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use na::{self, DVectorSliceMut, Isometry3, RealField, Translation3, Unit, Vector3};

use crate::joint::{Joint, JointMotor, RevoluteJoint, UnitJoint};
use crate::math::{JacobianSliceMut, Velocity};
use crate::object::{BodyPartHandle, Multibody, MultibodyLink};
use crate::solver::{ConstraintSet, GenericNonlinearConstraint, IntegrationParameters};

/// A joint that allows one degree of freedom between two multibody links.
///
/// The degree of freedom is the combination of a rotation and a translation along the same axis.
/// Both rotational and translational motions are coupled to generate a screw motion.
#[derive(Copy, Clone, Debug)]
pub struct HelicalJoint<N: RealField> {
    revo: RevoluteJoint<N>,
    pitch: N,
}

impl<N: RealField> HelicalJoint<N> {
    /// Create an helical joint with the given axis and initial angle.
    ///
    /// The `pitch` controls how much translation is generated for how much rotation.
    /// In particular, the translational displacement along `axis` is given by `angle * pitch`.
    pub fn new(axis: Unit<Vector3<N>>, pitch: N, angle: N) -> Self {
        HelicalJoint {
            revo: RevoluteJoint::new(axis, angle),
            pitch: pitch,
        }
    }

    /// The translational displacement along the joint axis.
    pub fn offset(&self) -> N {
        self.revo.angle() * self.pitch
    }

    /// The rotational displacement along the joint axis.
    pub fn angle(&self) -> N {
        self.revo.angle()
    }
}

impl<N: RealField> Joint<N> for HelicalJoint<N> {
    #[inline]
    fn ndofs(&self) -> usize {
        1
    }

    fn body_to_parent(&self, parent_shift: &Vector3<N>, body_shift: &Vector3<N>) -> Isometry3<N> {
        Translation3::from(self.revo.axis().as_ref() * self.revo.angle())
            * self.revo.body_to_parent(parent_shift, body_shift)
    }

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

    fn jacobian(&self, transform: &Isometry3<N>, out: &mut JacobianSliceMut<N>) {
        let mut jac = *self.revo.local_jacobian();
        jac.linear += self.revo.axis().as_ref() * self.pitch;
        out.copy_from(jac.transformed(transform).as_vector())
    }

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

    fn jacobian_dot_veldiff_mul_coordinates(
        &self,
        transform: &Isometry3<N>,
        acc: &[N],
        out: &mut JacobianSliceMut<N>,
    ) {
        self.revo
            .jacobian_dot_veldiff_mul_coordinates(transform, acc, out)
    }

    fn jacobian_mul_coordinates(&self, vels: &[N]) -> Velocity<N> {
        let mut jac = *self.revo.local_jacobian();
        jac.linear += self.revo.axis().as_ref() * self.pitch;
        jac * vels[0]
    }

    fn jacobian_dot_mul_coordinates(&self, vels: &[N]) -> Velocity<N> {
        self.revo.jacobian_dot_mul_coordinates(vels)
    }

    fn default_damping(&self, out: &mut DVectorSliceMut<N>) {
        out.fill(na::convert(0.1f64))
    }

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

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

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

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

    fn velocity_constraints(
        &self,
        parameters: &IntegrationParameters<N>,
        multibody: &Multibody<N>,
        link: &MultibodyLink<N>,
        assembly_id: usize,
        dof_id: usize,
        ext_vels: &[N],
        ground_j_id: &mut usize,
        jacobians: &mut [N],
        constraints: &mut ConstraintSet<N, (), (), usize>,
    ) {
        // XXX: is this correct even though we don't have the same jacobian?
        self.revo.velocity_constraints(
            parameters,
            multibody,
            link,
            assembly_id,
            dof_id,
            ext_vels,
            ground_j_id,
            jacobians,
            constraints,
        );
    }

    fn num_position_constraints(&self) -> usize {
        // NOTE: we don't test if constraints exist to simplify indexing.
        1
    }

    fn position_constraint(
        &self,
        _: usize,
        multibody: &Multibody<N>,
        link: &MultibodyLink<N>,
        handle: BodyPartHandle<()>,
        dof_id: usize,
        jacobians: &mut [N],
    ) -> Option<GenericNonlinearConstraint<N, ()>> {
        // XXX: is this correct even though we don't have the same jacobian?
        self.revo
            .position_constraint(0, multibody, link, handle, dof_id, jacobians)
    }
}

impl<N: RealField> UnitJoint<N> for HelicalJoint<N> {
    fn position(&self) -> N {
        self.revo.angle()
    }

    fn motor(&self) -> &JointMotor<N, N> {
        self.revo.motor()
    }

    fn min_position(&self) -> Option<N> {
        self.revo.min_angle()
    }

    fn max_position(&self) -> Option<N> {
        self.revo.max_angle()
    }
}

revolute_motor_limit_methods!(HelicalJoint, revo);