Bilib Geometry

Collaboration diagram for Bilib Geometry:

Functions
int	AffineToRotationMatrix (double *A, double *R, double *xRotation, double *yRotation, double *zRotation, int FirstOctant, double Tolerance, long MaxIterations, int *Status)
int	GetRotationMatrix (double *R, double xRotation, double yRotation, double zRotation)
int	GetScalingMatrix (double *S, double xScale, double yScale, double zScale)
int	GetTranslationMatrix (double *T, double xTranslation, double yTranslation, double zTranslation)
int	LineToLineIntersection (double P[], double Q[], double A[], double B[], double X[], long Lines, double Tolerance, long MaxIterations, int *Intersection, int *Status)
int	LineToLineIntersection3D (double P[], double q[], double A[], double b[], double X[], double Tolerance, int *Intersection)
int	LineToPlaneIntersection (double P[], double Q[], double A[], double B[], double C[], double X[], long Lines, double Tolerance, long MaxIterations, int *Intersection, int *Status)
int	LineToPlaneIntersection3D (double P[], double q[], double A[], double b[], double X[], double Tolerance, int *Intersection)
int	PointsToLine3D (double P[], double Q[], double A[], double b[], double Tolerance)
int	PointsToPlane3D (double P[], double Q[], double R[], double A[], double b[], double Tolerance)
int	PointToLineMembership (double P[], double A[], double B[], long Lines, double Tolerance, int *Membership, int *Status)
int	PointToLineMembership3D (double P[], double A[], double b[], double Tolerance, int *Membership)
int	PointToPlaneMembership (double P[], double A[], double B[], double C[], long Lines, double Tolerance, long MaxIterations, int *Membership, int *Status)
int	PointToPlaneMembership3D (double P[], double A[], double b[], double Tolerance, int *Membership)
int	ProjectPointToLine (double P[], double A[], double B[], double X[], long Lines, double Tolerance)
int	ProjectPointToLine3D (double P[], double A[], double b[], double X[], double Tolerance)
int	ProjectPointToPlane (double P[], double A[], double B[], double C[], double X[], long Lines, double Tolerance, long MaxIterations, int *Status)
int	ProjectPointToPlane3D (double P[], double A[], double b[], double X[], double Tolerance)
int	TestColinearVector (double U[], double V[], long Lines, double Tolerance, int *Colinear)
int	TestCoplanarVector (double U[], double V[], double W[], long Lines, double Tolerance, long MaxIterations, int *Coplanar, int *Status)

Detailed Description

Function Documentation

AffineToRotationMatrix()

int AffineToRotationMatrix	(	double *	A,
		double *	R,
		double *	xRotation,
		double *	yRotation,
		double *	zRotation,
		int	FirstOctant,
		double	Tolerance,
		long	MaxIterations,
		int *	Status
	)

Affine -> Rotation matrix. Approximate a (4 x 4) homogenous affine matrix by a (4 x 4) rotation matrix. The rotation matrix has the form R = Rx.Ry.Rz.

A and R are homogenous: (A, R) = {{*, *, *, 0}, {*, *, *, 0}, {*, *, *, 0}, {0, 0, 0, 1}}

The returned rotation angles are given in the unit of radian.

success: return(!ERROR); failure: return(ERROR)

GetRotationMatrix()

int GetRotationMatrix	(	double *	R,
		double	xRotation,
		double	yRotation,
		double	zRotation
	)

Produce Euler rotation matrix (X,Y,Z). Fill a rotation matrix R such that R = Rx.Ry.Rz. The size of the output matrix R is (4 x 4). R is homogenous: R = {{*, *, *, 0}, {*, *, *, 0}, {*, *, *, 0}, {0, 0, 0, 1}}. The rotation angles are given in the unit of radian.

success: return(!ERROR); failure: return(ERROR)

GetScalingMatrix()

int GetScalingMatrix	(	double *	S,
		double	xScale,
		double	yScale,
		double	zScale
	)

Produce scaling matrix. Fill a scaling matrix T. The size of the output matrix T is (4 x 4). T is homogenous: T = {{sx, 0, 0, 0}, {0, sy, 0, 0}, {0, 0, sz, 0}, {0, 0, 0, 1}}

success: return(!ERROR); failure: return(ERROR)

GetTranslationMatrix()

int GetTranslationMatrix	(	double *	T,
		double	xTranslation,
		double	yTranslation,
		double	zTranslation
	)

Produce a translation matrix. Fill a translation matrix T. The size of the output matrix T is (4 x 4) T is homogenous: T = {{1, 0, 0, dx}, {0, 1, 0, dy}, {0, 0, 1, dz}, {0, 0, 0, 1}}

success: return(!ERROR); failure: return(ERROR)

LineToLineIntersection()

int LineToLineIntersection	(	double	P[],
		double	Q[],
		double	A[],
		double	B[],
		double	X[],
		long	Lines,
		double	Tolerance,
		long	MaxIterations,
		int *	Intersection,
		int *	Status
	)

Do two lines intersect (n-D)?. Compute the intersection of the line (P,Q) with the line (A,B). All vectors have (Lines) elements. I.e., the dimension of the space is (Lines).

return Intersection = FALSE if there is no intersection. return Intersection = TRUE if the intersection is valid.

success: return(!ERROR); failure: return(ERROR)

LineToLineIntersection3D()

int LineToLineIntersection3D	(	double	P[],
		double	q[],
		double	A[],
		double	b[],
		double	X[],
		double	Tolerance,
		int *	Intersection
	)

Do two lines intersect (3-D)? Compute the intersection of the line (P,q) with the line (A,b). All points have 3 elements. All vectors have 3 elements.

A line is described by a point and a vector: X = P + t1 * q, X = A + t2 * b where (t1,t2) are free scalars.

The vectors (q, b) must have a normalized unit length.

return Intersection = FALSE if there is no intersection. return Intersection = TRUE if the intersection is valid.

success: return(!ERROR); failure: return(ERROR)

LineToPlaneIntersection()

int LineToPlaneIntersection	(	double	P[],
		double	Q[],
		double	A[],
		double	B[],
		double	C[],
		double	X[],
		long	Lines,
		double	Tolerance,
		long	MaxIterations,
		int *	Intersection,
		int *	Status
	)

Does a line intersect a plane (n-D)? Compute the intersection of the line (P,Q) with the plane (A,B,C). All vectors have (Lines) elements. I.e., the dimension of the space is (Lines).

return Intersection = FALSE if there is no intersection. return Intersection = TRUE if the intersection is valid.

success: return(!ERROR); failure: return(ERROR)

LineToPlaneIntersection3D()

int LineToPlaneIntersection3D	(	double	P[],
		double	q[],
		double	A[],
		double	b[],
		double	X[],
		double	Tolerance,
		int *	Intersection
	)

Does a line intersect a plane (3-D)? Compute the intersection of the line (P,q) with the plane (A,b). All points have 3 elements. All vectors have 3 elements.

A line is described by a point P and a vector q: X = P + t * q, with t a free scalar. A plane is described by a point A and a normal b: <AX, b> = 0. The vectors (q, b) must have a normalized unit length.

return Intersection = FALE if there is no intersection. return Intersection = TRUE if the intersection is valid.

success: return(!ERROR); failure: return(ERROR)

PointsToLine3D()

int PointsToLine3D	(	double	P[],
		double	Q[],
		double	A[],
		double	b[],
		double	Tolerance
	)

What is the line that passes through two points (3-D)?. Transform the points (P,Q) into the line (A,b). All points have 3 elements. All vectors have 3 elements.

A line is described by a point A and a vector b: X = A + t * b, with t a free scalar. The vector b has a normalized unit length.

success: return(!ERROR); failure: return(ERROR)

PointsToPlane3D()

int PointsToPlane3D	(	double	P[],
		double	Q[],
		double	R[],
		double	A[],
		double	b[],
		double	Tolerance
	)

What is the plane passing through 3 points (3-D)? Transform the points (P,Q,R) into the plane (A,b). All points have 3 elements. All vectors have 3 elements.

A plane is described by a point A and a normal b: <AX, b> = 0. The vectors b has a normalized unit length.

success: return(!ERROR); failure: return(ERROR)

PointToLineMembership()

int PointToLineMembership	(	double	P[],
		double	A[],
		double	B[],
		long	Lines,
		double	Tolerance,
		int *	Membership,
		int *	Status
	)

Does a point belong to a line (n-D)?. Test the membership of the point P to the line (A,B). All vectors have (Lines) elements.

return Membership = FALSE if P doesn't belong to (A,B). return Membership = TRUE if P does belong to (A,B).

success: return(!ERROR); failure: return(ERROR)

PointToLineMembership3D()

int PointToLineMembership3D	(	double	P[],
		double	A[],
		double	b[],
		double	Tolerance,
		int *	Membership
	)

Does a point belong to a line (3-D)? Test the membership of the point P to the line (A,b). All points have 3 elements. All vectors have 3 elements.

A line is described by a point A and a vector b: X = A + t * b, with t a free scalar. The vector b must have a normalized unit length.

return Membership = FALSE if P doesn't belong to (A,b). return Membership = TRUE if P does belong to (A,b).

success: return(!ERROR); failure: return(ERROR)

PointToPlaneMembership()

int PointToPlaneMembership	(	double	P[],
		double	A[],
		double	B[],
		double	C[],
		long	Lines,
		double	Tolerance,
		long	MaxIterations,
		int *	Membership,
		int *	Status
	)

Does a point belong to a plane (n-D)?. Test the membership of the point P to the plane (A,B,C). All vectors have (Lines) elements.

return Membership = FALSE if P doesn't belong to (A,B,C). return Membership = TRUE if P does belong to (A,B,C)

success: return(!ERROR); failure: return(ERROR)

PointToPlaneMembership3D()

int PointToPlaneMembership3D	(	double	P[],
		double	A[],
		double	b[],
		double	Tolerance,
		int *	Membership
	)

Does a point belong to a plane (3-D)? Test the membership of the point P to the plane (A,b). All points have 3 elements. All vectors have 3 elements.

A plane is described by a point A and a normal b: <AX, b> = 0. The vectors b must have a normalized unit length.

return Membership = FALSE if P doesn't belong to (A,b). return Membership = TRUE if P does belong to (A,b)

success: return(!ERROR); failure: return(ERROR)

ProjectPointToLine()

int ProjectPointToLine	(	double	P[],
		double	A[],
		double	B[],
		double	X[],
		long	Lines,
		double	Tolerance
	)

Project a point onto a line (n-D). Project the point P onto the line (A,B). All vectors have (Lines) elements.

success: return(!ERROR); failure: return(ERROR)

ProjectPointToLine3D()

int ProjectPointToLine3D	(	double	P[],
		double	A[],
		double	b[],
		double	X[],
		double	Tolerance
	)

Project a point onto a line (3-D). Project the point P onto the line (A,b). All points have 3 elements. All vectors have 3 elements.

A line is described by a point A and a vector b: X = A + t * b, with t a free scalar. The vector b must have a normalized unit length.

success: return(!ERROR); failure: return(ERROR)

ProjectPointToPlane()

int ProjectPointToPlane	(	double	P[],
		double	A[],
		double	B[],
		double	C[],
		double	X[],
		long	Lines,
		double	Tolerance,
		long	MaxIterations,
		int *	Status
	)

Project a point onto a plane (n-D). Project the point P onto the plane (A,B,C). All vectors have (Lines) elements.

success: return(!ERROR); failure: return(ERROR)

ProjectPointToPlane3D()

int ProjectPointToPlane3D	(	double	P[],
		double	A[],
		double	b[],
		double	X[],
		double	Tolerance
	)

Project a point onto a plane (3-D). Project the point P onto the plane (A,b). All points have 3 elements. All vectors have 3 elements.

A plane is described by a point A and a normal b: <AX, b> = 0. The vectors b must have a normalized unit length.

success: return(!ERROR); failure: return(ERROR)

TestColinearVector()

int TestColinearVector	(	double	U[],
		double	V[],
		long	Lines,
		double	Tolerance,
		int *	Colinear
	)

Are two vectors colinear (n-D)?. Determine whether the vectors U and V are colinear. The vectors U and V have (Lines) elements.

return Colinear = -1 if at least one of the vectors is degenerate. return Colinear = 0 if the vectors are not colinear. return Colinear = 1 if the vectors are colinear.

success: return(!ERROR); failure: return(ERROR)

TestCoplanarVector()

int TestCoplanarVector	(	double	U[],
		double	V[],
		double	W[],
		long	Lines,
		double	Tolerance,
		long	MaxIterations,
		int *	Coplanar,
		int *	Status
	)

Are three vectors coplanar (n-D)? Determine whether the vectors (U,V,W) are coplanar. The vectors (U,V,W) have (Lines) elements.

return Coplanar = -1 in degenerate cases. return Coplanar = 0 if the vectors are not coplanar. return Coplanar = 1 if the vectors are coplanar.

success: return(!ERROR); failure: return(ERROR)