tf.h File Reference

Low-level operations for SE(3) orientations and transformations. More...

#include <float.h>

Go to the source code of this file.

Classes
struct	aa_tf_vec3
	Memory layout for a vector of length 3. More...
struct	aa_tf_rotmat
	Memory layout for a rotation matrix. More...
struct	aa_tf_axang
	Axis-Angle rotation. More...
struct	aa_tf_quat
	Memory layout for a quaternion, x,y,z,w order. More...
struct	aa_tf_eulerzyx
	Memory layout for an Euler Angle in ZYX (yaw-pitch-roll) format. More...
struct	aa_tf_tfmat
	Memory layout for a transformation matrix. More...
struct	aa_tf_qv
	Memory layout for a Transformation as rotation quaternion and translation vector. More...
struct	aa_tf_duqu
	Memory layout for a dual quaternion . More...
struct	aa_tf_dx
	Memory layout for an SE(3) velocity. More...
struct	aa_tf_qv_dx
	Transform and spatial velocity. More...

Macros
#define	AA_TF_DEF_SERIES(name, a0, a1, a2)
#define	AA_TF_X   0
	Index of vector x element.
#define	AA_TF_Y   1
	Index of vector y element.
#define	AA_TF_Z   2
	Index of vector z element.
#define	AA_TF_QUAT_V   0
	Index of quaternion vector part.
#define	AA_TF_QUAT_XYZ   AA_TF_QUAT_V
	Index of quaternion vector part.
#define	AA_TF_QUAT_X   (AA_TF_QUAT_V + AA_TF_X)
	Index of quaternion vector x.
#define	AA_TF_QUAT_Y   (AA_TF_QUAT_V + AA_TF_Y)
	Index of quaternion vector y.
#define	AA_TF_QUAT_Z   (AA_TF_QUAT_V + AA_TF_Z)
	Index of quaternion vector z.
#define	AA_TF_QUAT_W   3
	Index of quaternion scalar part.
#define	AA_TF_TFMAT_R   0
	Index of rotation matrix part of transformation matrix.
#define	AA_TF_TFMAT_V   9
	Index of origin part of transformation matrix.
#define	AA_TF_TFMAT_X   9
	Index of origin x component of transformation matrix.
#define	AA_TF_TFMAT_Y   10
	Index of origin y component of transformation matrix.
#define	AA_TF_TFMAT_Z   11
	Index of origin z component of transformation matrix.
#define	AA_TF_DX_V   0
	Index of spatial velocity translational part.
#define	AA_TF_DX_W   3
	Index of spatial velocity translational part.
#define	AA_TF_QUTR_Q   0
	Index of quaternion-translation quaternion part.
#define	AA_TF_QUTR_QX   (AA_TF_QUTR_Q + AA_TF_QUAT_X)
	Index of quaternion-translation quaternion x.
#define	AA_TF_QUTR_QY   (AA_TF_QUTR_Q + AA_TF_QUAT_Y)
	Index of quaternion-translation quaternion y.
#define	AA_TF_QUTR_QZ   (AA_TF_QUTR_Q + AA_TF_QUAT_Z)
	Index of quaternion-translation quaternion z.
#define	AA_TF_QUTR_QW   (AA_TF_QUTR_Q + AA_TF_QUAT_W)
	Index of quaternion-translation quaternion w.
#define	AA_TF_QUTR_T   4
	Index of quaternion-translation translation part.
#define	AA_TF_QUTR_TX   (AA_TF_QUTR_T + AA_TF_X)
	Index of quaternion-translation translation x.
#define	AA_TF_QUTR_TY   (AA_TF_QUTR_T + AA_TF_Y)
	Index of quaternion-translation translation y.
#define	AA_TF_QUTR_TZ   (AA_TF_QUTR_T + AA_TF_Z)
	Index of quaternion-translation translation z.
#define	AA_TF_DUQU_REAL   0
	index of dual quaternion real part
#define	AA_TF_DUQU_DUAL   4
	index of dual quaternion dual part
#define	AA_TF_DUQU_REAL_W   (AA_TF_DUQU_REAL + AA_TF_QUAT_W)
	index of dual quaternion real w
#define	AA_TF_DUQU_REAL_XYZ   (AA_TF_DUQU_REAL + AA_TF_QUAT_XYZ)
	index of dual quaternion real xyz
#define	AA_TF_DUQU_REAL_X   (AA_TF_DUQU_REAL + AA_TF_QUAT_X)
	index of dual quaternion real x
#define	AA_TF_DUQU_REAL_Y   (AA_TF_DUQU_REAL + AA_TF_QUAT_Y)
	index of dual quaternion real y
#define	AA_TF_DUQU_REAL_Z   (AA_TF_DUQU_REAL + AA_TF_QUAT_Z)
	index of dual quaternion real z
#define	AA_TF_DUQU_DUAL_W   (AA_TF_DUQU_DUAL + AA_TF_QUAT_W)
	index of dual quaternion dual w
#define	AA_TF_DUQU_DUAL_XYZ   (AA_TF_DUQU_DUAL + AA_TF_QUAT_XYZ)
	index of dual quaternion dual xyz
#define	AA_TF_DUQU_DUAL_X   (AA_TF_DUQU_DUAL + AA_TF_QUAT_X)
	index of dual quaternion dual x
#define	AA_TF_DUQU_DUAL_Y   (AA_TF_DUQU_DUAL + AA_TF_QUAT_Y)
	index of dual quaternion dual y
#define	AA_TF_DUQU_DUAL_Z   (AA_TF_DUQU_DUAL + AA_TF_QUAT_Z)
	index of dual quaternion dual z
#define	AA_TF_EPSILON   .0001
	a small number
#define	AA_TF_IDENT_INITIALIZER   {1,0,0, 0,1,0, 0,0,1, 0,0,0}
	Static initializer for an identity transformation matrix.
#define	AA_TF_ROTMAT_IDENT_INITIALIZER   {1,0,0, 0,1,0, 0,0,1}
	Static initializer for an identity rotation matrix.
#define	AA_TF_QUAT_IDENT_INITIALIZER   {0,0,0,1}
	Static initializer for an identity quaternion.
#define	AA_TF_DUQU_IDENT_INITIALIZER   {0,0,0,1, 0,0,0,0}
	Static initializer for an identity dual quaternion.
#define	AA_TF_QUTR_IDENT_INITIALIZER   {0,0,0,1, 0,0,0}
	Static initializer for an identity quaternion-translation.
#define	AA_TF_AXANG_IDENT_INITIALIZER   {1,0,0,0}
	Static initializer for an identity axis-angle.
#define	AA_TF_ROTVEC_IDENT_INITIALIZER   {0,0,0}
	Static initializer for an identity rotation-vector.
#define	AA_TF_VEC_IDENT_INITIALIZER   {0,0,0}
	Static initializer for an identity vector-3.
#define	AA_TF_IDENT   ( (double[12]) AA_TF_IDENT_INITIALIZER )
	Identity transform.
#define	AA_TF_ROTMAT_IDENT   ( (double[9] AA_TF_ROTMAT_IDENT_INITIALIZER )
	Identity rotation matrix.
#define	AA_TF_QUAT_IDENT   ( (double[4]) AA_TF_QUAT_IDENT_INITIALIZER )
	Identity quaternion.
#define	AA_TF_AXANG_IDENT   ( (double[4]) AA_TF_AXANG_IDENT_INITIALIZER )
	Identity axis-angle.
#define	AA_TF_ROTVEC_IDENT   ( (double[3]) AA_TF_ROTVEC_IDENT_INITIALIZER )
	Identity Rotation Vector.
#define	AA_TF_DOTX(a, b)   ((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2])
	Macro to compute a dot product of length 3 vectors. More...
#define	AA_TF_CROSSX(a, b, c)
	Macro to compute the cross product of length 3 vectors. More...
#define	AA_TF_QUTR_Q   0
	Index of quaternion-translation quaternion part.
#define	AA_TF_QUTR_V   4
#define	AA_TF_DEF_EULER(letters)

Typedefs
typedef struct aa_tf_vec3	aa_tf_vec3_t
	Memory layout for a vector of length 3.
typedef struct aa_tf_rotmat	aa_tf_rotmat_t
	Memory layout for a rotation matrix. More...
typedef struct aa_tf_axang	aa_tf_axang_t
	Axis-Angle rotation.
typedef struct aa_tf_quat	aa_tf_quat_t
	Memory layout for a quaternion, x,y,z,w order.
typedef struct aa_tf_eulerzyx	aa_tf_eulerzyx_t
	Memory layout for an Euler Angle in ZYX (yaw-pitch-roll) format.
typedef struct aa_tf_tfmat	aa_tf_tfmat_t
	Memory layout for a transformation matrix. More...
typedef struct aa_tf_qv	aa_tf_qv_t
	Memory layout for a Transformation as rotation quaternion and translation vector.
typedef struct aa_tf_duqu	aa_tf_duqu_t
	Memory layout for a dual quaternion .

Functions
static void	aa_tf_sinccos2 (double theta2, double *sc, double *c)
static void	aa_tf_sinccos (double theta, double *sc, double *c)
static double	aa_tf_sinc (double theta)
AA_API void	aa_tf_12 (const double T[AA_RESTRICT 12], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 3])
	apply a euclidean transform
AA_API void	aa_tf_93 (const double R[AA_RESTRICT 9], const double v[AA_RESTRICT 3], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 4])
	apply a euclidean transform
AA_API void	aa_tf_tf_qv (const double quat[AA_RESTRICT 4], const double v[AA_RESTRICT 3], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 4])
	apply a euclidean transform
AA_API void	aa_tf_9 (const double R[AA_RESTRICT 9], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 4])
	apply a euclidean transform
AA_API void	aa_tf_12inv (const double T[AA_RESTRICT 12], double Ti[AA_RESTRICT 12])
	invert transform
AA_API void	aa_tf_93inv (const double R[AA_RESTRICT 9], const double v[AA_RESTRICT 3], double Ri[AA_RESTRICT 9], double vi[AA_RESTRICT 3])
	invert transform
AA_API void	aa_tf_qv_conj (const double q[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double qc[AA_RESTRICT 4], double vc[AA_RESTRICT 3])
	Invert transform. More...
AA_API void	aa_tf_12chain (const double T1[AA_RESTRICT 12], const double T2[AA_RESTRICT 12], double T[AA_RESTRICT 12])
	chain two transforms
AA_API void	aa_tf_v12chain (double T[AA_RESTRICT 12], const double T1[AA_RESTRICT 12], const double T2[AA_RESTRICT 12],...)
	Varargs transform chain.
AA_API void	aa_tf_93chain (const double R0[AA_RESTRICT 9], const double v0[AA_RESTRICT 3], const double R1[AA_RESTRICT 9], const double v1[AA_RESTRICT 3], double R[AA_RESTRICT 9], double v[AA_RESTRICT 3])
	chain two transforms
AA_API void	aa_tf_qv_chain (const double q0[AA_RESTRICT 4], const double v0[AA_RESTRICT 3], const double q1[AA_RESTRICT 4], const double v1[AA_RESTRICT 3], double q[AA_RESTRICT 4], double v[AA_RESTRICT 3])
	chain two transforms
AA_API void	aa_tf_93rel (const double R1[AA_RESTRICT 9], const double v1[AA_RESTRICT 3], const double R2[AA_RESTRICT 9], const double v2[AA_RESTRICT 3], double Rrel[AA_RESTRICT 9], double vrel[AA_RESTRICT 3])
	relative transform
AA_API void	aa_tf_12rel (const double T1[AA_RESTRICT 12], const double T2[AA_RESTRICT 12], double Trel[AA_RESTRICT 12])
	relative transform
AA_API void	aa_tf_skewsym_scal2 (double a, double b, const double u[3], double R[9])
AA_API void	aa_tf_skewsym_scal_c (const double u[AA_RESTRICT 3], const double a[AA_RESTRICT 3], const double b[AA_RESTRICT 3], double R[9])
AA_API void	aa_tf_rotmat_mul (const double R0[AA_RESTRICT 9], const double R1[AA_RESTRICT 9], double R[AA_RESTRICT 9])
AA_API void	aa_tf_tfmat_mul (const double T0[AA_RESTRICT 12], const double T1[AA_RESTRICT 12], double T[AA_RESTRICT 12])
AA_API void	aa_tf_tfmat2_mul (const double R0[AA_RESTRICT 9], const double v0[AA_RESTRICT 3], const double R1[AA_RESTRICT 9], const double v1[AA_RESTRICT 3], double R[AA_RESTRICT 9], double v[AA_RESTRICT 3])
AA_API void	aa_tf_rotmat_imul (const double R0[AA_RESTRICT 9], const double R1[AA_RESTRICT 9], double R[AA_RESTRICT 9])
AA_API void	aa_tf_rotmat_muli (const double R0[AA_RESTRICT 9], const double R1[AA_RESTRICT 9], double R[AA_RESTRICT 9])
AA_API void	aa_tf_tfmat_imul (const double T0[AA_RESTRICT 12], const double T1[AA_RESTRICT 12], double T[AA_RESTRICT 12])
AA_API void	aa_tf_tfmat_muli (const double T0[AA_RESTRICT 12], const double T1[AA_RESTRICT 12], double T[AA_RESTRICT 12])
AA_API void	aa_tf_tfmat2_imul (const double R0[AA_RESTRICT 9], const double v0[AA_RESTRICT 3], const double R1[AA_RESTRICT 9], const double v1[AA_RESTRICT 3], double R[AA_RESTRICT 9], double v[AA_RESTRICT 3])
AA_API void	aa_tf_tfmat2_muli (const double R0[AA_RESTRICT 9], const double v0[AA_RESTRICT 3], const double R1[AA_RESTRICT 9], const double v1[AA_RESTRICT 3], double R[AA_RESTRICT 9], double v[AA_RESTRICT 3])
AA_API void	aa_tf_rotmat_rot (const double R[AA_RESTRICT 9], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 3])
AA_API void	aa_tf_tfmat_tf (const double T[AA_RESTRICT 12], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 3])
AA_API void	aa_tf_tfmat2_tf (const double R[AA_RESTRICT 9], const double v[AA_RESTRICT 3], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 4])
AA_API void	aa_tf_rotmat_inv1 (double R[AA_RESTRICT 9])
	Invert a rotation in place.
AA_API void	aa_tf_rotmat_inv2 (const double R[AA_RESTRICT 9], double Ri[AA_RESTRICT 9])
	Invert a rotation.
AA_API void	aa_tf_tfmat_inv1 (double T[AA_RESTRICT 12])
	Invert a transform in place.
AA_API void	aa_tf_tfmat_inv2 (const double T[AA_RESTRICT 12], double Ti[AA_RESTRICT 12])
	Invert a transform.
AA_API int	aa_tf_isrotmat (const double R[AA_RESTRICT 9])
	tests if R is a rotation matrix
AA_API void	aa_tf_9mul (const double R0[AA_RESTRICT 9], const double R1[AA_RESTRICT 9], double R[AA_RESTRICT 9])
	Multiply two rotation matrices.
AA_API void	aa_tf_9rot (const double R[AA_RESTRICT 9], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 3])
	rotate p0 by R
AA_API void	aa_tf_9rel (const double R1[AA_RESTRICT 9], const double R2[AA_RESTRICT 9], double Ri[AA_RESTRICT 9])
	relative transform from R1 to R2
AA_API void	aa_tf_rotmat_exp_aa (const double aa[AA_RESTRICT 4], double R[AA_RESTRICT 9])
	Rotation Matrix exponential from axis angle.
AA_API void	aa_tf_rotmat_expv (const double rv[AA_RESTRICT 3], double R[AA_RESTRICT 9])
	Rotation Matrix exponential from rotation vector.
AA_API void	aa_tf_rotmat_lnv (const double R[AA_RESTRICT 9], double v[AA_RESTRICT 3])
	Rotation Matrix logarithm.
AA_API void	aa_tf_tfmat_expv (const double v[AA_RESTRICT 6], double T[AA_RESTRICT 12])
	Transformation Matrix exponential.
AA_API void	aa_tf_tfmat_lnv (const double T[AA_RESTRICT 12], double v[AA_RESTRICT 6])
	Transformation Matrix logarithm.
AA_API void	aa_tf_rotmat_vel2diff (const double R[AA_RESTRICT 9], const double w[AA_RESTRICT 3], double dR[AA_RESTRICT 9])
	Velocity to rotation matrix derivative.
AA_API void	aa_tf_rotmat_diff2vel (const double R[AA_RESTRICT 9], const double dR[AA_RESTRICT 9], double w[AA_RESTRICT 3])
	Rotation matrix derivative to velocity.
AA_API void	aa_tf_rotmat_svel (const double R0[AA_RESTRICT 9], const double w[AA_RESTRICT 3], double dt, double R1[AA_RESTRICT 9])
	Integrate rotational velocity.
AA_API void	aa_tf_tfmat_svel (const double T0[AA_RESTRICT 12], const double w[AA_RESTRICT 3], double dt, double T1[AA_RESTRICT 12])
	Integrate rotational velocity.
AA_API void	aa_tf_v9mul (double R[AA_RESTRICT 9], const double R1[AA_RESTRICT 9], const double R2[AA_RESTRICT 9],...)
	Vararg multiply two rotation matrices.
AA_API void	aa_tf_rotmat_xy (const double x_axis[AA_RESTRICT 3], const double y_axis[AA_RESTRICT 3], double R[AA_RESTRICT 9])
	Construct rotation matrix from an x and y axis of the child frame.
AA_API void	aa_tf_rotmat_yz (const double y_axis[AA_RESTRICT 3], const double z_axis[AA_RESTRICT 3], double R[AA_RESTRICT 9])
	Construct rotation matrix from a y and z axis of the child frame.
AA_API void	aa_tf_rotmat_zx (const double z_axis[AA_RESTRICT 3], const double x_axis[AA_RESTRICT 3], double R[AA_RESTRICT 9])
	Construct rotation matrix from a z and x axis of the child frame.
static double	AA_TF_VDOT (const double a[AA_RESTRICT 3], const double b[AA_RESTRICT 3])
	Inlined vector dot product.
static float	AA_TF_VDOTF (const float a[AA_RESTRICT 3], const float b[AA_RESTRICT 3])
	Inlined vector dot product.
AA_API double	aa_tf_vdot (const double a[AA_RESTRICT 3], const double b[AA_RESTRICT 3])
	Vector dot product.
AA_API float	aa_tf_vdotf (const float a[AA_RESTRICT 3], const float b[AA_RESTRICT 3])
	Vector dot product.
static void	AA_TF_CROSS (const double a[AA_RESTRICT 3], const double b[AA_RESTRICT 3], double c[AA_RESTRICT 3])
	Inlined Vector cross product.
static void	AA_TF_CROSSF (const float a[AA_RESTRICT 3], const float b[AA_RESTRICT 3], float c[AA_RESTRICT 3])
	Inlined Vector cross product.
AA_API void	aa_tf_cross (const double a[AA_RESTRICT 3], const double b[AA_RESTRICT 3], double c[AA_RESTRICT 3])
	Vector cross product.
AA_API void	aa_tf_crossf (const float a[AA_RESTRICT 3], const float b[AA_RESTRICT 3], float c[AA_RESTRICT 3])
	Vector cross product.
AA_API void	aa_tf_vnormalize (double v[AA_RESTRICT 3])
	Normalize Vector.
AA_API void	aa_tf_vnormalizef (float v[AA_RESTRICT 3])
	Normalize Vector.
static double	AA_TF_QDOT (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4])
	Inlined quaternion dot product.
double	aa_tf_qdot (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4])
	Quaternion dot product.
AA_API void	aa_tf_qnormalize (double q[AA_RESTRICT 4])
	Normalize Quaternion. More...
AA_API double	aa_tf_qnorm (const double q[AA_RESTRICT 4])
	Return norm of the quaternion.
AA_API void	aa_tf_qminimize (double q[AA_RESTRICT 4])
	Minimize angle represented by the quaternion. More...
AA_API void	aa_tf_qminimize2 (const double q[AA_RESTRICT 4], double qmin[AA_RESTRICT 4])
AA_API void	aa_tf_qnormalize2 (const double q[AA_RESTRICT 4], double qnorm[AA_RESTRICT 4])
	Normailize quaternion.
AA_API void	aa_tf_qconj (const double q[AA_RESTRICT 4], double r[AA_RESTRICT 4])
	Quaternion conjugate.
AA_API void	aa_tf_qexp (const double q[AA_RESTRICT 4], double r[AA_RESTRICT 4])
	Quaternion exponential.
AA_API void	aa_tf_qln (const double q[AA_RESTRICT 4], double r[AA_RESTRICT 4])
	Quaternion natural log.
AA_API void	aa_tf_qduln (const double q[AA_RESTRICT 4], const double dq[AA_RESTRICT 4], double dln[AA_RESTRICT 3])
	Derivative of the Unit Quaternion Logarithm. More...
AA_API void	aa_tf_qdulnj (const double q[AA_RESTRICT 4], const double dq[AA_RESTRICT 4], double dln[AA_RESTRICT 3])
AA_API void	aa_tf_qdpexp (const double e[AA_RESTRICT 3], const double de[AA_RESTRICT 3], double dq[AA_RESTRICT 4])
	Derivative of the Pure Quaternion Exponential. More...
AA_API void	aa_tf_qdpexpj (const double e[AA_RESTRICT 3], const double de[AA_RESTRICT 3], double dq[AA_RESTRICT 4])
double	aa_tf_qangle (const double q[AA_RESTRICT 4])
	Return the angle of the quaternion. More...
double	aa_tf_qangle_rel (const double *q, const double *p)
double	aa_tf_quhypangle2 (const double q[AA_RESTRICT 4], const double p[AA_RESTRICT 4])
	Return the angle between unit quaterniosn in 4D space.
AA_API void	aa_tf_qinv (const double q[AA_RESTRICT 4], double r[AA_RESTRICT 4])
	Quaternion inverse.
AA_API void	aa_tf_qadd (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion addition. More...
AA_API void	aa_tf_qsub (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion subtraction. More...
AA_API void	aa_tf_qmul (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion multiplication. More...
AA_API void	aa_tf_qmulnorm (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion multiplication and normalize. More...
AA_API void	aa_tf_qmul_qv (const double q[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double c[AA_RESTRICT 4])
	Quaternion multiplication. More...
AA_API void	aa_tf_qmul_vq (const double v[AA_RESTRICT 3], const double q[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion multiplication. More...
AA_API void	aa_tf_qcmul (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion conjugate a and multiply by b. More...
AA_API void	aa_tf_qmulc (const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion multiply a by conjugate b. More...
AA_API void	aa_tf_qrot1 (const double q[AA_RESTRICT 4], double v[AA_RESTRICT 3])
	Quaternion point rotation, in place.
AA_API void	aa_tf_qrot (const double q[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double p[AA_RESTRICT 3])
	Quaternion point rotation. More...
AA_API void	aa_tf_qrel (const double q1[AA_RESTRICT 4], const double q2[AA_RESTRICT 4], double q_rel[AA_RESTRICT 4])
	Relative orientation. More...
AA_API void	aa_tf_qslerp (double tau, const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion SLERP. More...
AA_API void	aa_tf_qslerpalg (double tau, const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Quaternion SLERP, computed algebraicly. More...
AA_API void	aa_tf_qslerpdiff (double tau, const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Derivative of quaternation SLERP WRT tau. More...
AA_API void	aa_tf_qslerpdiffalg (double tau, const double a[AA_RESTRICT 4], const double b[AA_RESTRICT 4], double c[AA_RESTRICT 4])
	Derivative of quaternation SLERP WRT tau, computed algebraicly.
AA_API void	aa_tf_qslerpchaindiff (double u, double du, const double q1[AA_RESTRICT 4], const double dq1[AA_RESTRICT 4], const double q2[AA_RESTRICT 4], const double dq2[AA_RESTRICT 4], double q[AA_RESTRICT 4], double dq[AA_RESTRICT 4])
	Chain-rule slerp differentiation.
AA_API void	aa_tf_qslerp3diff (double u12, double du12, const double q1[AA_RESTRICT 4], const double q2[AA_RESTRICT 4], double u34, double du34, const double q3[AA_RESTRICT 4], const double q4[AA_RESTRICT 4], double u, double du, double q[AA_RESTRICT 4], double dq[AA_RESTRICT 4])
	Triad sequence of slerp differentiation.
AA_API void	aa_tf_qdiff2vel (const double q[AA_RESTRICT 4], const double dq_dt[AA_RESTRICT 4], double v[AA_RESTRICT 3])
AA_API void	aa_tf_qvel2diff (const double q[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double dq_dt[AA_RESTRICT 4])
AA_API void	aa_tf_rotvec_diff2vel (const double v[3], const double dv[3], double w[3])
AA_API void	aa_tf_qrk1 (const double q0[AA_RESTRICT 4], const double dq[AA_RESTRICT 4], double dt, double q1[AA_RESTRICT 4])
	Integrate unit quaternion, Runge-Kutta-1 (euler) integration. More...
AA_API void	aa_tf_qvelrk1 (const double q0[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double dt, double q1[AA_RESTRICT 4])
	Integrate unit quaternion from angular velocity, Runge-Kutta-1 (euler) integration. More...
AA_API void	aa_tf_qvelrk4 (const double q0[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double dt, double q1[AA_RESTRICT 4])
	Integrate unit quaternion from angular velocity, Runge-Kutta-4 (euler) integration. More...
AA_API void	aa_tf_qsvel (const double q0[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double dt, double q1[AA_RESTRICT 4])
	Integrate unit quaternion from constant angular velocity. More...
AA_API void	aa_tf_qsdiff (const double q0[AA_RESTRICT 4], const double dq[AA_RESTRICT 4], double dt, double q1[AA_RESTRICT 4])
	Integrate unit quaternion from quaternion derivative. More...
AA_API void	aa_tf_xangle2quat (double theta_x, double q[AA_RESTRICT 4])
	Unit quaternion for angle about x axis.
AA_API void	aa_tf_yangle2quat (double theta_y, double q[AA_RESTRICT 4])
	Unit quaternion for angle about y axis.
AA_API void	aa_tf_zangle2quat (double theta_z, double q[AA_RESTRICT 4])
	Unit quaternion for angle about z axis.
AA_API void	aa_tf_quat_davenport_matrix (size_t n, const double *w, const double *q, size_t ldqq, double *M)
AA_API void	aa_tf_quat_davenport (size_t n, const double *w, const double *Q, size_t ldq, double *y)
AA_API void	aa_tf_qmatrix_l (const double *q, double *M, size_t ldm)
	Construct matrix for left quaternion multiply q*p = M*p.
AA_API void	aa_tf_qmatrix_r (const double *q, double *M, size_t ldm)
	Construct matrix for right quaternion multiply p*q = M*p.
void	aa_tf_qurand (double q[4])
	Generate random unit quaternion.
AA_API void	aa_tf_axang_make (double x, double y, double z, double theta, double axang[AA_RESTRICT 4])
	copy x,y,z,theta into axang
AA_API void	aa_tf_axang_permute (const double rv[AA_RESTRICT 4], int k, double rv_p[AA_RESTRICT 4])
	Scales angle by k * 2 * pi.
AA_API void	aa_tf_rotvec_permute (const double rv[AA_RESTRICT 3], int k, double rv_p[AA_RESTRICT 3])
	find alternate equivalent representations of rv
AA_API void	aa_tf_rotvec_near (const double rv[AA_RESTRICT 3], const double rv_near[AA_RESTRICT 3], double rv_p[AA_RESTRICT 3])
	Scales rv by multiple of 2pi to minimized SSD with rv_near.
void	aa_tf_qv_conj (const double q[4], const double v[3], double qc[4], double vc[3])
	quaternion-translation conjugate
void	aa_tf_qutr2duqu (const double e[7], double s[8])
	quaternion-translation to dual quaternion
void	aa_tf_qutr2tfmat (const double e[7], double T[12])
	quaternion-translation to transformation matrix
void	aa_tf_tfmat2qutr (const double T[12], double e[7])
	transformation matrix to quaternion-translation
void	aa_tf_duqu2qutr (const double s[8], double e[7])
	dual quaternion to quaternion-translation
void	aa_tf_qutr_mul (const double a[7], const double b[7], double c[7])
	quaternion-translation multiply
AA_API void	aa_tf_qutr_tf (const double E[AA_RESTRICT 7], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 3])
	Transform a point,.
void	aa_tf_qutr_mulnorm (const double a[7], const double b[7], double c[7])
	quaternion-translation multiply and normalize
void	aa_tf_qutr_conj (const double a[7], double c[7])
	quaternion-translation conjugate
void	aa_tf_qutr_mulc (const double a[7], const double b[7], double c[7])
	quaternion-translation conjugate multiply
void	aa_tf_qutr_cmul (const double a[7], const double b[7], double c[7])
	quaternion-translation conjugate multiply
void	aa_tf_qutr_diff2vel (const double e[7], const double de[7], double dx[6])
	Quaternion-translation derivative to spatial velocity.
void	aa_tf_qutr_vel2diff (const double e[7], const double dx[6], double de[7])
	Quaternion-translation spatial velocity to derivative.
void	aa_tf_qutr_svel (const double e0[7], const double dx[6], double dt, double e1[7])
	Integrate a quaternion-translation.
void	aa_tf_qutr_sdiff (const double e0[7], const double de[7], double dt, double e1[7])
	Integrate a quaternion-translation.
void	aa_tf_qutr_wavg (size_t n, const double *w, const double *EE, size_t ldee, double *a)
	Weighted average transform.
void	aa_tf_qutr_rand (double E[7])
	Generate random transform.
AA_API void	aa_tf_quat2axang (const double q[AA_RESTRICT 4], double axang[AA_RESTRICT 4])
	Quaternion to axis-angle. More...
AA_API void	aa_tf_axang2quat (const double axang[AA_RESTRICT 4], double q[AA_RESTRICT 4])
	axis-angle to quaternion. More...
AA_API void	aa_tf_axang2quat2 (const double axis[AA_RESTRICT 3], double angle, double q[AA_RESTRICT 4])
	axis-angle to quaternion. More...
AA_API void	aa_tf_vecs2quat (const double u[AA_RESTRICT 3], const double v[AA_RESTRICT 3], double q[AA_RESTRICT 4])
	Convert rotation between two vectors to a quaternion.
AA_API void	aa_tf_axang2rotvec (const double axang[AA_RESTRICT 4], double rotvec[AA_RESTRICT 3])
	convert axis-angle to rotation vector
AA_API void	aa_tf_rotvec2axang (const double rotvec[AA_RESTRICT 3], double axang[AA_RESTRICT 4])
	convert rotation vector to axis-angle
AA_API void	aa_tf_rotvec2quat (const double rotvec[AA_RESTRICT 3], double q[AA_RESTRICT 4])
	covert rotation vector to quaternion
AA_API void	aa_tf_quat2rotvec (const double q[AA_RESTRICT 4], double rotvec[AA_RESTRICT 3])
	covert quaternion to rotation vector
AA_API void	aa_tf_quat2rotvec_near (const double q[AA_RESTRICT 4], const double rv_near[AA_RESTRICT 3], double rotvec[AA_RESTRICT 3])
	covert quaternion to rotation vector minimizing distance from rv_near
AA_API void	aa_tf_quat2rotmat (const double quat[AA_RESTRICT 4], double rotmat[AA_RESTRICT 9])
	convert quaternion to rotation matrix
AA_API void	aa_tf_rotmat2quat (const double rotmat[AA_RESTRICT 9], double quat[AA_RESTRICT 4])
	convert rotation matrix to quaternion
AA_API void	aa_tf_rotmat2axang (const double R[AA_RESTRICT 9], double ra[AA_RESTRICT 4])
	convert rotation matrix to axis angle
AA_API void	aa_tf_rotmat2rotvec (const double R[AA_RESTRICT 9], double rv[AA_RESTRICT 3])
	convert axis rotation matrix to rotation vector
AA_API void	aa_tf_axang2rotmat (const double ra[AA_RESTRICT 4], double R[AA_RESTRICT 9])
	convert axis angle to rotation matrix
AA_API void	aa_tf_rotvec2rotmat (const double rv[AA_RESTRICT 3], double R[AA_RESTRICT 9])
	convert rotatoin vector to rotation matrix
AA_API void	aa_tf_qv2tfmat (const double q[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double T[AA_RESTRICT 12])
	Convert orientation unit quaternion and translation vector to transformation matrix. More...
AA_API void	aa_tf_rotmat2eulerzyx (const double R[AA_RESTRICT 9], double e[AA_RESTRICT 3])
	Convert Rotation Matrix to ZYX Euler Angles.
AA_API void	aa_tf_quat2eulerzyx (const double q[AA_RESTRICT 4], double e[AA_RESTRICT 3])
	Convert quaternion to ZYX Euler Angles.
AA_API void	aa_tf_xangle2rotmat (double theta_x, double R[AA_RESTRICT 9])
	Angle about x axis.
AA_API void	aa_tf_yangle2rotmat (double theta_y, double R[AA_RESTRICT 9])
	Angle about y axis.
AA_API void	aa_tf_zangle2rotmat (double theta_z, double R[AA_RESTRICT 9])
	Angle about z axis.
AA_API void	aa_tf_rotmat_mzlook (const double eye[AA_RESTRICT 3], const double target[AA_RESTRICT 3], const double up[AA_RESTRICT 3], double R[AA_RESTRICT 9])
	Find the camera frame, looking in negative z direction.
AA_API void	aa_tf_tfmat_mzlook (const double eye[AA_RESTRICT 3], const double target[AA_RESTRICT 3], const double up[AA_RESTRICT 3], double T[AA_RESTRICT 12])
	Find the camera frame, looking in negative z direction.
AA_API void	aa_tf_qmzlook (const double eye[AA_RESTRICT 3], const double target[AA_RESTRICT 3], const double up[AA_RESTRICT 3], double q[AA_RESTRICT 4])
	Find the camera frame, looking in negative z direction.
AA_API void	aa_tf_qv_mzlook (const double eye[AA_RESTRICT 3], const double target[AA_RESTRICT 3], const double up[AA_RESTRICT 3], double q[AA_RESTRICT 4], double v[AA_RESTRICT 3])
	Find the camera frame, looking in negative z direction.
AA_API void	aa_tf_qutr_mzlook (const double eye[AA_RESTRICT 3], const double target[AA_RESTRICT 3], const double up[AA_RESTRICT 3], double T[AA_RESTRICT 12])
	Find the camera frame, looking in negative z direction.
AA_API void	aa_tf_duqu_add (const double d1[AA_RESTRICT 8], const double d2[AA_RESTRICT 8], double d3[AA_RESTRICT 8])
	Dual quaternion addition.
AA_API void	aa_tf_duqu_sub (const double d1[AA_RESTRICT 8], const double d2[AA_RESTRICT 8], double d3[AA_RESTRICT 8])
	Dual quaternion subtraction.
AA_API void	aa_tf_duqu_smul (const double d1[AA_RESTRICT 8], const double d2[AA_RESTRICT 8], double d3[AA_RESTRICT 8])
	Dual quaternion scalar multiplication.
AA_API void	aa_tf_duqu_mul (const double d1[AA_RESTRICT 8], const double d2[AA_RESTRICT 8], double d3[AA_RESTRICT 8])
	Dual quaternion multiplication.
AA_API void	aa_tf_duqu_matrix_l (const double *q, double *M, size_t ldm)
	Construct matrix for left dual quaternion multiply q*p = M*p.
AA_API void	aa_tf_duqu_matrix_r (const double *q, double *M, size_t ldm)
	Construct matrix for right dual quaternion multiply p*q = M*p.
AA_API void	aa_tf_duqu_cmul (const double d1[AA_RESTRICT 8], const double d2[AA_RESTRICT 8], double d3[AA_RESTRICT 8])
	Dual quaternion multiply conjugate of d1 by d2.
AA_API void	aa_tf_duqu_mulc (const double d1[AA_RESTRICT 8], const double d2[AA_RESTRICT 8], double d3[AA_RESTRICT 8])
	Dual quaternion multiply d1 by conjugate of d2.
AA_API void	aa_tf_duqu_conj (const double d[AA_RESTRICT 8], double dconj[AA_RESTRICT 8])
	Dual quaternion conjugate.
AA_API void	aa_tf_duqu_exp (const double d[AA_RESTRICT 8], double e[AA_RESTRICT 8])
	Dual quaternion exponential.
AA_API void	aa_tf_duqu_ln (const double d[AA_RESTRICT 8], double e[AA_RESTRICT 8])
	Dual quaternion natural logarithm.
AA_API void	aa_tf_duqu_norm (const double d[AA_RESTRICT 8], double *nreal, double *ndual)
	Dual quaternion norm.
AA_API void	aa_tf_duqu_normalize (double d[AA_RESTRICT 8])
	Dual quaternion normalization.
AA_API void	aa_tf_duqu_minimize (double d[AA_RESTRICT 8])
	Dual quaternion angle minimization.
AA_API void	aa_tf_tf_duqu (const double d[AA_RESTRICT 8], const double p0[AA_RESTRICT 3], double p1[AA_RESTRICT 3])
	Dual quaternion transformation.
AA_API void	aa_tf_duqu_trans (const double d[AA_RESTRICT 8], double v[AA_RESTRICT 3])
	Extract dual quaternion translation vector.
AA_API void	aa_tf_duqu2tfmat (const double d[AA_RESTRICT 8], double T[AA_RESTRICT 12])
	Convert dual quaternion to transformation matrix.
AA_API void	aa_tf_tfmat2duqu (const double T[AA_RESTRICT 12], double d[AA_RESTRICT 8])
	Convert transformation matrix to dual quaternion.
AA_API void	aa_tf_qv2duqu (const double q[AA_RESTRICT 4], const double v[AA_RESTRICT 3], double d[AA_RESTRICT 8])
	Convert orientation unit quaternion and translation vector to dual quaternion. More...
AA_API void	aa_tf_xyz2duqu (double x, double y, double z, double d[AA_RESTRICT 8])
	Pure translation dual quaternion. More...
AA_API void	aa_tf_xxyz2duqu (double theta, double x, double y, double z, double d[AA_RESTRICT 8])
	Convert x angle and translation to dual quaternion. More...
AA_API void	aa_tf_yxyz2duqu (double theta, double x, double y, double z, double d[AA_RESTRICT 8])
	Convert y angle and translation to dual quaternion. More...
AA_API void	aa_tf_zxyz2duqu (double theta, double x, double y, double z, double d[AA_RESTRICT 8])
	Convert z angle and translation to dual quaternion. More...
AA_API void	aa_tf_duqu2qv (const double d[AA_RESTRICT 8], double q[AA_RESTRICT 4], double v[AA_RESTRICT 3])
	Convert dual quaternion to orientation unit quaternion and translation vector. More...
void	aa_tf_tfmat2av (const double T[12], double q[AA_RESTRICT 4], double v[AA_RESTRICT 3])
	transformation matrix to quaternion-translation
AA_API void	aa_tf_duqu_vel2twist (const double d[AA_RESTRICT 8], const double dx[AA_RESTRICT 6], double t[AA_RESTRICT 8])
	Dual quaternion twist from velocity.
AA_API void	aa_tf_duqu_twist2vel (const double d[AA_RESTRICT 8], const double t[AA_RESTRICT 8], double dx[AA_RESTRICT 6])
	Dual quaternion twist to velocity.
AA_API void	aa_tf_duqu_twist2diff (const double d[AA_RESTRICT 8], const double t[AA_RESTRICT 8], double dd[AA_RESTRICT 8])
	Dual quaternion twist to derivative.
AA_API void	aa_tf_duqu_vel2diff (const double d[AA_RESTRICT 8], const double dx[AA_RESTRICT 6], double dd[AA_RESTRICT 8])
	Dual quaternion derivative from velocity.
AA_API void	aa_tf_duqu_diff2vel (const double d[AA_RESTRICT 8], const double dd[AA_RESTRICT 8], double dx[AA_RESTRICT 6])
	Dual quaternion derivative to spatial velocity.
AA_API void	aa_tf_duqu_diff2twist (const double d[AA_RESTRICT 8], const double dd[AA_RESTRICT 8], double twist[AA_RESTRICT 8])
	Convert dual quaternion derivative to dual quaternion twist.
AA_API void	aa_tf_duqu_stwist (const double d0[AA_RESTRICT 8], const double twist[AA_RESTRICT 8], double dt, double d1[AA_RESTRICT 6])
	Dual quaternion twist integration. More...
AA_API void	aa_tf_duqu_svel (const double d0[AA_RESTRICT 8], const double dx[AA_RESTRICT 6], double dt, double d1[AA_RESTRICT 6])
	Dual quaternion velocity integration. More...
AA_API void	aa_tf_duqu_sdiff (const double d0[AA_RESTRICT 8], const double dd[AA_RESTRICT 8], double dt, double d1[AA_RESTRICT 6])
	Dual quaternion derivative integration. More...
void	aa_tf_relx_mean (size_t n, const double *R, const double *X, size_t ldx, const double *Y, size_t ldy, double rel[3])
void	aa_tf_relx_median (size_t n, const double *R, const double *X, size_t ldx, const double *Y, size_t ldy, double rel[3])

Variables
static const double	aa_tf_ident [12] = AA_TF_IDENT_INITIALIZER
	Identity transformation matrix array.
static const double	aa_tf_tfmat_ident [12] = AA_TF_IDENT_INITIALIZER
	Identity transformation matrix array.
static const double	aa_tf_rotmat_ident [9] = AA_TF_ROTMAT_IDENT_INITIALIZER
	Identity rotation matrix array.
static const double	aa_tf_quat_ident [4] = AA_TF_QUAT_IDENT_INITIALIZER
	Identity quaternion array.
static const double	aa_tf_duqu_ident [8] = AA_TF_DUQU_IDENT_INITIALIZER
	Identity dual quaternion array.
static const double	aa_tf_qutr_ident [7] = AA_TF_QUTR_IDENT_INITIALIZER
	Identity quaternion-translation array.
static const double	aa_tf_axang_ident [4] = AA_TF_AXANG_IDENT_INITIALIZER
	Identity axis-angle array.
static const double	aa_tf_rotvec_ident [3] = AA_TF_ROTVEC_IDENT_INITIALIZER
	Identity rotation vector array.
static const double	aa_tf_vec_ident [3] = AA_TF_ROTVEC_IDENT_INITIALIZER
	Identity vector-3 array.
static const double	aa_tf_vec_x [3] = {1, 0, 0}
	An X axis.
static const double	aa_tf_vec_y [3] = {0, 1, 0}
	A Y axis.
static const double	aa_tf_vec_z [3] = {0, 0, 1}
	A Z axis.

Detailed Description

Low-level operations for SE(3) orientations and transformations.

See also

tf.hpp provides a higher-level object-oriented interface which may ease conversion between different representations.

Definition in file tf.h.

Macro Definition Documentation

#define AA_TF_CROSSX	(		a,
			b,
			c
	)

Value:

(c)[0] =  (a)[1]*(b)[2] - (a)[2]*(b)[1]; \
    (c)[1] =  (a)[2]*(b)[0] - (a)[0]*(b)[2]; \
    (c)[2] =  (a)[0]*(b)[1] - (a)[1]*(b)[0]; \

Macro to compute the cross product of length 3 vectors.

May evaluate its arguments multiple times.

Definition at line 796 of file tf.h.

#define AA_TF_DEF_EULER

(

letters

)

Value:

AA_API void                                                         \
    aa_tf_euler ## letters ## 2rotmat( double e1, double e2, double e3, \
                                       double R[AA_RESTRICT 9] );       \
    AA_API void                                                         \
    aa_tf_euler ## letters ## 2quat( double e1, double e2, double e3,   \
                                    double q[AA_RESTRICT 4] );

Definition at line 1346 of file tf.h.

#define AA_TF_DEF_SERIES	(		name,
			a0,
			a1,
			a2
	)

Value:

static inline double                                    \
    aa_tf_ ## name ##_series2(double theta2)                \
    {                                                       \
        return aa_horner3( theta2, a0, a1, a2 );            \
    }                                                       \
    static inline double                                    \
    aa_tf_ ## name ## _series(double theta)                 \
    {                                                       \
        return aa_tf_ ## name ## _series2(theta*theta);     \
    }                                                       \

Definition at line 69 of file tf.h.

#define AA_TF_DOTX	(		a,
			b
	)		((a)[0]*(b)[0] + (a)[1]*(b)[1] + (a)[2]*(b)[2])

Macro to compute a dot product of length 3 vectors.

May evaluate its arguments multiple times.

Definition at line 757 of file tf.h.

Typedef Documentation

typedef struct aa_tf_rotmat aa_tf_rotmat_t

Memory layout for a rotation matrix.

column major

The matrix is in column-major order.

typedef struct aa_tf_tfmat aa_tf_tfmat_t

Memory layout for a transformation matrix.

It is a column-major matrix, but the bottom row is omitted because this row is the same for all SE(3) transformation matrices.

The first 9 elements are a column major rotation matrix. The last 3 elements are the origin vector.

Function Documentation

AA_API void aa_tf_axang2quat	(	const double	axang[AA_RESTRICT 4],
		double	q[AA_RESTRICT 4]
	)

axis-angle to quaternion.

AA_API void aa_tf_axang2quat2	(	const double	axis[AA_RESTRICT 3],
		double	angle,
		double	q[AA_RESTRICT 4]
	)

axis-angle to quaternion.

AA_API void aa_tf_duqu2qv	(	const double	d[AA_RESTRICT 8],
		double	q[AA_RESTRICT 4],
		double	v[AA_RESTRICT 3]
	)

Convert dual quaternion to orientation unit quaternion and translation vector.

AA_API void aa_tf_duqu_sdiff	(	const double	d0[AA_RESTRICT 8],
		const double	dd[AA_RESTRICT 8],
		double	dt,
		double	d1[AA_RESTRICT 6]
	)

Dual quaternion derivative integration.

Parameters

d0	initial position, dual quaternion
dd	dual quaternion derivative
dt	time step
d1	final position, dual quaternion

AA_API void aa_tf_duqu_stwist	(	const double	d0[AA_RESTRICT 8],
		const double	twist[AA_RESTRICT 8],
		double	dt,
		double	d1[AA_RESTRICT 6]
	)

Dual quaternion twist integration.

Parameters

d0	initial position, dual quaternion
twist	dual quaternion twist
dt	time step
d1	final position, dual quaternion

AA_API void aa_tf_duqu_svel	(	const double	d0[AA_RESTRICT 8],
		const double	dx[AA_RESTRICT 6],
		double	dt,
		double	d1[AA_RESTRICT 6]
	)

Dual quaternion velocity integration.

Parameters

d0	initial position, dual quaternion
dx	spatial velocity
dt	time step
d1	final position, dual quaternion

AA_API void aa_tf_qadd	(	const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion addition.

double aa_tf_qangle

(

const double

q[AA_RESTRICT 4]

)

Return the angle of the quaternion.

Note that this result is half the 3D angle.

AA_API void aa_tf_qcmul	(	const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion conjugate a and multiply by b.

AA_API void aa_tf_qdpexp	(	const double	e[AA_RESTRICT 3],
		const double	de[AA_RESTRICT 3],
		double	dq[AA_RESTRICT 4]
	)

Derivative of the Pure Quaternion Exponential.

Parameters

e	A pure quaternion
de	The derivative of e
dq	The derivative of exp(e)

AA_API void aa_tf_qduln	(	const double	q[AA_RESTRICT 4],
		const double	dq[AA_RESTRICT 4],
		double	dln[AA_RESTRICT 3]
	)

Derivative of the Unit Quaternion Logarithm.

Parameters

q	A unit quaternion
dq	The derivative of q
dln	The derivative of ln(dq)

AA_API void aa_tf_qminimize

(

double

q[AA_RESTRICT 4]

)

Minimize angle represented by the quaternion.

This puts the quaternion in the right-hand side of the complex plane. Its w value will be positive.

AA_API void aa_tf_qmul	(	const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion multiplication.

AA_API void aa_tf_qmul_qv	(	const double	q[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	c[AA_RESTRICT 4]
	)

Quaternion multiplication.

AA_API void aa_tf_qmul_vq	(	const double	v[AA_RESTRICT 3],
		const double	q[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion multiplication.

AA_API void aa_tf_qmulc	(	const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion multiply a by conjugate b.

AA_API void aa_tf_qmulnorm	(	const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion multiplication and normalize.

AA_API void aa_tf_qnormalize

(

double

q[AA_RESTRICT 4]

)

Normalize Quaternion.

\[ \bf{q} \leftarrow \frac{\bf q}{\Arrowvert {\bf q} \Arrowvert} \]

AA_API void aa_tf_qrel	(	const double	q1[AA_RESTRICT 4],
		const double	q2[AA_RESTRICT 4],
		double	q_rel[AA_RESTRICT 4]
	)

Relative orientation.

\[ q_{\rm rel} = q_1 q_2^{-1} \]

AA_API void aa_tf_qrk1	(	const double	q0[AA_RESTRICT 4],
		const double	dq[AA_RESTRICT 4],
		double	dt,
		double	q1[AA_RESTRICT 4]
	)

Integrate unit quaternion, Runge-Kutta-1 (euler) integration.

Parameters

q0	Initial rotation quaternion
dq	Quaternion derivative
dt	Time step
q1	Final rotation quaternion

AA_API void aa_tf_qrot	(	const double	q[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	p[AA_RESTRICT 3]
	)

Quaternion point rotation.

AA_API void aa_tf_qsdiff	(	const double	q0[AA_RESTRICT 4],
		const double	dq[AA_RESTRICT 4],
		double	dt,
		double	q1[AA_RESTRICT 4]
	)

Integrate unit quaternion from quaternion derivative.

Parameters

q0	Initial rotation quaternion
dq	Quaternion derivative
dt	Time step
q1	Final rotation quaternion

AA_API void aa_tf_qslerp	(	double	tau,
		const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion SLERP.

AA_API void aa_tf_qslerpalg	(	double	tau,
		const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion SLERP, computed algebraicly.

AA_API void aa_tf_qslerpdiff	(	double	tau,
		const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Derivative of quaternation SLERP WRT tau.

This is NOT a time derivative. Use the chain rule: (dq/dt = * (dq/dtau)*(dt/dtau) )

AA_API void aa_tf_qsub	(	const double	a[AA_RESTRICT 4],
		const double	b[AA_RESTRICT 4],
		double	c[AA_RESTRICT 4]
	)

Quaternion subtraction.

AA_API void aa_tf_qsvel	(	const double	q0[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	dt,
		double	q1[AA_RESTRICT 4]
	)

Integrate unit quaternion from constant angular velocity.

Parameters

q0	Initial rotation quaternion
v	Rotational velocity
dt	Time step
q1	Final rotation quaternion

AA_API void aa_tf_quat2axang	(	const double	q[AA_RESTRICT 4],
		double	axang[AA_RESTRICT 4]
	)

Quaternion to axis-angle.

AA_API void aa_tf_qv2duqu	(	const double	q[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	d[AA_RESTRICT 8]
	)

Convert orientation unit quaternion and translation vector to dual quaternion.

AA_API void aa_tf_qv2tfmat	(	const double	q[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	T[AA_RESTRICT 12]
	)

Convert orientation unit quaternion and translation vector to transformation matrix.

AA_API void aa_tf_qv_conj	(	const double	q[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	qc[AA_RESTRICT 4],
		double	vc[AA_RESTRICT 3]
	)

Invert transform.

Unit quaternion inverse is equal to the conjuage

AA_API void aa_tf_qvelrk1	(	const double	q0[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	dt,
		double	q1[AA_RESTRICT 4]
	)

Integrate unit quaternion from angular velocity, Runge-Kutta-1 (euler) integration.

Parameters

q0	Initial rotation quaternion
v	Rotational velocity
dt	Time step
q1	Final rotation quaternion

AA_API void aa_tf_qvelrk4	(	const double	q0[AA_RESTRICT 4],
		const double	v[AA_RESTRICT 3],
		double	dt,
		double	q1[AA_RESTRICT 4]
	)

Integrate unit quaternion from angular velocity, Runge-Kutta-4 (euler) integration.

Parameters

q0	Initial rotation quaternion
v	Rotational velocity
dt	Time step
q1	Final rotation quaternion

AA_API void aa_tf_xxyz2duqu	(	double	theta,
		double	x,
		double	y,
		double	z,
		double	d[AA_RESTRICT 8]
	)

Convert x angle and translation to dual quaternion.

AA_API void aa_tf_xyz2duqu	(	double	x,
		double	y,
		double	z,
		double	d[AA_RESTRICT 8]
	)

Pure translation dual quaternion.

AA_API void aa_tf_yxyz2duqu	(	double	theta,
		double	x,
		double	y,
		double	z,
		double	d[AA_RESTRICT 8]
	)

Convert y angle and translation to dual quaternion.

AA_API void aa_tf_zxyz2duqu	(	double	theta,
		double	x,
		double	y,
		double	z,
		double	d[AA_RESTRICT 8]
	)

Convert z angle and translation to dual quaternion.