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

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

/// A joint that allows 1 rotational and 2 translational degrees of freedom.
#[derive(Copy, Clone, Debug)]
pub struct PlanarJoint<N: RealField> {
prism1: PrismaticJoint<N>,
prism2: PrismaticJoint<N>,
revo: RevoluteJoint<N>,
}

impl<N: RealField> PlanarJoint<N> {
/// Create a new planar joint where both translational degrees of freedoms are along the provide axii.
///
/// The rotational degree of freedom is along an axis orthogonal to `axis1` and `axis2`. Idealy, the two
/// provided axii should be orthogonal. All axis are in the local coordinate space of the attached multibody links.
///
/// Panics if `axis1` and `axis2` are near-colinear.
pub fn new(
axis1: Unit<Vector3<N>>,
axis2: Unit<Vector3<N>>,
pos1: N,
pos2: N,
angle: N,
) -> Self {
let cross = axis1.cross(&*axis2);
let normal = Unit::try_new(cross, N::default_epsilon())
.expect("A planar joint cannot be defined from two collinear axis.");
let prism1 = PrismaticJoint::new(axis1, pos1);
let prism2 = PrismaticJoint::new(axis2, pos2);
let revo = RevoluteJoint::new(normal, angle);

PlanarJoint {
prism1,
prism2,
revo,
}
}
}

impl<N: RealField> Joint<N> for PlanarJoint<N> {
#[inline]
fn ndofs(&self) -> usize {
3
}

fn body_to_parent(&self, parent_shift: &Vector3<N>, body_shift: &Vector3<N>) -> Isometry3<N> {
self.prism1.translation()
* self.prism2.translation()
* self.revo.body_to_parent(parent_shift, body_shift)
}

fn update_jacobians(&mut self, body_shift: &Vector3<N>, vels: &[N]) {
self.prism1.update_jacobians(body_shift, vels);
self.prism2.update_jacobians(body_shift, &vels[1..]);
self.revo.update_jacobians(body_shift, &vels[2..]);
}

fn jacobian(&self, transform: &Isometry3<N>, out: &mut JacobianSliceMut<N>) {
self.prism1.jacobian(transform, &mut out.columns_mut(0, 1));
self.prism2.jacobian(transform, &mut out.columns_mut(1, 1));
self.revo.jacobian(transform, &mut out.columns_mut(2, 1));
}

fn jacobian_dot(&self, transform: &Isometry3<N>, out: &mut JacobianSliceMut<N>) {
self.prism1
.jacobian_dot(transform, &mut out.columns_mut(0, 1));
self.prism2
.jacobian_dot(transform, &mut out.columns_mut(1, 1));
self.revo
.jacobian_dot(transform, &mut out.columns_mut(2, 1));
}

fn jacobian_dot_veldiff_mul_coordinates(
&self,
transform: &Isometry3<N>,
vels: &[N],
out: &mut JacobianSliceMut<N>,
) {
self.prism1.jacobian_dot_veldiff_mul_coordinates(
transform,
vels,
&mut out.columns_mut(0, 1),
);
self.prism2.jacobian_dot_veldiff_mul_coordinates(
transform,
&[vels[1]],
&mut out.columns_mut(1, 1),
);
self.revo.jacobian_dot_veldiff_mul_coordinates(
transform,
&[vels[2]],
&mut out.columns_mut(2, 1),
);
}

fn jacobian_mul_coordinates(&self, vels: &[N]) -> Velocity<N> {
self.prism1.jacobian_mul_coordinates(vels)
+ self.prism2.jacobian_mul_coordinates(&[vels[1]])
+ self.revo.jacobian_mul_coordinates(&[vels[2]])
}

fn jacobian_dot_mul_coordinates(&self, vels: &[N]) -> Velocity<N> {
// NOTE: The two folowing are zero.
// self.prism1.jacobian_dot_mul_coordinates(vels)       +
// self.prism2.jacobian_dot_mul_coordinates(&[vels[1]]) +
self.revo.jacobian_dot_mul_coordinates(&[vels[2]])
}

fn default_damping(&self, out: &mut DVectorSliceMut<N>) {
self.prism1.default_damping(&mut out.rows_mut(0, 1));
self.prism2.default_damping(&mut out.rows_mut(1, 1));
self.revo.default_damping(&mut out.rows_mut(2, 1));
}

fn integrate(&mut self, parameters: &IntegrationParameters<N>, vels: &[N]) {
self.prism1.integrate(parameters, vels);
self.prism2.integrate(parameters, &[vels[1]]);
self.revo.integrate(parameters, &[vels[2]]);
}

fn apply_displacement(&mut self, disp: &[N]) {
self.prism1.apply_displacement(disp);
self.prism2.apply_displacement(&[disp[1]]);
self.revo.apply_displacement(&[disp[2]]);
}

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

fn num_velocity_constraints(&self) -> usize {
self.prism1.num_velocity_constraints()
+ self.prism2.num_velocity_constraints()
+ 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>,
) {
self.prism1.velocity_constraints(
parameters,
multibody,
link,
assembly_id,
dof_id,
ext_vels,
ground_j_id,
jacobians,
constraints,
);
self.prism2.velocity_constraints(
parameters,
multibody,
link,
assembly_id,
dof_id + 1,
ext_vels,
ground_j_id,
jacobians,
constraints,
);
self.revo.velocity_constraints(
parameters,
multibody,
link,
assembly_id,
dof_id + 2,
ext_vels,
ground_j_id,
jacobians,
constraints,
);
}

fn num_position_constraints(&self) -> usize {
// NOTE: we don't test if constraints exist to simplify indexing.
3
}

fn position_constraint(
&self,
i: usize,
multibody: &Multibody<N>,
link: &MultibodyLink<N>,
handle: BodyPartHandle<()>,
dof_id: usize,
jacobians: &mut [N],
) -> Option<GenericNonlinearConstraint<N, ()>> {
if i == 0 {
self.prism1
.position_constraint(0, multibody, link, handle, dof_id, jacobians)
} else if i == 1 {
self.prism2
.position_constraint(0, multibody, link, handle, dof_id + 1, jacobians)
} else {
self.revo
.position_constraint(0, multibody, link, handle, dof_id + 2, jacobians)
}
}
}

prismatic_motor_limit_methods_1!(PlanarJoint, prism1);
prismatic_motor_limit_methods_2!(PlanarJoint, prism2);
revolute_motor_limit_methods!(PlanarJoint, revo);