Merge pull request #146 from dimforge/implicit_friction_cone

Projection friction impulses on an implicit cone instead of a pyramid approximation.

12 files changed, 785 insertions, 483 deletions

diff --git a/src/dynamics/coefficient_combine_rule.rs b/src/dynamics/coefficient_combine_rule.rs
index 5e8b4a0..2c66888 100644
--- a/src/dynamics/coefficient_combine_rule.rs
+++ b/src/dynamics/coefficient_combine_rule.rs
@@ -25,7 +25,7 @@ impl CoefficientCombineRule {
         let effective_rule = rule_value1.max(rule_value2);
 
         match effective_rule {
-            0 => (coeff1 + coeff1) / 2.0,
+            0 => (coeff1 + coeff2) / 2.0,
             1 => coeff1.min(coeff2),
             2 => coeff1 * coeff2,
             _ => coeff1.max(coeff2),
diff --git a/src/dynamics/solver/delta_vel.rs b/src/dynamics/solver/delta_vel.rs
index 378d302..b50cb76 100644
--- a/src/dynamics/solver/delta_vel.rs
+++ b/src/dynamics/solver/delta_vel.rs
@@ -1,5 +1,6 @@
 use crate::math::{AngVector, Vector};
 use na::{Scalar, SimdRealField};
+use std::ops::AddAssign;
 
 #[derive(Copy, Clone, Debug)]
 //#[repr(align(64))]
@@ -16,3 +17,10 @@ impl<N: SimdRealField> DeltaVel<N> {
         }
     }
 }
+
+impl<N: SimdRealField> AddAssign for DeltaVel<N> {
+    fn add_assign(&mut self, rhs: Self) {
+        self.linear += rhs.linear;
+        self.angular += rhs.angular;
+    }
+}
diff --git a/src/dynamics/solver/mod.rs b/src/dynamics/solver/mod.rs
index 090d0f3..33b6f9a 100644
--- a/src/dynamics/solver/mod.rs
+++ b/src/dynamics/solver/mod.rs
@@ -24,9 +24,11 @@ pub(self) use position_ground_constraint::*;
 #[cfg(feature = "simd-is-enabled")]
 pub(self) use position_ground_constraint_wide::*;
 pub(self) use velocity_constraint::*;
+pub(self) use velocity_constraint_element::*;
 #[cfg(feature = "simd-is-enabled")]
 pub(self) use velocity_constraint_wide::*;
 pub(self) use velocity_ground_constraint::*;
+pub(self) use velocity_ground_constraint_element::*;
 #[cfg(feature = "simd-is-enabled")]
 pub(self) use velocity_ground_constraint_wide::*;
 
@@ -55,9 +57,11 @@ mod position_solver;
 #[cfg(not(feature = "parallel"))]
 mod solver_constraints;
 mod velocity_constraint;
+mod velocity_constraint_element;
 #[cfg(feature = "simd-is-enabled")]
 mod velocity_constraint_wide;
 mod velocity_ground_constraint;
+mod velocity_ground_constraint_element;
 #[cfg(feature = "simd-is-enabled")]
 mod velocity_ground_constraint_wide;
 #[cfg(not(feature = "parallel"))]
diff --git a/src/dynamics/solver/velocity_constraint.rs b/src/dynamics/solver/velocity_constraint.rs
index 243d7d7..643facb 100644
--- a/src/dynamics/solver/velocity_constraint.rs
+++ b/src/dynamics/solver/velocity_constraint.rs
@@ -1,12 +1,12 @@
-use super::DeltaVel;
 use crate::dynamics::solver::VelocityGroundConstraint;
 #[cfg(feature = "simd-is-enabled")]
 use crate::dynamics::solver::{WVelocityConstraint, WVelocityGroundConstraint};
 use crate::dynamics::{IntegrationParameters, RigidBodySet};
 use crate::geometry::{ContactManifold, ContactManifoldIndex};
-use crate::math::{AngVector, Real, Vector, DIM, MAX_MANIFOLD_POINTS};
+use crate::math::{Real, Vector, DIM, MAX_MANIFOLD_POINTS};
 use crate::utils::{WAngularInertia, WBasis, WCross, WDot};
-use simba::simd::SimdPartialOrd;
+
+use super::{DeltaVel, VelocityConstraintElement, VelocityConstraintNormalPart};
 
 //#[repr(align(64))]
 #[derive(Copy, Clone, Debug)]
@@ -78,46 +78,12 @@ impl AnyVelocityConstraint {
 }
 
 #[derive(Copy, Clone, Debug)]
-pub(crate) struct VelocityConstraintElementPart {
-    pub gcross1: AngVector<Real>,
-    pub gcross2: AngVector<Real>,
-    pub rhs: Real,
-    pub impulse: Real,
-    pub r: Real,
-}
-
-#[cfg(not(target_arch = "wasm32"))]
-impl VelocityConstraintElementPart {
-    fn zero() -> Self {
-        Self {
-            gcross1: na::zero(),
-            gcross2: na::zero(),
-            rhs: 0.0,
-            impulse: 0.0,
-            r: 0.0,
-        }
-    }
-}
-
-#[derive(Copy, Clone, Debug)]
-pub(crate) struct VelocityConstraintElement {
-    pub normal_part: VelocityConstraintElementPart,
-    pub tangent_part: [VelocityConstraintElementPart; DIM - 1],
-}
-
-#[cfg(not(target_arch = "wasm32"))]
-impl VelocityConstraintElement {
-    pub fn zero() -> Self {
-        Self {
-            normal_part: VelocityConstraintElementPart::zero(),
-            tangent_part: [VelocityConstraintElementPart::zero(); DIM - 1],
-        }
-    }
-}
-
-#[derive(Copy, Clone, Debug)]
 pub(crate) struct VelocityConstraint {
     pub dir1: Vector<Real>, // Non-penetration force direction for the first body.
+    #[cfg(feature = "dim3")]
+    pub tangent1: Vector<Real>, // One of the friction force directions.
+    #[cfg(feature = "dim3")]
+    pub tangent_rot1: na::UnitComplex<Real>, // Orientation of the tangent basis wrt. the reference basis.
     pub im1: Real,
     pub im2: Real,
     pub limit: Real,
@@ -126,7 +92,7 @@ pub(crate) struct VelocityConstraint {
     pub manifold_id: ContactManifoldIndex,
     pub manifold_contact_id: [u8; MAX_MANIFOLD_POINTS],
     pub num_contacts: u8,
-    pub elements: [VelocityConstraintElement; MAX_MANIFOLD_POINTS],
+    pub elements: [VelocityConstraintElement<Real>; MAX_MANIFOLD_POINTS],
 }
 
 impl VelocityConstraint {
@@ -156,6 +122,12 @@ impl VelocityConstraint {
         let force_dir1 = -manifold.data.normal;
         let warmstart_coeff = manifold.data.warmstart_multiplier * params.warmstart_coeff;
 
+        #[cfg(feature = "dim2")]
+        let tangents1 = force_dir1.orthonormal_basis();
+        #[cfg(feature = "dim3")]
+        let (tangents1, tangent_rot1) =
+            super::compute_tangent_contact_directions(&force_dir1, &rb1.linvel, &rb2.linvel);
+
         for (_l, manifold_points) in manifold
             .data
             .solver_contacts
@@ -165,6 +137,10 @@ impl VelocityConstraint {
             #[cfg(not(target_arch = "wasm32"))]
             let mut constraint = VelocityConstraint {
                 dir1: force_dir1,
+                #[cfg(feature = "dim3")]
+                tangent1: tangents1[0],
+                #[cfg(feature = "dim3")]
+                tangent_rot1,
                 elements: [VelocityConstraintElement::zero(); MAX_MANIFOLD_POINTS],
                 im1: rb1.effective_inv_mass,
                 im2: rb2.effective_inv_mass,
@@ -203,7 +179,7 @@ impl VelocityConstraint {
                     .as_nongrouped_mut()
                     .unwrap()
             } else {
-                unreachable!(); // We don't have parallelization on WASM yet, so this is unreachable.
+                unreachable!(); // We don't have parallelization on WASM yet, so this is unreachable.
             };
 
             #[cfg(target_arch = "wasm32")]
@@ -254,7 +230,7 @@ impl VelocityConstraint {
                     rhs *= is_bouncy + is_resting * params.velocity_solve_fraction;
                     rhs += is_resting * velocity_based_erp_inv_dt * manifold_point.dist.min(0.0);
 
-                    constraint.elements[k].normal_part = VelocityConstraintElementPart {
+                    constraint.elements[k].normal_part = VelocityConstraintNormalPart {
                         gcross1,
                         gcross2,
                         rhs,
@@ -265,7 +241,12 @@ impl VelocityConstraint {
 
                 // Tangent parts.
                 {
-                    let tangents1 = force_dir1.orthonormal_basis();
+                    #[cfg(feature = "dim3")]
+                    let impulse =
+                        tangent_rot1 * manifold_points[k].data.tangent_impulse * warmstart_coeff;
+                    #[cfg(feature = "dim2")]
+                    let impulse = [manifold_points[k].data.tangent_impulse * warmstart_coeff];
+                    constraint.elements[k].tangent_part.impulse = impulse;
 
                     for j in 0..DIM - 1 {
                         let gcross1 = rb1
@@ -281,18 +262,11 @@ impl VelocityConstraint {
                                 + gcross2.gdot(gcross2));
                         let rhs =
                             (vel1 - vel2 + manifold_point.tangent_velocity).dot(&tangents1[j]);
-                        #[cfg(feature = "dim2")]
-                        let impulse = manifold_point.data.tangent_impulse * warmstart_coeff;
-                        #[cfg(feature = "dim3")]
-                        let impulse = manifold_point.data.tangent_impulse[j] * warmstart_coeff;
-
-                        constraint.elements[k].tangent_part[j] = VelocityConstraintElementPart {
-                            gcross1,
-                            gcross2,
-                            rhs,
-                            impulse,
-                            r,
-                        };
+
+                        constraint.elements[k].tangent_part.gcross1[j] = gcross1;
+                        constraint.elements[k].tangent_part.gcross2[j] = gcross2;
+                        constraint.elements[k].tangent_part.rhs[j] = rhs;
+                        constraint.elements[k].tangent_part.r[j] = r;
                     }
                 }
             }
@@ -311,79 +285,36 @@ impl VelocityConstraint {
         let mut mj_lambda1 = DeltaVel::zero();
         let mut mj_lambda2 = DeltaVel::zero();
 
-        for i in 0..self.num_contacts as usize {
-            let elt = &self.elements[i].normal_part;
-            mj_lambda1.linear += self.dir1 * (self.im1 * elt.impulse);
-            mj_lambda1.angular += elt.gcross1 * elt.impulse;
-
-            mj_lambda2.linear += self.dir1 * (-self.im2 * elt.impulse);
-            mj_lambda2.angular += elt.gcross2 * elt.impulse;
-
-            // FIXME: move this out of the for loop?
-            let tangents1 = self.dir1.orthonormal_basis();
-
-            for j in 0..DIM - 1 {
-                let elt = &self.elements[i].tangent_part[j];
-                mj_lambda1.linear += tangents1[j] * (self.im1 * elt.impulse);
-                mj_lambda1.angular += elt.gcross1 * elt.impulse;
-
-                mj_lambda2.linear += tangents1[j] * (-self.im2 * elt.impulse);
-                mj_lambda2.angular += elt.gcross2 * elt.impulse;
-            }
-        }
-
-        mj_lambdas[self.mj_lambda1 as usize].linear += mj_lambda1.linear;
-        mj_lambdas[self.mj_lambda1 as usize].angular += mj_lambda1.angular;
-        mj_lambdas[self.mj_lambda2 as usize].linear += mj_lambda2.linear;
-        mj_lambdas[self.mj_lambda2 as usize].angular += mj_lambda2.angular;
+        VelocityConstraintElement::warmstart_group(
+            &self.elements[..self.num_contacts as usize],
+            &self.dir1,
+            #[cfg(feature = "dim3")]
+            &self.tangent1,
+            self.im1,
+            self.im2,
+            &mut mj_lambda1,
+            &mut mj_lambda2,
+        );
+
+        mj_lambdas[self.mj_lambda1 as usize] += mj_lambda1;
+        mj_lambdas[self.mj_lambda2 as usize] += mj_lambda2;
     }
 
     pub fn solve(&mut self, mj_lambdas: &mut [DeltaVel<Real>]) {
         let mut mj_lambda1 = mj_lambdas[self.mj_lambda1 as usize];
         let mut mj_lambda2 = mj_lambdas[self.mj_lambda2 as usize];
 
-        // Solve friction.
-        for i in 0..self.num_contacts as usize {
-            let tangents1 = self.dir1.orthonormal_basis();
-
-            for j in 0..DIM - 1 {
-                let normal_elt = &self.elements[i].normal_part;
-                let elt = &mut self.elements[i].tangent_part[j];
-                let dimpulse = tangents1[j].dot(&mj_lambda1.linear)
-                    + elt.gcross1.gdot(mj_lambda1.angular)
-                    - tangents1[j].dot(&mj_lambda2.linear)
-                    + elt.gcross2.gdot(mj_lambda2.angular)
-                    + elt.rhs;
-                let limit = self.limit * normal_elt.impulse;
-                let new_impulse = (elt.impulse - elt.r * dimpulse).simd_clamp(-limit, limit);
-                let dlambda = new_impulse - elt.impulse;
-                elt.impulse = new_impulse;
-
-                mj_lambda1.linear += tangents1[j] * (self.im1 * dlambda);
-                mj_lambda1.angular += elt.gcross1 * dlambda;
-
-                mj_lambda2.linear += tangents1[j] * (-self.im2 * dlambda);
-                mj_lambda2.angular += elt.gcross2 * dlambda;
-            }
-        }
-
-        // Solve non-penetration.
-        for i in 0..self.num_contacts as usize {
-            let elt = &mut self.elements[i].normal_part;
-            let dimpulse = self.dir1.dot(&mj_lambda1.linear) + elt.gcross1.gdot(mj_lambda1.angular)
-                - self.dir1.dot(&mj_lambda2.linear)
-                + elt.gcross2.gdot(mj_lambda2.angular)
-                + elt.rhs;
-            let new_impulse = (elt.impulse - elt.r * dimpulse).max(0.0);
-            let dlambda = new_impulse - elt.impulse;
-            elt.impulse = new_impulse;
-
-            mj_lambda1.linear += self.dir1 * (self.im1 * dlambda);
-            mj_lambda1.angular += elt.gcross1 * dlambda;
-
-            mj_lambda2.linear += self.dir1 * (-self.im2 * dlambda);
-            mj_lambda2.angular += elt.gcross2 * dlambda;
-        }
+        VelocityConstraintElement::solve_group(
+            &mut self.elements[..self.num_contacts as usize],
+            &self.dir1,
+            #[cfg(feature = "dim3")]
+            &self.tangent1,
+            self.im1,
+            self.im2,
+            self.limit,
+            &mut mj_lambda1,
+            &mut mj_lambda2,
+        );
 
         mj_lambdas[self.mj_lambda1 as usize] = mj_lambda1;
         mj_lambdas[self.mj_lambda2 as usize] = mj_lambda2;
@@ -398,15 +329,58 @@ impl VelocityConstraint {
             active_contact.data.impulse = self.elements[k].normal_part.impulse;
             #[cfg(feature = "dim2")]
             {
-                active_contact.data.tangent_impulse = self.elements[k].tangent_part[0].impulse;
+                active_contact.data.tangent_impulse = self.elements[k].tangent_part.impulse[0];
             }
             #[cfg(feature = "dim3")]
             {
-                active_contact.data.tangent_impulse = [
-                    self.elements[k].tangent_part[0].impulse,
-                    self.elements[k].tangent_part[1].impulse,
-                ];
+                active_contact.data.tangent_impulse = self
+                    .tangent_rot1
+                    .inverse_transform_vector(&self.elements[k].tangent_part.impulse);
             }
         }
     }
 }
+
+#[inline(always)]
+#[cfg(feature = "dim3")]
+pub(crate) fn compute_tangent_contact_directions<N>(
+    force_dir1: &Vector<N>,
+    linvel1: &Vector<N>,
+    linvel2: &Vector<N>,
+) -> ([Vector<N>; DIM - 1], na::UnitComplex<N>)
+where
+    N: na::SimdRealField,
+    N::Element: na::RealField,
+    Vector<N>: WBasis,
+{
+    use na::SimdValue;
+
+    // Compute the tangent direction. Pick the direction of
+    // the linear relative velocity, if it is not too small.
+    // Otherwise use a fallback direction.
+    let relative_linvel = linvel1 - linvel2;
+    let mut tangent_relative_linvel =
+        relative_linvel - force_dir1 * (force_dir1.dot(&relative_linvel));
+    let tangent_linvel_norm = tangent_relative_linvel.normalize_mut();
+    let threshold: N::Element = na::convert(1.0e-4);
+    let use_fallback = tangent_linvel_norm.simd_lt(N::splat(threshold));
+    let tangent_fallback = force_dir1.orthonormal_vector();
+
+    let tangent1 = tangent_fallback.select(use_fallback, tangent_relative_linvel);
+    let bitangent1 = force_dir1.cross(&tangent1);
+
+    // Rotation such that: rot * tangent_fallback = tangent1
+    // (when projected in the tangent plane.) This is needed to ensure the
+    // warmstart impulse has the correct orientation. Indeed, at frame n + 1,
+    // we need to reapply the same impulse as we did in frame n. However the
+    // basis on which the tangent impulse is expresses may change at each frame
+    // (because the the relative linvel may change direction at each frame).
+    // So we need this rotation to:
+    // - Project the impulse back to the "reference" basis at after friction is resolved.
+    // - Project the old impulse on the new basis before the friction is resolved.
+    let rot = na::UnitComplex::new_unchecked(na::Complex::new(
+        tangent1.dot(&tangent_fallback),
+        bitangent1.dot(&tangent_fallback),
+    ));
+    ([tangent1, bitangent1], rot)
+}
diff --git a/src/dynamics/solver/velocity_constraint_element.rs b/src/dynamics/solver/velocity_constraint_element.rs
new file mode 100644
index 0000000..1324c35
--- /dev/null
+++ b/src/dynamics/solver/velocity_constraint_element.rs
@@ -0,0 +1,261 @@
+use super::DeltaVel;
+use crate::math::{AngVector, Vector, DIM};
+use crate::utils::{WBasis, WDot};
+use na::SimdRealField;
+
+#[derive(Copy, Clone, Debug)]
+pub(crate) struct VelocityConstraintTangentPart<N: SimdRealField> {
+    pub gcross1: [AngVector<N>; DIM - 1],
+    pub gcross2: [AngVector<N>; DIM - 1],
+    pub rhs: [N; DIM - 1],
+    #[cfg(feature = "dim2")]
+    pub impulse: [N; DIM - 1],
+    #[cfg(feature = "dim3")]
+    pub impulse: na::Vector2<N>,
+    pub r: [N; DIM - 1],
+}
+
+impl<N: SimdRealField> VelocityConstraintTangentPart<N> {
+    #[cfg(not(target_arch = "wasm32"))]
+    fn zero() -> Self {
+        Self {
+            gcross1: [na::zero(); DIM - 1],
+            gcross2: [na::zero(); DIM - 1],
+            rhs: [na::zero(); DIM - 1],
+            #[cfg(feature = "dim2")]
+            impulse: [na::zero(); DIM - 1],
+            #[cfg(feature = "dim3")]
+            impulse: na::zero(),
+            r: [na::zero(); DIM - 1],
+        }
+    }
+
+    #[inline]
+    pub fn warmstart(
+        &self,
+        tangents1: [&Vector<N>; DIM - 1],
+        im1: N,
+        im2: N,
+        mj_lambda1: &mut DeltaVel<N>,
+        mj_lambda2: &mut DeltaVel<N>,
+    ) where
+        AngVector<N>: WDot<AngVector<N>, Result = N>,
+        N::Element: SimdRealField,
+    {
+        for j in 0..DIM - 1 {
+            mj_lambda1.linear += tangents1[j] * (im1 * self.impulse[j]);
+            mj_lambda1.angular += self.gcross1[j] * self.impulse[j];
+
+            mj_lambda2.linear += tangents1[j] * (-im2 * self.impulse[j]);
+            mj_lambda2.angular += self.gcross2[j] * self.impulse[j];
+        }
+    }
+
+    #[inline]
+    pub fn solve(
+        &mut self,
+        tangents1: [&Vector<N>; DIM - 1],
+        im1: N,
+        im2: N,
+        limit: N,
+        mj_lambda1: &mut DeltaVel<N>,
+        mj_lambda2: &mut DeltaVel<N>,
+    ) where
+        AngVector<N>: WDot<AngVector<N>, Result = N>,
+        N::Element: SimdRealField,
+    {
+        #[cfg(feature = "dim2")]
+        {
+            let dimpulse = tangents1[0].dot(&mj_lambda1.linear)
+                + self.gcross1[0].gdot(mj_lambda1.angular)
+                - tangents1[0].dot(&mj_lambda2.linear)
+                + self.gcross2[0].gdot(mj_lambda2.angular)
+                + self.rhs[0];
+            let new_impulse = (self.impulse[0] - self.r[0] * dimpulse).simd_clamp(-limit, limit);
+            let dlambda = new_impulse - self.impulse[0];
+            self.impulse[0] = new_impulse;
+
+            mj_lambda1.linear += tangents1[0] * (im1 * dlambda);
+            mj_lambda1.angular += self.gcross1[0] * dlambda;
+
+            mj_lambda2.linear += tangents1[0] * (-im2 * dlambda);
+            mj_lambda2.angular += self.gcross2[0] * dlambda;
+        }
+
+        #[cfg(feature = "dim3")]
+        {
+            let dimpulse_0 = tangents1[0].dot(&mj_lambda1.linear)
+                + self.gcross1[0].gdot(mj_lambda1.angular)
+                - tangents1[0].dot(&mj_lambda2.linear)
+                + self.gcross2[0].gdot(mj_lambda2.angular)
+                + self.rhs[0];
+            let dimpulse_1 = tangents1[1].dot(&mj_lambda1.linear)
+                + self.gcross1[1].gdot(mj_lambda1.angular)
+                - tangents1[1].dot(&mj_lambda2.linear)
+                + self.gcross2[1].gdot(mj_lambda2.angular)
+                + self.rhs[1];
+
+            let new_impulse = na::Vector2::new(
+                self.impulse[0] - self.r[0] * dimpulse_0,
+                self.impulse[1] - self.r[1] * dimpulse_1,
+            );
+            let new_impulse = new_impulse.simd_cap_magnitude(limit);
+            let dlambda = new_impulse - self.impulse;
+            self.impulse = new_impulse;
+
+            mj_lambda1.linear +=
+                tangents1[0] * (im1 * dlambda[0]) + tangents1[1] * (im1 * dlambda[1]);
+            mj_lambda1.angular += self.gcross1[0] * dlambda[0] + self.gcross1[1] * dlambda[1];
+
+            mj_lambda2.linear +=
+                tangents1[0] * (-im2 * dlambda[0]) + tangents1[1] * (-im2 * dlambda[1]);
+            mj_lambda2.angular += self.gcross2[0] * dlambda[0] + self.gcross2[1] * dlambda[1];
+        }
+    }
+}
+
+#[derive(Copy, Clone, Debug)]
+pub(crate) struct VelocityConstraintNormalPart<N: SimdRealField> {
+    pub gcross1: AngVector<N>,
+    pub gcross2: AngVector<N>,
+    pub rhs: N,
+    pub impulse: N,
+    pub r: N,
+}
+
+impl<N: SimdRealField> VelocityConstraintNormalPart<N> {
+    #[cfg(not(target_arch = "wasm32"))]
+    fn zero() -> Self {
+        Self {
+            gcross1: na::zero(),
+            gcross2: na::zero(),
+            rhs: na::zero(),
+            impulse: na::zero(),
+            r: na::zero(),
+        }
+    }
+
+    #[inline]
+    pub fn warmstart(
+        &self,
+        dir1: &Vector<N>,
+        im1: N,
+        im2: N,
+        mj_lambda1: &mut DeltaVel<N>,
+        mj_lambda2: &mut DeltaVel<N>,
+    ) where
+        AngVector<N>: WDot<AngVector<N>, Result = N>,
+    {
+        mj_lambda1.linear += dir1 * (im1 * self.impulse);
+        mj_lambda1.angular += self.gcross1 * self.impulse;
+
+        mj_lambda2.linear += dir1 * (-im2 * self.impulse);
+        mj_lambda2.angular += self.gcross2 * self.impulse;
+    }
+
+    #[inline]
+    pub fn solve(
+        &mut self,
+        dir1: &Vector<N>,
+        im1: N,
+        im2: N,
+        mj_lambda1: &mut DeltaVel<N>,
+        mj_lambda2: &mut DeltaVel<N>,
+    ) where
+        AngVector<N>: WDot<AngVector<N>, Result = N>,
+    {
+        let dimpulse = dir1.dot(&mj_lambda1.linear) + self.gcross1.gdot(mj_lambda1.angular)
+            - dir1.dot(&mj_lambda2.linear)
+            + self.gcross2.gdot(mj_lambda2.angular)
+            + self.rhs;
+        let new_impulse = (self.impulse - self.r * dimpulse).simd_max(N::zero());
+        let dlambda = new_impulse - self.impulse;
+        self.impulse = new_impulse;
+
+        mj_lambda1.linear += dir1 * (im1 * dlambda);
+        mj_lambda1.angular += self.gcross1 * dlambda;
+
+        mj_lambda2.linear += dir1 * (-im2 * dlambda);
+        mj_lambda2.angular += self.gcross2 * dlambda;
+    }
+}
+
+#[derive(Copy, Clone, Debug)]
+pub(crate) struct VelocityConstraintElement<N: SimdRealField> {
+    pub normal_part: VelocityConstraintNormalPart<N>,
+    pub tangent_part: VelocityConstraintTangentPart<N>,
+}
+
+impl<N: SimdRealField> VelocityConstraintElement<N> {
+    #[cfg(not(target_arch = "wasm32"))]
+    pub fn zero() -> Self {
+        Self {
+            normal_part: VelocityConstraintNormalPart::zero(),
+            tangent_part: VelocityConstraintTangentPart::zero(),
+        }
+    }
+
+    #[inline]
+    pub fn warmstart_group(
+        elements: &[Self],
+        dir1: &Vector<N>,
+        #[cfg(feature = "dim3")] tangent1: &Vector<N>,
+        im1: N,
+        im2: N,
+        mj_lambda1: &mut DeltaVel<N>,
+        mj_lambda2: &mut DeltaVel<N>,
+    ) where
+        Vector<N>: WBasis,
+        AngVector<N>: WDot<AngVector<N>, Result = N>,
+        N::Element: SimdRealField,
+    {
+        #[cfg(feature = "dim3")]
+        let tangents1 = [tangent1, &dir1.cross(&tangent1)];
+        #[cfg(feature = "dim2")]
+        let tangents1 = [&dir1.orthonormal_vector()];
+
+        for element in elements {
+            element
+                .tangent_part
+                .warmstart(tangents1, im1, im2, mj_lambda1, mj_lambda2);
+            element
+                .normal_part
+                .warmstart(dir1, im1, im2, mj_lambda1, mj_lambda2);
+        }
+    }
+
+    #[inline]
+    pub fn solve_group(
+        elements: &mut [Self],
+        dir1: &Vector<N>,
+        #[cfg(feature = "dim3")] tangent1: &Vector<N>,
+        im1: N,
+        im2: N,
+        limit: N,
+        mj_lambda1: &mut DeltaVel<N>,
+        mj_lambda2: &mut DeltaVel<N>,
+    ) where
+        Vector<N>: WBasis,
+        AngVector<N>: WDot<AngVector<N>, Result = N>,
+        N::Element: SimdRealField,
+    {
+        // Solve friction.
+        #[cfg(feature = "dim3")]
+        let tangents1 = [tangent1, &dir1.cross(&tangent1)];
+        #[cfg(feature = "dim2")]
+        let tangents1 = [&dir1.orthonormal_vector()];
+
+        for element in elements.iter_mut() {
+            let limit = limit * element.normal_part.impulse;
+            let part = &mut element.tangent_part;
+            part.solve(tangents1, im1, im2, limit, mj_lambda1, mj_lambda2);
+        }
+
+        // Solve penetration.
+        for element in elements.iter_mut() {
+            element
+                .normal_part
+                .solve(&dir1, im1, im2, mj_lambda1, mj_lambda2);
+        }
+    }
+}
diff --git a/src/dynamics/solver/velocity_constraint_wide.rs b/src/dynamics/solver/velocity_constraint_wide.rs
index d97602c..673af54 100644
--- a/src/dynamics/solver/velocity_constraint_wide.rs
+++ b/src/dynamics/solver/velocity_constraint_wide.rs
@@ -1,53 +1,25 @@
-use super::{AnyVelocityConstraint, DeltaVel};
+use super::{
+    AnyVelocityConstraint, DeltaVel, VelocityConstraintElement, VelocityConstraintNormalPart,
+};
 use crate::dynamics::{IntegrationParameters, RigidBodySet};
 use crate::geometry::{ContactManifold, ContactManifoldIndex};
 use crate::math::{
     AngVector, AngularInertia, Point, Real, SimdReal, Vector, DIM, MAX_MANIFOLD_POINTS, SIMD_WIDTH,
 };
-use crate::utils::{WAngularInertia, WBasis, WCross, WDot};
+#[cfg(feature = "dim2")]
+use crate::utils::WBasis;
+use crate::utils::{WAngularInertia, WCross, WDot};
 use num::Zero;
 use simba::simd::{SimdPartialOrd, SimdValue};
 
 #[derive(Copy, Clone, Debug)]
-pub(crate) struct WVelocityConstraintElementPart {
-    pub gcross1: AngVector<SimdReal>,
-    pub gcross2: AngVector<SimdReal>,
-    pub rhs: SimdReal,
-    pub impulse: SimdReal,
-    pub r: SimdReal,
-}
-
-impl WVelocityConstraintElementPart {
-    pub fn zero() -> Self {
-        Self {
-            gcross1: AngVector::zero(),
-            gcross2: AngVector::zero(),
-            rhs: SimdReal::zero(),
-            impulse: SimdReal::zero(),
-            r: SimdReal::zero(),
-        }
-    }
-}
-
-#[derive(Copy, Clone, Debug)]
-pub(crate) struct WVelocityConstraintElement {
-    pub normal_part: WVelocityConstraintElementPart,
-    pub tangent_parts: [WVelocityConstraintElementPart; DIM - 1],
-}
-
-impl WVelocityConstraintElement {
-    pub fn zero() -> Self {
-        Self {
-            normal_part: WVelocityConstraintElementPart::zero(),
-            tangent_parts: [WVelocityConstraintElementPart::zero(); DIM - 1],
-        }
-    }
-}
-
-#[derive(Copy, Clone, Debug)]
 pub(crate) struct WVelocityConstraint {
     pub dir1: Vector<SimdReal>, // Non-penetration force direction for the first body.
-    pub elements: [WVelocityConstraintElement; MAX_MANIFOLD_POINTS],
+    #[cfg(feature = "dim3")]
+    pub tangent1: Vector<SimdReal>, // One of the friction force directions.
+    #[cfg(feature = "dim3")]
+    pub tangent_rot1: na::UnitComplex<SimdReal>, // Orientation of the tangent basis wrt. the reference basis.
+    pub elements: [VelocityConstraintElement<SimdReal>; MAX_MANIFOLD_POINTS],
     pub num_contacts: u8,
     pub im1: SimdReal,
     pub im2: SimdReal,
@@ -108,6 +80,12 @@ impl WVelocityConstraint {
         let warmstart_coeff = warmstart_multiplier * SimdReal::splat(params.warmstart_coeff);
         let num_active_contacts = manifolds[0].data.num_active_contacts();
 
+        #[cfg(feature = "dim2")]
+        let tangents1 = force_dir1.orthonormal_basis();
+        #[cfg(feature = "dim3")]
+        let (tangents1, tangent_rot1) =
+            super::compute_tangent_contact_directions(&force_dir1, &linvel1, &linvel2);
+
         for l in (0..num_active_contacts).step_by(MAX_MANIFOLD_POINTS) {
             let manifold_points = array![|ii|
                 &manifolds[ii].data.solver_contacts[l..num_active_contacts]; SIMD_WIDTH
@@ -116,7 +94,11 @@ impl WVelocityConstraint {
 
             let mut constraint = WVelocityConstraint {
                 dir1: force_dir1,
-                elements: [WVelocityConstraintElement::zero(); MAX_MANIFOLD_POINTS],
+                #[cfg(feature = "dim3")]
+                tangent1: tangents1[0],
+                #[cfg(feature = "dim3")]
+                tangent_rot1,
+                elements: [VelocityConstraintElement::zero(); MAX_MANIFOLD_POINTS],
                 im1,
                 im2,
                 limit: SimdReal::splat(0.0),
@@ -169,7 +151,7 @@ impl WVelocityConstraint {
                     rhs +=
                         dist.simd_min(SimdReal::zero()) * (velocity_based_erp_inv_dt * is_resting);
 
-                    constraint.elements[k].normal_part = WVelocityConstraintElementPart {
+                    constraint.elements[k].normal_part = VelocityConstraintNormalPart {
                         gcross1,
                         gcross2,
                         rhs,
@@ -179,31 +161,30 @@ impl WVelocityConstraint {
                 }
 
                 // tangent parts.
-                let tangents1 = force_dir1.orthonormal_basis();
+                #[cfg(feature = "dim2")]
+                let impulse = [SimdReal::from(
+                    array![|ii| manifold_points[ii][k].data.tangent_impulse; SIMD_WIDTH],
+                )];
 
-                for j in 0..DIM - 1 {
-                    #[cfg(feature = "dim2")]
-                    let impulse = SimdReal::from(
+                #[cfg(feature = "dim3")]
+                let impulse = tangent_rot1
+                    * na::Vector2::from(
                         array![|ii| manifold_points[ii][k].data.tangent_impulse; SIMD_WIDTH],
                     );
-                    #[cfg(feature = "dim3")]
-                    let impulse = SimdReal::from(
-                        array![|ii| manifold_points[ii][k].data.tangent_impulse[j]; SIMD_WIDTH],
-                    );
 
+                constraint.elements[k].tangent_part.impulse = impulse;
+
+                for j in 0..DIM - 1 {
                     let gcross1 = ii1.transform_vector(dp1.gcross(tangents1[j]));
                     let gcross2 = ii2.transform_vector(dp2.gcross(-tangents1[j]));
                     let r = SimdReal::splat(1.0)
                         / (im1 + im2 + gcross1.gdot(gcross1) + gcross2.gdot(gcross2));
                     let rhs = (vel1 - vel2 + tangent_velocity).dot(&tangents1[j]);
 
-                    constraint.elements[k].tangent_parts[j] = WVelocityConstraintElementPart {
-                        gcross1,
-                        gcross2,
-                        rhs,
-                        impulse: impulse * warmstart_coeff,
-                        r,
-                    };
+                    constraint.elements[k].tangent_part.gcross1[j] = gcross1;
+                    constraint.elements[k].tangent_part.gcross2[j] = gcross2;
+                    constraint.elements[k].tangent_part.rhs[j] = rhs;
+                    constraint.elements[k].tangent_part.r[j] = r;
                 }
             }
 
@@ -235,26 +216,16 @@ impl WVelocityConstraint {
             ),
         };
 
-        for i in 0..self.num_contacts as usize {
-            let elt = &self.elements[i].normal_part;
-            mj_lambda1.linear += self.dir1 * (self.im1 * elt.impulse);
-            mj_lambda1.angular += elt.gcross1 * elt.impulse;
-
-            mj_lambda2.linear += self.dir1 * (-self.im2 * elt.impulse);
-            mj_lambda2.angular += elt.gcross2 * elt.impulse;
-
-            // FIXME: move this out of the for loop?
-            let tangents1 = self.dir1.orthonormal_basis();
-
-            for j in 0..DIM - 1 {
-                let elt = &self.elements[i].tangent_parts[j];
-                mj_lambda1.linear += tangents1[j] * (self.im1 * elt.impulse);
-                mj_lambda1.angular += elt.gcross1 * elt.impulse;
-
-                mj_lambda2.linear += tangents1[j] * (-self.im2 * elt.impulse);
-                mj_lambda2.angular += elt.gcross2 * elt.impulse;
-            }
-        }
+        VelocityConstraintElement::warmstart_group(
+            &self.elements[..self.num_contacts as usize],
+            &self.dir1,
+            #[cfg(feature = "dim3")]
+            &self.tangent1,
+            self.im1,
+            self.im2,