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Wotos-mpv/lib/cglm/docs/source/quat.rst
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.. default-domain:: C
quaternions
===========
Header: cglm/quat.h
**Important:** *cglm* stores quaternion as **[x, y, z, w]** in memory
since **v0.4.0** it was **[w, x, y, z]**
before v0.4.0 ( **v0.3.5 and earlier** ). w is real part.
What you can do with quaternions with existing functions is (Some of them):
- You can rotate transform matrix using quaterion
- You can rotate vector using quaterion
- You can create view matrix using quaterion
- You can create a lookrotation (from source point to dest)
Table of contents (click to go):
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Macros:
1. GLM_QUAT_IDENTITY_INIT
#. GLM_QUAT_IDENTITY
Functions:
1. :c:func:`glm_quat_identity`
#. :c:func:`glm_quat_identity_array`
#. :c:func:`glm_quat_init`
#. :c:func:`glm_quat`
#. :c:func:`glm_quatv`
#. :c:func:`glm_quat_copy`
#. :c:func:`glm_quat_from_vecs`
#. :c:func:`glm_quat_norm`
#. :c:func:`glm_quat_normalize`
#. :c:func:`glm_quat_normalize_to`
#. :c:func:`glm_quat_dot`
#. :c:func:`glm_quat_conjugate`
#. :c:func:`glm_quat_inv`
#. :c:func:`glm_quat_add`
#. :c:func:`glm_quat_sub`
#. :c:func:`glm_quat_real`
#. :c:func:`glm_quat_imag`
#. :c:func:`glm_quat_imagn`
#. :c:func:`glm_quat_imaglen`
#. :c:func:`glm_quat_angle`
#. :c:func:`glm_quat_axis`
#. :c:func:`glm_quat_mul`
#. :c:func:`glm_quat_mat4`
#. :c:func:`glm_quat_mat4t`
#. :c:func:`glm_quat_mat3`
#. :c:func:`glm_quat_mat3t`
#. :c:func:`glm_quat_lerp`
#. :c:func:`glm_quat_nlerp`
#. :c:func:`glm_quat_slerp`
#. :c:func:`glm_quat_look`
#. :c:func:`glm_quat_for`
#. :c:func:`glm_quat_forp`
#. :c:func:`glm_quat_rotatev`
#. :c:func:`glm_quat_rotate`
#. :c:func:`glm_quat_rotate_at`
#. :c:func:`glm_quat_rotate_atm`
Functions documentation
~~~~~~~~~~~~~~~~~~~~~~~
.. c:function:: void glm_quat_identity(versor q)
| makes given quat to identity
Parameters:
| *[in, out]* **q** quaternion
.. c:function:: void glm_quat_identity_array(versor * __restrict q, size_t count)
| make given quaternion array's each element identity quaternion
Parameters:
| *[in, out]* **q** quat array (must be aligned (16) if alignment is not disabled)
| *[in]* **count** count of quaternions
.. c:function:: void glm_quat_init(versor q, float x, float y, float z, float w)
| inits quaternion with given values
Parameters:
| *[out]* **q** quaternion
| *[in]* **x** imag.x
| *[in]* **y** imag.y
| *[in]* **z** imag.z
| *[in]* **w** w (real part)
.. c:function:: void glm_quat(versor q, float angle, float x, float y, float z)
| creates NEW quaternion with individual axis components
| given axis will be normalized
Parameters:
| *[out]* **q** quaternion
| *[in]* **angle** angle (radians)
| *[in]* **x** axis.x
| *[in]* **y** axis.y
| *[in]* **z** axis.z
.. c:function:: void glm_quatv(versor q, float angle, vec3 axis)
| creates NEW quaternion with axis vector
| given axis will be normalized
Parameters:
| *[out]* **q** quaternion
| *[in]* **angle** angle (radians)
| *[in]* **axis** axis (will be normalized)
.. c:function:: void glm_quat_copy(versor q, versor dest)
| copy quaternion to another one
Parameters:
| *[in]* **q** source quaternion
| *[out]* **dest** destination quaternion
.. c:function:: void glm_quat_from_vecs(vec3 a, vec3 b, versor dest)
| compute unit quaternion needed to rotate a into b
References:
* `Finding quaternion representing the rotation from one vector to another <https://stackoverflow.com/a/11741520/183120>`_
* `Quaternion from two vectors <http://lolengine.net/blog/2014/02/24/quaternion-from-two-vectors-final>`_
* `Angle between vectors <http://www.euclideanspace.com/maths/algebra/vectors/angleBetween/minorlogic.htm>`_
Parameters:
| *[in]* **a** unit vector
| *[in]* **b** unit vector
| *[in]* **dest** unit quaternion
.. c:function:: float glm_quat_norm(versor q)
| returns norm (magnitude) of quaternion
Parameters:
| *[in]* **a** quaternion
Returns:
norm (magnitude)
.. c:function:: void glm_quat_normalize_to(versor q, versor dest)
| normalize quaternion and store result in dest, original one will not be normalized
Parameters:
| *[in]* **q** quaternion to normalize into
| *[out]* **dest** destination quaternion
.. c:function:: void glm_quat_normalize(versor q)
| normalize quaternion
Parameters:
| *[in, out]* **q** quaternion
.. c:function:: float glm_quat_dot(versor p, versor q)
dot product of two quaternion
Parameters:
| *[in]* **p** quaternion 1
| *[in]* **q** quaternion 2
Returns:
dot product
.. c:function:: void glm_quat_conjugate(versor q, versor dest)
conjugate of quaternion
Parameters:
| *[in]* **q** quaternion
| *[in]* **dest** conjugate
.. c:function:: void glm_quat_inv(versor q, versor dest)
inverse of non-zero quaternion
Parameters:
| *[in]* **q** quaternion
| *[in]* **dest** inverse quaternion
.. c:function:: void glm_quat_add(versor p, versor q, versor dest)
add (componentwise) two quaternions and store result in dest
Parameters:
| *[in]* **p** quaternion 1
| *[in]* **q** quaternion 2
| *[in]* **dest** result quaternion
.. c:function:: void glm_quat_sub(versor p, versor q, versor dest)
subtract (componentwise) two quaternions and store result in dest
Parameters:
| *[in]* **p** quaternion 1
| *[in]* **q** quaternion 2
| *[in]* **dest** result quaternion
.. c:function:: float glm_quat_real(versor q)
returns real part of quaternion
Parameters:
| *[in]* **q** quaternion
Returns:
real part (quat.w)
.. c:function:: void glm_quat_imag(versor q, vec3 dest)
returns imaginary part of quaternion
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** imag
.. c:function:: void glm_quat_imagn(versor q, vec3 dest)
returns normalized imaginary part of quaternion
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** imag
.. c:function:: float glm_quat_imaglen(versor q)
returns length of imaginary part of quaternion
Parameters:
| *[in]* **q** quaternion
Returns:
norm of imaginary part
.. c:function:: float glm_quat_angle(versor q)
returns angle of quaternion
Parameters:
| *[in]* **q** quaternion
Returns:
angles of quat (radians)
.. c:function:: void glm_quat_axis(versor q, versor dest)
axis of quaternion
Parameters:
| *[in]* **p** quaternion
| *[out]* **dest** axis of quaternion
.. c:function:: void glm_quat_mul(versor p, versor q, versor dest)
| multiplies two quaternion and stores result in dest
| this is also called Hamilton Product
| According to WikiPedia:
| The product of two rotation quaternions [clarification needed] will be
equivalent to the rotation q followed by the rotation p
Parameters:
| *[in]* **p** quaternion 1 (first rotation)
| *[in]* **q** quaternion 2 (second rotation)
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_mat4(versor q, mat4 dest)
| convert quaternion to mat4
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_mat4t(versor q, mat4 dest)
| convert quaternion to mat4 (transposed). This is transposed version of glm_quat_mat4
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_mat3(versor q, mat3 dest)
| convert quaternion to mat3
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_mat3t(versor q, mat3 dest)
| convert quaternion to mat3 (transposed). This is transposed version of glm_quat_mat3
Parameters:
| *[in]* **q** quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_lerp(versor from, versor to, float t, versor dest)
| interpolates between two quaternions
| using spherical linear interpolation (LERP)
Parameters:
| *[in]* **from** from
| *[in]* **to** to
| *[in]* **t** interpolant (amount) clamped between 0 and 1
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_nlerp(versor q, versor r, float t, versor dest)
| interpolates between two quaternions
| taking the shortest rotation path using
| normalized linear interpolation (NLERP)
| This is a cheaper alternative to slerp; most games use nlerp
| for animations as it visually makes little difference.
References:
* `Understanding Slerp, Then Not Using it <http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It>`_
* `Lerp, Slerp and Nlerp <https://keithmaggio.wordpress.com/2011/02/15/math-magician-lerp-slerp-and-nlerp/>`_
Parameters:
| *[in]* **from** from
| *[in]* **to** to
| *[in]* **t** interpolant (amount) clamped between 0 and 1
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_slerp(versor q, versor r, float t, versor dest)
| interpolates between two quaternions
| using spherical linear interpolation (SLERP)
Parameters:
| *[in]* **from** from
| *[in]* **to** to
| *[in]* **t** interpolant (amount) clamped between 0 and 1
| *[out]* **dest** result quaternion
.. c:function:: void glm_quat_look(vec3 eye, versor ori, mat4 dest)
| creates view matrix using quaternion as camera orientation
Parameters:
| *[in]* **eye** eye
| *[in]* **ori** orientation in world space as quaternion
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_for(vec3 dir, vec3 up, versor dest)
| creates look rotation quaternion
Parameters:
| *[in]* **dir** direction to look
| *[in]* **up** up vector
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_forp(vec3 from, vec3 to, vec3 up, versor dest)
| creates look rotation quaternion using source and destination positions p suffix stands for position
| this is similar to glm_quat_for except this computes direction for glm_quat_for for you.
Parameters:
| *[in]* **from** source point
| *[in]* **to** destination point
| *[in]* **up** up vector
| *[out]* **dest** result matrix
.. c:function:: void glm_quat_rotatev(versor q, vec3 v, vec3 dest)
| crotate vector using using quaternion
Parameters:
| *[in]* **q** quaternion
| *[in]* **v** vector to rotate
| *[out]* **dest** rotated vector
.. c:function:: void glm_quat_rotate(mat4 m, versor q, mat4 dest)
| rotate existing transform matrix using quaternion
instead of passing identity matrix, consider to use quat_mat4 functions
Parameters:
| *[in]* **m** existing transform matrix to rotate
| *[in]* **q** quaternion
| *[out]* **dest** rotated matrix/transform
.. c:function:: void glm_quat_rotate_at(mat4 m, versor q, vec3 pivot)
| rotate existing transform matrix using quaternion at pivot point
Parameters:
| *[in, out]* **m** existing transform matrix to rotate
| *[in]* **q** quaternion
| *[in]* **pivot** pivot
.. c:function:: void glm_quat_rotate_atm(mat4 m, versor q, vec3 pivot)
| rotate NEW transform matrix using quaternion at pivot point
| this creates rotation matrix, it assumes you don't have a matrix
| this should work faster than glm_quat_rotate_at because it reduces one glm_translate.
Parameters:
| *[in, out]* **m** existing transform matrix to rotate
| *[in]* **q** quaternion
| *[in]* **pivot** pivot
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