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use std::f32;
use std::ops::{AddAssign, SubAssign};
use cgmath::{EuclideanSpace, InnerSpace, SquareMatrix, Rotation,
Matrix, Matrix3, Point3, Quaternion, Vector3, One, Zero};
use bounds::*;
use compound::*;
use collision::*;
use geom::*;
use manifold::*;
pub trait Inertia {
fn tensor(&self, m: f32) -> Matrix3<f32>;
}
impl Inertia for Sphere {
fn tensor(&self, m: f32) -> Matrix3<f32> {
let i = 0.4 * m * self.r * self.r;
Matrix3::new(i, 0.0, 0.0, 0.0, i, 0.0, 0.0, 0.0, i)
}
}
impl Inertia for Capsule {
fn tensor(&self, m: f32) -> Matrix3<f32> {
let h = self.d.magnitude();
let r = self.r;
let mh = m * 2.0 * r / (4.0 * r + 3.0 * h);
let mc = m * h / (4.0 / 3.0 * r + h);
let ic_x = 1.0 / 12.0 * mc * (3.0 * r * r + h * h);
let ic_y = 0.5 * mc * r * r;
let ic_z = ic_x;
let is_x = mh * (3.0 * r + 2.0 * h) / 4.0 * h;
let is_y = 4.0 / 5.0 * mh * r * r;
let is_z = is_x;
let (i_x, i_y, i_z) = (ic_x + is_x, ic_y + is_y, ic_z + is_z);
let dst = self.d;
let src = Vector3::new(0.0, 1.0, 0.0) * h;
let rot = Matrix3::<f32>::from(Quaternion::from_arc(src, dst, None));
rot * Matrix3::new(i_x, 0.0, 0.0, 0.0, i_y, 0.0, 0.0, 0.0, i_z) * rot.transpose()
}
}
impl Inertia for Component {
fn tensor(&self, m: f32) -> Matrix3<f32> {
match self {
&Component::Sphere(s) => s.tensor(m),
&Component::Capsule(c) => c.tensor(m),
}
}
}
#[derive(Clone)]
pub struct RigidBody {
pub restitution: f32,
pub friction: f32,
pub total_inv_mass: f32,
pub inv_moment_body: Matrix3<f32>,
pub inv_moment: Matrix3<f32>,
pub v: Vector3<f32>,
pub omega: Vector3<f32>,
pub v_step: Vector3<f32>,
pub linear_m: Vector3<f32>,
pub angular_m: Vector3<f32>,
pub force: Vector3<f32>,
pub torque: Vector3<f32>,
pub collider: Compound,
pub component_masses: Vec<f32>,
}
impl RigidBody {
pub fn new(
restitution: f32,
friction: f32,
world_force: Vector3<f32>,
mut shapes: Vec<Component>,
masses: Vec<f32>
) -> Self {
let mut total_mass = 0.0;
let mut center = Point3::new(0.0, 0.0, 0.0);
for (shape, mass) in shapes.iter().zip(masses.iter()) {
center += shape.center().to_vec() * *mass;
total_mass += *mass;
}
let inv_mass = 1.0 / total_mass;
center *= inv_mass;
for shape in shapes.iter_mut() {
*shape -= center.to_vec();
}
let tensor = shapes.iter().zip(masses.iter())
.fold(Matrix3::zero(), |tensor_sum, (shape, mass)| {
let disp = shape.center().to_vec();
let outer_prod = Matrix3::from_cols(
disp * disp.x,
disp * disp.y,
disp * disp.z
);
tensor_sum + shape.tensor(*mass)
+ *mass * (Matrix3::one() * disp.magnitude2() - outer_prod)
});
let inv_moment = tensor.invert().unwrap();
RigidBody {
restitution,
friction,
total_inv_mass: inv_mass,
inv_moment_body: inv_moment,
inv_moment,
v: Vector3::zero(),
omega: Vector3::zero(),
v_step: Vector3::zero(),
linear_m: Vector3::zero(),
angular_m: Vector3::zero(),
force: world_force / inv_mass,
torque: Vector3::zero(),
collider: Compound::new(shapes),
component_masses: masses,
}
}
}
impl AddAssign<Vector3<f32>> for RigidBody {
fn add_assign(&mut self, v: Vector3<f32>) {
self.collider.disp += v
}
}
impl SubAssign<Vector3<f32>> for RigidBody {
fn sub_assign(&mut self, v: Vector3<f32>) {
self.collider.disp -= v
}
}
impl Shape for RigidBody {
fn center(&self) -> Point3<f32> {
Point3::from_vec(self.collider.disp)
}
}
impl Delta for RigidBody {
fn delta(&self) -> Vector3<f32> {
self.v_step
}
}
impl BoundedBy<AABB> for RigidBody {
fn bounds(&self) -> AABB {
let b1 = self.collider.bounds();
let b2 = b1 + self.v_step;
Bound::combine(&b1, &b2)
}
}
impl BoundedBy<Sphere> for RigidBody {
fn bounds(&self) -> Sphere {
let b1 = self.collider.bounds();
let b2 = b1 + self.v_step;
Bound::combine(&b1, &b2)
}
}
impl<RHS> Contacts<RHS> for RigidBody
where
RHS: Contacts<Moving<Component>> + BoundedBy<AABB>
{
fn contacts<F: FnMut(Contact)>(&self, rhs: &RHS, mut callback: F) -> bool {
let conj_rot = self.collider.rot.conjugate();
let mut rhs_bounds = rhs.bounds().rotate(conj_rot);
let rhs_center = rhs_bounds.center();
let bounds_disp = conj_rot.rotate_point(rhs_center + -self.collider.disp) + self.collider.disp;
rhs_bounds.set_pos(bounds_disp);
let rhs_bounds: AABB = Moving::sweep(rhs_bounds, -self.v_step).bounds();
let mut collided = false;
self.collider.bvh.query(&rhs_bounds, |&comp_i| {
let shape = Moving::sweep(
self.collider.shapes[comp_i].rotate(self.collider.rot) + self.collider.disp,
self.v_step
);
rhs.contacts(&shape, |c| { collided = true; callback(-c) });
});
collided
}
}
pub struct StaticBody<'a, S: Shape + 'a> {
pub friction: f32,
pub shape: &'a S,
}
impl<'a, S: Shape + 'a> StaticBody<'a, S> {
pub fn new(friction: f32, shape: &'a S) -> Self {
StaticBody {
friction,
shape
}
}
}
impl<'a, S, B> BoundedBy<B> for StaticBody<'a, S>
where
B: Bound,
S: Shape + BoundedBy<B>
{
fn bounds(&self) -> B {
self.shape.bounds()
}
}
impl<'a, S, RHS> Intersects<RHS> for StaticBody<'a, S>
where
S: Intersects<RHS> + Shape
{
fn intersection(&self, rhs: &RHS) -> Option<Intersection> {
self.shape.intersection(rhs)
}
}
impl<'a, S, RHS> Contacts<RHS> for StaticBody<'a, S>
where
S: Contacts<RHS> + Shape
{
fn contacts<F: FnMut(Contact)>(&self, rhs: &RHS, callback: F) -> bool {
self.shape.contacts(rhs, callback)
}
}
impl<'a, S, Recv> LocalContacts<StaticBody<'a, S>> for Recv
where
S: Shape,
Recv: Contacts<S> + Shape + Delta
{
fn local_contacts<F: FnMut(LocalContact)>(&self, rhs: &StaticBody<'a, S>, mut callback: F) -> bool {
self.contacts(rhs.shape, |c| {
let a_c = self.center() + self.delta() * c.t;
let b_c = rhs.shape.center();
callback(LocalContact {
local_b: c.a + -a_c.to_vec(),
local_a: c.b + -b_c.to_vec(),
global: c
})
})
}
}
#[derive(Copy, Clone)]
pub struct PhysicsState {
pub restitution: f32,
pub friction: f32,
pub inv_mass: f32,
pub inv_moment: Matrix3<f32>,
pub x: Point3<f32>,
pub v: Vector3<f32>,
pub omega: Vector3<f32>,
}
pub trait PhysicsObject {
fn integrate(&mut self, dt: f32);
fn state(&self) -> PhysicsState;
fn apply_impulse(&mut self, linear: Vector3<f32>, angular: Vector3<f32>);
fn update_dx(&mut self);
}
impl PhysicsObject for RigidBody {
fn integrate(&mut self, dt: f32) {
self.collider += self.v_step;
self.collider.rot = (self.collider.rot
+ Quaternion::from_sv(0.0, self.omega)
* 0.5 * self.collider.rot).normalize();
let r = Matrix3::from(self.collider.rot);
self.inv_moment = r * self.inv_moment_body * r.transpose();
self.linear_m += self.force * dt;
self.angular_m += self.torque * dt;
self.update_dx();
self.v_step = self.v * dt;
}
fn state(&self) -> PhysicsState {
PhysicsState {
restitution: self.restitution,
friction: self.friction,
inv_mass: self.total_inv_mass,
inv_moment: self.inv_moment,
x: self.collider.center() + self.v_step,
v: self.v,
omega: self.omega,
}
}
fn apply_impulse(&mut self, linear: Vector3<f32>, angular: Vector3<f32>) {
self.linear_m += linear;
self.angular_m += angular;
}
fn update_dx(&mut self) {
self.v = self.linear_m * self.total_inv_mass;
self.omega = self.inv_moment * self.angular_m;
}
}
impl<'a, S: Shape + 'a> PhysicsObject for StaticBody<'a, S> {
#[inline(always)]
fn integrate(&mut self, _dt: f32) {
}
fn state(&self) -> PhysicsState {
PhysicsState {
restitution: 0.0,
friction: self.friction,
inv_mass: 0.0,
inv_moment: Matrix3::zero(),
x: self.shape.center(),
v: Vector3::zero(),
omega: Vector3::zero(),
}
}
#[inline(always)]
fn apply_impulse(&mut self, _linear: Vector3<f32>, _angular: Vector3<f32>) {
}
#[inline(always)]
fn update_dx(&mut self) {
}
}
pub trait PhysicsConfig {
const PENETRATION_SLOP: f32;
const BAUMGARTE: f32;
}
pub struct DefaultPhysConfig {}
impl PhysicsConfig for DefaultPhysConfig {
const PENETRATION_SLOP: f32 = 0.005;
const BAUMGARTE: f32 = 0.2;
}
impl PhysicsState {
pub fn resolve_contact<Config, ObjA, ObjB>(
obj_a: &mut ObjA,
obj_b: &mut ObjB,
contact: &LocalContact,
dt: f32
) where Config: PhysicsConfig,
ObjA: PhysicsObject,
ObjB: PhysicsObject
{
let (state_a, state_b) = (obj_a.state(), obj_b.state());
let (xa, va, oa) = (state_a.x, state_a.v, state_a.omega);
let (xb, vb, ob) = (state_b.x, state_b.v, state_b.omega);
let ca = contact.local_a.to_vec() + xa.to_vec();
let cb = contact.local_b.to_vec() + xb.to_vec();
let ra = ca - xa.to_vec();
let rb = cb - xb.to_vec();
let ra_cn = ra.cross(contact.global.n);
let rb_cn = rb.cross(contact.global.n);
let pen = (cb - ca).dot(contact.global.n);
let max_restitution = state_a.restitution.max(state_b.restitution);
let dv = vb + ob.cross(rb) - va - oa.cross(ra);
let rel_v = dv.dot(contact.global.n);
let bias = Config::BAUMGARTE / dt * if pen > 0.0 {
0.0
} else {
-pen + Config::PENETRATION_SLOP
} + if rel_v < -1.0 {
-max_restitution * rel_v
} else {
0.0
};
let normal_mass = 1.0 /
(state_a.inv_mass + ra_cn.dot(state_a.inv_moment * ra_cn)
+ state_b.inv_mass + rb_cn.dot(state_b.inv_moment * rb_cn));
let lambda = (normal_mass * (-rel_v + bias)).max(0.0);
let impulse = contact.global.n * lambda;
obj_a.apply_impulse(-impulse, -state_a.inv_moment * ra.cross(impulse));
obj_b.apply_impulse( impulse, state_b.inv_moment * rb.cross(impulse));
let normal_impulse = lambda / 5.0;
let mix_friction = (state_a.friction * state_b.friction).sqrt();
let tangents = contact.global.compute_basis();
let mut impulse = Vector3::zero();
for tangent in tangents.iter() {
let ra_ct = ra.cross(*tangent);
let rb_ct = rb.cross(*tangent);
let tangent_mass = 1.0 /
(state_a.inv_mass + ra_ct.dot(state_a.inv_moment * ra_ct)
+ state_b.inv_mass + rb_ct.dot(state_b.inv_moment * rb_ct));
let lambda = -dv.dot(*tangent) * tangent_mass;
let max_lambda = mix_friction * normal_impulse;
let clamped = lambda.max(-max_lambda).min(max_lambda);
impulse += clamped * tangent;
}
obj_a.apply_impulse(-impulse, -state_a.inv_moment * ra.cross(impulse));
obj_b.apply_impulse( impulse, state_b.inv_moment * rb.cross(impulse));
}
pub fn resolve_manifold<Config, ObjA, ObjB>(
obj_a: &mut ObjA,
obj_b: &mut ObjB,
manifold: &Manifold,
dt: f32
) where Config: PhysicsConfig,
ObjA: PhysicsObject,
ObjB: PhysicsObject
{
for contact in &manifold.contacts {
PhysicsState::resolve_contact::<Config, ObjA, ObjB>(obj_a, obj_b, contact, dt);
}
obj_a.update_dx();
obj_b.update_dx();
}
}
#[cfg(test)]
mod tests {
mod physics {
use cgmath::{Vector3, Point3, One, Zero};
use geom::*;
use physics::*;
#[test]
fn test_rigid_body() {
let body_sample = RigidBody::new(1.0, 0.0, Vector3::zero(),
vec![ Component::from(Sphere{ c: Point3::new(-5.0, 0.0, 0.0),
r: 1.0 }),
Component::from(Sphere{ c: Point3::new(5.0, 0.0, 0.0),
r: 1.0 }) ],
vec![ 1.0, 1.0 ]);
let mut body1 = body_sample.clone();
let mut body2 = body1.clone();
body1.set_pos(Point3::new(-10.0, 0.0, 0.0));
body1.apply_impulse(Vector3::new(5.0, 0.0, 0.0) * 2.0, Vector3::zero());
body1.integrate(1.0);
body2.set_pos(Point3::new(10.0, 0.0, 0.0));
body2.apply_impulse(Vector3::new(-5.0, 0.0, 0.0) * 2.0, Vector3::zero());
body2.integrate(1.0);
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c| {
manifold.push(c);
}));
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(-5.2005005, 0.0, 0.0));
assert_eq!(body2.v, Vector3::new(5.2005005, 0.0, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
assert_eq!(body2.collider.rot, Quaternion::one());
let mut body1 = body_sample.clone();
let mut body2 = body_sample.clone();
body1.set_pos(Point3::new(-10.0, 0.0, 0.0));
body1.apply_impulse(Vector3::new(4.0, 0.0, 0.0) * 2.0, Vector3::zero());
body1.integrate(1.0);
body2.set_pos(Point3::new(10.0, 0.0, 0.0));
body2.apply_impulse(Vector3::new(-4.0, 0.0, 0.0) * 2.0, Vector3::zero());
body2.integrate(1.0);
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c| {
manifold.push(c);
}));
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(-4.0004997, 0.0, 0.0));
assert_eq!(body2.v, Vector3::new(4.0004997, 0.0, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
assert_eq!(body2.collider.rot, Quaternion::one());
let mut body1 = body_sample.clone();
let mut body2 = body_sample.clone();
body1 += Vector3::new(0.0, 5.0, 0.0);
body1.apply_impulse(Vector3::new(0.0, -4.0, 0.0) * 2.0, Vector3::zero());
body1.integrate(1.0);
body2 -= Vector3::new(0.0, 5.0, 0.0);
body2.apply_impulse(Vector3::new(0.0, 4.0, 0.0) * 2.0, Vector3::zero());
body2.integrate(1.0);
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c| {
manifold.push(c);
}));
assert_eq!(manifold.contacts.len(), 2);
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(0.0, 4.0639954, 0.0));
assert_eq!(body2.v, Vector3::new(0.0, -4.0639954, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
assert_eq!(body2.collider.rot, Quaternion::one());
let capsule_sample = RigidBody::new(1.0, 0.0, Vector3::zero(),
vec![ Component::from(Capsule{ a: Point3::new(-5.0, 0.0, 0.0),
d: Vector3::new(10.0, 0.0, 0.0),
r: 1.0 }) ],
vec![ 2.0 ]);
let mut body1 = capsule_sample.clone();
let mut body2 = body_sample.clone();
body1 += Vector3::new(0.0, 5.0, 0.0);
body1.apply_impulse(Vector3::new(0.0, -4.0, 0.0) * 2.0, Vector3::zero());
body1.integrate(1.0);
body2 -= Vector3::new(0.0, 5.0, 0.0);
body2.apply_impulse(Vector3::new(0.0, 4.0, 0.0) * 2.0, Vector3::zero());
body2.integrate(1.0);
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c| {
manifold.push(c);
}));
assert_eq!(manifold.contacts.len(), 2);
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(0.0, 2.0769472, 0.0));
assert_eq!(body2.v, Vector3::new(0.0, -2.0769472, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
assert_eq!(body2.collider.rot, Quaternion::one());
let mut body1 = capsule_sample.clone();
let mut body2 = capsule_sample.clone();
body1 += Vector3::new(0.0, 5.0, 0.0);
body1.apply_impulse(Vector3::new(0.0, -4.0, 0.0) * 2.0, Vector3::zero());
body1.integrate(1.0);
body2 -= Vector3::new(0.0, 5.0, 0.0);
body2.apply_impulse(Vector3::new(0.0, 4.0, 0.0) * 2.0, Vector3::zero());
body2.integrate(1.0);
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c| {
manifold.push(c);
}));
assert_eq!(manifold.contacts.len(), 1);
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(0.0, 4.0004997, 0.0));
assert_eq!(body2.v, Vector3::new(0.0, -4.0004997, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
assert_eq!(body2.collider.rot, Quaternion::one());
let raft = RigidBody::new(
1.0,
0.0,
Vector3::zero(),
vec![
Component::from(Capsule{
a: Point3::new(0.0, 0.0, 0.0),
d: Vector3::new(2.0, 0.0, 0.0),
r: 1.0,
}),
Component::from(Capsule{
a: Point3::new(2.0, 0.0, 0.0),
d: Vector3::new(0.0, 0.0, 2.0),
r: 1.0,
}),
Component::from(Capsule{
a: Point3::new(2.0, 0.0, 2.0),
d: Vector3::new(-2.0, 0.0, 0.0),
r: 1.0,
}),
Component::from(Capsule{
a: Point3::new(0.0, 0.0, 2.0),
d: Vector3::new(0.0, 0.0, -2.0),
r: 1.0,
})
],
vec![ 1.0, 1.0, 1.0, 1.0 ]
);
let mut body1 = raft.clone();
let mut body2 = raft.clone();
body1 += Vector3::new(0.0, 5.0, 0.0);
body1.apply_impulse(Vector3::new(0.0, -4.0, 0.0) * 4.0, Vector3::zero());
body1.integrate(1.0);
body2 -= Vector3::new(0.0, 5.0, 0.0);
body2.apply_impulse(Vector3::new(0.0, 4.0, 0.0) * 4.0, Vector3::zero());
body2.integrate(1.0);
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c: LocalContact| {
manifold.push(c);
}));
assert_eq!(manifold.contacts.len(), 4);
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(0.0, 8.338712, 0.0));
assert_eq!(body2.v, Vector3::new(0.0, -8.338712, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
assert_eq!(body2.collider.rot, Quaternion::one());
let static_rect = Rect {
c: Point3::new(0.0, 0.0, 0.0),
u: [ Vector3::new(1.0, 0.0, 0.0), Vector3::new(0.0, 0.0, 1.0) ],
e: [ 5.0, 5.0 ],
};
let mut body1 = raft.clone();
let mut body2 = StaticBody::new(0.0, &static_rect);
body1 += Vector3::new(0.0, 5.0, 0.0);
body1.apply_impulse(Vector3::new(0.0, -4.0, 0.0) * 4.0, Vector3::zero());
body1.integrate(1.0);
assert_eq!(body1.v, Vector3::new(0.0, -4.0, 0.0));
let mut manifold = Manifold::new();
assert!(body1.local_contacts(&body2, |c: LocalContact| {
manifold.push(c);
}));
assert_eq!(manifold.contacts.len(), 4);
PhysicsState::resolve_manifold::<DefaultPhysConfig, _, _>(&mut body1, &mut body2, &manifold, 1.0);
assert_eq!(body1.v, Vector3::new(0.0, 8.337941, 0.0));
assert_eq!(body1.collider.rot, Quaternion::one());
}
}
}