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authorsanine <sanine.not@pm.me>2022-06-14 00:06:42 -0500
committersanine <sanine.not@pm.me>2022-06-14 00:06:42 -0500
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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