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

#include <ER_CAPI.H>

Inheritance diagram for ER_CAPI_SYS_MATHEMATICS:

Static Public Member Functions
static ER_DllExport int	vec_to_frame_idx (float vec, frame T, int rotation_idx)
	Converts an euler vector or quaternion into a frame. Vector `vec` is converted into a frame `T` A frame FRAME is a homogeneous 4x4 transformation matrix. Depending on the rotation index `rotation_idx`, which is one of ROT_XYZ = RotX * RotY' * RotZ'' default, ROT_XYZ, ROT_ZYX, ROT_YXZ, ROT_ZYZ,ROT_XYX, ROT_RPY, ROT_QUAT, ROT_CA, ROT_ZYpZ, ROT_Y9XZ, ROT_Z9XY, ROT_Z9XZ, ROT_Z9YX, ROT_IJK, ROT_ANGLE_1 See also frame_to_vec_idx() More...

static ER_DllExport int	frame_to_vec_idx (float vec, frame T, int rotation_idx)
	Converts a frame into an euler vector or quaternion. Frame `T` is converted into a vector `vec` A frame FRAME is a homogeneous 4x4 transformation matrix. Depending on the rotation index `rotation_idx`, which is one of ROT_XYZ = RotX * RotY' * RotZ'' default, ROT_XYZ, ROT_ZYX, ROT_YXZ, ROT_ZYZ,ROT_XYX, ROT_RPY, ROT_QUAT, ROT_CA, ROT_ZYpZ, ROT_Y9XZ, ROT_Z9XY, ROT_Z9XZ, ROT_Z9YX, ROT_IJK, ROT_ANGLE_1 See also vec_to_frame_idx() More...

static ER_DllExport void	vec_to_frame (float vec, frame T)
	Converts an euler vector with ROT_XYZ representation into a frame. Vector `vec` is converted into a frame `T` A frame FRAME is a homogeneous 4x4 transformation matrix. See also frame_to_vec() More...

static ER_DllExport void	frame_to_vec (float vec, frame T)
	Converts a frame into an euler vector with ROT_XYZ representation. Frame `T` is converted into a vector `vec` A frame FRAME is a homogeneous 4x4 transformation matrix. See also vec_to_frame() More...

static ER_DllExport int *	inq_rob_kin_controller_rot_idx (void)
	Returns the Controller rotation index for the cRobot. The Controller index is one of ROT_XYZ = RotX * RotY' * RotZ'' default, ROT_XYZ, ROT_ZYX, ROT_YXZ, ROT_ZYZ,ROT_XYX, ROT_RPY, ROT_QUAT, ROT_CA, ROT_ZYpZ, ROT_Y9XZ, ROT_Z9XY, ROT_Z9XZ, ROT_Z9YX, ROT_IJK, ROT_ANGLE_1 . More...

static ER_DllExport char *	inq_rob_kin_controller_name (void)
	Returns the Controller name for the cRobot. More...

static ER_DllExport void	inv_T (FRAME To, FRAME Ti)
	Builds the inverse of a homogeneous 4x4 transformation matrix `Ti`. To = inv(Ti) = ( Ri' , -Ri'*pi ), Ri' is transpose of Ri A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	inv_R (FRAME Ro, FRAME 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 FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	incr_T (FRAME Ti1, FRAME Ti2, int res)
	Multiplication of two homogeneous 4x4 transformation matrices. Depending in `res` , the result is copied to `Ti1` or `Ti2`. If `res` is 1, Ti1 = Ti1 * Ti2 If `res` is 2, Ti2 = Ti1 * Ti2 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	incr_R (FRAME Ri1, FRAME Ri2, int res)
	Orientation multiplication of two homogeneous 4x4 transformation matrices. Depending in `res` , the result is copied to `Ri1` or `Ri2`. If `res` is 1, Ri1 = Ri1 * Ri2 If `res` is 2, Ri2 = Ri1 * Ri2 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	cpy_R (FRAME Ro, FRAME Ri)
	Copies the Orientation from frame `Ri` into frame `Ro` A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport float *	delta_T (float dx, frame Ts, frame *Ti)
	Builds the difference between frame Ts and frame Ti Position dx[0..2] = Ts->p[0..2] - Ti->p[0..2] Orientation dx[3..5]= 'inv(Ri)Rs'. Remarks* It is assumed that the orientation of Ts and Ti are "close by". More...

static ER_DllExport void	mul_R_R (FRAME Ro, FRAME Ri1, FRAME *Ri2)
	Orientation multiplication of two homogeneous 4x4 transformation matrices. Ro = Ri1 * Ri2 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_T (FRAME To, FRAME Ti1, FRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = Ti1 * Ti2 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_invT (FRAME To, FRAME Ti1, FRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = Ti1 * inv(Ti2) Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_T (FRAME To, FRAME Ti1, FRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = inv(Ti1) * Ti2 Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_invT (FRAME To, FRAME Ti1, FRAME *Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. To = inv(Ti1) * inv(Ti2) Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_pos (float po, FRAME T, float *pi)
	Multiplication of a 3x1 position with a homogeneous 4x4 transformation matrices. po = T * pi, pi is vector of size DIM po = R*pi + p, with T = ( R , p) A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_pos (float po, FRAME T, float *pi)
	Multiplication of a 3x1 position with the inverse of a homogeneous 4x4 transformation matrices. po = inv(T) * pi, pi is vector of size DIM Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_R_pos (float po, FRAME R, float *pi)
	Multiplication of a 3x1 position with the 3x3 orientation of a homogeneous 4x4 transformation matrices. po = R * pi, pi is vector of size DIM A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invR_pos (float po, FRAME R, float *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 DIM Remarks R' = inv(R) is the transpose of R, see inv_R() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_T_T (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * Ti2 * Ti3 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_T_invT (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * Ti2 * inv(Ti3) Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_invT_T (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * inv(Ti2) * Ti3 Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_T_invT_invT (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = Ti1 * inv(Ti2) * inv(Ti3) Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_T_T (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * Ti2 * Ti3 Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_T_invT (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * Ti2 * inv(Ti3) Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_invT_T (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * inv(Ti2) * Ti3 Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	mul_invT_invT_invT (FRAME To, FRAME Ti1, FRAME Ti2, FRAME Ti3)
	Tripple multiplication of homogeneous 4x4 transformation matrices. To = inv(Ti1) * inv(Ti2) * inv(Ti3) Remarks inv(T) is the inverse of T, see inv_T() A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	rob_kin_T_mal_T (frame Ti1, frame Ti2)
	Multiplication of two homogeneous 4x4 transformation matrices. Ti1 = Ti1 * Ti2 Remarks same as incr_T() with res=1 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	rob_kin_R_mal_R (frame Ti1, frame Ti2)
	Orientation multiplication of two homogeneous 4x4 transformation matrices. Ri1 = Ri1 * Ri2 Remarks same as incr_R() with res=1 A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	rob_kin_frame_ident (frame *T)
	Set the homogeneous 4x4 transformation matrix `T` to identity. T = Ident A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	rob_kin_rot (int rotation_idx, double q, frame *T)
	Set orientation of homogeneous 4x4 transformation matrix. T = f(q,rotation_idx) The rotation index `rotation_idx`, is one of ROT_IDENT = default, ROT_X, ROT_Y or ROT_Z A frame FRAME is a homogeneous 4x4 transformation matrix. More...

static ER_DllExport void	rob_kin_rot_xyz (frame *T, float Rx, float Ry, float Rz)
	Converts an euler represented rotation index ROT_XYZ into a frame. Rotation angle `Rx`, `Ry`, `Rz` are converted into a frame `T` A frame FRAME is a homogeneous 4x4 transformation matrix. Remarks Use rob_kin_trans() to set the position. More...

static ER_DllExport void	rob_kin_trans (frame *T, double x, double y, double z)
	Converts a position into a frame. Location `x`, `y`, `z` are converted into a frame `T` , T->p = [x,y,z] A frame FRAME is a homogeneous 4x4 transformation matrix. Remarks Use rob_kin_rot_xyz() to set the orientation. More...

static ER_DllExport void	dh_to_frame (ROB_DH rdh, frame T)
	Converts Denavit Hartenberg Parameter ROB_DH parameter into a homogeneous frame FRAME. More...

static ER_DllExport float	sass (float s1, float beta, float s2)
	Triangle calculation, calculates the opposite site of angle `beta` Using cosine rule c^2 = a^2 + b^2 - 2abcos(beta) Remarks* See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	sasa (float s1, float beta, float s2)
	Triangle calculation, calculates the angle at side `s2` Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	asss (float beta, float s1, float s2)
	Triangle calculation, calculates 3rd side s3 Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	assa (float beta, float s1, float s2)
	Triangle calculation, calculates angle between `s1` and `s2` Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	assa2 (float beta, float s1, float s2)
	Triangle calculation, calculates angle between `s2` and `s3` Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	sssa (float s1, float s2, float s3)
	Triangle calculation, calculates angle opposite of `s1` Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	sasssa (float s1, float beta, float s2, float s3, float s4)
	Quadrangle calculation, calculates angle between `s2` of `s3` Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport float	sasssa2 (float s1, float beta, float s2, float s3, float s4)
	Quadrangle calculation, calculates angle between `s3` of `s4` Remarks See EASY-ROB-ERPL-eng.pdf "parser functions". More...

static ER_DllExport int	inq_errorflg (void)
	Parser error flag Remarks call this function after calling parser_calc() More...

static ER_DllExport double	parser_calc (char str, int error)
	Formel parser calculation Remarks call inq_errorflg() to get parser error. More...

static ER_DllExport double	rob_kin_atan2 (double y, double x)
	Calculates math function atan2 If x=y=0, this function return 0. More...

static ER_DllExport int	circ_center_point (float p1, float p2, float p3, frame pTc, float radius, float phi, float *dphi=NULL)
	Circle calculation from three points `p1` over `p2` to `p3`. Calculates center of circle, radius and angle. More...

Additional Inherited Members
Static Public Attributes inherited from ER_CAPI_SYS
static ER_CAPI_SYS_UTILITIES	er_capi_sys_utilities
	Method class for helping functions, color conversion, etc. More...

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

static ER_CAPI_SYS_VIEW	er_capi_sys_view
	Method class for graphical update of the 3D scene, refreshing dialogs, etc. More...

static ER_CAPI_SYS_PREVIEW	er_capi_sys_preview
	Method class for the CAD-Preview. More...

static ER_CAPI_SYS_STATUS	er_capi_sys_status
	Method class for unloading objects (work cells, robots, tools, programs, etc.) simulation status. More...

static ER_CAPI_SYS_UNITS	er_capi_sys_units
	Method class for setting and calculating units. More...

static ER_CAPI_SYS_USERDLL	er_capi_sys_userdll
	Method class to access API UserDll. More...

static ER_CAPI_SYS_APIDLL	er_capi_sys_apidll
	Method class to access API Dll for inverse kinematics, robot trajectory planner and robot dynamics. More...

Static Public Attributes inherited from ER_CAPI
static ER_CAPI_USER_IO	er_capi_user_io
	Method class for interaction with EASY-ROB. More...

static ER_CAPI_DEVICES	er_capi_devices
	Method class to create, attach, update devices, for kinematics calculations and for trajectory planning and -execution. More...

static ER_CAPI_SIM	er_capi_sim
	Method class for simulation settings. More...

static ER_CAPI_TARGETS	er_capi_targets
	Method class for paths and tags. More...

static ER_CAPI_CAD	er_capi_cad
	Method class for for 3D CAD Data import and -export, changing attributes and positions. More...

static ER_CAPI_SYS	er_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

◆ assa()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::assa	(	float	beta,
		float	s1,
		float	s2
	)

static

Triangle calculation, calculates angle between s1 and s2
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	beta	angle between s1 and s3, [rad]
[in]	s1	side
[in]	s2	side

Return values

angle between s1 and s2

◆ assa2()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::assa2	(	float	beta,
		float	s1,
		float	s2
	)

static

Triangle calculation, calculates angle between s2 and s3
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	beta	angle between s1 and s3, [rad]
[in]	s1	side
[in]	s2	side

Return values

angle between s2 and s3

◆ asss()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::asss	(	float	beta,
		float	s1,
		float	s2
	)

static

Triangle calculation, calculates 3rd side s3
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	beta	angle between s1 and s3, [rad]
[in]	s1	side
[in]	s2	side

Return values

s3 side

◆ circ_center_point()

static ER_DllExport int ER_CAPI_SYS_MATHEMATICS::circ_center_point	(	float *	p1,
		float *	p2,
		float *	p3,
		frame *	pTc,
		float *	radius,
		float *	phi,
		float *	dphi = `NULL`
	)

static

Circle calculation from three points p1 over p2 to p3.
Calculates center of circle, radius and angle.

Parameters

[in]	p1	1st point, DIM
[in]	p2	2nd point, DIM
[in]	p3	3rd point, DIM
[out]	pTc	center of circle, FRAME
[out]	radius	of circle
[out]	phi	angle of complete circle segment from `p1` over `p2` to `p3`
[out]	dphi	angle of circle segment from `p1` to `p2`

Return values

0	- OK
1	- Error, cannot calculate circle, maybe p1, p2 and p3 are on a line

◆ cpy_R()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::cpy_R	(	FRAME *	Ro,
		FRAME *	Ri
	)

static

Copies the Orientation from frame Ri into frame Ro
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	Ro	1st FRAME
[in]	Ri	2nd FRAME

◆ delta_T()

static ER_DllExport float* ER_CAPI_SYS_MATHEMATICS::delta_T	(	float *	dx,
		frame *	Ts,
		frame *	Ti
	)

static

Builds the difference between frame Ts and frame Ti
Position dx[0..2] = Ts->p[0..2] - Ti->p[0..2]
Orientation dx[3..5]= 'inv(Ri)*Rs'.
Remarks
It is assumed that the orientation of Ts and Ti are "close by".

Parameters

[out]	dx	difference between Ts and Ti, DOF6
[in]	Ts	1st frame FRAME
[in]	Ti	2nd frame FRAME

Return values

pointer to dx

◆ dh_to_frame()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::dh_to_frame	(	ROB_DH *	rdh,
		frame *	T
	)

static

Converts Denavit Hartenberg Parameter ROB_DH parameter into a homogeneous frame FRAME.

Parameters

[in]	rdh	Denavit Hartenberg Parameter, ROB_DH
[out]	T	homegeneous matrix FRAME

◆ frame_to_vec()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::frame_to_vec	(	float *	vec,
		frame *	T
	)

static

Converts a frame into an euler vector with ROT_XYZ representation.
Frame T is converted into a vector vec
A frame FRAME is a homogeneous 4x4 transformation matrix.
See also vec_to_frame()

Parameters

[out]	vec	vector, max size is DOF6
[in]	T	homegeneous matrix FRAME

Return values

0	- OK
1	- Error

◆ frame_to_vec_idx()

static ER_DllExport int ER_CAPI_SYS_MATHEMATICS::frame_to_vec_idx	(	float *	vec,
		frame *	T,
		int	rotation_idx
	)

static

Converts a frame into an euler vector or quaternion.
Frame T is converted into a vector vec
A frame FRAME is a homogeneous 4x4 transformation matrix.
Depending on the rotation index rotation_idx, which is one of
ROT_XYZ = RotX * RotY' * RotZ'' default,
ROT_XYZ, ROT_ZYX, ROT_YXZ, ROT_ZYZ,ROT_XYX, ROT_RPY, ROT_QUAT, ROT_CA, ROT_ZYpZ,
ROT_Y9XZ, ROT_Z9XY, ROT_Z9XZ, ROT_Z9YX, ROT_IJK, ROT_ANGLE_1
See also vec_to_frame_idx()

Parameters

[out]	vec	vector (euler, quaternion), max size is DOF6 or DOF_QUAT for ROT_QUAT
[in]	T	homegeneous matrix FRAME
[in]	rotation_idx	rotation index

Return values

0	- OK
1	- Error, invalid rotation_idx

◆ incr_R()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::incr_R	(	FRAME *	Ri1,
		FRAME *	Ri2,
		int	res
	)

static

Orientation multiplication of two homogeneous 4x4 transformation matrices.
Depending in res , the result is copied to Ri1 or Ri2.
If res is 1, Ri1 = Ri1 * Ri2
If res is 2, Ri2 = Ri1 * Ri2
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[in,out]	Ri1	frame FRAME out if res=1
[in,out]	Ri2	frame FRAME out if res=2
[in]	res	Result copied to Ri1 or Ri2

◆ incr_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::incr_T	(	FRAME *	Ti1,
		FRAME *	Ti2,
		int	res
	)

static

Multiplication of two homogeneous 4x4 transformation matrices.
Depending in res , the result is copied to Ti1 or Ti2.
If res is 1, Ti1 = Ti1 * Ti2
If res is 2, Ti2 = Ti1 * Ti2
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[in,out]	Ti1	frame FRAME out if res=1
[in,out]	Ti2	frame FRAME out if res=2
[in]	res	Result copied to Ti1 or Ti2

◆ inq_errorflg()

static ER_DllExport int ER_CAPI_SYS_MATHEMATICS::inq_errorflg ( void )

static

Parser error flag
Remarks
call this function after calling parser_calc()

Return values

0	- Ok
1	- Error

◆ inq_rob_kin_controller_name()

static ER_DllExport char* ER_CAPI_SYS_MATHEMATICS::inq_rob_kin_controller_name ( void )

static

Returns the Controller name for the cRobot.

Return values

name	Controller name, MAXSTR

◆ inq_rob_kin_controller_rot_idx()

static ER_DllExport int* ER_CAPI_SYS_MATHEMATICS::inq_rob_kin_controller_rot_idx ( void )

static

Returns the Controller rotation index for the cRobot.
The Controller index is one of
ROT_XYZ = RotX * RotY' * RotZ'' default,
ROT_XYZ, ROT_ZYX, ROT_YXZ, ROT_ZYZ,ROT_XYX, ROT_RPY, ROT_QUAT, ROT_CA, ROT_ZYpZ,
ROT_Y9XZ, ROT_Z9XY, ROT_Z9XZ, ROT_Z9YX, ROT_IJK, ROT_ANGLE_1
.

Return values

rot_idx Controller rotation index

◆ inv_R()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::inv_R	(	FRAME *	Ro,
		FRAME *	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 FRAME is a homogeneous 4x4 transformation matrix.

Parameters

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

◆ inv_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::inv_T	(	FRAME *	To,
		FRAME *	Ti
	)

static

Builds the inverse of a homogeneous 4x4 transformation matrix Ti.
To = inv(Ti) = ( Ri' , -Ri'*pi ), Ri' is transpose of Ri
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

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

◆ mul_invR_pos()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invR_pos	(	float *	po,
		FRAME *	R,
		float *	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 DIM
Remarks
R' = inv(R) is the transpose of R, see inv_R()
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

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

◆ mul_invT_invT()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_invT	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2
	)

static

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

Parameters

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

◆ mul_invT_invT_invT()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_invT_invT	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	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 inv_T()
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

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

◆ mul_invT_invT_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_invT_T	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ mul_invT_pos()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_pos	(	float *	po,
		FRAME *	T,
		float *	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 DIM
Remarks
inv(T) is the inverse of T, see inv_T()
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	po	position product of inv(T) and pi DIM
[in]	T	frame FRAME
[in]	pi	position DIM

◆ mul_invT_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_T	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2
	)

static

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

Parameters

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

◆ mul_invT_T_invT()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_T_invT	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ mul_invT_T_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_invT_T_T	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ mul_R_pos()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_R_pos	(	float *	po,
		FRAME *	R,
		float *	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 DIM
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[out]	po	position product of R and pi DIM
[in]	R	3x3 orientation frame FRAME
[in]	pi	position DIM

◆ mul_R_R()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_R_R	(	FRAME *	Ro,
		FRAME *	Ri1,
		FRAME *	Ri2
	)

static

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

Parameters

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

◆ mul_T_invT()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_invT	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2
	)

static

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

Parameters

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

◆ mul_T_invT_invT()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_invT_invT	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ mul_T_invT_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_invT_T	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ mul_T_pos()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_pos	(	float *	po,
		FRAME *	T,
		float *	pi
	)

static

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

Parameters

[out]	po	position product of T and pi DIM
[in]	T	frame FRAME
[in]	pi	position DIM

◆ mul_T_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_T	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2
	)

static

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

Parameters

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

◆ mul_T_T_invT()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_T_invT	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ mul_T_T_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::mul_T_T_T	(	FRAME *	To,
		FRAME *	Ti1,
		FRAME *	Ti2,
		FRAME *	Ti3
	)

static

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

Parameters

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

◆ parser_calc()

static ER_DllExport double ER_CAPI_SYS_MATHEMATICS::parser_calc	(	char *	str,
		int *	error
	)

static

Formel parser calculation
Remarks
call inq_errorflg() to get parser error.

Parameters

[in]	str	formular
[out]	error	flag, 0-Ok, 1-Error

Return values

result calculated parser result

◆ rob_kin_atan2()

static ER_DllExport double ER_CAPI_SYS_MATHEMATICS::rob_kin_atan2	(	double	y,
		double	x
	)

static

Calculates math function atan2
If x=y=0, this function return 0.

Parameters

[in]	y
[in]	x

Return values

atan2

◆ rob_kin_frame_ident()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::rob_kin_frame_ident ( frame * T )

static

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

Parameters

[in,out] T frame identity FRAME

◆ rob_kin_R_mal_R()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::rob_kin_R_mal_R	(	frame *	Ti1,
		frame *	Ti2
	)

static

Orientation multiplication of two homogeneous 4x4 transformation matrices.
Ri1 = Ri1 * Ri2
Remarks
same as incr_R() with res=1
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[in,out]	Ti1	product of Ti1 and Ti2 FRAME
[in]	Ti2	2nd frame FRAME

◆ rob_kin_rot()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::rob_kin_rot	(	int	rotation_idx,
		double	q,
		frame *	T
	)

static

Set orientation of homogeneous 4x4 transformation matrix.
T = f(q,rotation_idx)
The rotation index rotation_idx, is one of
ROT_IDENT = default, ROT_X, ROT_Y or ROT_Z
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

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

◆ rob_kin_rot_xyz()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::rob_kin_rot_xyz	(	frame *	T,
		float	Rx,
		float	Ry,
		float	Rz
	)

static

Converts an euler represented rotation index ROT_XYZ into a frame.
Rotation angle Rx, Ry, Rz are converted into a frame T
A frame FRAME is a homogeneous 4x4 transformation matrix.
Remarks
Use rob_kin_trans() to set the position.

Parameters

[out]	T	homegeneous matrix FRAME
[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]

◆ rob_kin_T_mal_T()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::rob_kin_T_mal_T	(	frame *	Ti1,
		frame *	Ti2
	)

static

Multiplication of two homogeneous 4x4 transformation matrices.
Ti1 = Ti1 * Ti2
Remarks
same as incr_T() with res=1
A frame FRAME is a homogeneous 4x4 transformation matrix.

Parameters

[in,out]	Ti1	product of Ti1 and Ti2 FRAME
[in]	Ti2	2nd frame FRAME

◆ rob_kin_trans()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::rob_kin_trans	(	frame *	T,
		double	x,
		double	y,
		double	z
	)

static

Converts a position into a frame.
Location x, y, z are converted into a frame T , T->p = [x,y,z]
A frame FRAME is a homogeneous 4x4 transformation matrix.
Remarks
Use rob_kin_rot_xyz() to set the orientation.

Parameters

[out]	T	homegeneous matrix FRAME
[in]	x	X position
[in]	y	Y position
[in]	z	Z position

◆ sasa()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::sasa	(	float	s1,
		float	beta,
		float	s2
	)

static

Triangle calculation, calculates the angle at side s2
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	s1	side
[in]	beta	angle between s1 and s2, [rad]
[in]	s2	side

Return values

angle at side s2

◆ sass()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::sass	(	float	s1,
		float	beta,
		float	s2
	)

static

Triangle calculation, calculates the opposite site of angle beta
Using cosine rule c^2 = a^2 + b^2 - 2ab*cos(beta)
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	s1	side
[in]	beta	angle between s1 and s2, [rad]
[in]	s2	side

Return values

s3	opposite site of angle `beta`

◆ sasssa()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::sasssa	(	float	s1,
		float	beta,
		float	s2,
		float	s3,
		float	s4
	)

static

Quadrangle calculation, calculates angle between s2 of s3
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	s1	side
[in]	beta	angle between `s1` and `s2`
[in]	s2	side
[in]	s3	side
[in]	s4	side

Return values

angle between s2 of s3

◆ sasssa2()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::sasssa2	(	float	s1,
		float	beta,
		float	s2,
		float	s3,
		float	s4
	)

static

Quadrangle calculation, calculates angle between s3 of s4
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	s1	side
[in]	beta	angle between `s1` and `s2`
[in]	s2	side
[in]	s3	side
[in]	s4	side

Return values

angle between s3 of s4

◆ sssa()

static ER_DllExport float ER_CAPI_SYS_MATHEMATICS::sssa	(	float	s1,
		float	s2,
		float	s3
	)

static

Triangle calculation, calculates angle opposite of s1
Remarks
See EASY-ROB-ERPL-eng.pdf "parser functions".

Parameters

[in]	s1	side
[in]	s2	side
[in]	s3	side

Return values

angle opposite of s1

◆ vec_to_frame()

static ER_DllExport void ER_CAPI_SYS_MATHEMATICS::vec_to_frame	(	float *	vec,
		frame *	T
	)

static

Converts an euler vector with ROT_XYZ representation into a frame.
Vector vec is converted into a frame T
A frame FRAME is a homogeneous 4x4 transformation matrix.
See also frame_to_vec()

Parameters

[in]	vec	vector, max size is DOF6
[out]	T	homegeneous matrix FRAME

Return values

0	- OK
1	- Error

◆ vec_to_frame_idx()

static ER_DllExport int ER_CAPI_SYS_MATHEMATICS::vec_to_frame_idx	(	float *	vec,
		frame *	T,
		int	rotation_idx
	)

static

Converts an euler vector or quaternion into a frame.
Vector vec is converted into a frame T
A frame FRAME is a homogeneous 4x4 transformation matrix.
Depending on the rotation index rotation_idx, which is one of
ROT_XYZ = RotX * RotY' * RotZ'' default,
ROT_XYZ, ROT_ZYX, ROT_YXZ, ROT_ZYZ,ROT_XYX, ROT_RPY, ROT_QUAT, ROT_CA, ROT_ZYpZ,
ROT_Y9XZ, ROT_Z9XY, ROT_Z9XZ, ROT_Z9YX, ROT_IJK, ROT_ANGLE_1
See also frame_to_vec_idx()

Parameters

[in]	vec	vector (euler, quaternion), max size is DOF6 or DOF_QUAT for ROT_QUAT
[out]	T	homegeneous matrix FRAME
[in]	rotation_idx	rotation index

Return values

0	- OK
1	- Error, invalid rotation idx

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

ER_CAPI.H

Static Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ assa()

◆ assa2()

◆ asss()

◆ circ_center_point()

◆ cpy_R()

◆ delta_T()

◆ dh_to_frame()

◆ frame_to_vec()

◆ frame_to_vec_idx()

◆ incr_R()

◆ incr_T()

◆ inq_errorflg()

◆ inq_rob_kin_controller_name()

◆ inq_rob_kin_controller_rot_idx()

◆ inv_R()

◆ inv_T()

◆ mul_invR_pos()

◆ mul_invT_invT()

◆ mul_invT_invT_invT()

◆ mul_invT_invT_T()

◆ mul_invT_pos()

◆ mul_invT_T()

◆ mul_invT_T_invT()

◆ mul_invT_T_T()

◆ mul_R_pos()

◆ mul_R_R()

◆ mul_T_invT()

◆ mul_T_invT_invT()

◆ mul_T_invT_T()

◆ mul_T_pos()

◆ mul_T_T()

◆ mul_T_T_invT()

◆ mul_T_T_T()

◆ parser_calc()

◆ rob_kin_atan2()

◆ rob_kin_frame_ident()

◆ rob_kin_R_mal_R()

◆ rob_kin_rot()

◆ rob_kin_rot_xyz()

◆ rob_kin_T_mal_T()

◆ rob_kin_trans()

◆ sasa()

◆ sass()

◆ sasssa()

◆ sasssa2()

◆ sssa()

◆ vec_to_frame()

◆ vec_to_frame_idx()