Low-level operations for SE(2), planar orientations and transformations. More...

Macros
#define	AA_TF_CMPLX(x, y) ((x) + _Complex_I * (y))
	Construct a complex number.

#define	AA_TF_CMPLX_REAL(c) (creal(c))
	Extract the real part of a complex number.

#define	AA_TF_CMPLX_IMAG(c) (cimag(c))
	Extract the imaginary part of a complex number.

#define	AA_TF_VEC2(x, y) AA_TF_CMPLX(x, y)
	Construct a 2D vector.

#define	AA_TF_VEC2_X(v) AA_TF_CMPLX_REAL(v)
	Extract the x-coordinate of a 2D vector.

#define	AA_TF_VEC2_Y(v) AA_TF_CMPLX_IMAG(v)
	Extract the y-coordinate of a 2D vector.

#define	AA_TF_VEC2_LD(ptr) AA_TF_VEC2((ptr)[0], (ptr)[1])
	Load a 2D vector from memory.

#define	AA_TF_VEC2_ST(v, ptr)
	Store a 2D vector in memory. More...

#define	AA_TF_ROTMATP_IDENT_INITIALIZER {1,0, 0,1};
	Initializer for planar rotation matrix identity element.

#define	AA_TF_COTR_IDENT_INITIALIZER {1,0, 0,0 };
	Initializer for complex number and translation identity element.

#define	AA_TF_TFMATP_IDENT_INITIALIZER {1,0, 0,1, 0,0};
	Initializer for planar transformation matrix identity element.

#define	AA_TF_CMPLX_IDENT AA_TF_CMPLX(1, 0)
	Constant for complex number identity element.

Functions
AA_API aa_tf_cmplx	aa_tf_cpexp (double theta)
	Exponential of a pure (zero real part) complex number. More...

AA_API double	aa_tf_culn (const aa_tf_cmplx c)
	Logarithm of a unit complex number. More...

AA_API void	aa_tf_rotmatp_pexp (double angle, double R[AA_RESTRICT 4])
	Exponential of a pure (zero real part) complex number as a rotation matrix.

AA_API double	aa_tf_rotmatp_uln (const double R[4])
	Logarithm of a planar rotation matrix.

AA_API aa_tf_vec2	aa_tf_crot (const aa_tf_cmplx c, const aa_tf_vec2 v)
	Apply a planar rotation via complex number.

AA_API aa_tf_vec2	aa_tf_rotmatp_rot (const double R[AA_RESTRICT 4], const aa_tf_vec2 v)
	Apply a planar rotation via rotation matrix.

AA_API aa_tf_cmplx	aa_tf_cconj (const aa_tf_cmplx c)
	Conjugate a complex number, giving the inverse rotation.

AA_API void	aa_tf_rotmatp_inv2 (const double R[AA_RESTRICT 4], double Ri[AA_RESTRICT 4])
	Invert a planar rotation matrix.

AA_API aa_tf_cmplx	aa_tf_cmul (const aa_tf_cmplx c1, const aa_tf_cmplx c2)
	Multiply complex numbers.

AA_API void	aa_tf_rotmatp_mul (const double R1[AA_RESTRICT 4], const double R2[AA_RESTRICT 4], double R12[AA_RESTRICT 4])
	Multiply planar rotation matrices.

AA_API double	aa_tf_cmplx2angle (const aa_tf_cmplx c)
	Convert a complex number to a rotation angle.

AA_API void	aa_tf_cmplx2rotmatp (const aa_tf_cmplx c, double R[AA_RESTRICT 4])
	Convert a unit complex number to a rotation matrix.

AA_API aa_tf_cmplx	aa_tf_angle2cmplx (double angle)
	Convert a rotation angle to a complex number.

AA_API void	aa_tf_angle2rotmatp (double angle, double R[AA_RESTRICT 4])
	Convert a rotation angle to a planar rotation matrix.

AA_API aa_tf_cmplx	aa_tf_rotmatp2cmplx (const double R[AA_RESTRICT 4])
	Convert a planar rotation matrix to a complex number.

AA_API double	aa_tf_rotmatp2angle (const double R[AA_RESTRICT 4])
	Convert a planar rotation matrix to a rotation angle.

AA_API aa_tf_vec2	aa_tf_cv_tf (const aa_tf_cmplx c, const aa_tf_vec2 v, const aa_tf_vec2 p)
	Apply a planar transform represented with a complex number and translation vector. More...

AA_API aa_tf_vec2	aa_tf_tfmatp_tf (const double T[AA_RESTRICT 6], const aa_tf_vec2 p)
	Apply a planar transform represented matrix.

AA_API void	aa_tf_cv2tfmatp (const aa_tf_cmplx c, const aa_tf_vec2 v, double T[AA_RESTRICT 6])
	Convert a complex number and translation vector to a planar transformation matrix.

AA_API void	aa_tf_tfmatp2cv (const double T[AA_RESTRICT 6], aa_tf_cmplx c, aa_tf_vec2 v)
	Convert a planar transformation matrix to a complex number and translation vector.

AA_API void	aa_tf_cv_mul (const aa_tf_cmplx c1, const aa_tf_vec2 v1, const aa_tf_cmplx c2, const aa_tf_vec2 v2, aa_tf_cmplx c12, aa_tf_vec2 v12)
	Multiply (chain) two complex number and translation vector planar transforms.

AA_API void	aa_tf_tfmatp_mul (const double T1[AA_RESTRICT 6], const double T2[AA_RESTRICT 6], double T12[AA_RESTRICT 6])
	Multiply (chain) two complex number and translation vector planar transforms.

AA_API void	aa_tf_cv_inv (const aa_tf_cmplx c, const aa_tf_vec2 v, aa_tf_cmplx ci, aa_tf_vec2 vi)
	Invert a complex number and translation vector planar transform.

AA_API void	aa_tf_tfmatp_inv2 (const double T[AA_RESTRICT 6], double Ti[AA_RESTRICT 6])
	Invert a planar transformation matrix.

Detailed Description

Low-level operations for SE(2), planar orientations and transformations.

Definition in file planar.h.

Macro Definition Documentation

◆ AA_TF_VEC2_ST

#define AA_TF_VEC2_ST	(	v,
		ptr
	)

Value:

    do {                            \
        (ptr)[0] = AA_TF_VEC2_X(v); \
        (ptr)[1] = AA_TF_VEC2_Y(v); \
    } while (0)

Store a 2D vector in memory.

Definition at line 67 of file planar.h.

Function Documentation

◆ aa_tf_cpexp()

AA_API aa_tf_cmplx aa_tf_cpexp ( double theta )

Exponential of a pure (zero real part) complex number.

\[ e^{\theta \imath} = \cos \theta + \imath \sin \theta \]

◆ aa_tf_culn()

AA_API double aa_tf_culn ( const aa_tf_cmplx c )

Logarithm of a unit complex number.

\[ \ln\left(a + b\imath\right) = \operatorname{atan2}\left(b,a\right)\;, \quad \text{where } \sqrt{a^2+b^2} = 1 \]

◆ aa_tf_cv_tf()

AA_API aa_tf_vec2 aa_tf_cv_tf	(	const aa_tf_cmplx	c,
		const aa_tf_vec2	v,
		const aa_tf_vec2	p
	)

Apply a planar transform represented with a complex number and translation vector.

Parameters

c	The rotation part of the transform
v	The translation part of the transform
p	The point to transform

Macros