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Intrinsic vs extrinsic take two...
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@bitshifter
bitshifter committed Jul 14, 2024
1 parent 95d5371 commit f0d6b5e
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124 changes: 62 additions & 62 deletions src/euler.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -2,78 +2,78 @@ use crate::{DMat3, DMat4, DQuat, DVec3, Mat3, Mat3A, Mat4, Quat, Vec3, Vec3A, Ve

/// Euler rotation sequences.
///
/// Both intrinsic and extrinsic rotation sequences are supported. Extrinsic rotations are most
/// commonly used and have no suffix, intrinsic sequences have an `In` suffix.
/// The three elemental rotations may be extrinsic (rotations about the axes xyz of the original
/// coordinate system, which is assumed to remain motionless), or intrinsic(rotations about the
/// axes of the rotating coordinate system XYZ, solidary with the moving body, which changes its
/// orientation after each elemental rotation).
///
/// Extrinsic rotation sequences are all defined with respect to a fixed frame. Rotations are
/// applied from right to left, for example `EulerRot::XYZ` will result in the following rotation
/// sequence:
///
/// ```
/// Rextrinsic = Rz(k) * Ry(j) * Rx(i)
/// ```
/// # use glam::{EulerRot, Mat3};
/// # let i = core::f32::consts::FRAC_PI_2;
/// # let j = core::f32::consts::FRAC_PI_4;
/// # let k = core::f32::consts::FRAC_PI_8;
/// let m_intrinsic = Mat3::from_rotation_x(i) * Mat3::from_rotation_y(j) * Mat3::from_rotation_z(k);
/// let n_intrinsic = Mat3::from_euler(EulerRot::XYZ, i, j, k);
/// assert!(m_intrinsic.abs_diff_eq(n_intrinsic, 2e-6));
///
/// Intrinsic rotations are all defined with respect to the rotating coordinate frame. Rotations
/// are applied from left to right, for example `EulerRot::XYZIn` with result in the following
/// rotation sequence:
///
/// ```
/// Rintrinsic = Rx(i) * Ry(j) * Rz(k)
/// let m_extrinsic = Mat3::from_rotation_z(k) * Mat3::from_rotation_y(j) * Mat3::from_rotation_x(i);
/// let n_extrinsic = Mat3::from_euler(EulerRot::XYZEx, i, j, k);
/// assert!(m_extrinsic.abs_diff_eq(n_extrinsic, 2e-6));
/// ```
///
#[derive(Debug, Clone, Copy, PartialEq, Eq, Hash)]
pub enum EulerRot {
/// Extrinsic three-axis rotation ZYX
/// Intrinsic three-axis rotation ZYX
ZYX,
/// Extrinsic three-axis rotation ZXY
/// Intrinsic three-axis rotation ZXY
ZXY,
/// Extrinsic three-axis rotation YXZ
/// Intrinsic three-axis rotation YXZ
YXZ,
/// Extrinsic three-axis rotation YZX
/// Intrinsic three-axis rotation YZX
YZX,
/// Extrinsic three-axis rotation XYZ
/// Intrinsic three-axis rotation XYZ
XYZ,
/// Extrinsic three-axis rotation XZY
/// Intrinsic three-axis rotation XZY
XZY,

/// Extrinsic two-axis rotation ZYZ
/// Intrinsic two-axis rotation ZYZ
ZYZ,
/// Extrinsic two-axis rotation ZXZ
/// Intrinsic two-axis rotation ZXZ
ZXZ,
/// Extrinsic two-axis rotation YXY
/// Intrinsic two-axis rotation YXY
YXY,
/// Extrinsic two-axis rotation YZY
/// Intrinsic two-axis rotation YZY
YZY,
/// Extrinsic two-axis rotation XYX
/// Intrinsic two-axis rotation XYX
XYX,
/// Extrinsic two-axis rotation XZX
/// Intrinsic two-axis rotation XZX
XZX,

/// Intrinsic three-axis rotation ZYX
ZYXIn,
/// Intrinsic three-axis rotation ZXY
ZXYIn,
/// Intrinsic three-axis rotation YXZ
YXZIn,
/// Intrinsic three-axis rotation YZX
YZXIn,
/// Intrinsic three-axis rotation XYZ
XYZIn,
/// Intrinsic three-axis rotation XZY
XZYIn,
/// Extrinsic three-axis rotation ZYX
ZYXEx,
/// Extrinsic three-axis rotation ZXY
ZXYEx,
/// Extrinsic three-axis rotation YXZ
YXZEx,
/// Extrinsic three-axis rotation YZX
YZXEx,
/// Extrinsic three-axis rotation XYZ
XYZEx,
/// Extrinsic three-axis rotation XZY
XZYEx,

/// Intrinsic two-axis rotation ZYZ
ZYZIn,
/// Intrinsic two-axis rotation ZXZ
ZXZIn,
/// Intrinsic two-axis rotation YXY
YXYIn,
/// Intrinsic two-axis rotation YZY
YZYIn,
/// Intrinsic two-axis rotation XYX
XYXIn,
/// Intrinsic two-axis rotation XZX
XZXIn,
/// Extrinsic two-axis rotation ZYZ
ZYZEx,
/// Extrinsic two-axis rotation ZXZ
ZXZEx,
/// Extrinsic two-axis rotation YXY
YXYEx,
/// Extrinsic two-axis rotation YZY
YZYEx,
/// Extrinsic two-axis rotation XYX
XYXEx,
/// Extrinsic two-axis rotation XZX
XZXEx,
}

pub(crate) trait ToEuler {
Expand Down Expand Up @@ -153,18 +153,18 @@ impl Order {
EulerRot::ZXZ => Self::new(Axis::Z, Parity::Even, Repeated::Yes, Frame::Static),
EulerRot::ZYX => Self::new(Axis::Z, Parity::Odd, Repeated::No, Frame::Static),
EulerRot::ZYZ => Self::new(Axis::Z, Parity::Odd, Repeated::Yes, Frame::Static),
EulerRot::ZYXIn => Self::new(Axis::X, Parity::Even, Repeated::No, Frame::Relative),
EulerRot::XYXIn => Self::new(Axis::X, Parity::Even, Repeated::Yes, Frame::Relative),
EulerRot::YZXIn => Self::new(Axis::X, Parity::Odd, Repeated::No, Frame::Relative),
EulerRot::XZXIn => Self::new(Axis::X, Parity::Odd, Repeated::Yes, Frame::Relative),
EulerRot::XZYIn => Self::new(Axis::Y, Parity::Even, Repeated::No, Frame::Relative),
EulerRot::YZYIn => Self::new(Axis::Y, Parity::Even, Repeated::Yes, Frame::Relative),
EulerRot::ZXYIn => Self::new(Axis::Y, Parity::Odd, Repeated::No, Frame::Relative),
EulerRot::YXYIn => Self::new(Axis::Y, Parity::Odd, Repeated::Yes, Frame::Relative),
EulerRot::YXZIn => Self::new(Axis::Z, Parity::Even, Repeated::No, Frame::Relative),
EulerRot::ZXZIn => Self::new(Axis::Z, Parity::Even, Repeated::Yes, Frame::Relative),
EulerRot::XYZIn => Self::new(Axis::Z, Parity::Odd, Repeated::No, Frame::Relative),
EulerRot::ZYZIn => Self::new(Axis::Z, Parity::Odd, Repeated::Yes, Frame::Relative),
EulerRot::ZYXEx => Self::new(Axis::X, Parity::Even, Repeated::No, Frame::Relative),
EulerRot::XYXEx => Self::new(Axis::X, Parity::Even, Repeated::Yes, Frame::Relative),
EulerRot::YZXEx => Self::new(Axis::X, Parity::Odd, Repeated::No, Frame::Relative),
EulerRot::XZXEx => Self::new(Axis::X, Parity::Odd, Repeated::Yes, Frame::Relative),
EulerRot::XZYEx => Self::new(Axis::Y, Parity::Even, Repeated::No, Frame::Relative),
EulerRot::YZYEx => Self::new(Axis::Y, Parity::Even, Repeated::Yes, Frame::Relative),
EulerRot::ZXYEx => Self::new(Axis::Y, Parity::Odd, Repeated::No, Frame::Relative),
EulerRot::YXYEx => Self::new(Axis::Y, Parity::Odd, Repeated::Yes, Frame::Relative),
EulerRot::YXZEx => Self::new(Axis::Z, Parity::Even, Repeated::No, Frame::Relative),
EulerRot::ZXZEx => Self::new(Axis::Z, Parity::Even, Repeated::Yes, Frame::Relative),
EulerRot::XYZEx => Self::new(Axis::Z, Parity::Odd, Repeated::No, Frame::Relative),
EulerRot::ZYZEx => Self::new(Axis::Z, Parity::Odd, Repeated::Yes, Frame::Relative),
}
}

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