Functions
template<typename T >
BALL_INLINE T	BALL::getDeterminant_ (const T *m, Size dim)

template<typename T >
T	BALL::getDeterminant (const T *m, Size dim)

template<typename T >
BALL_INLINE T	BALL::getDeterminant2 (const T *m)

template<typename T >
BALL_INLINE T	BALL::getDeterminant2 (const T &m00, const T &m01, const T &m10, const T &m11)

template<typename T >
BALL_INLINE T	BALL::getDeterminant3 (const T *m)

template<typename T >
BALL_INLINE T	BALL::getDeterminant3 (const T &m00, const T &m01, const T &m02, const T &m10, const T &m11, const T &m12, const T &m20, const T &m21, const T &m22)

template<typename T >
bool	BALL::SolveSystem (const T m, T x, const Size dim)

template<typename T >
BALL_INLINE bool	BALL::SolveSystem2 (const T &a1, const T &b1, const T &c1, const T &a2, const T &b2, const T &c2, T &x1, T &x2)

template<typename T >
short	BALL::SolveQuadraticEquation (const T &a, const T &b, const T &c, T &x1, T &x2)

template<typename T >
BALL_INLINE TVector3< T >	BALL::GetPartition (const TVector3< T > &a, const TVector3< T > &b)

template<typename T >
BALL_INLINE TVector3< T >	BALL::GetPartition (const TVector3< T > &a, const TVector3< T > &b, const T &r, const T &s)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TVector3< T > &a, const TVector3< T > &b)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TLine3< T > &line, const TVector3< T > &point)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TVector3< T > &point, const TLine3< T > &line)

template<typename T >
T	BALL::GetDistance (const TLine3< T > &a, const TLine3< T > &b)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TVector3< T > &point, const TPlane3< T > &plane)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TPlane3< T > &plane, const TVector3< T > &point)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TLine3< T > &line, const TPlane3< T > &plane)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TPlane3< T > &plane, const TLine3< T > &line)

template<typename T >
BALL_INLINE T	BALL::GetDistance (const TPlane3< T > &a, const TPlane3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TVector3< T > &a, const TVector3< T > &b, TAngle< T > &intersection_angle)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TLine3< T > &a, const TLine3< T > &b, TAngle< T > &intersection_angle)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TPlane3< T > &plane, const TVector3< T > &vector, TAngle< T > &intersection_angle)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TVector3< T > &vector, const TPlane3< T > &plane, TAngle< T > &intersection_angle)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TPlane3< T > &plane, const TLine3< T > &line, TAngle< T > &intersection_angle)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TLine3< T > &line, const TPlane3< T > &plane, TAngle< T > &intersection_angle)

template<typename T >
BALL_INLINE bool	BALL::GetAngle (const TPlane3< T > &a, const TPlane3< T > &b, TAngle< T > &intersection_angle)

template<typename T >
bool	BALL::GetIntersection (const TLine3< T > &a, const TLine3< T > &b, TVector3< T > &point)

template<typename T >
BALL_INLINE bool	BALL::GetIntersection (const TPlane3< T > &plane, const TLine3< T > &line, TVector3< T > &intersection_point)

template<typename T >
BALL_INLINE bool	BALL::GetIntersection (const TLine3< T > &line, const TPlane3< T > &plane, TVector3< T > &intersection_point)

template<typename T >
bool	BALL::GetIntersection (const TPlane3< T > &plane1, const TPlane3< T > &plane2, TLine3< T > &line)

template<typename T >
bool	BALL::GetIntersection (const TSphere3< T > &sphere, const TLine3< T > &line, TVector3< T > &intersection_point1, TVector3< T > &intersection_point2)

template<typename T >
BALL_INLINE bool	BALL::GetIntersection (const TLine3< T > &line, const TSphere3< T > &sphere, TVector3< T > &intersection_point1, TVector3< T > &intersection_point2)

template<typename T >
bool	BALL::GetIntersection (const TSphere3< T > &sphere, const TPlane3< T > &plane, TCircle3< T > &intersection_circle)

template<typename T >
BALL_INLINE bool	BALL::GetIntersection (const TPlane3< T > &plane, const TSphere3< T > &sphere, TCircle3< T > &intersection_circle)

template<typename T >
bool	BALL::GetIntersection (const TSphere3< T > &a, const TSphere3< T > &b, TCircle3< T > &intersection_circle)

template<class T >
bool	BALL::GetIntersection (const TSphere3< T > &s1, const TSphere3< T > &s2, const TSphere3< T > &s3, TVector3< T > &p1, TVector3< T > &p2, bool test=true)

template<typename T >
BALL_INLINE bool	BALL::isCollinear (const TVector3< T > &a, const TVector3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::isComplanar (const TVector3< T > &a, const TVector3< T > &b, const TVector3< T > &c)

template<typename T >
BALL_INLINE bool	BALL::isComplanar (const TVector3< T > &a, const TVector3< T > &b, const TVector3< T > &c, const TVector3< T > &d)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TVector3< T > &a, const TVector3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TVector3< T > &vector, const TLine3< T > &line)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TLine3< T > &line, const TVector3< T > &vector)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TLine3< T > &a, const TLine3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TVector3< T > &vector, const TPlane3< T > &plane)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TPlane3< T > &plane, const TVector3< T > &vector)

template<typename T >
BALL_INLINE bool	BALL::isOrthogonal (const TPlane3< T > &a, const TPlane3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TVector3< T > &point, const TLine3< T > &line)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TLine3< T > &line, const TVector3< T > &point)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TLine3< T > &a, const TLine3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TVector3< T > &point, const TPlane3< T > &plane)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TPlane3< T > &plane, const TVector3< T > &point)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TLine3< T > &line, const TPlane3< T > &plane)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TPlane3< T > &plane, const TLine3< T > &line)

template<typename T >
BALL_INLINE bool	BALL::isIntersecting (const TPlane3< T > &a, const TPlane3< T > &b)

template<typename T >
BALL_INLINE bool	BALL::isParallel (const TLine3< T > &line, const TPlane3< T > &plane)

template<typename T >
BALL_INLINE bool	BALL::isParallel (const TPlane3< T > &plane, const TLine3< T > &line)

template<typename T >
BALL_INLINE bool	BALL::isParallel (const TPlane3< T > &a, const TPlane3< T > &b)

template<typename T >
TAngle< T >	BALL::getOrientedAngle (const T &ax, const T &ay, const T &az, const T &bx, const T &by, const T &bz, const T &nx, const T &ny, const T &nz)

template<typename T >
BALL_INLINE TAngle< T >	BALL::getOrientedAngle (const TVector3< T > &a, const TVector3< T > &b, const TVector3< T > &normal)

template<typename T >
TAngle< T >	BALL::getTorsionAngle (const T &ax, const T &ay, const T &az, const T &bx, const T &by, const T &bz, const T &cx, const T &cy, const T &cz, const T &dx, const T &dy, const T &dz)

Detailed Description

representation of analytical geometry functions, using the classes: TAngle, TCircle3, TLine3, TPlane3, TSphere3, TVector3.

Function Documentation

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TVector3< T > &	a,
		const TVector3< T > &	b,
		TAngle< T > &	intersection_angle
	)

Get the angle between two Vector3.

Parameters

a	the first vector
b	the second vector
intersection_angle	the resulting angle

Returns: bool, always true

Definition at line 551 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TLine3< T > &	a,
		const TLine3< T > &	b,
		TAngle< T > &	intersection_angle
	)

Get the angle between two lines.

Parameters

a	the first line
b	the second line
intersection_angle	the resulting angle

Returns: bool, true if an angle can be calculated, otherwise false

Definition at line 570 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TPlane3< T > &	plane,
		const TVector3< T > &	vector,
		TAngle< T > &	intersection_angle
	)

Get the angle between a plane and a Vector3.

Parameters

plane	the plane
vector	the Vector3
intersection_angle	the resulting angle

Returns: bool, true if an angle can be calculated, otherwise false

Definition at line 590 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TVector3< T > &	vector,
		const TPlane3< T > &	plane,
		TAngle< T > &	intersection_angle
	)

Get the angle between a vector3 and a plane.

Parameters

vector	the vector3
plane	the plane
intersection_angle	the resulting angle

Returns: bool, true if an angle can be calculated, otherwise false

Definition at line 613 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TPlane3< T > &	plane,
		const TLine3< T > &	line,
		TAngle< T > &	intersection_angle
	)

Get the angle between a plane and a line.

Parameters

plane	the plane
line	the line
intersection_angle	the resulting angle

Returns: bool, true if an angle can be calculated, otherwise false

Definition at line 626 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TLine3< T > &	line,
		const TPlane3< T > &	plane,
		TAngle< T > &	intersection_angle
	)

Get the angle between a line and a plane.

Parameters

line	the line
plane	the plane
intersection_angle	the resulting angle

Returns: bool, true if an angle can be calculated, otherwise false

Definition at line 647 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetAngle	(	const TPlane3< T > &	a,
		const TPlane3< T > &	b,
		TAngle< T > &	intersection_angle
	)

Get the angle between two planes.

Parameters

a	the first plane
b	the second plane
intersection_angle	the resulting angle

Returns: bool, true if an angle can be calculated, otherwise false

Definition at line 661 of file analyticalGeometry.h.

template<typename T >

T BALL::getDeterminant	(	const T *	m,
		Size	dim
	)

Get the determinant of any matrix.

Parameters

m	pointer to matrix
dim	dimension of the matrix

Definition at line 93 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::getDeterminant2 ( const T * m )

Get the determinant of an 2x2 matrix.

Parameters

m	pointer to matrix

Definition at line 119 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::getDeterminant2	(	const T &	m00,
		const T &	m01,
		const T &	m10,
		const T &	m11
	)

Get the determinant of an 2x2 matrix.

Parameters

m00	first value of the matrix
m01	second value of the matrix
m10	third value of the matrix
m11	fourth value of the matrix

Definition at line 133 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::getDeterminant3 ( const T * m )

Get the determinant of an 3x3 matrix.

Parameters

m	pointer to matrix

Definition at line 143 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::getDeterminant3	(	const T &	m00,
		const T &	m01,
		const T &	m02,
		const T &	m10,
		const T &	m11,
		const T &	m12,
		const T &	m20,
		const T &	m21,
		const T &	m22
	)

Get the determinant of an 3x3 matrix.

Parameters

m00,m01,m02,m10,m11,m12,m20,m21,m22 the elements of the matrix

Definition at line 159 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::getDeterminant_	(	const T *	m,
		Size	dim
	)

Subroutine to get the determinant of any matrix. Direct usage of this function should be avoided. Instead use T getDeterminant(const T* m, Size dim)

Parameters

m	pointer to matrix
dim	dimension of the matrix

Definition at line 57 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TVector3< T > &	a,
		const TVector3< T > &	b
	)

Get the distance between two points.

Parameters

a	the first point
b	the second point

Returns: T the distance

Definition at line 387 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TLine3< T > &	line,
		const TVector3< T > &	point
	)

Get the distance between a line and a point.

Parameters

line	the line
point	the point

Returns: T the distance

Exceptions

Exception::DivisionByZero if the line has length 0

Definition at line 404 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TVector3< T > &	point,
		const TLine3< T > &	line
	)

Get the distance between a point and a line.

Parameters

point	the point
line	the line

Returns: T the distance

Exceptions

Exception::DivisionByZero if the line has length 0

Definition at line 421 of file analyticalGeometry.h.

template<typename T >

T BALL::GetDistance	(	const TLine3< T > &	a,
		const TLine3< T > &	b
	)

Get the distance between two lines.

Parameters

a	the first line
b	the second line

Returns: T the distance

Exceptions

Exception::DivisionByZero if the lines are parallel and a has length 0

Definition at line 433 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TVector3< T > &	point,
		const TPlane3< T > &	plane
	)

Get the distance between a point and a plane.

Parameters

point	the point
plane	the plane

Returns: T the distance

Exceptions

Exception::DivisionByZero if the normal vector of plane has zero length

Definition at line 470 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TPlane3< T > &	plane,
		const TVector3< T > &	point
	)

Get the distance between a plane and a point.

Parameters

plane	the plane
point	the point

Returns: T the distance

Exceptions

Exception::DivisionByZero if the normal vector of plane has zero length

Definition at line 489 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TLine3< T > &	line,
		const TPlane3< T > &	plane
	)

Get the distance between a line and a plane.

Parameters

line	the line
plane	the plane

Returns: T the distance

Exceptions

Exception::DivisionByZero if the normal vector of plane has zero length

Definition at line 502 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TPlane3< T > &	plane,
		const TLine3< T > &	line
	)

Get the distance between a plane and a line.

Parameters

plane	the plane
line	the line

Returns: T the distance

Exceptions

Exception::DivisionByZero if the normal vector of plane has zero length

Definition at line 520 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE T BALL::GetDistance	(	const TPlane3< T > &	a,
		const TPlane3< T > &	b
	)

Get the distance between two planes.

Parameters

a	the first plane
b	the second plane

Returns: T the distance

Exceptions

Exception::DivisionByZero if the normal vector of a has zero length

Definition at line 533 of file analyticalGeometry.h.

template<typename T >

bool BALL::GetIntersection	(	const TLine3< T > &	a,
		const TLine3< T > &	b,
		TVector3< T > &	point
	)

Get the intersection point between two lines.

Parameters

a	the first line
b	the second line
point	the resulting intersection

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 681 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetIntersection	(	const TPlane3< T > &	plane,
		const TLine3< T > &	line,
		TVector3< T > &	intersection_point
	)

Get the intersection point between a plane and a line.

Parameters

plane	the plane
line	the line
intersection_point	the resulting intersection

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 701 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetIntersection	(	const TLine3< T > &	line,
		const TPlane3< T > &	plane,
		TVector3< T > &	intersection_point
	)

Get the intersection point between a line and a plane.

Parameters

line	the line
plane	the plane
intersection_point	the resulting intersection

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 720 of file analyticalGeometry.h.

template<typename T >

bool BALL::GetIntersection	(	const TPlane3< T > &	plane1,
		const TPlane3< T > &	plane2,
		TLine3< T > &	line
	)

Get the intersection line between two planes.

Parameters

plane1	the first plane
plane2	the second plane
line	the resulting intersection

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 732 of file analyticalGeometry.h.

template<typename T >

bool BALL::GetIntersection	(	const TSphere3< T > &	sphere,
		const TLine3< T > &	line,
		TVector3< T > &	intersection_point1,
		TVector3< T > &	intersection_point2
	)

Get the intersection point between a sphere and a line.

Parameters

sphere	the sphere
line	the line
intersection_point1	the first intersection point
intersection_point2	the second intersection point

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 799 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetIntersection	(	const TLine3< T > &	line,
		const TSphere3< T > &	sphere,
		TVector3< T > &	intersection_point1,
		TVector3< T > &	intersection_point2
	)

Get the intersection point between a line and a sphere.

Parameters

line	the line
sphere	the sphere
intersection_point1	the first intersection point
intersection_point2	the second intersection point

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 824 of file analyticalGeometry.h.

template<typename T >

bool BALL::GetIntersection	(	const TSphere3< T > &	sphere,
		const TPlane3< T > &	plane,
		TCircle3< T > &	intersection_circle
	)

Get the intersection circle between a sphere and a plane.

Parameters

sphere	the sphere
plane	the plane
intersection_circle	the intersection circle

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 836 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::GetIntersection	(	const TPlane3< T > &	plane,
		const TSphere3< T > &	sphere,
		TCircle3< T > &	intersection_circle
	)

Get the intersection circle between a plane and a sphere.

Parameters

plane	the plane
sphere	the sphere
intersection_circle	the intersection circle

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 870 of file analyticalGeometry.h.

template<typename T >

bool BALL::GetIntersection	(	const TSphere3< T > &	a,
		const TSphere3< T > &	b,
		TCircle3< T > &	intersection_circle
	)

Get the intersection circle between two spheres. This methods returns false, if the two spheres are identical, since then no intersection circle exists.

Parameters

a	the first sphere
b	the second sphere
intersection_circle	the intersection circle

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 884 of file analyticalGeometry.h.

template<class T >

bool BALL::GetIntersection	(	const TSphere3< T > &	s1,
		const TSphere3< T > &	s2,
		const TSphere3< T > &	s3,
		TVector3< T > &	p1,
		TVector3< T > &	p2,
		bool	test = `true`
	)

Get the intersection points between three spheres.

Parameters

s1	the first sphere
s2	the second sphere
s3	the third sphere
p1	the first intersection point
p2	the second intersection point
test

Returns: bool, true if an intersection can be calculated, otherwise false

Definition at line 929 of file analyticalGeometry.h.

template<typename T >

TAngle<T> BALL::getOrientedAngle	(	const T &	ax,
		const T &	ay,
		const T &	az,
		const T &	bx,
		const T &	by,
		const T &	bz,
		const T &	nx,
		const T &	ny,
		const T &	nz
	)

Return the oriented angle of two vectors with a normal vector.

Exceptions

Exception::DivisionByZero if at least one vector is zero

Definition at line 1259 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE TAngle<T> BALL::getOrientedAngle	(	const TVector3< T > &	a,
		const TVector3< T > &	b,
		const TVector3< T > &	normal
	)

Return the oriented angle of two vectors with a normal vector.

Exceptions

Exception::DivisionByZero if at least one vector is zero

Definition at line 1300 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE TVector3<T> BALL::GetPartition	(	const TVector3< T > &	a,
		const TVector3< T > &	b
	)

Get the partition of two vectors.

Parameters

a	the first vector
b	the second vector

Returns: TVector3 the partition

Definition at line 351 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE TVector3<T> BALL::GetPartition	(	const TVector3< T > &	a,
		const TVector3< T > &	b,
		const T &	r,
		const T &	s
	)

Get the partition of two vectors, calculated with two ratio factors.

Parameters

a	the first vector
b	the second vector
r	the ratio factor of the first vector
s	the ratio factor of the second vector

Returns: TVector3 the partition

Exceptions

Exception::DivisionByZero if r+s == 0

Definition at line 367 of file analyticalGeometry.h.

template<typename T >

TAngle<T> BALL::getTorsionAngle	(	const T &	ax,
		const T &	ay,
		const T &	az,
		const T &	bx,
		const T &	by,
		const T &	bz,
		const T &	cx,
		const T &	cy,
		const T &	cz,
		const T &	dx,
		const T &	dy,
		const T &	dz
	)

Return the torsion angle of four points to each other.

Parameters

ax	1. vector x component
ay	1. vector y component
az	1. vector z component
bx	2. vector x component
by	2. vector y component
bz	2. vector z component
cx	3. vector x component
cy	3. vector y component
cz	3. vector z component
dx	4. vector x component
dy	4. vector y component
dz	4. vector z component

Returns: TAngle the torsion angle

Exceptions

Exception::DivisionByZero if one of the outer vectors is collinear with the middle one

Definition at line 1323 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isCollinear	(	const TVector3< T > &	a,
		const TVector3< T > &	b
	)

Test whether two vector3 are collinear

Parameters

a	the first vector3
b	the second vector3

Returns: bool, true or false

Definition at line 1006 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isComplanar	(	const TVector3< T > &	a,
		const TVector3< T > &	b,
		const TVector3< T > &	c
	)

Test whether three vector3 are complanar

Parameters

a	the first vector3
b	the second vector3
c	the third vector3

Returns: bool, true or false

Definition at line 1019 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isComplanar	(	const TVector3< T > &	a,
		const TVector3< T > &	b,
		const TVector3< T > &	c,
		const TVector3< T > &	d
	)

Test whether four vector3 are complanar

Parameters

a	the first vector3
b	the second vector3
c	the third vector3
d	the fourth vector3

Returns: bool, true or false

Definition at line 1033 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TVector3< T > &	point,
		const TLine3< T > &	line
	)

Test whether a line is intersecting a point.

Parameters

point	the point
line	the line

Returns: bool, true or false

Definition at line 1129 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TLine3< T > &	line,
		const TVector3< T > &	point
	)

Test whether a line is intersecting a point.

Parameters

line	the line
point	the point

Returns: bool, true or false

Definition at line 1141 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TLine3< T > &	a,
		const TLine3< T > &	b
	)

Test whether two lines are intersecting.

Parameters

a	the first line
b	the second line

Returns: bool, true or false

Definition at line 1153 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TVector3< T > &	point,
		const TPlane3< T > &	plane
	)

Test whether a point lies in a plane.

Parameters

point	the point
plane	the plane

Returns: bool, true or false

Definition at line 1165 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TPlane3< T > &	plane,
		const TVector3< T > &	point
	)

Test whether a point lies in a plane.

Parameters

plane	the plane
point	the point

Returns: bool, true or false

Definition at line 1177 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TLine3< T > &	line,
		const TPlane3< T > &	plane
	)

Test whether a line is intersecting a plane.

Parameters

line	the line
plane	the plane

Returns: bool, true or false

Definition at line 1189 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TPlane3< T > &	plane,
		const TLine3< T > &	line
	)

Test whether a plane is intersecting a line.

Parameters

plane	the plane
line	the line

Returns: bool, true or false

Definition at line 1201 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isIntersecting	(	const TPlane3< T > &	a,
		const TPlane3< T > &	b
	)

Test whether two planes are intersecting.

Parameters

a	the first plane
b	the second plane

Returns: bool, true or false

Definition at line 1213 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TVector3< T > &	a,
		const TVector3< T > &	b
	)

Test whether two vector3 are orthogonal

Parameters

a	the first vector3
b	the second vector3

Returns: bool, true or false

Definition at line 1045 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TVector3< T > &	vector,
		const TLine3< T > &	line
	)

Test whether a vector3 and a line are orthogonal

Parameters

vector	the vector
line	the line

Returns: bool, true or false

Definition at line 1057 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TLine3< T > &	line,
		const TVector3< T > &	vector
	)

Test whether a line and a vector3 are orthogonal

Parameters

line	the line
vector	the vector

Returns: bool, true or false

Definition at line 1069 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TLine3< T > &	a,
		const TLine3< T > &	b
	)

Test whether two lines are orthogonal.

Parameters

a	the first line
b	the second line

Returns: bool, true or false

Definition at line 1081 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TVector3< T > &	vector,
		const TPlane3< T > &	plane
	)

Test whether a vector3 and a plane are orthogonal.

Parameters

vector	the vector3
plane	the plane

Returns: bool, true or false

Definition at line 1093 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TPlane3< T > &	plane,
		const TVector3< T > &	vector
	)

Test whether a plane and a vector3 are orthogonal.

Parameters

plane	the plane
vector	the vector3

Returns: bool, true or false

Definition at line 1105 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isOrthogonal	(	const TPlane3< T > &	a,
		const TPlane3< T > &	b
	)

Test whether two planes are orthogonal.

Parameters

a	the first plane
b	the second plane

Returns: bool, true or false

Definition at line 1117 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isParallel	(	const TLine3< T > &	line,
		const TPlane3< T > &	plane
	)

Test whether a line and a plane are parallel.

Parameters

line	the line
plane	the plane

Returns: bool, true or false

Definition at line 1225 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isParallel	(	const TPlane3< T > &	plane,
		const TLine3< T > &	line
	)

Test whether a plane and a line are parallel.

Parameters

plane	the plane
line	the line

Returns: bool, true or false

Definition at line 1237 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::isParallel	(	const TPlane3< T > &	a,
		const TPlane3< T > &	b
	)

Test whether two planes are parallel.

Parameters

a	the first plane
b	the second plane

Returns: bool, true or false

Definition at line 1249 of file analyticalGeometry.h.

template<typename T >

short BALL::SolveQuadraticEquation	(	const T &	a,
		const T &	b,
		const T &	c,
		T &	x1,
		T &	x2
	)

Solve a quadratic equation of the form a $x^2 + b x + c = 0$ .

Parameters

a
b
c
x1	the first solution
x2	the second solution

Returns: short the number of solutions (0 - 2)

Definition at line 310 of file analyticalGeometry.h.

template<typename T >

bool BALL::SolveSystem	(	const T *	m,
		T *	x,
		const Size	dim
	)

Solve a system of linear equations. Given a system of linear equations

: $\begin{array}{ccccccccc} a_{1,1} x_1 & + & a_{1,2} x_2 & + & \ldots & + & a_{1,n} x_n & = & a_{1,(n+1)} \\ a_{2,1} x_1 & + & a_{2,2} x_2 & + & \ldots & + & a_{2,n} x_n & = & a_{2,(n+1)} \\ \vdots & & \vdots & & \ddots & & \vdots & & \vdots \\ a_{n,1} x_1 & + & a_{n,2} x_2 & + & \ldots & + & a_{n,n} x_n & = & a_{n,(n+1)} \\ \end{array}$

: in matrix form, identify the solution $x = (x_1, x_2,\ldots x_N)$ .

: m should point to a C-style array containing the $n\times(n+1)$ matrix A.

: The elements of A are row-ordered, i.e., they are ordered like this:

: $a_{1,1}, a_{1,2}, \cdot, a_{1,(n+1)}, a_{2,1}, \ldots a_{n,(n+1)}$

: x points to a C-style array that will contain the solution vector x upon successful termination of the function.

: If there is no solution or the system is under-determined, return false.

Parameters

m	pointer to the factors in the equations
x	pointer in which the results are stored
dim	the dimension of the equation system (number of variables)

Returns: bool true if a solution is found

Definition at line 191 of file analyticalGeometry.h.

template<typename T >

BALL_INLINE bool BALL::SolveSystem2	(	const T &	a1,
		const T &	b1,
		const T &	c1,
		const T &	a2,
		const T &	b2,
		const T &	c2,
		T &	x1,
		T &	x2
	)

Solve a system of two equations of the form $a_1 x_1 + b_1 x_2 = c_1$ and $a_2 x_1 + b_2 x_2 = c_2$ .

Parameters

a1,b1,c1,a2,b2,c2	constants of the system
x1	the first solution
x2	the second solution

Returns: bool true if a solution is found

Definition at line 285 of file analyticalGeometry.h.

Functions

Detailed Description

Function Documentation