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use approxeq::ApproxEq;
use num_traits::Float;
use trig::Trig;
use {Rotation3D, Transform3D, Vector3D};
/// A rigid transformation. All lengths are preserved under such a transformation.
///
///
/// Internally, this is a rotation and a translation, with the rotation
/// applied first (i.e. `Rotation * Translation`, in row-vector notation)
///
/// This can be more efficient to use over full matrices, especially if you
/// have to deal with the decomposed quantities often.
#[derive(Copy, Clone, Debug, PartialEq, Eq, Hash)]
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[repr(C)]
pub struct RigidTransform3D<T, Src, Dst> {
pub rotation: Rotation3D<T, Src, Dst>,
pub translation: Vector3D<T, Dst>,
}
// All matrix multiplication in this file is in row-vector notation,
// i.e. a vector `v` is transformed with `v * T`, and if you want to apply `T1`
// before `T2` you use `T1 * T2`
impl<T: Float + ApproxEq<T>, Src, Dst> RigidTransform3D<T, Src, Dst> {
/// Construct a new rigid transformation, where the `rotation` applies first
#[inline]
pub fn new(rotation: Rotation3D<T, Src, Dst>, translation: Vector3D<T, Dst>) -> Self {
Self {
rotation,
translation,
}
}
/// Construct an identity transform
#[inline]
pub fn identity() -> Self {
Self {
rotation: Rotation3D::identity(),
translation: Vector3D::zero(),
}
}
/// Construct a new rigid transformation, where the `translation` applies first
#[inline]
pub fn new_from_reversed(
translation: Vector3D<T, Src>,
rotation: Rotation3D<T, Src, Dst>,
) -> Self {
// T * R
// = (R * R^-1) * T * R
// = R * (R^-1 * T * R)
// = R * T'
//
// T' = (R^-1 * T * R) is also a translation matrix
// It is equivalent to the translation matrix obtained by rotating the
// translation by R
let translation = rotation.transform_vector3d(translation);
Self {
rotation,
translation,
}
}
#[inline]
pub fn from_rotation(rotation: Rotation3D<T, Src, Dst>) -> Self {
Self {
rotation,
translation: Vector3D::zero(),
}
}
#[inline]
pub fn from_translation(translation: Vector3D<T, Dst>) -> Self {
Self {
translation,
rotation: Rotation3D::identity(),
}
}
/// Decompose this into a translation and an rotation to be applied in the opposite order
///
/// i.e., the translation is applied _first_
#[inline]
pub fn decompose_reversed(&self) -> (Vector3D<T, Src>, Rotation3D<T, Src, Dst>) {
// self = R * T
// = R * T * (R^-1 * R)
// = (R * T * R^-1) * R)
// = T' * R
//
// T' = (R^ * T * R^-1) is T rotated by R^-1
let translation = self.rotation.inverse().transform_vector3d(self.translation);
(translation, self.rotation)
}
/// Returns the multiplication of the two transforms such that
/// other's transformation applies after self's transformation.
///
/// i.e., this produces `self * other` in row-vector notation
#[inline]
pub fn post_transform<Dst2>(
&self,
other: &RigidTransform3D<T, Dst, Dst2>,
) -> RigidTransform3D<T, Src, Dst2> {
// self = R1 * T1
// other = R2 * T2
// result = R1 * T1 * R2 * T2
// = R1 * (R2 * R2^-1) * T1 * R2 * T2
// = (R1 * R2) * (R2^-1 * T1 * R2) * T2
// = R' * T' * T2
// = R' * T''
//
// (R2^-1 * T2 * R2^) = T' = T2 rotated by R2
// R1 * R2 = R'
// T' * T2 = T'' = vector addition of translations T2 and T'
let t_prime = other
.rotation
.transform_vector3d(self.translation);
let r_prime = self.rotation.post_rotate(&other.rotation);
let t_prime2 = t_prime + other.translation;
RigidTransform3D {
rotation: r_prime,
translation: t_prime2,
}
}
/// Returns the multiplication of the two transforms such that
/// self's transformation applies after other's transformation.
///
/// i.e., this produces `other * self` in row-vector notation
#[inline]
pub fn pre_transform<Src2>(
&self,
other: &RigidTransform3D<T, Src2, Src>,
) -> RigidTransform3D<T, Src2, Dst> {
other.post_transform(&self)
}
/// Inverts the transformation
#[inline]
pub fn inverse(&self) -> RigidTransform3D<T, Dst, Src> {
// result = (self)^-1
// = (R * T)^-1
// = T^-1 * R^-1
// = (R^-1 * R) * T^-1 * R^-1
// = R^-1 * (R * T^-1 * R^-1)
// = R' * T'
//
// T' = (R * T^-1 * R^-1) = (-T) rotated by R^-1
// R' = R^-1
//
// An easier way of writing this is to use new_from_reversed() with R^-1 and T^-1
RigidTransform3D::new_from_reversed(
-self.translation,
self.rotation.inverse(),
)
}
pub fn to_transform(&self) -> Transform3D<T, Src, Dst>
where
T: Trig,
{
self.translation
.to_transform()
.pre_transform(&self.rotation.to_transform())
}
}
impl<T: Float + ApproxEq<T>, Src, Dst> From<Rotation3D<T, Src, Dst>>
for RigidTransform3D<T, Src, Dst>
{
fn from(rot: Rotation3D<T, Src, Dst>) -> Self {
Self::from_rotation(rot)
}
}
impl<T: Float + ApproxEq<T>, Src, Dst> From<Vector3D<T, Dst>>
for RigidTransform3D<T, Src, Dst>
{
fn from(t: Vector3D<T, Dst>) -> Self {
Self::from_translation(t)
}
}
#[cfg(test)]
mod test {
use super::RigidTransform3D;
use default::{Rotation3D, Transform3D, Vector3D};
#[test]
fn test_rigid_construction() {
let translation = Vector3D::new(12.1, 17.8, -5.5);
let rotation = Rotation3D::unit_quaternion(0.5, -7.8, 2.2, 4.3);
let rigid = RigidTransform3D::new(rotation, translation);
assert!(rigid
.to_transform()
.approx_eq(&translation.to_transform().pre_transform(&rotation.to_transform())));
let rigid = RigidTransform3D::new_from_reversed(translation, rotation);
assert!(rigid.to_transform().approx_eq(
&translation
.to_transform()
.post_transform(&rotation.to_transform())
));
}
#[test]
fn test_rigid_decomposition() {
let translation = Vector3D::new(12.1, 17.8, -5.5);
let rotation = Rotation3D::unit_quaternion(0.5, -7.8, 2.2, 4.3);
let rigid = RigidTransform3D::new(rotation, translation);
let (t2, r2) = rigid.decompose_reversed();
assert!(rigid
.to_transform()
.approx_eq(&t2.to_transform().post_transform(&r2.to_transform())));
}
#[test]
fn test_rigid_inverse() {
let translation = Vector3D::new(12.1, 17.8, -5.5);
let rotation = Rotation3D::unit_quaternion(0.5, -7.8, 2.2, 4.3);
let rigid = RigidTransform3D::new(rotation, translation);
let inverse = rigid.inverse();
assert!(rigid
.post_transform(&inverse)
.to_transform()
.approx_eq(&Transform3D::identity()));
assert!(inverse
.to_transform()
.approx_eq(&rigid.to_transform().inverse().unwrap()));
}
#[test]
fn test_rigid_multiply() {
let translation = Vector3D::new(12.1, 17.8, -5.5);
let rotation = Rotation3D::unit_quaternion(0.5, -7.8, 2.2, 4.3);
let translation2 = Vector3D::new(9.3, -3.9, 1.1);
let rotation2 = Rotation3D::unit_quaternion(0.1, 0.2, 0.3, -0.4);
let rigid = RigidTransform3D::new(rotation, translation);
let rigid2 = RigidTransform3D::new(rotation2, translation2);
assert!(rigid
.post_transform(&rigid2)
.to_transform()
.approx_eq(&rigid.to_transform().post_transform(&rigid2.to_transform())));
assert!(rigid
.pre_transform(&rigid2)
.to_transform()
.approx_eq(&rigid.to_transform().pre_transform(&rigid2.to_transform())));
}
}