Method class for mathematical calculations, multiplications of homogeneous matrices, conversion Euler angle, triangle calculations, formula parser, etc. More...

#include <erk_capi.h>

Inheritance diagram for ERK_CAPI_SYS_MATHEMATICS:

Static Public Member Functions
static DLLAPI int ER_STDCALL	erMath_FrameToVecIdx (DFRAME T, double vec, long rotation_idx=ER_ROT_XYZ)
	Converts a frame into an euler vector or quaternion. Frame `T` is converted into a vector `vec` A frame DFRAME is a homogeneous 4x4 transformation matrix. Depending on the rotation index `rotation_idx`, which is one of ER_ROT_XYZ = RotX * RotY' * RotZ'' default, ER_ROT_XYZ, ER_ROT_ZYX, ER_ROT_YXZ, ER_ROT_ZYZ,ER_ROT_XYX, ER_ROT_RPY, ER_ROT_QUAT, ER_ROT_CA, ER_ROT_ZYpZ, ER_ROT_Y9XZ, ER_ROT_Z9XY, ER_ROT_Z9XZ, ER_ROT_Z9YX, ER_ROT_IJK, ER_ROT_ANGLE_1 See also erMath_VecToFrameIdx() More...

static DLLAPI int ER_STDCALL	erMath_VecToFrameIdx (double vec, DFRAME T, long rotation_idx=ER_ROT_XYZ)
	Converts an euler vector or quaternion into a frame. Vector `vec` is converted into a frame `T` A frame DFRAME is a homogeneous 4x4 transformation matrix. Depending on the rotation index `rotation_idx`, which is one of ER_ROT_XYZ = RotX * RotY' * RotZ'' default, ER_ROT_XYZ, ER_ROT_ZYX, ER_ROT_YXZ, ER_ROT_ZYZ,ER_ROT_XYX, ER_ROT_RPY, ER_ROT_QUAT, ER_ROT_CA, ER_ROT_ZYpZ, ER_ROT_Y9XZ, ER_ROT_Z9XY, ER_ROT_Z9XZ, ER_ROT_Z9YX, ER_ROT_IJK, ER_ROT_ANGLE_1 See also erMath_FrameToVecIdx() More...

static DLLAPI int ER_STDCALL	erMath_PxyzRxyzToFrame (double x, double y, double z, double Rx, double Ry, double Rz, DFRAME *T)
	Converts an euler represented location with rotation index ER_ROT_XYZ into a frame. Location `x`, `y`, `z`, `Rx`, `Ry`, `Rz` are converted into a frame `T` A frame DFRAME is a homogeneous 4x4 transformation matrix. See also erMath_VecToFrameIdx(), erMath_FrameToVecIdx() More...

static DLLAPI int ER_STDCALL	erMath_Frame_Ident (DFRAME *T)
	Set the homogeneous 4x4 transformation matrix `T` to identity. T = Ident A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_Frame_Trans (DFRAME *T, double x, double y, double z)
	Set position of homogeneous 4x4 transformation matrix. T.p[] = [x,y,z] A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_Frame_Rot (DFRAME *T, double q, long rotation_idx=ER_ROT_IDENT)
	Set orientation of homogeneous 4x4 transformation matrix. T = f(q,rotation_idx) The rotation index `rotation_idx`, is one of ER_ROT_IDENT=default, ER_ROT_X, ER_ROT_Y or ER_ROT_Z A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_AngleBetween (DFRAME Ts, DFRAME Te, double angle, double k=NULL)
	Calculates the angle and the equivalent angle axis between two homogeneous 4x4 transformation matrices. Rotation from start frame `Ts` into end frame `Te` by angle of rotation `angle` about the equivalent angle axis `k` A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_DistBetween (DFRAME Ts, DFRAME Te, double dist, double dv=NULL)
	Calculates the distance and direction between two homogeneous 4x4 transformation matrices. Translation from start frame `Ts` into end frame `Te` by the distance `dist` in direction `vd` A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_CircCenterPoint (double ps, double pv, double pe, DFRAME pTc, double radius, double phi, double *phi_via=NULL)
	Circle calculation from three points `ps` over `pv` to `pe`. Calculates center of circle, radius and angle. More...

static DLLAPI int ER_STDCALL	erMath_invT (DFRAME To, DFRAME Ti)
	Builds the inverse of a homogeneous 4x4 transformation matrix `T`. To = inv(Ti) = ( Ri' , -Ri'*pi ), Ri' is transpose of Ri A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_invR (DFRAME Ro, DFRAME Ri)
	Builds the inverse of the 3x3 orientation matrix from a homogeneous 4x4 transformation matrix `T`. Ro = inv(Ri) = transpose(Ri) = Ri', with Ti = ( Ri , pi ) A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_R_R (DFRAME Ro, DFRAME Ri1, DFRAME *Ri2)
	Orientation multiplication of two homogeneous 4x4 transformation matrices. Ro = Ri1 * Ri2 A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_T (DFRAME To, DFRAME Ti1, DFRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = Ti1 * Ti2 A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_invT (DFRAME To, DFRAME Ti1, DFRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = Ti1 * inv(Ti2) Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_T (DFRAME To, DFRAME Ti1, DFRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = inv(Ti1) * Ti2 Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_invT (DFRAME To, DFRAME Ti1, DFRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = inv(Ti1) * inv(Ti2) Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_pos (double po, DFRAME T, double *pi)
	Multiplication of a 3x1 position with a homogeneous 4x4 transformation matrices. po = T * pi, pi is vector of size ER_DIM po = R*pi + p, with T = ( R , p) A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_pos (double po, DFRAME T, double *pi)
	Multiplication of a 3x1 position with the inverse of a homogeneous 4x4 transformation matrices. po = inv(T) * pi, pi is vector of size ER_DIM Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_R_pos (double po, DFRAME R, double *pi)
	Multiplication of a 3x1 position with the 3x3 orientation of a homogeneous 4x4 transformation matrices. po = R * pi, pi is vector of size ER_DIM A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invR_pos (double po, DFRAME R, double *pi)
	Multiplication of a 3x1 position with the transpose of a 3x3 orientation of a homogeneous 4x4 transformation matrices. po = R' * pi, pi is vector of size ER_DIM Remarks R' = inv(R) is the transpose of R, see erMath_invR() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_T_T (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * Ti2 * Ti3 A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_T_invT (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * Ti2 * inv(Ti3) Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_invT_T (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * inv(Ti2) * Ti3 Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_T_invT_invT (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * inv(Ti2) * inv(Ti3) Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_T_T (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * Ti2 * Ti3 Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_T_invT (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * Ti2 * inv(Ti3) Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_invT_T (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * inv(Ti2) * Ti3 Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI int ER_STDCALL	erMath_mul_invT_invT_invT (DFRAME To, DFRAME Ti1, DFRAME Ti2, DFRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * inv(Ti2) * inv(Ti3) Remarks inv(T) is the inverse of T, see erMath_invT() A frame DFRAME is a homogeneous 4x4 transformation matrix. More...

static DLLAPI double *ER_STDCALL	erMath_SetVec6 (double *vec, double q1, double q2, double q3, double q4, double q5, double q6)
	Cpy six values to a vector. More...

static DLLAPI double *ER_STDCALL	erMath_SetVec6PosOri (double *vec, double x, double y, double z, double Rx, double Ry, double Rz)
	Cpy and convert a target location (position+orientation) to a vector position x,y,z in [mm] converted to [m] by ER_mm2m orientation Rx,Ry,Rz in [deg] converted to [rad] by ER_RAD . More...

static DLLAPI DFRAME *ER_STDCALL	erMath_SetFramePosOri (DFRAME *To, double x, double y, double z, double Rx, double Ry, double Rz)
	Cpy and convert a target location (position+orientation) to a DFRAME position x,y,z in [mm] converted to [m] by ER_mm2m orientation Rx,Ry,Rz in [deg] converted to [rad] by ER_RAD . More...

static DLLAPI double *ER_STDCALL	erMath_SetVec_n (double *vec, int n, double q1, double q2, double q3, double q4, double q5, double q6)
	Cpy n values to a vector. More...

static DLLAPI double *ER_STDCALL	erMath_CpyVec (double dst, double src, int n)
	Cpy vector dst = src. More...

static DLLAPI double *ER_STDCALL	erMath_ResetVec (double *dst, int n)
	Reset vector dst = 0. More...

Additional Inherited Members
Static Public Attributes inherited from ERK_CAPI_SYS
static ERK_CAPI_SYS_UTILITIES	erk_capi_sys_utilities
	Method class for helping functions, color conversion, etc. More...

static ERK_CAPI_SYS_MATHEMATICS	erk_capi_sys_mathematics
	Method class for mathematical calculations, multiplications of homogeneous matrices, conversion Euler angle, triangle calculations, formula parser, etc. More...

Static Public Attributes inherited from ERK_CAPI
static ERK_CAPI_ADMIN	erk_capi_admin
	Method class to administrate this Robotics Simulation Kernel. More...

static ERK_CAPI_DEVICES	erk_capi_devices
	Method class to create, attach, update devices, for kinematics calculations and for motion planning and -execution. More...

static ERK_CAPI_SIM	erk_capi_sim
	Method class for simulation settings. More...

static ERK_CAPI_AUTOPATH	erk_capi_autopath
	Method class for collision free path planning. More...

static ERK_CAPI_TARGETS	erk_capi_targets
	Method class for paths and tags. More...

static ERK_CAPI_GEO	erk_capi_geo
	Method class to handle 3D Geometry Data. More...

static ERK_CAPI_SYS	erk_capi_sys
	Method class for mathematical calculations, simulation status, units. More...

Detailed Description

Method class for mathematical calculations, multiplications of homogeneous matrices, conversion Euler angle, triangle calculations, formula parser, etc.

Member Function Documentation

◆ erMath_AngleBetween()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_AngleBetween	(	DFRAME *	Ts,
		DFRAME *	Te,
		double *	angle,
		double *	k = `NULL`
	)

static

Calculates the angle and the equivalent angle axis between two homogeneous 4x4 transformation matrices.
Rotation from start frame Ts into end frame Te by angle of rotation angle about the equivalent angle axis k
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[in]	Ts	start frame DFRAME
[in]	Te	end frame DFRAME
[out]	angle	angle of rotation [rad]
[out]	k	normalized equivalent angle axis

Return values

0	- OK
1	- Error, invalid rotation idx, kernel not initialized

◆ erMath_CircCenterPoint()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_CircCenterPoint	(	double *	ps,
		double *	pv,
		double *	pe,
		DFRAME *	pTc,
		double *	radius,
		double *	phi,
		double *	phi_via = `NULL`
	)

static

Circle calculation from three points ps over pv to pe.
Calculates center of circle, radius and angle.

Parameters

[in]	ps	1st start point, ER_DIM
[in]	pv	2nd via point, ER_DIM
[in]	pe	3rd end point, ER_DIM
[out]	pTc	center of circle, DFRAME
[out]	radius	of circle
[out]	phi	angle of complete circle segment from `ps` over `pv` to `pe`
[out]	phi_via	angle of circle segment from `ps` to `pv`

Return values

0	- OK
1	- Error, cannot calculate circle, maybe ps, pv and pe are on a line

◆ erMath_CpyVec()

static DLLAPI double* ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_CpyVec	(	double *	dst,
		double *	src,
		int	n
	)

static

Cpy vector dst = src.

Parameters

[out]	dst	- destination
[in]	src	- source
[in]	n	- number of values to cpy

Return values

pointer to double of dst

◆ erMath_DistBetween()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_DistBetween	(	DFRAME *	Ts,
		DFRAME *	Te,
		double *	dist,
		double *	dv = `NULL`
	)

static

Calculates the distance and direction between two homogeneous 4x4 transformation matrices.
Translation from start frame Ts into end frame Te by the distance dist in direction vd
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[in]	Ts	start frame DFRAME
[in]	Te	end frame DFRAME
[out]	dist	distance
[out]	dv	normalized direction

Return values

0	- OK
1	- Error, invalid rotation idx, kernel not initialized

◆ erMath_Frame_Ident()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_Frame_Ident ( DFRAME * T )

static

Set the homogeneous 4x4 transformation matrix T to identity.
T = Ident
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out] T frame identity DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_Frame_Rot()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_Frame_Rot	(	DFRAME *	T,
		double	q,
		long	rotation_idx = `ER_ROT_IDENT`
	)

static

Set orientation of homogeneous 4x4 transformation matrix.
T = f(q,rotation_idx)
The rotation index rotation_idx, is one of
ER_ROT_IDENT=default, ER_ROT_X, ER_ROT_Y or ER_ROT_Z
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	T	frame DFRAME
[in]	q	rotation angle [rad]
[in]	rotation_idx	rotation index

Return values

0	- OK
1	- Error, invalid rotation idx, kernel not initialized

◆ erMath_Frame_Trans()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_Frame_Trans	(	DFRAME *	T,
		double	x,
		double	y,
		double	z
	)

static

Set position of homogeneous 4x4 transformation matrix.
T.p[] = [x,y,z]
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	T	frame DFRAME
[in]	x	X position
[in]	y	Y position
[in]	z	Z position

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_FrameToVecIdx()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_FrameToVecIdx	(	DFRAME *	T,
		double *	vec,
		long	rotation_idx = `ER_ROT_XYZ`
	)

static

Converts a frame into an euler vector or quaternion. Frame T is converted into a vector vec
A frame DFRAME is a homogeneous 4x4 transformation matrix.
Depending on the rotation index rotation_idx, which is one of
ER_ROT_XYZ = RotX * RotY' * RotZ'' default,
ER_ROT_XYZ, ER_ROT_ZYX, ER_ROT_YXZ, ER_ROT_ZYZ,ER_ROT_XYX, ER_ROT_RPY, ER_ROT_QUAT, ER_ROT_CA, ER_ROT_ZYpZ,
ER_ROT_Y9XZ, ER_ROT_Z9XY, ER_ROT_Z9XZ, ER_ROT_Z9YX, ER_ROT_IJK, ER_ROT_ANGLE_1
See also erMath_VecToFrameIdx()

Parameters

[in]	T	homegeneous matrix DFRAME
[out]	vec	vector (euler, quaternion in [rad]), max size is ER_DOF6 or ER_DOF_QUAT for ER_ROT_QUAT
[in]	rotation_idx	rotation index

Return values

0	- Error, invalid rotation_idx, no results calculated in vector `vec`
>=5	- number of valid calculated values in vector `vec`, depending on the rotation index `rotation_idx`

◆ erMath_invR()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_invR	(	DFRAME *	Ro,
		DFRAME *	Ri
	)

static

Builds the inverse of the 3x3 orientation matrix from a homogeneous 4x4 transformation matrix T.
Ro = inv(Ri) = transpose(Ri) = Ri', with Ti = ( Ri , pi )
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	Ro	inverse of Ri DFRAME
[in]	Ri	frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_invT	(	DFRAME *	To,
		DFRAME *	Ti
	)

static

Builds the inverse of a homogeneous 4x4 transformation matrix T.
To = inv(Ti) = ( Ri' , -Ri'*pi ), Ri' is transpose of Ri
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	inverse of Ti DFRAME
[in]	Ti	frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invR_pos()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invR_pos	(	double *	po,
		DFRAME *	R,
		double *	pi
	)

static

Multiplication of a 3x1 position with the transpose of a 3x3 orientation of a homogeneous 4x4 transformation matrices.
po = R' * pi, pi is vector of size ER_DIM
Remarks
R' = inv(R) is the transpose of R, see erMath_invR()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	po	position product of inv(R) and pi ER_DIM
[in]	R	3x3 orientation frame DFRAME
[in]	pi	position ER_DIM

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_invT	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2
	)

static

Multiplication of two homogeneous 4x4 transformation matrices.
To = inv(Ti1) * inv(Ti2)
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and inv(Ti2) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_invT_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_invT_invT	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = inv(Ti1) * inv(Ti2) * inv(Ti3)
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of inv(Ti1) and inv(Ti2) and inv(Ti3) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_invT_T()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_invT_T	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = inv(Ti1) * inv(Ti2) * Ti3
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of inv(Ti1) and inv(Ti2) and Ti3 DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_pos()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_pos	(	double *	po,
		DFRAME *	T,
		double *	pi
	)

static

Multiplication of a 3x1 position with the inverse of a homogeneous 4x4 transformation matrices.
po = inv(T) * pi, pi is vector of size ER_DIM
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	po	position product of inv(T) and pi ER_DIM
[in]	T	frame DFRAME
[in]	pi	position ER_DIM

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_T()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_T	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2
	)

static

Multiplication of two homogeneous 4x4 transformation matrices.
To = inv(Ti1) * Ti2
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and inv(Ti2) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_T_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_T_invT	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = inv(Ti1) * Ti2 * inv(Ti3)
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of inv(Ti1) and Ti2 and inv(Ti3) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_invT_T_T()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_invT_T_T	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = inv(Ti1) * Ti2 * Ti3
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of inv(Ti1) and Ti2 and Ti3 DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_R_pos()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_R_pos	(	double *	po,
		DFRAME *	R,
		double *	pi
	)

static

Multiplication of a 3x1 position with the 3x3 orientation of a homogeneous 4x4 transformation matrices.
po = R * pi, pi is vector of size ER_DIM
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	po	position product of R and pi ER_DIM
[in]	R	3x3 orientation frame DFRAME
[in]	pi	position ER_DIM

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_R_R()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_R_R	(	DFRAME *	Ro,
		DFRAME *	Ri1,
		DFRAME *	Ri2
	)

static

Orientation multiplication of two homogeneous 4x4 transformation matrices.
Ro = Ri1 * Ri2
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	Ro	product of Ri1 and Ri2 DFRAME
[in]	Ri1	1st frame orientation DFRAME
[in]	Ri2	2nd frame orientation DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_invT	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2
	)

static

Multiplication of two homogeneous 4x4 transformation matrices.
To = Ti1 * inv(Ti2)
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and inv(Ti2) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_invT_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_invT_invT	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = Ti1 * inv(Ti2) * inv(Ti3)
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and inv(Ti2) and inv(Ti3) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_invT_T()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_invT_T	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = Ti1 * inv(Ti2) * Ti3
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and inv(Ti2) and Ti3 DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_pos()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_pos	(	double *	po,
		DFRAME *	T,
		double *	pi
	)

static

Multiplication of a 3x1 position with a homogeneous 4x4 transformation matrices.
po = T * pi, pi is vector of size ER_DIM
po = R*pi + p, with T = ( R , p) A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	po	position product of T and pi ER_DIM
[in]	T	frame DFRAME
[in]	pi	position ER_DIM

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_T()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_T	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2
	)

static

Multiplication of two homogeneous 4x4 transformation matrices.
To = Ti1 * Ti2
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and Ti2 DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_T_invT()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_T_invT	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = Ti1 * Ti2 * inv(Ti3)
Remarks
inv(T) is the inverse of T, see erMath_invT()
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and Ti2 and inv(Ti3) DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_mul_T_T_T()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_mul_T_T_T	(	DFRAME *	To,
		DFRAME *	Ti1,
		DFRAME *	Ti2,
		DFRAME *	Ti3
	)

static

Tripple multiplication of homogeneous 4x4 transformation matrices.
To = Ti1 * Ti2 * Ti3
A frame DFRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	To	product of Ti1 and Ti2 and Ti3 DFRAME
[in]	Ti1	1st frame DFRAME
[in]	Ti2	2nd frame DFRAME
[in]	Ti3	3rd frame DFRAME

Return values

0	- OK
1	- Error, kernel not initialized

◆ erMath_PxyzRxyzToFrame()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_PxyzRxyzToFrame	(	double	x,
		double	y,
		double	z,
		double	Rx,
		double	Ry,
		double	Rz,
		DFRAME *	T
	)

static

Converts an euler represented location with rotation index ER_ROT_XYZ into a frame.
Location x, y, z, Rx, Ry, Rz are converted into a frame T
A frame DFRAME is a homogeneous 4x4 transformation matrix.
See also erMath_VecToFrameIdx(), erMath_FrameToVecIdx()

Parameters

[in]	x	X position
[in]	y	Y position
[in]	z	Z position
[in]	Rx	rotation angle about X axis in [rad]
[in]	Ry	rotation angle about Y axis in [rad]
[in]	Rz	rotation angle about Z axis in [rad]
[out]	T	homegeneous matrix DFRAME

Return values

0	- OK
1	- Error, invalid rotation idx, kernel not initialized

◆ erMath_ResetVec()

static DLLAPI double* ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_ResetVec	(	double *	dst,
		int	n
	)

static

Reset vector dst = 0.

Parameters

[out]	dst	- destination
[in]	n	- number of values to reset to 0

Return values

pointer to double of dst

◆ erMath_SetFramePosOri()

static DLLAPI DFRAME* ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_SetFramePosOri	(	DFRAME *	To,
		double	x,
		double	y,
		double	z,
		double	Rx,
		double	Ry,
		double	Rz
	)

static

Cpy and convert a target location (position+orientation) to a DFRAME
position x,y,z in [mm] converted to [m] by ER_mm2m
orientation Rx,Ry,Rz in [deg] converted to [rad] by ER_RAD
.

Parameters

[in,out]	To	- DFRAME
[in]	x	- x position
[in]	y	- y position
[in]	z	- z position
[in]	Rx	- x rotation
[in]	Ry	- y rotation
[in]	Rz	- z rotation

Return values

pointer to DFRAME of To

◆ erMath_SetVec6()

static DLLAPI double* ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_SetVec6	(	double *	vec,
		double	q1,
		double	q2,
		double	q3,
		double	q4,
		double	q5,
		double	q6
	)

static

Cpy six values to a vector.

Parameters

[in,out]	vec	- [q1,q2,q3, q4,q5,q6]
[in]	q1	- 1st value
[in]	q2	- 2nd value
[in]	q3	- 3rd value
[in]	q4	- 4th value
[in]	q5	- 5th value
[in]	q6	- 6th value

Return values

pointer to double of vec

◆ erMath_SetVec6PosOri()

static DLLAPI double* ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_SetVec6PosOri	(	double *	vec,
		double	x,
		double	y,
		double	z,
		double	Rx,
		double	Ry,
		double	Rz
	)

static

Cpy and convert a target location (position+orientation) to a vector
position x,y,z in [mm] converted to [m] by ER_mm2m
orientation Rx,Ry,Rz in [deg] converted to [rad] by ER_RAD
.

Parameters

[in,out]	vec	- [x,y,z, Rx,Ry,Rz]
[in]	x	- x position
[in]	y	- y position
[in]	z	- z position
[in]	Rx	- x rotation
[in]	Ry	- y rotation
[in]	Rz	- z rotation

Return values

pointer to double of vec

◆ erMath_SetVec_n()

static DLLAPI double* ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_SetVec_n	(	double *	vec,
		int	n,
		double	q1,
		double	q2,
		double	q3,
		double	q4,
		double	q5,
		double	q6
	)

static

Cpy n values to a vector.

Parameters

[in,out]	vec	- [q1,q2,q3, q4,q5,q6]
[in]	n	- number of values to cpy, maximum is 6
[in]	q1	- 1st value
[in]	q2	- 2nd value
[in]	q3	- 3rd value
[in]	q4	- 4th value
[in]	q5	- 5th value
[in]	q6	- 6th value

Return values

pointer to double of vec

◆ erMath_VecToFrameIdx()

static DLLAPI int ER_STDCALL ERK_CAPI_SYS_MATHEMATICS::erMath_VecToFrameIdx	(	double *	vec,
		DFRAME *	T,
		long	rotation_idx = `ER_ROT_XYZ`
	)

static

Converts an euler vector or quaternion into a frame. Vector vec is converted into a frame T
A frame DFRAME is a homogeneous 4x4 transformation matrix.
Depending on the rotation index rotation_idx, which is one of
ER_ROT_XYZ = RotX * RotY' * RotZ'' default,
ER_ROT_XYZ, ER_ROT_ZYX, ER_ROT_YXZ, ER_ROT_ZYZ,ER_ROT_XYX, ER_ROT_RPY, ER_ROT_QUAT, ER_ROT_CA, ER_ROT_ZYpZ,
ER_ROT_Y9XZ, ER_ROT_Z9XY, ER_ROT_Z9XZ, ER_ROT_Z9YX, ER_ROT_IJK, ER_ROT_ANGLE_1
See also erMath_FrameToVecIdx()

Parameters

[in]	vec	vector (euler, quaternion in [rad]), max size is ER_DOF6 or ER_DOF_QUAT for ER_ROT_QUAT
[out]	T	homegeneous matrix DFRAME
[in]	rotation_idx	rotation index

Return values

0	- OK
1	- Error, invalid rotation idx, kernel not initialized

The documentation for this class was generated from the following file:

erk_capi.h

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ erMath_AngleBetween()

◆ erMath_CircCenterPoint()

◆ erMath_CpyVec()

◆ erMath_DistBetween()

◆ erMath_Frame_Ident()

◆ erMath_Frame_Rot()

◆ erMath_Frame_Trans()

◆ erMath_FrameToVecIdx()

◆ erMath_invR()

◆ erMath_invT()

◆ erMath_mul_invR_pos()

◆ erMath_mul_invT_invT()

◆ erMath_mul_invT_invT_invT()

◆ erMath_mul_invT_invT_T()

◆ erMath_mul_invT_pos()

◆ erMath_mul_invT_T()

◆ erMath_mul_invT_T_invT()

◆ erMath_mul_invT_T_T()

◆ erMath_mul_R_pos()

◆ erMath_mul_R_R()

◆ erMath_mul_T_invT()

◆ erMath_mul_T_invT_invT()

◆ erMath_mul_T_invT_T()

◆ erMath_mul_T_pos()

◆ erMath_mul_T_T()

◆ erMath_mul_T_T_invT()

◆ erMath_mul_T_T_T()

◆ erMath_PxyzRxyzToFrame()

◆ erMath_ResetVec()

◆ erMath_SetFramePosOri()

◆ erMath_SetVec6()

◆ erMath_SetVec6PosOri()

◆ erMath_SetVec_n()

◆ erMath_VecToFrameIdx()