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use crate::core::{
storage::XYZ,
traits::{
scalar::{FloatEx, NumEx},
vector::*,
},
};
pub trait Quaternion<T: FloatEx>: FloatVector4<T> {
type SIMDVector3;
#[inline]
fn from_axis_angle(axis: XYZ<T>, angle: T) -> Self {
glam_assert!(FloatVector3::is_normalized(axis));
let (s, c) = (angle * T::HALF).sin_cos();
let v = axis.mul_scalar(s);
Self::new(v.x, v.y, v.z, c)
}
#[inline]
fn from_rotation_x(angle: T) -> Self {
let (s, c) = (angle * T::HALF).sin_cos();
Self::new(s, T::ZERO, T::ZERO, c)
}
#[inline]
fn from_rotation_y(angle: T) -> Self {
let (s, c) = (angle * T::HALF).sin_cos();
Self::new(T::ZERO, s, T::ZERO, c)
}
#[inline]
fn from_rotation_z(angle: T) -> Self {
let (s, c) = (angle * T::HALF).sin_cos();
Self::new(T::ZERO, T::ZERO, s, c)
}
/// From the columns of a 3x3 rotation matrix.
#[inline]
fn from_rotation_axes(x_axis: XYZ<T>, y_axis: XYZ<T>, z_axis: XYZ<T>) -> Self {
// Based on https://github.com/microsoft/DirectXMath `XM$quaternionRotationMatrix`
// TODO: sse2 version
let (m00, m01, m02) = x_axis.into_tuple();
let (m10, m11, m12) = y_axis.into_tuple();
let (m20, m21, m22) = z_axis.into_tuple();
if m22 <= T::ZERO {
// x^2 + y^2 >= z^2 + w^2
let dif10 = m11 - m00;
let omm22 = T::ONE - m22;
if dif10 <= T::ZERO {
// x^2 >= y^2
let four_xsq = omm22 - dif10;
let inv4x = T::HALF / four_xsq.sqrt();
Self::new(
four_xsq * inv4x,
(m01 + m10) * inv4x,
(m02 + m20) * inv4x,
(m12 - m21) * inv4x,
)
} else {
// y^2 >= x^2
let four_ysq = omm22 + dif10;
let inv4y = T::HALF / four_ysq.sqrt();
Self::new(
(m01 + m10) * inv4y,
four_ysq * inv4y,
(m12 + m21) * inv4y,
(m20 - m02) * inv4y,
)
}
} else {
// z^2 + w^2 >= x^2 + y^2
let sum10 = m11 + m00;
let opm22 = T::ONE + m22;
if sum10 <= T::ZERO {
// z^2 >= w^2
let four_zsq = opm22 - sum10;
let inv4z = T::HALF / four_zsq.sqrt();
Self::new(
(m02 + m20) * inv4z,
(m12 + m21) * inv4z,
four_zsq * inv4z,
(m01 - m10) * inv4z,
)
} else {
// w^2 >= z^2
let four_wsq = opm22 + sum10;
let inv4w = T::HALF / four_wsq.sqrt();
Self::new(
(m12 - m21) * inv4w,
(m20 - m02) * inv4w,
(m01 - m10) * inv4w,
four_wsq * inv4w,
)
}
}
}
fn to_axis_angle(self) -> (XYZ<T>, T) {
// const EPSILON: f32 = 1.0e-8;
// const EPSILON_SQUARED: f32 = EPSILON * EPSILON;
let (x, y, z, w) = Vector4::into_tuple(self);
let angle = w.acos_approx() * T::TWO;
let scale_sq = NumEx::max(T::ONE - w * w, T::ZERO);
// TODO: constants for epslions?
if scale_sq >= T::from_f32(1.0e-8 * 1.0e-8) {
(XYZ { x, y, z }.mul_scalar(scale_sq.sqrt().recip()), angle)
} else {
(Vector3Const::X, angle)
}
}
#[inline]
fn is_near_identity(self) -> bool {
// Based on https://github.com/nfrechette/rtm `rtm::quat_near_identity`
let threshold_angle = T::from_f64(0.002_847_144_6);
// Because of floating point precision, we cannot represent very small rotations.
// The closest f32 to 1.0 that is not 1.0 itself yields:
// 0.99999994.acos() * 2.0 = 0.000690533954 rad
//
// An error threshold of 1.e-6 is used by default.
// (1.0 - 1.e-6).acos() * 2.0 = 0.00284714461 rad
// (1.0 - 1.e-7).acos() * 2.0 = 0.00097656250 rad
//
// We don't really care about the angle value itself, only if it's close to 0.
// This will happen whenever quat.w is close to 1.0.
// If the quat.w is close to -1.0, the angle will be near 2*PI which is close to
// a negative 0 rotation. By forcing quat.w to be positive, we'll end up with
// the shortest path.
let positive_w_angle = self.as_ref_xyzw().w.abs().acos_approx() * T::TWO;
positive_w_angle < threshold_angle
}
fn conjugate(self) -> Self;
fn lerp(self, end: Self, s: T) -> Self;
fn slerp(self, end: Self, s: T) -> Self;
fn mul_quaternion(self, other: Self) -> Self;
fn mul_vector3(self, other: XYZ<T>) -> XYZ<T>;
fn mul_float4_as_vector3(self, other: Self::SIMDVector3) -> Self::SIMDVector3;
}