typename T >
double	giveAverageCoord (std::vector< T > &points, int cIndex)
	Calculates the average coordinate of the given points. More...
template<typename T >
void	projectPointsToXYPlane (std::vector< T > &points)
	Sets the z-coordinate of the given points to the zero. More...

Detailed Description

Set of functions supporting mathematic operations.

Function Documentation

double angleBetweenPlanes	(	double	a1,
		double	b1,
		double	c1,
		double	a2,
		double	b2,
		double	c2
	)

Calculates the angle between two planes ( ).

Parameters

a1	Coefficient a of the first plane
b1	Coefficient b of the first plane
c1	Coefficient c of the first plane
a1	Coefficient a of the second plane
b1	Coefficient b of the second plane
c1	Coefficient c of the second plane

Returns

Angle between the planes

double angleBetweenPlanes	(	double	n1[3],
		double	n2[3]
	)

Calculates the angle between two planes given by normal vectors.

Parameters

n1	Normal vector of the first plane
n2	Normal vector of the second plane

Returns

Angle between the planes

template<typename T >

void averageD	(	std::vector< T > &	points,
		double(&)	v1[3],
		double &	averageD
	)

Calculates the average coefficient d for the plane ( ) given by normal vector and interpolated through the given points.

Parameters

points	Plane points
v1	Plane normal vector
averageD	Return parameter storing the calculated coefficient

void cross	(	double(&)	a[3],
		double(&)	b[3],
		double(&)	result[3]
	)

Calculates the cross product of two vectors.

Parameters

a	The first vector
b	The second vector
result	Return parameter storing the resulting cross product

void cubicEq	(	double	au,
		double	bu,
		double	cu,
		double	du,
		double(&)	result[3]
	)

Calculates the solution of a cubic equation ( ).

Parameters

au	Coefficient a
bu	Coefficient b
cu	Coefficient c
du	Coefficient d
result	Return parameter storing the calculated solution

double det2	(	double	a1,
		double	b1,
		double	c1,
		double	d1
	)

Calculates the determinant of the given 2x2 matrix.

Parameters

a1	Matrix element (1,1)
b1	Matrix element (1,2)
c1	Matrix element (2,1)
d1	Matrix element (2,2)

Returns

Determinant

double det3

(

double

matrix[3][3]

)

Calculates the determinant of the given 3x3 matrix.

Parameters

matrix

3x3 matrix

Returns

Determinant

double dot	(	double	ax,
		double	ay,
		double	az,
		double	bx,
		double	by,
		double	bz
	)

Calculates the dot product of two vectors.

Parameters

ax	X component of the first vector
ay	Y component of the first vector
az	Z component of the first vector
bx	X component of the second vector
by	Y component of the second vector
bz	Z component of the second vector

Returns

Resulting dot product

void eig3	(	double	matrix[3][3],
		double	lambda,
		double(&)	result[3]
	)

Calculates eigenvector of the given 3x3 matrix for the given eigenvalue.

Parameters

matrix	3x3 matrix
lambda	Eigenvalue
result	Return parameter storing the calculated eigenvector

template<typename T >

double giveAverageCoord	(	std::vector< T > &	points,
		int	cIndex
	)

Calculates the average coordinate of the given points.

Parameters

points	The points for calculation of the average coordinate
index	Index specifying which coordinate to calculate (0~x, 1~y, 2~z)

Returns

The average coordinate calculated

template<typename T >

void giveLocalCS	(	std::vector< T > &	points,
		double(&)	locx[3],
		double(&)	locy[3],
		double(&)	locz[3]
	)

Calculates local coordinate system of the plane defined by the given points.

Parameters

points	Points defining the plane for which to calculate the local coordinate system
locx	Return parameter storing local x-axis (in plane, horizontal)
locy	Return parameter storing local y-axis (in plane, vertical)
locz	Return parameter storing local z-axis (normal vector)

void giveLtoGVectorsFromLocalCS	(	double(&)	locx[3],
		double(&)	locy[3],
		double(&)	locz[3],
		double(&)	l2g1[3],
		double(&)	l2g2[3],
		double(&)	l2g3[3]
	)

Calculates the global-to-local (G2L) transformation vectors to local-to-global (L2G) transformation vectors.

Parameters

locx	The first G2L transformation vector
locy	The second G2L transformation vector
locz	The third G2L transformation vector
l2g1	In-out parameter storing the first L2G transformation vector
l2g1	In-out parameter storing the second L2G transformation vector
l2g1	In-out parameter storing the third L2G transformation vector

template<typename T >

void moveBackCSorigin	(	std::vector< T > &	points,
		T	O
	)

Recalculates the coordinates of the points when the origin of the coordinate system is reset from the given O to (0, 0, 0).

Parameters

pt	In-Out parameter storing the points to be transformed
O	Actual origin coordinates

template<typename T >

void moveCSorigin	(	std::vector< T > &	points,
		T	O
	)

Recalculates the coordinates of the points when the new origin of the coordinate system is set.

Parameters

pt	In-Out parameter storing the points to be transformed
O	New origin coordinates

void normalize

(

double(&)

vec[3]

)

Normalizes the given vector.

Parameters

vec	In-Out parameter storing the vector to be normalized

template<typename T >

void planeFromPoints	(	std::vector< T > &	points,
		std::vector< int > &	indexes,
		double(&)	v1[3],
		double &	averageD
	)

Interpolates the plane through the given points.

Parameters

points	Points for the calculation
indexes	Indexes specifying which points to use for the plane calculation
v1	Return parametr storing the normal vector of the plane
averageD	Coefficient d of the plane equation ( )

template<typename T >

void planeFromPoints	(	std::vector< T > &	points,
		double(&)	v1[3],
		double(&)	v2[3],
		double(&)	v3[3],
		double &	averageD
	)

Interpolates the plane through the given points.

Parameters

points	Points through which to interpolate the plane
v1	Return parametr storing the normal vector of the plane
v2	Return parametr storing the first in-plane vector
v3	Return parametr storing the second in-plane vector
averageD	Coefficient d of the plane equation ( )

template<typename T >

void projectPointsToXYPlane

(

std::vector< T > &

points

)

Sets the z-coordinate of the given points to the zero.

Parameters

points

In-Out parameter storing the points to be projected

template<typename T >

void rotatePoint	(	T &	pt,
		double(&)	v1[3],
		double(&)	v2[3],
		double(&)	v3[3]
	)

Rotates point in the local coordinate system given by its base vectors.

Parameters

pt	In-Out parameter storing the point to be rotated
v1	The first base vector of the local coordinate system
v2	The second base vector of the local coordinate system
v3	The third base vector of the local coordinate system

template<typename T >

void rotatePoints	(	std::vector< T > &	points,
		double(&)	v1[3],
		double(&)	v2[3],
		double(&)	v3[3]
	)

Rotates points in the local coordinate system given by its base vectors.

Parameters

pt	In-Out parameter storing the points to be rotated
v1	The first base vector of the local coordinate system
v2	The second base vector of the local coordinate system
v3	The third base vector of the local coordinate system

template<typename T >

void rotatePointsToLocal	(	std::vector< T > &	points,
		double(&)	locx[3],
		double(&)	locy[3]
	)

Rotates points in the local coordinate system (z = 0).

Parameters

points	In-Out parameter storing the points to be rotated
locx	Local x vector
locy	Local y vector