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```
```use na::{DVectorSliceMut, Isometry3, RealField, Unit, Vector3};

use crate::joint::{Joint, PrismaticJoint, RevoluteJoint};
use crate::math::{JacobianSliceMut, Velocity};
use crate::solver::{ConstraintSet, GenericNonlinearConstraint, IntegrationParameters};

/// A joint that allows one translational and one rotational degrees of freedom.
///
/// Both are not required to be along the same direction.
#[derive(Copy, Clone, Debug)]
pub struct PinSlotJoint<N: RealField> {
prism: PrismaticJoint<N>,
revo: RevoluteJoint<N>,
}

impl<N: RealField> PinSlotJoint<N> {
/// Create a new pin-slot joint with axii expressed in the local coordinate frame of the attached bodies, and
/// with initial linear position and angle.
pub fn new(axis_v: Unit<Vector3<N>>, axis_w: Unit<Vector3<N>>, position: N, angle: N) -> Self {
let prism = PrismaticJoint::new(axis_v, position);
let revo = RevoluteJoint::new(axis_w, angle);

PinSlotJoint { prism, revo }
}

/// The linear displacement.
pub fn offset(&self) -> N {
self.prism.offset()
}

/// The angular displacement.
pub fn angle(&self) -> N {
self.revo.angle()
}
}

impl<N: RealField> Joint<N> for PinSlotJoint<N> {
#[inline]
fn ndofs(&self) -> usize {
2
}

fn body_to_parent(&self, parent_shift: &Vector3<N>, body_shift: &Vector3<N>) -> Isometry3<N> {
self.prism.translation() * self.revo.body_to_parent(parent_shift, body_shift)
}

fn update_jacobians(&mut self, body_shift: &Vector3<N>, vels: &[N]) {
self.prism.update_jacobians(body_shift, vels);
self.revo.update_jacobians(body_shift, &[vels[1]]);
}

fn jacobian(&self, transform: &Isometry3<N>, out: &mut JacobianSliceMut<N>) {
self.prism.jacobian(transform, &mut out.columns_mut(0, 1));
self.revo.jacobian(transform, &mut out.columns_mut(1, 1));
}

fn jacobian_dot(&self, transform: &Isometry3<N>, out: &mut JacobianSliceMut<N>) {
self.prism
.jacobian_dot(transform, &mut out.columns_mut(0, 1));
self.revo
.jacobian_dot(transform, &mut out.columns_mut(1, 1));
}

fn jacobian_dot_veldiff_mul_coordinates(
&self,
transform: &Isometry3<N>,
vels: &[N],
out: &mut JacobianSliceMut<N>,
) {
self.prism.jacobian_dot_veldiff_mul_coordinates(
transform,
vels,
&mut out.columns_mut(0, 1),
);
self.revo.jacobian_dot_veldiff_mul_coordinates(
transform,
&[vels[1]],
&mut out.columns_mut(1, 1),
);
}

fn jacobian_mul_coordinates(&self, vels: &[N]) -> Velocity<N> {
self.prism.jacobian_mul_coordinates(vels) + self.revo.jacobian_mul_coordinates(&[vels[1]])
}

fn jacobian_dot_mul_coordinates(&self, vels: &[N]) -> Velocity<N> {
// NOTE: The following is zero.
// self.prism.jacobian_dot_mul_coordinates(vels) +
self.revo.jacobian_dot_mul_coordinates(&[vels[1]])
}

fn default_damping(&self, out: &mut DVectorSliceMut<N>) {
self.prism.default_damping(&mut out.rows_mut(0, 1));
self.revo.default_damping(&mut out.rows_mut(1, 1));
}

fn integrate(&mut self, parameters: &IntegrationParameters<N>, vels: &[N]) {
self.prism.integrate(parameters, vels);
self.revo.integrate(parameters, &[vels[1]]);
}

fn apply_displacement(&mut self, disp: &[N]) {
self.prism.apply_displacement(disp);
self.revo.apply_displacement(&[disp[1]]);
}

#[inline]
fn clone(&self) -> Box<dyn Joint<N>> {
Box::new(*self)
}

fn num_velocity_constraints(&self) -> usize {
self.prism.num_velocity_constraints() + self.revo.num_velocity_constraints()
}

fn velocity_constraints(
&self,
parameters: &IntegrationParameters<N>,
multibody: &Multibody<N>,
assembly_id: usize,
dof_id: usize,
ext_vels: &[N],
ground_j_id: &mut usize,
jacobians: &mut [N],
constraints: &mut ConstraintSet<N, (), (), usize>,
) {
self.prism.velocity_constraints(
parameters,
multibody,
assembly_id,
dof_id,
ext_vels,
ground_j_id,
jacobians,
constraints,
);
self.revo.velocity_constraints(
parameters,
multibody,
assembly_id,
dof_id + 1,
ext_vels,
ground_j_id,
jacobians,
constraints,
);
}

fn num_position_constraints(&self) -> usize {
// NOTE: we don't test if constraints exist to simplify indexing.
2
}

fn position_constraint(
&self,
i: usize,
multibody: &Multibody<N>,
handle: BodyPartHandle<()>,
dof_id: usize,
jacobians: &mut [N],
) -> Option<GenericNonlinearConstraint<N, ()>> {
if i == 0 {
self.prism
.position_constraint(0, multibody, link, handle, dof_id, jacobians)
} else {
self.revo
.position_constraint(0, multibody, link, handle, dof_id + 1, jacobians)
}
}
}

prismatic_motor_limit_methods!(PinSlotJoint, prism);
revolute_motor_limit_methods!(PinSlotJoint, revo);
```