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use crate::dynamics::solver::solver_body::SolverBody;
use crate::dynamics::solver::xpbd;
use crate::prelude::*;
/// An angular constraint applies an angular correction around a given axis.
pub trait AngularConstraint {
/// Applies an angular correction to two bodies.
///
/// Returns the angular impulse that is applied proportional
/// to the inverse moments of inertia of the bodies.
#[cfg(feature = "2d")]
fn apply_angular_lagrange_update(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
delta_lagrange: Scalar,
) -> Scalar {
if delta_lagrange.abs() <= Scalar::EPSILON {
return 0.0;
}
self.apply_angular_impulse(
body1,
body2,
inv_angular_inertia1,
inv_angular_inertia2,
-delta_lagrange,
)
}
/// Applies an angular impulse to two bodies.
///
/// Returns the impulse that is applied proportional
/// to the inverse moments of inertia of the bodies.
#[cfg(feature = "2d")]
fn apply_angular_impulse(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
impulse: Scalar,
) -> Scalar {
// Apply rotational updates
let delta_angle = Self::get_delta_rot(inv_angular_inertia1, impulse);
body1.delta_rotation = body1.delta_rotation.add_angle_fast(delta_angle);
let delta_angle = Self::get_delta_rot(inv_angular_inertia2, -impulse);
body2.delta_rotation = body2.delta_rotation.add_angle_fast(delta_angle);
impulse
}
/// Applies an angular correction to two bodies.
///
/// Returns the angular impulse that is applied proportional
/// to the inverse moments of inertia of the bodies.
#[cfg(feature = "3d")]
fn apply_angular_lagrange_update(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
delta_lagrange: Scalar,
axis: Vector,
) -> Vector {
if delta_lagrange.abs() <= Scalar::EPSILON {
return Vector::ZERO;
}
let impulse = -delta_lagrange * axis;
self.apply_angular_impulse(
body1,
body2,
inv_angular_inertia1,
inv_angular_inertia2,
impulse,
)
}
/// Applies an angular impulse to two bodies.
///
/// Returns the impulse that is applied proportional
/// to the inverse moments of inertia of the bodies.
#[cfg(feature = "3d")]
fn apply_angular_impulse(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
impulse: Vector,
) -> Vector {
// Apply rotational updates
let delta_quat = Self::get_delta_rot(inv_angular_inertia1, impulse);
body1.delta_rotation.0 = delta_quat * body1.delta_rotation.0;
let delta_quat = Self::get_delta_rot(inv_angular_inertia2, -impulse);
body2.delta_rotation.0 = delta_quat * body2.delta_rotation.0;
impulse
}
/// Applies an angular correction that aligns the orientation of the bodies.
///
/// Returns the Lagrange multiplier update.
#[cfg(feature = "2d")]
fn align_orientation(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
angle: Scalar,
lagrange: Scalar,
compliance: Scalar,
dt: Scalar,
) -> AngularVector {
if angle.abs() <= Scalar::EPSILON {
return AngularVector::ZERO;
}
let w = [inv_angular_inertia1, inv_angular_inertia2];
// Compute Lagrange multiplier update
let delta_lagrange = xpbd::compute_lagrange_update(lagrange, angle, &w, compliance, dt);
// Apply angular correction to aling the bodies
self.apply_angular_lagrange_update(
body1,
body2,
inv_angular_inertia1,
inv_angular_inertia2,
delta_lagrange,
);
// Return Lagrange multiplier update
delta_lagrange
}
/// Applies an angular correction that aligns the orientation of the bodies.
///
/// Returns the Lagrange multiplier update.
#[cfg(feature = "3d")]
fn align_orientation(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
rotation_difference: Vector,
lagrange: Scalar,
compliance: Scalar,
dt: Scalar,
) -> AngularVector {
let angle = rotation_difference.length();
if angle <= Scalar::EPSILON {
return AngularVector::ZERO;
}
let axis = rotation_difference / angle;
// Compute generalized inverse masses
let w1 =
AngularConstraint::compute_generalized_inverse_mass(self, inv_angular_inertia1, axis);
let w2 =
AngularConstraint::compute_generalized_inverse_mass(self, inv_angular_inertia2, axis);
let w = [w1, w2];
// Compute Lagrange multiplier update
let delta_lagrange = xpbd::compute_lagrange_update(lagrange, angle, &w, compliance, dt);
// Apply angular correction to aling the bodies
self.apply_angular_lagrange_update(
body1,
body2,
inv_angular_inertia1,
inv_angular_inertia2,
delta_lagrange,
axis,
);
// Return Lagrange multiplier update
delta_lagrange * axis
}
/// Applies angular constraints for interactions between two bodies.
///
/// Here in 2D, `axis` is a unit vector with the Z coordinate set to 1 or -1. It controls if the body should rotate counterclockwise or clockwise.
///
/// Returns the angular impulse that is applied proportional to the inverse masses of the bodies.
#[cfg(feature = "2d")]
fn apply_angular_correction(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
delta_lagrange: Scalar,
axis: Vector3,
) -> Scalar {
if delta_lagrange.abs() <= Scalar::EPSILON {
return 0.0;
}
// Compute angular impulse
// `axis.z` is 1 or -1 and it controls if the body should rotate counterclockwise or clockwise
let p = -delta_lagrange * axis.z;
// Apply rotational updates
let delta_angle = Self::get_delta_rot(inv_angular_inertia1, p);
body1.delta_rotation = body1.delta_rotation.add_angle_fast(delta_angle);
let delta_angle = Self::get_delta_rot(inv_angular_inertia2, -p);
body2.delta_rotation = body2.delta_rotation.add_angle_fast(delta_angle);
p
}
/// Applies angular constraints for interactions between two bodies.
///
/// Returns the angular impulse that is applied proportional to the inverse masses of the bodies.
#[cfg(feature = "3d")]
fn apply_angular_correction(
&self,
body1: &mut SolverBody,
body2: &mut SolverBody,
inv_angular_inertia1: SymmetricTensor,
inv_angular_inertia2: SymmetricTensor,
delta_lagrange: Scalar,
axis: Vector,
) -> Vector {
if delta_lagrange.abs() <= Scalar::EPSILON {
return Vector::ZERO;
}
// Compute angular impulse
let p = -delta_lagrange * axis;
// Apply rotational updates
let delta_quat = Self::get_delta_rot(inv_angular_inertia1, p);
body1.delta_rotation.0 = delta_quat * body1.delta_rotation.0;
let delta_quat = Self::get_delta_rot(inv_angular_inertia2, -p);
body2.delta_rotation.0 = delta_quat * body2.delta_rotation.0;
p
}
/// Computes the generalized inverse mass of a body when applying an angular correction
/// around `axis`.
///
/// In 2D, `axis` should only have the z axis set to either -1 or 1 to indicate counterclockwise or
/// clockwise rotation.
fn compute_generalized_inverse_mass(
&self,
inv_angular_inertia: SymmetricTensor,
axis: Vector3,
) -> Scalar {
axis.dot(inv_angular_inertia * axis)
}
/// Computes the update in rotation when applying an angular correction `p`.
#[cfg(feature = "2d")]
fn get_delta_rot(inverse_inertia: SymmetricTensor, p: Scalar) -> Scalar {
// Equation 8/9 but in 2D
inverse_inertia * p
}
/// Computes the update in rotation when applying an angular correction `p`.
#[cfg(feature = "3d")]
fn get_delta_rot(inverse_inertia: SymmetricTensor, p: Vector) -> Quaternion {
// Equation 8/9
Quaternion::from_scaled_axis(inverse_inertia * p)
}
/// Computes the torque acting along the constraint using the equation `tau = lambda * n / h^2`,
/// where `n` is the Z axis in 2D.
#[cfg(feature = "2d")]
fn compute_torque(&self, lagrange: Scalar, dt: Scalar) -> AngularVector {
// Eq (17)
lagrange / dt.powi(2)
}
/// Computes the torque acting along the constraint using the equation `tau = lambda * n / h^2`
#[cfg(feature = "3d")]
fn compute_torque(&self, lagrange: Scalar, axis: Vector, dt: Scalar) -> AngularVector {
// Eq (17)
lagrange * axis / dt.powi(2)
}
}