Merge pull request #6 from dimforge/collider_removal

Add collider removal + fix rigid-bodies with multiple colliders

20 files changed, 405 insertions, 72 deletions

diff --git a/src/dynamics/mass_properties.rs b/src/dynamics/mass_properties.rs
index cc2979c..22e7da5 100644
--- a/src/dynamics/mass_properties.rs
+++ b/src/dynamics/mass_properties.rs
@@ -1,7 +1,7 @@
 use crate::math::{AngVector, AngularInertia, Isometry, Point, Rotation, Vector};
 use crate::utils;
 use num::Zero;
-use std::ops::{Add, AddAssign};
+use std::ops::{Add, AddAssign, Sub, SubAssign};
 #[cfg(feature = "dim3")]
 use {na::Matrix3, std::ops::MulAssign};
 
@@ -91,6 +91,18 @@ impl MassProperties {
     }
 
     #[cfg(feature = "dim3")]
+    /// Reconstructs the inverse angular inertia tensor of the rigid body from its principal inertia values and axii.
+    pub fn reconstruct_inverse_inertia_matrix(&self) -> Matrix3<f32> {
+        let inv_principal_inertia = self.inv_principal_inertia_sqrt.map(|e| e * e);
+        self.principal_inertia_local_frame.to_rotation_matrix()
+            * Matrix3::from_diagonal(&inv_principal_inertia)
+            * self
+                .principal_inertia_local_frame
+                .inverse()
+                .to_rotation_matrix()
+    }
+
+    #[cfg(feature = "dim3")]
     /// Reconstructs the angular inertia tensor of the rigid body from its principal inertia values and axii.
     pub fn reconstruct_inertia_matrix(&self) -> Matrix3<f32> {
         let principal_inertia = self.inv_principal_inertia_sqrt.map(|e| utils::inv(e * e));
@@ -125,6 +137,19 @@ impl MassProperties {
             Matrix3::zeros()
         }
     }
+
+    /// Transform each element of the mass properties.
+    pub fn transform_by(&self, m: &Isometry<f32>) -> Self {
+        // NOTE: we don't apply the parallel axis theorem here
+        // because the center of mass is also transformed.
+        Self {
+            local_com: m * self.local_com,
+            inv_mass: self.inv_mass,
+            inv_principal_inertia_sqrt: self.inv_principal_inertia_sqrt,
+            #[cfg(feature = "dim3")]
+            principal_inertia_local_frame: m.rotation * self.principal_inertia_local_frame,
+        }
+    }
 }
 
 impl Zero for MassProperties {
@@ -143,6 +168,68 @@ impl Zero for MassProperties {
     }
 }
 
+impl Sub<MassProperties> for MassProperties {
+    type Output = Self;
+
+    #[cfg(feature = "dim2")]
+    fn sub(self, other: MassProperties) -> Self {
+        if self.is_zero() || other.is_zero() {
+            return self;
+        }
+
+        let m1 = utils::inv(self.inv_mass);
+        let m2 = utils::inv(other.inv_mass);
+        let inv_mass = utils::inv(m1 - m2);
+
+        let local_com = (self.local_com * m1 - other.local_com.coords * m2) * inv_mass;
+        let i1 = self.construct_shifted_inertia_matrix(local_com - self.local_com);
+        let i2 = other.construct_shifted_inertia_matrix(local_com - other.local_com);
+        let inertia = i1 - i2;
+        // NOTE: we drop the negative eigenvalues that may result from subtraction rounding errors.
+        let inv_principal_inertia_sqrt = utils::inv(inertia.max(0.0).sqrt());
+
+        Self {
+            local_com,
+            inv_mass,
+            inv_principal_inertia_sqrt,
+        }
+    }
+
+    #[cfg(feature = "dim3")]
+    fn sub(self, other: MassProperties) -> Self {
+        if self.is_zero() || other.is_zero() {
+            return self;
+        }
+
+        let m1 = utils::inv(self.inv_mass);
+        let m2 = utils::inv(other.inv_mass);
+        let inv_mass = utils::inv(m1 - m2);
+        let local_com = (self.local_com * m1 - other.local_com.coords * m2) * inv_mass;
+        let i1 = self.construct_shifted_inertia_matrix(local_com - self.local_com);
+        let i2 = other.construct_shifted_inertia_matrix(local_com - other.local_com);
+        let inertia = i1 - i2;
+        let eigen = inertia.symmetric_eigen();
+        let principal_inertia_local_frame =
+            Rotation::from_matrix_eps(&eigen.eigenvectors, 1.0e-6, 10, na::one());
+        let principal_inertia = eigen.eigenvalues;
+        // NOTE: we drop the negative eigenvalues that may result from subtraction rounding errors.
+        let inv_principal_inertia_sqrt = principal_inertia.map(|e| utils::inv(e.max(0.0).sqrt()));
+
+        Self {
+            local_com,
+            inv_mass,
+            inv_principal_inertia_sqrt,
+            principal_inertia_local_frame,
+        }
+    }
+}
+
+impl SubAssign<MassProperties> for MassProperties {
+    fn sub_assign(&mut self, rhs: MassProperties) {
+        *self = *self - rhs
+    }
+}
+
 impl Add<MassProperties> for MassProperties {
     type Output = Self;
 
@@ -186,7 +273,8 @@ impl Add<MassProperties> for MassProperties {
         let i2 = other.construct_shifted_inertia_matrix(local_com - other.local_com);
         let inertia = i1 + i2;
         let eigen = inertia.symmetric_eigen();
-        let principal_inertia_local_frame = Rotation::from_matrix(&eigen.eigenvectors);
+        let principal_inertia_local_frame =
+            Rotation::from_matrix_eps(&eigen.eigenvectors, 1.0e-6, 10, na::one());
         let principal_inertia = eigen.eigenvalues;
         let inv_principal_inertia_sqrt = principal_inertia.map(|e| utils::inv(e.sqrt()));
 
@@ -204,3 +292,101 @@ impl AddAssign<MassProperties> for MassProperties {
         *self = *self + rhs
     }
 }
+
+impl approx::AbsDiffEq for MassProperties {
+    type Epsilon = f32;
+    fn default_epsilon() -> Self::Epsilon {
+        f32::default_epsilon()
+    }
+
+    fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool {
+        #[cfg(feature = "dim2")]
+        let inertia_is_ok = self
+            .inv_principal_inertia_sqrt
+            .abs_diff_eq(&other.inv_principal_inertia_sqrt, epsilon);
+
+        #[cfg(feature = "dim3")]
+        let inertia_is_ok = self
+            .reconstruct_inverse_inertia_matrix()
+            .abs_diff_eq(&other.reconstruct_inverse_inertia_matrix(), epsilon);
+
+        inertia_is_ok
+            && self.local_com.abs_diff_eq(&other.local_com, epsilon)
+            && self.inv_mass.abs_diff_eq(&other.inv_mass, epsilon)
+            && self
+                .inv_principal_inertia_sqrt
+                .abs_diff_eq(&other.inv_principal_inertia_sqrt, epsilon)
+    }
+}
+
+impl approx::RelativeEq for MassProperties {
+    fn default_max_relative() -> Self::Epsilon {
+        f32::default_max_relative()
+    }
+
+    fn relative_eq(
+        &self,
+        other: &Self,
+        epsilon: Self::Epsilon,
+        max_relative: Self::Epsilon,
+    ) -> bool {
+        #[cfg(feature = "dim2")]
+        let inertia_is_ok = self.inv_principal_inertia_sqrt.relative_eq(
+            &other.inv_principal_inertia_sqrt,
+            epsilon,
+            max_relative,
+        );
+
+        #[cfg(feature = "dim3")]
+        let inertia_is_ok = self.reconstruct_inverse_inertia_matrix().relative_eq(
+            &other.reconstruct_inverse_inertia_matrix(),
+            epsilon,
+            max_relative,
+        );
+
+        inertia_is_ok
+            && self
+                .local_com
+                .relative_eq(&other.local_com, epsilon, max_relative)
+            && self
+                .inv_mass
+                .relative_eq(&other.inv_mass, epsilon, max_relative)
+    }
+}
+
+#[cfg(test)]
+mod test {
+    use super::MassProperties;
+    use crate::geometry::ColliderBuilder;
+    use approx::assert_relative_eq;
+    use num::Zero;
+
+    #[test]
+    fn mass_properties_add_sub() {
+        // Check that addition and subtraction of mass properties behave as expected.
+        let c1 = ColliderBuilder::capsule_x(1.0, 2.0).build();
+        let c2 = ColliderBuilder::capsule_y(3.0, 4.0).build();
+        let c3 = ColliderBuilder::ball(5.0).build();
+
+        let m1 = c1.mass_properties();
+        let m2 = c2.mass_properties();
+        let m3 = c3.mass_properties();
+        let m1m2m3 = m1 + m2 + m3;
+
+        assert_relative_eq!(m1 + m2, m2 + m1, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - m1, m2 + m3, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - m2, m1 + m3, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - m3, m1 + m2, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - (m1 + m2), m3, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - (m1 + m3), m2, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - (m2 + m3), m1, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - m1 - m2, m3, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - m1 - m3, m2, epsilon = 1.0e-6);
+        assert_relative_eq!(m1m2m3 - m2 - m3, m1, epsilon = 1.0e-6);
+        assert_relative_eq!(
+            m1m2m3 - m1 - m2 - m3,
+            MassProperties::zero(),
+            epsilon = 1.0e-6
+        );
+    }
+}
diff --git a/src/dynamics/rigid_body.rs b/src/dynamics/rigid_body.rs
index 584dc96..a2fcacc 100644
--- a/src/dynamics/rigid_body.rs
+++ b/src/dynamics/rigid_body.rs
@@ -1,5 +1,5 @@
 use crate::dynamics::MassProperties;
-use crate::geometry::{ColliderHandle, InteractionGraph, RigidBodyGraphIndex};
+use crate::geometry::{Collider, ColliderHandle, InteractionGraph, RigidBodyGraphIndex};
 use crate::math::{AngVector, AngularInertia, Isometry, Point, Rotation, Translation, Vector};
 use crate::utils::{WCross, WDot};
 use num::Zero;
@@ -137,6 +137,28 @@ impl RigidBody {
         crate::utils::inv(self.mass_properties.inv_mass)
     }
 
+    /// Adds a collider to this rigid-body.
+    pub(crate) fn add_collider_internal(&mut self, handle: ColliderHandle, coll: &Collider) {
+        let mass_properties = coll
+            .mass_properties()
+            .transform_by(coll.position_wrt_parent());
+        self.colliders.push(handle);
+        self.mass_properties += mass_properties;
+        self.update_world_mass_properties();
+    }
+
+    /// Removes a collider from this rigid-body.
+    pub(crate) fn remove_collider_internal(&mut self, handle: ColliderHandle, coll: &Collider) {
+        if let Some(i) = self.colliders.iter().position(|e| *e == handle) {
+            self.colliders.swap_remove(i);
+            let mass_properties = coll
+                .mass_properties()
+                .transform_by(coll.position_wrt_parent());
+            self.mass_properties -= mass_properties;
+            self.update_world_mass_properties();
+        }
+    }
+
     /// Put this rigid body to sleep.
     ///
     /// A sleeping body no longer moves and is no longer simulated by the physics engine unless
@@ -171,7 +193,7 @@ impl RigidBody {
     }
 
     fn integrate_velocity(&self, dt: f32) -> Isometry<f32> {
-        let com = &self.position * self.mass_properties.local_com; // FIXME: use non-origin center of masses.
+        let com = &self.position * self.mass_properties.local_com;
         let shift = Translation::from(com.coords);
         shift * Isometry::new(self.linvel * dt, self.angvel * dt) * shift.inverse()
     }
diff --git a/src/dynamics/solver/position_constraint.rs b/src/dynamics/solver/position_constraint.rs
index 608a342..69fcf57 100644
--- a/src/dynamics/solver/position_constraint.rs
+++ b/src/dynamics/solver/position_constraint.rs
@@ -104,8 +104,8 @@ impl PositionConstraint {
             let mut local_p2 = [Point::origin(); MAX_MANIFOLD_POINTS];
 
             for l in 0..manifold_points.len() {
-                local_p1[l] = manifold_points[l].local_p1 + shift1;
-                local_p2[l] = manifold_points[l].local_p2 + shift2;
+                local_p1[l] = manifold.delta1 * (manifold_points[l].local_p1 + shift1);
+                local_p2[l] = manifold.delta2 * (manifold_points[l].local_p2 + shift2);
             }
 
             let constraint = PositionConstraint {
diff --git a/src/dynamics/solver/position_constraint_wide.rs b/src/dynamics/solver/position_constraint_wide.rs
index 8828c3d..0633926 100644
--- a/src/dynamics/solver/position_constraint_wide.rs
+++ b/src/dynamics/solver/position_constraint_wide.rs
@@ -51,6 +51,9 @@ impl WPositionConstraint {
         let radius1 = SimdFloat::from(array![|ii| manifolds[ii].kinematics.radius1; SIMD_WIDTH]);
         let radius2 = SimdFloat::from(array![|ii| manifolds[ii].kinematics.radius2; SIMD_WIDTH]);
 
+        let delta1 = Isometry::from(array![|ii| manifolds[ii].delta1; SIMD_WIDTH]);
+        let delta2 = Isometry::from(array![|ii| manifolds[ii].delta2; SIMD_WIDTH]);
+
         let rb1 = array![|ii| rbs1[ii].active_set_offset; SIMD_WIDTH];
         let rb2 = array![|ii| rbs2[ii].active_set_offset; SIMD_WIDTH];
 
@@ -85,8 +88,8 @@ impl WPositionConstraint {
                 let local_p2 =
                     Point::from(array![|ii| manifold_points[ii][i].local_p2; SIMD_WIDTH]);
 
-                constraint.local_p1[i] = local_p1 + shift1;
-                constraint.local_p2[i] = local_p2 + shift2;
+                constraint.local_p1[i] = delta1 * (local_p1 + shift1);
+                constraint.local_p2[i] = delta2 * (local_p2 + shift2);
             }
 
             if push {
diff --git a/src/dynamics/solver/position_ground_constraint.rs b/src/dynamics/solver/position_ground_constraint.rs
index e6e83c6..dcd2d64 100644
--- a/src/dynamics/solver/position_ground_constraint.rs
+++ b/src/dynamics/solver/position_ground_constraint.rs
@@ -34,22 +34,30 @@ impl PositionGroundConstraint {
 
         let local_n1;
         let local_n2;
+        let delta1;
+        let delta2;
 
         if flip {
             std::mem::swap(&mut rb1, &mut rb2);
             local_n1 = manifold.local_n2;
             local_n2 = manifold.local_n1;
+            delta1 = &manifold.delta2;
+            delta2 = &manifold.delta1;
         } else {
             local_n1 = manifold.local_n1;
             local_n2 = manifold.local_n2;
+            delta1 = &manifold.delta1;
+            delta2 = &manifold.delta2;
         };
 
+        let coll_pos1 = rb1.position * delta1;
         let shift1 = local_n1 * -manifold.kinematics.radius1;
         let shift2 = local_n2 * -manifold.kinematics.radius2;
+        let n1 = coll_pos1 * local_n1;
         let radius =
             manifold.kinematics.radius1 + manifold.kinematics.radius2 /* - params.allowed_linear_error */;
 
-        for (l, manifold_points) in manifold
+        for (l, manifold_contacts) in manifold
             .active_contacts()
             .chunks(MAX_MANIFOLD_POINTS)
             .enumerate()
@@ -59,16 +67,16 @@ impl PositionGroundConstraint {
 
             if flip {
                 // Don't forget that we already swapped rb1 and rb2 above.
-                // So if we flip, only manifold_points[k].{local_p1,local_p2} have to
+                // So if we flip, only manifold_contacts[k].{local_p1,local_p2} have to
                 // be swapped.
-                for k in 0..manifold_points.len() {
-                    p1[k] = rb1.predicted_position * (manifold_points[k].local_p2 + shift1);
-                    local_p2[k] = manifold_points[k].local_p1 + shift2;
+                for k in 0..manifold_contacts.len() {
+                    p1[k] = coll_pos1 * (manifold_contacts[k].local_p2 + shift1);
+                    local_p2[k] = delta2 * (manifold_contacts[k].local_p1 + shift2);
                 }
             } else {
-                for k in 0..manifold_points.len() {
-                    p1[k] = rb1.predicted_position * (manifold_points[k].local_p1 + shift1);
-                    local_p2[k] = manifold_points[k].local_p2 + shift2;
+                for k in 0..manifold_contacts.len() {
+                    p1[k] = coll_pos1 * (manifold_contacts[k].local_p1 + shift1);
+                    local_p2[k] = delta2 * (manifold_contacts[k].local_p2 + shift2);
                 }
             }
 
@@ -76,11 +84,11 @@ impl PositionGroundConstraint {
                 rb2: rb2.active_set_offset,
                 p1,
                 local_p2,
-                n1: rb1.predicted_position * local_n1,
+                n1,
                 radius,
                 im2: rb2.mass_properties.inv_mass,
                 ii2: rb2.world_inv_inertia_sqrt.squared(),
-                num_contacts: manifold_points.len() as u8,
+                num_contacts: manifold_contacts.len() as u8,
                 erp: params.erp,
                 max_linear_correction: params.max_linear_correction,
             };
diff --git a/src/dynamics/solver/position_ground_constraint_wide.rs b/src/dynamics/solver/position_ground_constraint_wide.rs
index faa928b..e423c0a 100644
--- a/src/dynamics/solver/position_ground_constraint_wide.rs
+++ b/src/dynamics/solver/position_ground_constraint_wide.rs
@@ -54,16 +54,24 @@ impl WPositionGroundConstraint {
             array![|ii| if flipped[ii] { manifolds[ii].local_n1 } else { manifolds[ii].local_n2 }; SIMD_WIDTH],
         );
 
+        let delta1 = Isometry::from(
+            array![|ii| if flipped[ii] { manifolds[ii].delta2 } else { manifolds[ii].delta1 }; SIMD_WIDTH],
+        );
+        let delta2 = Isometry::from(
+            array![|ii| if flipped[ii] { manifolds[ii].delta1 } else { manifolds[ii].delta2 }; SIMD_WIDTH],
+        );
+
         let radius1 = SimdFloat::from(array![|ii| manifolds[ii].kinematics.radius1; SIMD_WIDTH]);
         let radius2 = SimdFloat::from(array![|ii| manifolds[ii].kinematics.radius2; SIMD_WIDTH]);
 
-        let position1 = Isometry::from(array![|ii| rbs1[ii].predicted_position; SIMD_WIDTH]);
+        let coll_pos1 =
+            delta1 * Isometry::from(array![|ii| rbs1[ii].predicted_position; SIMD_WIDTH]);
 
         let rb2 = array![|ii| rbs2[ii].active_set_offset; SIMD_WIDTH];
 
         let radius = radius1 + radius2 /*- SimdFloat::splat(params.allowed_linear_error)*/;
 
-        let n1 = position1 * local_n1;
+        let n1 = coll_pos1 * local_n1;
 
         for l in (0..manifolds[0].num_active_contacts()).step_by(MAX_MANIFOLD_POINTS) {
             let manifold_points = array![|ii| &manifolds[ii].active_contacts()[l..]; SIMD_WIDTH];
@@ -90,8 +98,8 @@ impl WPositionGroundConstraint {
                     array![|ii| if flipped[ii] { manifold_points[ii][i].local_p1 } else { manifold_points[ii][i].local_p2 }; SIMD_WIDTH],
                 );
 
-                constraint.p1[i] = position1 * local_p1 - n1 * radius1;
-                constraint.local_p2[i] = local_p2 - local_n2 * radius2;
+                constraint.p1[i] = coll_pos1 * local_p1 - n1 * radius1;
+                constraint.local_p2[i] = delta2 * (local_p2 - local_n2 * radius2);
             }
 
             if push {
diff --git a/src/dynamics/solver/velocity_constraint.rs b/src/dynamics/solver/velocity_constraint.rs
index 9212e89..190076d 100644
--- a/src/dynamics/solver/velocity_constraint.rs
+++ b/src/dynamics/solver/velocity_constraint.rs
@@ -148,7 +148,9 @@ impl VelocityConstraint {
         let rb2 = &bodies[manifold.body_pair.body2];
         let mj_lambda1 = rb1.active_set_offset;
         let mj_lambda2 = rb2.active_set_offset;
-        let force_dir1 = rb1.position * (-manifold.local_n1);
+        let pos_coll1 = rb1.position * manifold.delta1;
+        let pos_coll2 = rb2.position * manifold.delta2;
+        let force_dir1 = pos_coll1 * (-manifold.local_n1);
         let warmstart_coeff = manifold.warmstart_multiplier * params.warmstart_coeff;
 
         for (l, manifold_points) in manifold
@@ -215,10 +217,8 @@ impl VelocityConstraint {
 
             for k in 0..manifold_points.len() {
                 let manifold_point = &manifold_points[k];
-                let dp1 = (rb1.position * manifold_point.local_p1).coords
-                    - rb1.position.translation.vector;
-                let dp2 = (rb2.position * manifold_point.local_p2).coords
-                    - rb2.position.translation.vector;
+                let dp1 = (pos_coll1 * manifold_point.local_p1) - rb1.world_com;
+                let dp2 = (pos_coll2 * manifold_point.local_p2) - rb2.world_com;
 
                 let vel1 = rb1.linvel + rb1.angvel.gcross(dp1);
                 let vel2 = rb2.linvel + rb2.angvel.gcross(dp2);
@@ -355,7 +355,7 @@ impl VelocityConstraint {
             }
         }
 
-        // Solve penetration.
+        // 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)
diff --git a/src/dynamics/solver/velocity_constraint_wide.rs b/src/dynamics/solver/velocity_constraint_wide.rs
index 8f387a5..f515d5e 100644
--- a/src/dynamics/solver/velocity_constraint_wide.rs
+++ b/src/dynamics/solver/velocity_constraint_wide.rs
@@ -72,6 +72,9 @@ impl WVelocityConstraint {
         let rbs1 = array![|ii| &bodies[manifolds[ii].body_pair.body1]; SIMD_WIDTH];
         let rbs2 = array![|ii| &bodies[manifolds[ii].body_pair.body2]; SIMD_WIDTH];
 
+        let delta1 = Isometry::from(array![|ii| manifolds[ii].delta1; SIMD_WIDTH]);
+        let delta2 = Isometry::from(array![|ii| manifolds[ii].delta2; SIMD_WIDTH]);
+
         let im1 = SimdFloat::from(array![|ii| rbs1[ii].mass_properties.inv_mass; SIMD_WIDTH]);
         let ii1: AngularInertia<SimdFloat> =
             AngularInertia::from(array![|ii| rbs1[ii].world_inv_inertia_sqrt; SIMD_WIDTH]);
@@ -79,7 +82,8 @@ impl WVelocityConstraint {
         let linvel1 = Vector::from(array![|ii| rbs1[ii].linvel; SIMD_WIDTH]);
         let angvel1 = AngVector::<SimdFloat>::from(array![|ii| rbs1[ii].angvel; SIMD_WIDTH]);
 
-        let position1 = Isometry::from(array![|ii| rbs1[ii].position; SIMD_WIDTH]);
+        let pos1 = Isometry::from(array![|ii| rbs1[ii].position; SIMD_WIDTH]);
+        let world_com1 = Point::from(array![|ii| rbs1[ii].world_com; SIMD_WIDTH]);
 
         let im2 = SimdFloat::from(array![|ii| rbs2[ii].mass_properties.inv_mass; SIMD_WIDTH]);
         let ii2: AngularInertia<SimdFloat> =
@@ -88,9 +92,13 @@ impl WVelocityConstraint {
         let linvel2 = Vector::from(array![|ii| rbs2[ii].linvel; SIMD_WIDTH]);
         let angvel2 = AngVector::<SimdFloat>::from(array![|ii| rbs2[ii].angvel; SIMD_WIDTH]);
 
-        let position2 = Isometry::from(array![|ii| rbs2[ii].position; SIMD_WIDTH]);
+        let pos2 = Isometry::from(array![|ii| rbs2[ii].position; SIMD_WIDTH]);
+        let world_com2 = Point::from(array![|ii| rbs2[ii].world_com; SIMD_WIDTH]);
+
+        let coll_pos1 = pos1 * delta1;
+        let coll_pos2 = pos2 * delta2;
 
-        let force_dir1 = position1 * -Vector::from(array![|ii| manifolds[ii].local_n1; SIMD_WIDTH]);
+        let force_dir1 = coll_pos1 * -Vector::from(array![|ii| manifolds[ii].local_n1; SIMD_WIDTH]);
 
         let mj_lambda1 = array![|ii| rbs1[ii].active_set_offset; SIMD_WIDTH];
         let mj_lambda2 = array![|ii| rbs2[ii].active_set_offset; SIMD_WIDTH];
@@ -118,11 +126,11 @@ impl WVelocityConstraint {
             };
 
             for k in 0..num_points {
-                // FIXME: can we avoid the multiplications by position1/position2 here?
+                // FIXME: can we avoid the multiplications by coll_pos1/coll_pos2 here?
                 // By working as much as possible in local-space.
-                let p1 = position1
+                let p1 = coll_pos1
                     * Point::from(array![|ii| manifold_points[ii][k].local_p1; SIMD_WIDTH]);
-                let p2 = position2
+                let p2 = coll_pos2
                     * Point::from(array![|ii| manifold_points[ii][k].local_p2; SIMD_WIDTH]);
 
                 let dist = SimdFloat::from(array![|ii| manifold_points[ii][k].dist; SIMD_WIDTH]);
@@ -130,8 +138,8 @@ impl WVelocityConstraint {
                 let impulse =
                     SimdFloat::from(array![|ii| manifold_points[ii][k].impulse; SIMD_WIDTH]);
 
-                let dp1 = p1.coords - position1.translation.vector;
-                let dp2 = p2.coords - position2.translation.vector;
+                let dp1 = p1 - world_com1;
+                let dp2 = p2 - world_com2;
 
                 let vel1 = linvel1 + angvel1.gcross(dp1);
                 let vel2 = linvel2 + angvel2.gcross(dp2);
diff --git a/src/dynamics/solver/velocity_ground_constraint.rs b/src/dynamics/solver/velocity_ground_constraint.rs
index 457c3b3..d9229ff 100644
--- a/src/dynamics/solver/velocity_ground_constraint.rs
+++ b/src/dynamics/solver/velocity_ground_constraint.rs
@@ -66,20 +66,22 @@ impl VelocityGroundConstraint {
         let mut rb1 = &bodies[manifold.body_pair.body1];
         let mut rb2 = &bodies[manifold.body_pair.body2];
         let flipped = !rb2.is_dynamic();
+        let force_dir1;
+        let coll_pos1;
+        let coll_pos2;
 
         if flipped {
+            coll_pos1 = rb2.position * manifold.delta2;
+            coll_pos2 = rb1.position * manifold.delta1;
+            force_dir1 = coll_pos1 * (-manifold.local_n2);
             std::mem::swap(&mut rb1, &mut rb2);
+        } else {
+            coll_pos1 = rb1.position * manifold.delta1;
+            coll_pos2 = rb2.position * manifold.delta2;
+            force_dir1 = coll_pos1 * (-manifold.local_n1);
         }
 
         let mj_lambda2 = rb2.active_set_offset;
-        let force_dir1 = if flipped {
-            // NOTE: we already swapped rb1 and rb2
-            // so we multiply by rb1.position.
-            rb1.position * (-manifold.local_n2)
-        } else {
-            rb1.position * (-manifold.local_n1)
-        };
-
         let warmstart_coeff = manifold.warmstart_multiplier * params.warmstart_coeff;
 
         for (l, manifold_points) in manifold
@@ -144,19 +146,19 @@ impl VelocityGroundConstraint {
                 let manifold_point = &manifold_points[k];
                 let (p1, p2) = if flipped {
                     // NOTE: we already swapped rb1 and rb2
-                    // so we multiply by rb2.position.
+                    // so we multiply by coll_pos1/coll_pos2.
                     (
-                        rb1.position * manifold_point.local_p2,
-                        rb2.position * manifold_point.local_p1,
+                        coll_pos1 * manifold_point.local_p2,
+                        coll_pos2 * manifold_point.local_p1,
                     )
                 } else {
                     (
-                        rb1.position * manifold_point.local_p1,
-                        rb2.position * manifold_point.local_p2,
+                        coll_pos1 * manifold_point.local_p1,
+                        coll_pos2 * manifold_point.local_p2,
                     )
                 };
-                let dp2 = p2.coords - rb2.position.translation.vector;
-                let dp1 = p1.coords - rb1.position.translation.vector;
+                let dp2 = p2 - rb2.world_com;
+                let dp1 = p1 - rb1.world_com;
                 let vel1 = rb1.linvel + rb1.angvel.gcross(dp1);
                 let vel2 = rb2.linvel + rb2.angvel.gcross(dp2);
 
diff --git a/src/dynamics/solver/velocity_ground_constraint_wide.rs b/src/dynamics/solver/velocity_ground_constraint_wide.rs
index ec9e186..18e9257 100644
--- a/src/dynamics/solver/velocity_ground_constraint_wide.rs
+++ b/src/dynamics/solver/velocity_ground_constraint_wide.rs
@@ -86,10 +86,23 @@ impl WVelocityGroundConstraint {
         let linvel2 = Vector::from(array![|ii| rbs2[ii].linvel; SIMD_WIDTH]);
         let angvel2 = AngVector::<SimdFloat>::from(array![|ii| rbs2[ii].angvel; SIMD_WIDTH]);
 
-        let position1 = Isometry::from(array![|ii| rbs1[ii].position; SIMD_WIDTH]);
-        let position2 = Isometry::from(array![|ii| rbs2[ii].position; SIMD_WIDTH]);
+        let pos1 = Isometry::from(array![|ii| rbs1[ii].position; SIMD_WIDTH]);
+        let pos2 = Isometry::from(array![|ii| rbs2[ii].position; SIMD_WIDTH]);
 
-        let force_dir1 = position1
+        let delta1 = Isometry::from(
+            array![|ii| if flipped[ii] { manifolds[ii].delta2 } else { manifolds[ii].delta1 }; SIMD_WIDTH],
+        );
+        let delta2 = Isometry::from(
+            array![|ii| if flipped[ii] { manifolds[ii].delta1 } else { manifolds[ii].delta2 }; SIMD_WIDTH],
+        );
+
+        let coll_pos1 = pos1 * delta1;
+        let coll_pos2 = pos2 * delta2;
+
+        let world_com1 = Point::from(array![|ii| rbs1[ii].world_com; SIMD_WIDTH]);
+        let world_com2 = Point::from(array![|ii| rbs2[ii].world_com; SIMD_WIDTH]);
+
+        let force_dir1 = coll_pos1
             * -Vector::from(
                 array![|ii| if flipped[ii] { manifolds[ii].local_n2 } else { manifolds[ii].local_n1 }; SIMD_WIDTH],
             );
@@ -117,11 +130,11 @@ impl WVelocityGroundConstraint {
             };
 
             for k in 0..num_points {
-                let p1 = position1
+                let p1 = coll_pos1
                     * Point::from(
                         array![|ii| if flipped[ii] { manifold_points[ii][k].local_p2 } else { manifold_points[ii][k].local_p1 }; SIMD_WIDTH],
                     );
-                let p2 = position2
+                let p2 = coll_pos2
                     * Point::from(
                         array![|ii| if flipped[ii] { manifold_points[ii][k].local_p1 } else { manifold_points[ii][k].local_p2 }; SIMD_WIDTH],
                     );
@@ -130,8 +143,8 @@ impl WVelocityGroundConstraint {
 
                 let impulse =
                     SimdFloat::from(array![|ii| manifold_points[ii][k].impulse; SIMD_WIDTH]);
-                let dp1 = p1.coords - position1.translation.vector;
-                let dp2 = p2.coords - position2.translation.vector;
+                let dp1 = p1 - world_com1;
+                let dp2 = p2 - world_com2;
 
                 let vel1 = linvel1 + angvel1.gcross(dp1);
                 let vel2 = linvel2 + angvel2.gcross(dp2);
diff --git a/src/geometry/broad_phase_multi_sap.rs b/src/geometry/broad_phase_multi_sap.rs
index 0505e21..054fccf 100644
--- a/src/geometry/broad_phase_multi_sap.rs
+++ b/src/geometry/broad_phase_multi_sap.rs
@@ -662,7 +662,7 @@ mod test {
         let rb = RigidBodyBuilder::new_dynamic().build();
         let co = ColliderBuilder::ball(0.5).build();
         let hrb = bodies.insert(rb);
-        let hco = colliders.insert(co, hrb, &mut bodies);
+        colliders.insert(co, hrb, &mut bodies);
 
         broad_phase.update_aabbs(0.0, &bodies, &mut colliders);
 
@@ -681,7 +681,7 @@ mod test {
         let rb = RigidBodyBuilder::new_dynamic().build();
         let co = ColliderBuilder::ball(0.5).build();
         let hrb = bodies.insert(rb);
-        let hco = colliders.insert(co, hrb, &mut bodies);
+        colliders.insert(co, hrb, &mut bodies);
 
         // Make sure the proxy handles is recycled properly.
         broad_phase.update_aabbs(0.0, &bodies, &mut colliders);
diff --git a/src/geometry/collider.rs b/src/geometry/collider.rs
index 2457212..aed76c8 100644
--- a/src/geometry/collider.rs
+++ b/src/geometry/collider.rs
@@ -3,7 +3,7 @@ use crate::geometry::{
     Ball, Capsule, ColliderGraphIndex, Contact, Cuboid, HeightField, InteractionGraph, Polygon,
     Proximity, Triangle, Trimesh,
 };
-use crate::math::{Isometry, Point, Vector};
+use crate::math::{AngVector, Isometry, Point, Rotation, Vector};
 use na::Point3;
 use ncollide::bounding_volume::{HasBoundingVolume, AABB};
 use num::Zero;
@@ -150,6 +150,7 @@ impl Collider {