avian3d 0.6.0

use super::FixedAngleConstraintShared;
use crate::{
    dynamics::{
        joints::MotorModel,
        solver::{
            solver_body::{SolverBody, SolverBodyInertia},
            xpbd::*,
        },
    },
    prelude::*,
};
use bevy::prelude::*;

/// Constraint data required by the XPBD constraint solver for a [`PrismaticJoint`].
#[derive(Component, Clone, Copy, Debug, Default, PartialEq, Reflect)]
#[cfg_attr(feature = "serialize", derive(serde::Serialize, serde::Deserialize))]
#[cfg_attr(feature = "serialize", reflect(Serialize, Deserialize))]
#[reflect(Component, Debug, PartialEq)]
pub struct PrismaticJointSolverData {
    pub(super) world_r1: Vector,
    pub(super) world_r2: Vector,
    pub(super) center_difference: Vector,
    pub(super) free_axis1: Vector,
    pub(super) total_position_lagrange: Vector,
    pub(super) angle_constraint: FixedAngleConstraintShared,
    /// Accumulated motor Lagrange multiplier for this frame.
    pub(super) total_motor_lagrange: Scalar,
    /// Motor Lagrange multiplier from the previous frame, used for warm starting.
    /// This is zeroed after being applied in the first substep.
    pub(super) warm_start_motor_lagrange: Scalar,
}

impl XpbdConstraintSolverData for PrismaticJointSolverData {
    fn clear_lagrange_multipliers(&mut self) {
        self.total_position_lagrange = Vector::ZERO;
        self.angle_constraint.clear_lagrange_multipliers();
        // Save motor lagrange for warm starting before clearing.
        self.warm_start_motor_lagrange = self.total_motor_lagrange;
        self.total_motor_lagrange = 0.0;
    }

    fn total_position_lagrange(&self) -> Vector {
        self.total_position_lagrange
    }

    fn total_rotation_lagrange(&self) -> AngularVector {
        self.angle_constraint.total_rotation_lagrange()
    }

    fn total_motor_lagrange(&self) -> Scalar {
        self.total_motor_lagrange
    }
}

impl XpbdConstraint<2> for PrismaticJoint {
    type SolverData = PrismaticJointSolverData;

    fn prepare(
        &mut self,
        bodies: [&RigidBodyQueryReadOnlyItem; 2],
        solver_data: &mut PrismaticJointSolverData,
    ) {
        let [body1, body2] = bodies;

        let Some(local_anchor1) = self.local_anchor1() else {
            return;
        };
        let Some(local_anchor2) = self.local_anchor2() else {
            return;
        };
        let Some(local_basis1) = self.local_basis1() else {
            return;
        };
        let Some(local_basis2) = self.local_basis2() else {
            return;
        };

        // Prepare the point-to-point constraint.
        solver_data.angle_constraint.prepare(
            body1.rotation,
            body2.rotation,
            local_basis1,
            local_basis2,
        );

        // Prepare the prismatic joint.
        solver_data.world_r1 = body1.rotation * (local_anchor1 - body1.center_of_mass.0);
        solver_data.world_r2 = body2.rotation * (local_anchor2 - body2.center_of_mass.0);
        solver_data.center_difference = (body2.position.0 - body1.position.0)
            + (body2.rotation * body2.center_of_mass.0 - body1.rotation * body1.center_of_mass.0);
        solver_data.free_axis1 = *body1.rotation * local_basis1 * self.slider_axis;
    }

    fn solve(
        &mut self,
        bodies: [&mut SolverBody; 2],
        inertias: [&SolverBodyInertia; 2],
        solver_data: &mut PrismaticJointSolverData,
        dt: Scalar,
    ) {
        let [body1, body2] = bodies;

        // Solve the angular constraint.
        solver_data
            .angle_constraint
            .solve([body1, body2], inertias, self.angle_compliance, dt);

        // Solve motors before limits to give limits higher priority.
        self.apply_motor(body1, body2, inertias[0], inertias[1], solver_data, dt);

        // Constrain the relative positions of the bodies, only allowing translation along one free axis.
        self.constrain_positions(body1, body2, inertias[0], inertias[1], solver_data, dt);
    }

    fn warm_start_motors(
        &self,
        bodies: [&mut SolverBody; 2],
        inertias: [&SolverBodyInertia; 2],
        solver_data: &mut PrismaticJointSolverData,
        _dt: Scalar,
        warm_start_coefficient: Scalar,
    ) {
        if !self.motor.enabled {
            return;
        }

        let [body1, body2] = bodies;
        let [inertia1, inertia2] = inertias;

        let inv_mass1 = inertia1.effective_inv_mass();
        let inv_mass2 = inertia2.effective_inv_mass();
        let inv_angular_inertia1 = inertia1.effective_inv_angular_inertia();
        let inv_angular_inertia2 = inertia2.effective_inv_angular_inertia();

        let axis = body1.delta_rotation * solver_data.free_axis1;
        let world_r1 = body1.delta_rotation * solver_data.world_r1;
        let world_r2 = body2.delta_rotation * solver_data.world_r2;

        let impulse = warm_start_coefficient * solver_data.warm_start_motor_lagrange * axis;

        body1.linear_velocity -= impulse * inv_mass1;
        body2.linear_velocity += impulse * inv_mass2;
        body1.angular_velocity -= inv_angular_inertia1 * cross(world_r1, impulse);
        body2.angular_velocity += inv_angular_inertia2 * cross(world_r2, impulse);

        solver_data.warm_start_motor_lagrange = 0.0;
    }
}

impl PrismaticJoint {
    /// Constrains the relative positions of the bodies, only allowing translation along one free axis.
    ///
    /// Returns the force exerted by this constraint.
    fn constrain_positions(
        &self,
        body1: &mut SolverBody,
        body2: &mut SolverBody,
        inertia1: &SolverBodyInertia,
        inertia2: &SolverBodyInertia,
        solver_data: &mut PrismaticJointSolverData,
        dt: Scalar,
    ) {
        // Compute the effective inverse masses and angular inertias of the bodies.
        let inv_mass1 = inertia1.effective_inv_mass();
        let inv_mass2 = inertia2.effective_inv_mass();
        let inv_angular_inertia1 = inertia1.effective_inv_angular_inertia();
        let inv_angular_inertia2 = inertia2.effective_inv_angular_inertia();

        let world_r1 = body1.delta_rotation * solver_data.world_r1;
        let world_r2 = body2.delta_rotation * solver_data.world_r2;

        let mut delta_x = Vector::ZERO;

        let axis1 = body1.delta_rotation * solver_data.free_axis1;
        if let Some(limits) = self.limits {
            let separation = (body2.delta_position - body1.delta_position)
                + (world_r2 - world_r1)
                + solver_data.center_difference;
            delta_x += limits.compute_correction_along_axis(separation, axis1);
        }

        let zero_distance_limit = DistanceLimit::ZERO;

        #[cfg(feature = "2d")]
        {
            let axis2 = Vector::new(axis1.y, -axis1.x);

            let separation = (body2.delta_position - body1.delta_position)
                + (world_r2 - world_r1)
                + solver_data.center_difference;
            delta_x += zero_distance_limit.compute_correction_along_axis(separation, axis2);
        }
        #[cfg(feature = "3d")]
        {
            let axis2 = axis1.any_orthogonal_vector();
            let axis3 = axis1.cross(axis2);

            let separation = (body2.delta_position - body1.delta_position)
                + (world_r2 - world_r1)
                + solver_data.center_difference;
            delta_x += zero_distance_limit.compute_correction_along_axis(separation, axis2);

            let separation = (body2.delta_position - body1.delta_position)
                + (world_r2 - world_r1)
                + solver_data.center_difference;
            delta_x += zero_distance_limit.compute_correction_along_axis(separation, axis3);
        }

        let magnitude = delta_x.length();

        if magnitude <= Scalar::EPSILON {
            return;
        }

        let dir = delta_x / magnitude;

        // Compute generalized inverse masses
        let w1 = PositionConstraint::compute_generalized_inverse_mass(
            self,
            inv_mass1.max_element(),
            inv_angular_inertia1,
            world_r1,
            dir,
        );
        let w2 = PositionConstraint::compute_generalized_inverse_mass(
            self,
            inv_mass2.max_element(),
            inv_angular_inertia2,
            world_r2,
            dir,
        );

        // Compute Lagrange multiplier update
        let delta_lagrange =
            compute_lagrange_update(0.0, magnitude, &[w1, w2], self.align_compliance, dt);
        let impulse = delta_lagrange * dir;
        solver_data.total_position_lagrange += impulse;

        // Apply positional correction to align the positions of the bodies
        self.apply_positional_impulse(
            body1, body2, inertia1, inertia2, impulse, world_r1, world_r2,
        );
    }
}

impl PrismaticJoint {
    /// Applies motor forces to drive the joint towards the target velocity and/or position.
    fn apply_motor(
        &self,
        body1: &mut SolverBody,
        body2: &mut SolverBody,
        inertia1: &SolverBodyInertia,
        inertia2: &SolverBodyInertia,
        solver_data: &mut PrismaticJointSolverData,
        dt: Scalar,
    ) {
        let motor = &self.motor;

        if !motor.enabled {
            return;
        }

        let axis1 = body1.delta_rotation * solver_data.free_axis1;
        let world_r1 = body1.delta_rotation * solver_data.world_r1;
        let world_r2 = body2.delta_rotation * solver_data.world_r2;

        let separation = (body2.delta_position - body1.delta_position)
            + (world_r2 - world_r1)
            + solver_data.center_difference;
        let current_position = separation.dot(axis1);
        let current_velocity = (body2.linear_velocity - body1.linear_velocity).dot(axis1);

        let inv_mass1 = inertia1.effective_inv_mass();
        let inv_mass2 = inertia2.effective_inv_mass();
        let inv_angular_inertia1 = inertia1.effective_inv_angular_inertia();
        let inv_angular_inertia2 = inertia2.effective_inv_angular_inertia();

        let w1 = PositionConstraint::compute_generalized_inverse_mass(
            self,
            inv_mass1.max_element(),
            inv_angular_inertia1,
            world_r1,
            axis1,
        );
        let w2 = PositionConstraint::compute_generalized_inverse_mass(
            self,
            inv_mass2.max_element(),
            inv_angular_inertia2,
            world_r2,
            axis1,
        );

        let w_sum = w1 + w2;
        if w_sum <= Scalar::EPSILON {
            return;
        }

        let velocity_error = motor.target_velocity - current_velocity;
        let position_error = motor.target_position - current_position;

        let target_velocity_change = match motor.motor_model {
            MotorModel::SpringDamper {
                frequency,
                damping_ratio,
            } => {
                // Implicit Euler formulation for stable spring-damper behavior.
                let omega = TAU * frequency;
                let omega_sq = omega * omega;
                let two_zeta_omega = 2.0 * damping_ratio * omega;
                let inv_denominator = 1.0 / (1.0 + two_zeta_omega * dt + omega_sq * dt * dt);
                (omega_sq * position_error + two_zeta_omega * velocity_error) * dt * inv_denominator
            }
            MotorModel::AccelerationBased { stiffness, damping } => {
                damping * velocity_error + stiffness * position_error * dt
            }
            MotorModel::ForceBased { stiffness, damping } => {
                // Velocity change = (stiffness * pos_error + damping * vel_error) * inv_mass
                (stiffness * position_error + damping * velocity_error) * w_sum
            }
        };

        let correction = target_velocity_change * dt;
        if correction.abs() <= Scalar::EPSILON {
            return;
        }

        let delta_lagrange = correction / w_sum;

        // Clamp to limit instantaneous force per substep.
        let delta_lagrange = if motor.max_force < Scalar::MAX && motor.max_force > 0.0 {
            let max_delta = motor.max_force * dt * dt;
            delta_lagrange.clamp(-max_delta, max_delta)
        } else {
            delta_lagrange
        };

        solver_data.total_motor_lagrange += delta_lagrange;

        let impulse = delta_lagrange * axis1;
        solver_data.total_position_lagrange += impulse;

        // Negate impulse: apply_positional_impulse convention is opposite to motor direction.
        self.apply_positional_impulse(
            body1, body2, inertia1, inertia2, -impulse, world_r1, world_r2,
        );
    }
}

impl PositionConstraint for PrismaticJoint {}

impl AngularConstraint for PrismaticJoint {}