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/*
Conversion from quaternions to Euler rotation sequences.
From: http://bediyap.com/programming/convert-quaternion-to-euler-rotations/
*/
use super::{DQuat, Quat};
#[cfg(feature = "libm")]
#[allow(unused_imports)]
use num_traits::Float;
/// Euler rotation sequences.
///
/// The angles are applied starting from the right.
/// E.g. XYZ will first apply the z-axis rotation.
///
/// YXZ can be used for yaw (y-axis), pitch (x-axis), roll (z-axis).
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
#[cfg_attr(feature = "serde", derive(serde::Deserialize, serde::Serialize))]
pub enum EulerRot {
/// Intrinsic three-axis rotation ZYX
ZYX,
/// Intrinsic three-axis rotation ZXY
ZXY,
/// Intrinsic three-axis rotation YXZ
YXZ,
/// Intrinsic three-axis rotation YZX
YZX,
/// Intrinsic three-axis rotation XYZ
XYZ,
/// Intrinsic three-axis rotation XZY
XZY,
}
impl Default for EulerRot {
/// Default `YXZ` as yaw (y-axis), pitch (x-axis), roll (z-axis).
fn default() -> Self {
Self::YXZ
}
}
/// Conversion from quaternion to euler angles.
pub(crate) trait EulerFromQuaternion<Q: Copy>: Sized + Copy {
type Output;
/// Compute the angle of the first axis (X-x-x)
fn first(self, q: Q) -> Self::Output;
/// Compute then angle of the second axis (x-X-x)
fn second(self, q: Q) -> Self::Output;
/// Compute then angle of the third axis (x-x-X)
fn third(self, q: Q) -> Self::Output;
/// Compute all angles of a rotation in the notation order
fn convert_quat(self, q: Q) -> (Self::Output, Self::Output, Self::Output) {
(self.first(q), self.second(q), self.third(q))
}
}
/// Conversion from euler angles to quaternion.
pub(crate) trait EulerToQuaternion<T>: Copy {
type Output;
/// Create the rotation quaternion for the three angles of this euler rotation sequence.
fn new_quat(self, u: T, v: T, w: T) -> Self::Output;
}
/// Adds a atan2 that handles the negative zero case.
/// Basically forces positive zero in the x-argument for atan2.
pub(crate) trait Atan2Fixed<T = Self> {
fn atan2_fixed(self, other: T) -> T;
}
impl Atan2Fixed for f32 {
fn atan2_fixed(self, other: f32) -> f32 {
self.atan2(if other == 0.0f32 { 0.0f32 } else { other })
}
}
impl Atan2Fixed for f64 {
fn atan2_fixed(self, other: f64) -> f64 {
self.atan2(if other == 0.0f64 { 0.0f64 } else { other })
}
}
macro_rules! impl_from_quat {
($t:ty, $quat:ident) => {
impl EulerFromQuaternion<$quat> for EulerRot {
type Output = $t;
fn first(self, q: $quat) -> $t {
use EulerRot::*;
match self {
ZYX => (2.0 * (q.x * q.y + q.w * q.z))
.atan2(q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z),
ZXY => (-2.0 * (q.x * q.y - q.w * q.z))
.atan2(q.w * q.w - q.x * q.x + q.y * q.y - q.z * q.z),
YXZ => (2.0 * (q.x * q.z + q.w * q.y))
.atan2(q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z),
YZX => (-2.0 * (q.x * q.z - q.w * q.y))
.atan2(q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z),
XYZ => (-2.0 * (q.y * q.z - q.w * q.x))
.atan2(q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z),
XZY => (2.0 * (q.y * q.z + q.w * q.x))
.atan2(q.w * q.w - q.x * q.x + q.y * q.y - q.z * q.z),
}
}
fn second(self, q: $quat) -> $t {
use EulerRot::*;
/// Clamp number to range [-1,1](-1,1) for asin() and acos(), else NaN is possible.
#[inline(always)]
fn arc_clamp(val: $t) -> $t {
<$t>::min(<$t>::max(val, -1.0), 1.0)
}
match self {
ZYX => arc_clamp(-2.0 * (q.x * q.z - q.w * q.y)).asin(),
ZXY => arc_clamp(2.0 * (q.y * q.z + q.w * q.x)).asin(),
YXZ => arc_clamp(-2.0 * (q.y * q.z - q.w * q.x)).asin(),
YZX => arc_clamp(2.0 * (q.x * q.y + q.w * q.z)).asin(),
XYZ => arc_clamp(2.0 * (q.x * q.z + q.w * q.y)).asin(),
XZY => arc_clamp(-2.0 * (q.x * q.y - q.w * q.z)).asin(),
}
}
fn third(self, q: $quat) -> $t {
use EulerRot::*;
match self {
ZYX => (2.0 * (q.y * q.z + q.w * q.x))
.atan2(q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z),
ZXY => (-2.0 * (q.x * q.z - q.w * q.y))
.atan2(q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z),
YXZ => (2.0 * (q.x * q.y + q.w * q.z))
.atan2(q.w * q.w - q.x * q.x + q.y * q.y - q.z * q.z),
YZX => (-2.0 * (q.y * q.z - q.w * q.x))
.atan2(q.w * q.w - q.x * q.x + q.y * q.y - q.z * q.z),
XYZ => (-2.0 * (q.x * q.y - q.w * q.z))
.atan2(q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z),
XZY => (2.0 * (q.x * q.z + q.w * q.y))
.atan2(q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z),
}
}
}
// End - impl EulerFromQuaternion
};
}
macro_rules! impl_to_quat {
($t:ty, $quat:ident) => {
impl EulerToQuaternion<$t> for EulerRot {
type Output = $quat;
#[inline(always)]
fn new_quat(self, u: $t, v: $t, w: $t) -> $quat {
use EulerRot::*;
#[inline(always)]
fn rot_x(a: $t) -> $quat {
$quat::from_rotation_x(a)
}
#[inline(always)]
fn rot_y(a: $t) -> $quat {
$quat::from_rotation_y(a)
}
#[inline(always)]
fn rot_z(a: $t) -> $quat {
$quat::from_rotation_z(a)
}
match self {
ZYX => rot_z(u) * rot_y(v) * rot_x(w),
ZXY => rot_z(u) * rot_x(v) * rot_y(w),
YXZ => rot_y(u) * rot_x(v) * rot_z(w),
YZX => rot_y(u) * rot_z(v) * rot_x(w),
XYZ => rot_x(u) * rot_y(v) * rot_z(w),
XZY => rot_x(u) * rot_z(v) * rot_y(w),
}
.normalize()
}
}
// End - impl EulerToQuaternion
};
}
impl_from_quat!(f32, Quat);
impl_from_quat!(f64, DQuat);
impl_to_quat!(f32, Quat);
impl_to_quat!(f64, DQuat);
|
