Carthesian Namespace Reference

Classes
class	Point3D
class	Segment3D
class	Vector3D
class	Matrix3D
Functions
bool	intersection (const Carthesian::Point3D &p1, const Carthesian::Point3D &p2, const Carthesian::Point3D &p3, const Carthesian::Point3D &p4, Carthesian::Point3D &pa, Carthesian::Point3D &pb, double &mua, double &mub)
	Calculate the line segment PaPb that is the shortest route between the segments P1P2 and P3P4. Calculate the line segment PaPb that is the shortest route between two lines P1P2 and P3P4. Calculate also the values of mua and mub where Pa = P1 + mua (P2 - P1) Pb = P3 + mub (P4 - P3) source : http://paulbourke.net/geometry/lineline3d.
bool	intersection (const Carthesian::Segment3D &p1p2, const Carthesian::Segment3D &p3p4, Carthesian::Segment3D &papb, double &mua, double &mub)
	Calculate the line segment PaPb that is the shortest route between the segments P1P2 and P3P4. Calculate the line segment PaPb that is the shortest route between two lines P1P2 and P3P4. Calculate also the values of mua and mub where Pa = P1 + mua (P2 - P1) Pb = P3 + mub (P4 - P3) source : http://paulbourke.net/geometry/lineline3d.
double	angle (const Carthesian::Vector3D &v1, const Carthesian::Vector3D &v2)
	compute the angle in radians between 2 vectors
double	dotproduct (const Carthesian::Vector3D &v1, const Carthesian::Vector3D &v2)
	compute the scalar product between 2 vectors
void	dotproduct (const Carthesian::Matrix3D &m, const Carthesian::Vector3D &v, Carthesian::Vector3D &vout)
	compute the dot product between a matrix and a vector
Carthesian::Vector3D	dotproduct (const Carthesian::Matrix3D &m, const Carthesian::Vector3D &v)
	compute the dot product between a matrix and a vector
void	crossproduct (const Carthesian::Vector3D &v1, const Carthesian::Vector3D &v2, Carthesian::Vector3D &vout)
	compute the cross product between 2 vectors
Carthesian::Vector3D	crossproduct (const Carthesian::Vector3D &v1, const Carthesian::Vector3D &v2)
	compute the cross product between 2 vectors
void	rotation_matrix (const Carthesian::Vector3D &axis, const double theta, Carthesian::Matrix3D &matrix)
	construct the rotation matrix of an angle theta in radians using the vector axis as rotation axis Uses the Rodrigues' Rotation Formula set in http://mathworld.wolfram.com/RodriguesRotationFormula.html
void	rotate (const Carthesian::Vector3D &v, const Carthesian::Vector3D &axis, const double theta, Carthesian::Vector3D &vout)
	construct the vector issued of the rotation of v by an angle theta in radians using the vector axis as rotation axis Uses the Rodrigues' Rotation Formula set in http://mathworld.wolfram.com/RodriguesRotationFormula.html
Carthesian::Vector3D	rotate (const Carthesian::Vector3D &v, const Carthesian::Vector3D &axis, const double theta)
	construct the vector issued of the rotation of v by an angle theta in radians using the vector axis as rotation axis Uses the Rodrigues' Rotation Formula set in http://mathworld.wolfram.com/RodriguesRotationFormula.html

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Detailed Description

Carthesian geometry kernel

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Function Documentation

double Carthesian::angle	(	const Carthesian::Vector3D &	v1,
		const Carthesian::Vector3D &	v2
	)

compute the angle in radians between 2 vectors

Parameters:

	v1	first vector
	v2	second vector

Returns:

the oriented angle in radians

References crossproduct(), dotproduct(), and Carthesian::Vector3D::norm().

Carthesian::Vector3D Carthesian::crossproduct	(	const Carthesian::Vector3D &	v1,
		const Carthesian::Vector3D &	v2
	)

compute the cross product between 2 vectors

Parameters:

	v1	first vector
	v2	second vector

Returns:

the cross product vector

References crossproduct().

void Carthesian::crossproduct	(	const Carthesian::Vector3D &	v1,
		const Carthesian::Vector3D &	v2,
		Carthesian::Vector3D &	vout
	)

compute the cross product between 2 vectors

Parameters:

	v1	[IN] first vector
	v2	[IN] second vector
	vout	[OUT] the cross product vector

References Carthesian::Vector3D::set().

Referenced by angle(), crossproduct(), and Viewing::earth_to_sat_from_range().

double Carthesian::dotproduct	(	const Carthesian::Vector3D &	v1,
		const Carthesian::Vector3D &	v2
	)

compute the scalar product between 2 vectors

Parameters:

	v1	first vector
	v2	second vector

Returns:

the scalar product

Referenced by angle(), dotproduct(), and rotate().

void Carthesian::dotproduct	(	const Carthesian::Matrix3D &	m,
		const Carthesian::Vector3D &	v,
		Carthesian::Vector3D &	vout
	)

compute the dot product between a matrix and a vector

Parameters:

	m	[IN] a matrix
	v	[IN] a vector
	vout	[OUT] resulting vector

References Carthesian::Vector3D::set().

Carthesian::Vector3D Carthesian::dotproduct	(	const Carthesian::Matrix3D &	m,
		const Carthesian::Vector3D &	v
	)

compute the dot product between a matrix and a vector

Parameters:

	m	a matrix
	v	a vector

Returns:

the resulting vector

References dotproduct().

bool Carthesian::intersection	(	const Carthesian::Segment3D &	p1p2,
		const Carthesian::Segment3D &	p3p4,
		Carthesian::Segment3D &	papb,
		double &	mua,
		double &	mub
	)

Calculate the line segment PaPb that is the shortest route between the segments P1P2 and P3P4. Calculate the line segment PaPb that is the shortest route between two lines P1P2 and P3P4. Calculate also the values of mua and mub where Pa = P1 + mua (P2 - P1) Pb = P3 + mub (P4 - P3) source : http://paulbourke.net/geometry/lineline3d.

Parameters:

	p1p2	[IN] first segment
	p3p4	[IN] 2nd segment start point
	papb	[OUT] intersection segment
	mua	[OUT] ratio as Pa = P1 + mua (P2 - P1)
	mub	[OUT] ratio as Pb = P3 + mub (P4 - P3)

Returns:

Return false if no solution exists, true else

References intersection(), Carthesian::Segment3D::p1, and Carthesian::Segment3D::p2.

bool Carthesian::intersection	(	const Carthesian::Point3D &	p1,
		const Carthesian::Point3D &	p2,
		const Carthesian::Point3D &	p3,
		const Carthesian::Point3D &	p4,
		Carthesian::Point3D &	pa,
		Carthesian::Point3D &	pb,
		double &	mua,
		double &	mub
	)

Calculate the line segment PaPb that is the shortest route between the segments P1P2 and P3P4. Calculate the line segment PaPb that is the shortest route between two lines P1P2 and P3P4. Calculate also the values of mua and mub where Pa = P1 + mua (P2 - P1) Pb = P3 + mub (P4 - P3) source : http://paulbourke.net/geometry/lineline3d.

Parameters:

	p1	[IN] first segment start point
	p2	[IN] first segment end point
	p3	[IN] 2nd segment start point
	p4	[IN] 2nd segment end point
	pa	[OUT] intersection point on P1P2
	pb	[OUT] intersection point on P3P4
	mua	[OUT] ratio as Pa = P1 + mua (P2 - P1)
	mub	[OUT] ratio as Pb = P3 + mub (P4 - P3)

Returns:

Return false if no solution exists, true else

Referenced by intersection().

Carthesian::Vector3D Carthesian::rotate	(	const Carthesian::Vector3D &	v,
		const Carthesian::Vector3D &	axis,
		const double	theta
	)

construct the vector issued of the rotation of v by an angle theta in radians using the vector axis as rotation axis Uses the Rodrigues' Rotation Formula set in http://mathworld.wolfram.com/RodriguesRotationFormula.html

Parameters:

	v1	vector to rotate
	axis	vector used as rotation axis
	theta	rotation angle in radians

Returns:

the vector issued of the rotation

References rotate().

void Carthesian::rotate	(	const Carthesian::Vector3D &	v,
		const Carthesian::Vector3D &	axis,
		const double	theta,
		Carthesian::Vector3D &	vout
	)

construct the vector issued of the rotation of v by an angle theta in radians using the vector axis as rotation axis Uses the Rodrigues' Rotation Formula set in http://mathworld.wolfram.com/RodriguesRotationFormula.html

Parameters:

	v	[IN] vector to rotate
	axis	[IN] vector used as rotation axis
	theta	[IN] rotation angle in radians
	vout	[OUT] vector issued of the rotation

References dotproduct(), and rotation_matrix().

Referenced by Viewing::earth_to_sat_from_range(), and rotate().

void Carthesian::rotation_matrix	(	const Carthesian::Vector3D &	axis,
		const double	theta,
		Carthesian::Matrix3D &	matrix
	)

construct the rotation matrix of an angle theta in radians using the vector axis as rotation axis Uses the Rodrigues' Rotation Formula set in http://mathworld.wolfram.com/RodriguesRotationFormula.html

Parameters:

	axis	[IN] vector used as rotation axis
	theta	[IN] rotation angle in radians
	matrix	[OUT] rotation matrix

Referenced by rotate().