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orbit-plus/include/cglm/quat.h

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2023-02-12 04:18:45 +00:00
/*
* Copyright (c), Recep Aslantas.
*
* MIT License (MIT), http://opensource.org/licenses/MIT
* Full license can be found in the LICENSE file
*/
/*
Macros:
GLM_QUAT_IDENTITY_INIT
GLM_QUAT_IDENTITY
Functions:
CGLM_INLINE void glm_quat_identity(versor q);
CGLM_INLINE void glm_quat_init(versor q, float x, float y, float z, float w);
CGLM_INLINE void glm_quat(versor q, float angle, float x, float y, float z);
CGLM_INLINE void glm_quatv(versor q, float angle, vec3 axis);
CGLM_INLINE void glm_quat_copy(versor q, versor dest);
CGLM_INLINE void glm_quat_from_vecs(vec3 a, vec3 b, versor dest);
CGLM_INLINE float glm_quat_norm(versor q);
CGLM_INLINE void glm_quat_normalize(versor q);
CGLM_INLINE void glm_quat_normalize_to(versor q, versor dest);
CGLM_INLINE float glm_quat_dot(versor p, versor q);
CGLM_INLINE void glm_quat_conjugate(versor q, versor dest);
CGLM_INLINE void glm_quat_inv(versor q, versor dest);
CGLM_INLINE void glm_quat_add(versor p, versor q, versor dest);
CGLM_INLINE void glm_quat_sub(versor p, versor q, versor dest);
CGLM_INLINE float glm_quat_real(versor q);
CGLM_INLINE void glm_quat_imag(versor q, vec3 dest);
CGLM_INLINE void glm_quat_imagn(versor q, vec3 dest);
CGLM_INLINE float glm_quat_imaglen(versor q);
CGLM_INLINE float glm_quat_angle(versor q);
CGLM_INLINE void glm_quat_axis(versor q, vec3 dest);
CGLM_INLINE void glm_quat_mul(versor p, versor q, versor dest);
CGLM_INLINE void glm_quat_mat4(versor q, mat4 dest);
CGLM_INLINE void glm_quat_mat4t(versor q, mat4 dest);
CGLM_INLINE void glm_quat_mat3(versor q, mat3 dest);
CGLM_INLINE void glm_quat_mat3t(versor q, mat3 dest);
CGLM_INLINE void glm_quat_lerp(versor from, versor to, float t, versor dest);
CGLM_INLINE void glm_quat_lerpc(versor from, versor to, float t, versor dest);
CGLM_INLINE void glm_quat_slerp(versor q, versor r, float t, versor dest);
CGLM_INLINE void glm_quat_nlerp(versor q, versor r, float t, versor dest);
CGLM_INLINE void glm_quat_look(vec3 eye, versor ori, mat4 dest);
CGLM_INLINE void glm_quat_for(vec3 dir, vec3 fwd, vec3 up, versor dest);
CGLM_INLINE void glm_quat_forp(vec3 from,
vec3 to,
vec3 fwd,
vec3 up,
versor dest);
CGLM_INLINE void glm_quat_rotatev(versor q, vec3 v, vec3 dest);
CGLM_INLINE void glm_quat_rotate(mat4 m, versor q, mat4 dest);
*/
#ifndef cglm_quat_h
#define cglm_quat_h
#include "common.h"
#include "vec3.h"
#include "vec4.h"
#include "mat4.h"
#include "mat3.h"
#include "affine-mat.h"
#include "affine.h"
#ifdef CGLM_SSE_FP
# include "simd/sse2/quat.h"
#endif
#ifdef CGLM_NEON_FP
# include "simd/neon/quat.h"
#endif
CGLM_INLINE void glm_quat_normalize(versor q);
/*
* IMPORTANT:
* ----------------------------------------------------------------------------
* cglm stores quat as [x, y, z, w] since v0.3.6
*
* it was [w, x, y, z] before v0.3.6 it has been changed to [x, y, z, w]
* with v0.3.6 version.
* ----------------------------------------------------------------------------
*/
#define GLM_QUAT_IDENTITY_INIT {0.0f, 0.0f, 0.0f, 1.0f}
#define GLM_QUAT_IDENTITY ((versor)GLM_QUAT_IDENTITY_INIT)
/*!
* @brief makes given quat to identity
*
* @param[in, out] q quaternion
*/
CGLM_INLINE
void
glm_quat_identity(versor q) {
CGLM_ALIGN(16) versor v = GLM_QUAT_IDENTITY_INIT;
glm_vec4_copy(v, q);
}
/*!
* @brief make given quaternion array's each element identity quaternion
*
* @param[in, out] q quat array (must be aligned (16)
* if alignment is not disabled)
*
* @param[in] count count of quaternions
*/
CGLM_INLINE
void
glm_quat_identity_array(versor * __restrict q, size_t count) {
CGLM_ALIGN(16) versor v = GLM_QUAT_IDENTITY_INIT;
size_t i;
for (i = 0; i < count; i++) {
glm_vec4_copy(v, q[i]);
}
}
/*!
* @brief inits quaterion with raw values
*
* @param[out] q quaternion
* @param[in] x x
* @param[in] y y
* @param[in] z z
* @param[in] w w (real part)
*/
CGLM_INLINE
void
glm_quat_init(versor q, float x, float y, float z, float w) {
q[0] = x;
q[1] = y;
q[2] = z;
q[3] = w;
}
/*!
* @brief creates NEW quaternion with axis vector
*
* @param[out] q quaternion
* @param[in] angle angle (radians)
* @param[in] axis axis
*/
CGLM_INLINE
void
glm_quatv(versor q, float angle, vec3 axis) {
CGLM_ALIGN(8) vec3 k;
float a, c, s;
a = angle * 0.5f;
c = cosf(a);
s = sinf(a);
glm_normalize_to(axis, k);
q[0] = s * k[0];
q[1] = s * k[1];
q[2] = s * k[2];
q[3] = c;
}
/*!
* @brief creates NEW quaternion with individual axis components
*
* @param[out] q quaternion
* @param[in] angle angle (radians)
* @param[in] x axis.x
* @param[in] y axis.y
* @param[in] z axis.z
*/
CGLM_INLINE
void
glm_quat(versor q, float angle, float x, float y, float z) {
CGLM_ALIGN(8) vec3 axis = {x, y, z};
glm_quatv(q, angle, axis);
}
/*!
* @brief copy quaternion to another one
*
* @param[in] q quaternion
* @param[out] dest destination
*/
CGLM_INLINE
void
glm_quat_copy(versor q, versor dest) {
glm_vec4_copy(q, dest);
}
/*!
* @brief compute quaternion rotating vector A to vector B
*
* @param[in] a vec3 (must have unit length)
* @param[in] b vec3 (must have unit length)
* @param[out] dest quaternion (of unit length)
*/
CGLM_INLINE
void
glm_quat_from_vecs(vec3 a, vec3 b, versor dest) {
CGLM_ALIGN(8) vec3 axis;
float cos_theta;
float cos_half_theta;
cos_theta = glm_vec3_dot(a, b);
if (cos_theta >= 1.f - GLM_FLT_EPSILON) { /* a ∥ b */
glm_quat_identity(dest);
return;
}
if (cos_theta < -1.f + GLM_FLT_EPSILON) { /* angle(a, b) = π */
glm_vec3_ortho(a, axis);
cos_half_theta = 0.f; /* cos π/2 */
} else {
glm_vec3_cross(a, b, axis);
cos_half_theta = 1.0f + cos_theta; /* cos 0 + cos θ */
}
glm_quat_init(dest, axis[0], axis[1], axis[2], cos_half_theta);
glm_quat_normalize(dest);
}
/*!
* @brief returns norm (magnitude) of quaternion
*
* @param[in] q quaternion
*/
CGLM_INLINE
float
glm_quat_norm(versor q) {
return glm_vec4_norm(q);
}
/*!
* @brief normalize quaternion and store result in dest
*
* @param[in] q quaternion to normalze
* @param[out] dest destination quaternion
*/
CGLM_INLINE
void
glm_quat_normalize_to(versor q, versor dest) {
#if defined( __SSE2__ ) || defined( __SSE2__ )
__m128 xdot, x0;
float dot;
x0 = glmm_load(q);
xdot = glmm_vdot(x0, x0);
dot = _mm_cvtss_f32(xdot);
if (dot <= 0.0f) {
glm_quat_identity(dest);
return;
}
glmm_store(dest, _mm_div_ps(x0, _mm_sqrt_ps(xdot)));
#else
float dot;
dot = glm_vec4_norm2(q);
if (dot <= 0.0f) {
glm_quat_identity(dest);
return;
}
glm_vec4_scale(q, 1.0f / sqrtf(dot), dest);
#endif
}
/*!
* @brief normalize quaternion
*
* @param[in, out] q quaternion
*/
CGLM_INLINE
void
glm_quat_normalize(versor q) {
glm_quat_normalize_to(q, q);
}
/*!
* @brief dot product of two quaternion
*
* @param[in] p quaternion 1
* @param[in] q quaternion 2
*/
CGLM_INLINE
float
glm_quat_dot(versor p, versor q) {
return glm_vec4_dot(p, q);
}
/*!
* @brief conjugate of quaternion
*
* @param[in] q quaternion
* @param[out] dest conjugate
*/
CGLM_INLINE
void
glm_quat_conjugate(versor q, versor dest) {
glm_vec4_negate_to(q, dest);
dest[3] = -dest[3];
}
/*!
* @brief inverse of non-zero quaternion
*
* @param[in] q quaternion
* @param[out] dest inverse quaternion
*/
CGLM_INLINE
void
glm_quat_inv(versor q, versor dest) {
CGLM_ALIGN(16) versor conj;
glm_quat_conjugate(q, conj);
glm_vec4_scale(conj, 1.0f / glm_vec4_norm2(q), dest);
}
/*!
* @brief add (componentwise) two quaternions and store result in dest
*
* @param[in] p quaternion 1
* @param[in] q quaternion 2
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_add(versor p, versor q, versor dest) {
glm_vec4_add(p, q, dest);
}
/*!
* @brief subtract (componentwise) two quaternions and store result in dest
*
* @param[in] p quaternion 1
* @param[in] q quaternion 2
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_sub(versor p, versor q, versor dest) {
glm_vec4_sub(p, q, dest);
}
/*!
* @brief returns real part of quaternion
*
* @param[in] q quaternion
*/
CGLM_INLINE
float
glm_quat_real(versor q) {
return q[3];
}
/*!
* @brief returns imaginary part of quaternion
*
* @param[in] q quaternion
* @param[out] dest imag
*/
CGLM_INLINE
void
glm_quat_imag(versor q, vec3 dest) {
dest[0] = q[0];
dest[1] = q[1];
dest[2] = q[2];
}
/*!
* @brief returns normalized imaginary part of quaternion
*
* @param[in] q quaternion
*/
CGLM_INLINE
void
glm_quat_imagn(versor q, vec3 dest) {
glm_normalize_to(q, dest);
}
/*!
* @brief returns length of imaginary part of quaternion
*
* @param[in] q quaternion
*/
CGLM_INLINE
float
glm_quat_imaglen(versor q) {
return glm_vec3_norm(q);
}
/*!
* @brief returns angle of quaternion
*
* @param[in] q quaternion
*/
CGLM_INLINE
float
glm_quat_angle(versor q) {
/*
sin(theta / 2) = length(x*x + y*y + z*z)
cos(theta / 2) = w
theta = 2 * atan(sin(theta / 2) / cos(theta / 2))
*/
return 2.0f * atan2f(glm_quat_imaglen(q), glm_quat_real(q));
}
/*!
* @brief axis of quaternion
*
* @param[in] q quaternion
* @param[out] dest axis of quaternion
*/
CGLM_INLINE
void
glm_quat_axis(versor q, vec3 dest) {
glm_quat_imagn(q, dest);
}
/*!
* @brief 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
*
* @param[in] p quaternion 1
* @param[in] q quaternion 2
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_mul(versor p, versor q, versor dest) {
/*
+ (a1 b2 + b1 a2 + c1 d2 − d1 c2)i
+ (a1 c2 − b1 d2 + c1 a2 + d1 b2)j
+ (a1 d2 + b1 c2 − c1 b2 + d1 a2)k
a1 a2 − b1 b2 − c1 c2 − d1 d2
*/
#if defined( __SSE__ ) || defined( __SSE2__ )
glm_quat_mul_sse2(p, q, dest);
#elif defined(CGLM_NEON_FP)
glm_quat_mul_neon(p, q, dest);
#else
dest[0] = p[3] * q[0] + p[0] * q[3] + p[1] * q[2] - p[2] * q[1];
dest[1] = p[3] * q[1] - p[0] * q[2] + p[1] * q[3] + p[2] * q[0];
dest[2] = p[3] * q[2] + p[0] * q[1] - p[1] * q[0] + p[2] * q[3];
dest[3] = p[3] * q[3] - p[0] * q[0] - p[1] * q[1] - p[2] * q[2];
#endif
}
/*!
* @brief convert quaternion to mat4
*
* @param[in] q quaternion
* @param[out] dest result matrix
*/
CGLM_INLINE
void
glm_quat_mat4(versor q, mat4 dest) {
float w, x, y, z,
xx, yy, zz,
xy, yz, xz,
wx, wy, wz, norm, s;
norm = glm_quat_norm(q);
s = norm > 0.0f ? 2.0f / norm : 0.0f;
x = q[0];
y = q[1];
z = q[2];
w = q[3];
xx = s * x * x; xy = s * x * y; wx = s * w * x;
yy = s * y * y; yz = s * y * z; wy = s * w * y;
zz = s * z * z; xz = s * x * z; wz = s * w * z;
dest[0][0] = 1.0f - yy - zz;
dest[1][1] = 1.0f - xx - zz;
dest[2][2] = 1.0f - xx - yy;
dest[0][1] = xy + wz;
dest[1][2] = yz + wx;
dest[2][0] = xz + wy;
dest[1][0] = xy - wz;
dest[2][1] = yz - wx;
dest[0][2] = xz - wy;
dest[0][3] = 0.0f;
dest[1][3] = 0.0f;
dest[2][3] = 0.0f;
dest[3][0] = 0.0f;
dest[3][1] = 0.0f;
dest[3][2] = 0.0f;
dest[3][3] = 1.0f;
}
/*!
* @brief convert quaternion to mat4 (transposed)
*
* @param[in] q quaternion
* @param[out] dest result matrix as transposed
*/
CGLM_INLINE
void
glm_quat_mat4t(versor q, mat4 dest) {
float w, x, y, z,
xx, yy, zz,
xy, yz, xz,
wx, wy, wz, norm, s;
norm = glm_quat_norm(q);
s = norm > 0.0f ? 2.0f / norm : 0.0f;
x = q[0];
y = q[1];
z = q[2];
w = q[3];
xx = s * x * x; xy = s * x * y; wx = s * w * x;
yy = s * y * y; yz = s * y * z; wy = s * w * y;
zz = s * z * z; xz = s * x * z; wz = s * w * z;
dest[0][0] = 1.0f - yy - zz;
dest[1][1] = 1.0f - xx - zz;
dest[2][2] = 1.0f - xx - yy;
dest[1][0] = xy + wz;
dest[2][1] = yz + wx;
dest[0][2] = xz + wy;
dest[0][1] = xy - wz;
dest[1][2] = yz - wx;
dest[2][0] = xz - wy;
dest[0][3] = 0.0f;
dest[1][3] = 0.0f;
dest[2][3] = 0.0f;
dest[3][0] = 0.0f;
dest[3][1] = 0.0f;
dest[3][2] = 0.0f;
dest[3][3] = 1.0f;
}
/*!
* @brief convert quaternion to mat3
*
* @param[in] q quaternion
* @param[out] dest result matrix
*/
CGLM_INLINE
void
glm_quat_mat3(versor q, mat3 dest) {
float w, x, y, z,
xx, yy, zz,
xy, yz, xz,
wx, wy, wz, norm, s;
norm = glm_quat_norm(q);
s = norm > 0.0f ? 2.0f / norm : 0.0f;
x = q[0];
y = q[1];
z = q[2];
w = q[3];
xx = s * x * x; xy = s * x * y; wx = s * w * x;
yy = s * y * y; yz = s * y * z; wy = s * w * y;
zz = s * z * z; xz = s * x * z; wz = s * w * z;
dest[0][0] = 1.0f - yy - zz;
dest[1][1] = 1.0f - xx - zz;
dest[2][2] = 1.0f - xx - yy;
dest[0][1] = xy + wz;
dest[1][2] = yz + wx;
dest[2][0] = xz + wy;
dest[1][0] = xy - wz;
dest[2][1] = yz - wx;
dest[0][2] = xz - wy;
}
/*!
* @brief convert quaternion to mat3 (transposed)
*
* @param[in] q quaternion
* @param[out] dest result matrix
*/
CGLM_INLINE
void
glm_quat_mat3t(versor q, mat3 dest) {
float w, x, y, z,
xx, yy, zz,
xy, yz, xz,
wx, wy, wz, norm, s;
norm = glm_quat_norm(q);
s = norm > 0.0f ? 2.0f / norm : 0.0f;
x = q[0];
y = q[1];
z = q[2];
w = q[3];
xx = s * x * x; xy = s * x * y; wx = s * w * x;
yy = s * y * y; yz = s * y * z; wy = s * w * y;
zz = s * z * z; xz = s * x * z; wz = s * w * z;
dest[0][0] = 1.0f - yy - zz;
dest[1][1] = 1.0f - xx - zz;
dest[2][2] = 1.0f - xx - yy;
dest[1][0] = xy + wz;
dest[2][1] = yz + wx;
dest[0][2] = xz + wy;
dest[0][1] = xy - wz;
dest[1][2] = yz - wx;
dest[2][0] = xz - wy;
}
/*!
* @brief interpolates between two quaternions
* using linear interpolation (LERP)
*
* @param[in] from from
* @param[in] to to
* @param[in] t interpolant (amount)
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_lerp(versor from, versor to, float t, versor dest) {
glm_vec4_lerp(from, to, t, dest);
}
/*!
* @brief interpolates between two quaternions
* using linear interpolation (LERP)
*
* @param[in] from from
* @param[in] to to
* @param[in] t interpolant (amount) clamped between 0 and 1
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_lerpc(versor from, versor to, float t, versor dest) {
glm_vec4_lerpc(from, to, t, dest);
}
/*!
* @brief interpolates between two quaternions
* taking the shortest rotation path using
* normalized linear interpolation (NLERP)
*
* @param[in] from from
* @param[in] to to
* @param[in] t interpolant (amount)
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_nlerp(versor from, versor to, float t, versor dest) {
versor target;
float dot;
dot = glm_vec4_dot(from, to);
glm_vec4_scale(to, (dot >= 0) ? 1.0f : -1.0f, target);
glm_quat_lerp(from, target, t, dest);
glm_quat_normalize(dest);
}
/*!
* @brief interpolates between two quaternions
* using spherical linear interpolation (SLERP)
*
* @param[in] from from
* @param[in] to to
* @param[in] t amout
* @param[out] dest result quaternion
*/
CGLM_INLINE
void
glm_quat_slerp(versor from, versor to, float t, versor dest) {
CGLM_ALIGN(16) vec4 q1, q2;
float cosTheta, sinTheta, angle;
cosTheta = glm_quat_dot(from, to);
glm_quat_copy(from, q1);
if (fabsf(cosTheta) >= 1.0f) {
glm_quat_copy(q1, dest);
return;
}
if (cosTheta < 0.0f) {
glm_vec4_negate(q1);
cosTheta = -cosTheta;
}
sinTheta = sqrtf(1.0f - cosTheta * cosTheta);
/* LERP to avoid zero division */
if (fabsf(sinTheta) < 0.001f) {
glm_quat_lerp(from, to, t, dest);
return;
}
/* SLERP */
angle = acosf(cosTheta);
glm_vec4_scale(q1, sinf((1.0f - t) * angle), q1);
glm_vec4_scale(to, sinf(t * angle), q2);
glm_vec4_add(q1, q2, q1);
glm_vec4_scale(q1, 1.0f / sinTheta, dest);
}
/*!
* @brief creates view matrix using quaternion as camera orientation
*
* @param[in] eye eye
* @param[in] ori orientation in world space as quaternion
* @param[out] dest view matrix
*/
CGLM_INLINE
void
glm_quat_look(vec3 eye, versor ori, mat4 dest) {
/* orientation */
glm_quat_mat4t(ori, dest);
/* translate */
glm_mat4_mulv3(dest, eye, 1.0f, dest[3]);
glm_vec3_negate(dest[3]);
}
/*!
* @brief creates look rotation quaternion
*
* @param[in] dir direction to look
* @param[in] up up vector
* @param[out] dest destination quaternion
*/
CGLM_INLINE
void
glm_quat_for(vec3 dir, vec3 up, versor dest) {
CGLM_ALIGN_MAT mat3 m;
glm_vec3_normalize_to(dir, m[2]);
/* No need to negate in LH, but we use RH here */
glm_vec3_negate(m[2]);
glm_vec3_crossn(up, m[2], m[0]);
glm_vec3_cross(m[2], m[0], m[1]);
glm_mat3_quat(m, dest);
}
/*!
* @brief creates look rotation quaternion using source and
* destination positions p suffix stands for position
*
* @param[in] from source point
* @param[in] to destination point
* @param[in] up up vector
* @param[out] dest destination quaternion
*/
CGLM_INLINE
void
glm_quat_forp(vec3 from, vec3 to, vec3 up, versor dest) {
CGLM_ALIGN(8) vec3 dir;
glm_vec3_sub(to, from, dir);
glm_quat_for(dir, up, dest);
}
/*!
* @brief rotate vector using using quaternion
*
* @param[in] q quaternion
* @param[in] v vector to rotate
* @param[out] dest rotated vector
*/
CGLM_INLINE
void
glm_quat_rotatev(versor q, vec3 v, vec3 dest) {
CGLM_ALIGN(16) versor p;
CGLM_ALIGN(8) vec3 u, v1, v2;
float s;
glm_quat_normalize_to(q, p);
glm_quat_imag(p, u);
s = glm_quat_real(p);
glm_vec3_scale(u, 2.0f * glm_vec3_dot(u, v), v1);
glm_vec3_scale(v, s * s - glm_vec3_dot(u, u), v2);
glm_vec3_add(v1, v2, v1);
glm_vec3_cross(u, v, v2);
glm_vec3_scale(v2, 2.0f * s, v2);
glm_vec3_add(v1, v2, dest);
}
/*!
* @brief rotate existing transform matrix using quaternion
*
* @param[in] m existing transform matrix
* @param[in] q quaternion
* @param[out] dest rotated matrix/transform
*/
CGLM_INLINE
void
glm_quat_rotate(mat4 m, versor q, mat4 dest) {
CGLM_ALIGN_MAT mat4 rot;
glm_quat_mat4(q, rot);
glm_mul_rot(m, rot, dest);
}
/*!
* @brief rotate existing transform matrix using quaternion at pivot point
*
* @param[in, out] m existing transform matrix
* @param[in] q quaternion
* @param[out] pivot pivot
*/
CGLM_INLINE
void
glm_quat_rotate_at(mat4 m, versor q, vec3 pivot) {
CGLM_ALIGN(8) vec3 pivotInv;
glm_vec3_negate_to(pivot, pivotInv);
glm_translate(m, pivot);
glm_quat_rotate(m, q, m);
glm_translate(m, pivotInv);
}
/*!
* @brief 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.
*
* @param[out] m existing transform matrix
* @param[in] q quaternion
* @param[in] pivot pivot
*/
CGLM_INLINE
void
glm_quat_rotate_atm(mat4 m, versor q, vec3 pivot) {
CGLM_ALIGN(8) vec3 pivotInv;
glm_vec3_negate_to(pivot, pivotInv);
glm_translate_make(m, pivot);
glm_quat_rotate(m, q, m);
glm_translate(m, pivotInv);
}
#endif /* cglm_quat_h */
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