use crate::math::{AngVector, AngularInertia, Isometry, Point, Rotation, Vector};
use crate::utils;
use num::Zero;
use std::ops::{Add, AddAssign, Sub, SubAssign};
#[cfg(feature = "dim3")]
use {na::Matrix3, std::ops::MulAssign};
#[derive(Copy, Clone, Debug, PartialEq)]
#[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
pub struct MassProperties {
pub local_com: Point<f32>,
pub inv_mass: f32,
pub inv_principal_inertia_sqrt: AngVector<f32>,
#[cfg(feature = "dim3")]
pub principal_inertia_local_frame: Rotation<f32>,
}
impl MassProperties {
#[cfg(feature = "dim2")]
pub fn new(local_com: Point<f32>, mass: f32, principal_inertia: f32) -> Self {
let inv_mass = utils::inv(mass);
let inv_principal_inertia_sqrt = utils::inv(principal_inertia.sqrt());
Self {
local_com,
inv_mass,
inv_principal_inertia_sqrt,
}
}
#[cfg(feature = "dim3")]
pub fn new(local_com: Point<f32>, mass: f32, principal_inertia: AngVector<f32>) -> Self {
Self::with_principal_inertia_frame(local_com, mass, principal_inertia, Rotation::identity())
}
#[cfg(feature = "dim3")]
pub fn with_principal_inertia_frame(
local_com: Point<f32>,
mass: f32,
principal_inertia: AngVector<f32>,
principal_inertia_local_frame: Rotation<f32>,
) -> Self {
let inv_mass = utils::inv(mass);
let inv_principal_inertia_sqrt = principal_inertia.map(|e| utils::inv(e.sqrt()));
Self {
local_com,
inv_mass,
inv_principal_inertia_sqrt,
principal_inertia_local_frame,
}
}
pub fn world_com(&self, pos: &Isometry<f32>) -> Point<f32> {
pos * self.local_com
}
#[cfg(feature = "dim2")]
pub fn world_inv_inertia_sqrt(&self, _rot: &Rotation<f32>) -> AngularInertia<f32> {
self.inv_principal_inertia_sqrt
}
#[cfg(feature = "dim3")]
pub fn world_inv_inertia_sqrt(&self, rot: &Rotation<f32>) -> AngularInertia<f32> {
if !self.inv_principal_inertia_sqrt.is_zero() {
let mut lhs = (rot * self.principal_inertia_local_frame)
.to_rotation_matrix()
.into_inner();
let rhs = lhs.transpose();
lhs.column_mut(0)
.mul_assign(self.inv_principal_inertia_sqrt.x);
lhs.column_mut(1)
.mul_assign(self.inv_principal_inertia_sqrt.y);
lhs.column_mut(2)
.mul_assign(self.inv_principal_inertia_sqrt.z);
let inertia = lhs * rhs;
AngularInertia::from_sdp_matrix(inertia)
} else {
AngularInertia::zero()
}
}
#[cfg(feature = "dim3")]
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")]
pub fn reconstruct_inertia_matrix(&self) -> Matrix3<f32> {
let principal_inertia = self.inv_principal_inertia_sqrt.map(|e| utils::inv(e * e));
self.principal_inertia_local_frame.to_rotation_matrix()
* Matrix3::from_diagonal(&principal_inertia)
* self
.principal_inertia_local_frame
.inverse()
.to_rotation_matrix()
}
#[cfg(feature = "dim2")]
pub(crate) fn construct_shifted_inertia_matrix(&self, shift: Vector<f32>) -> f32 {
let i = utils::inv(self.inv_principal_inertia_sqrt * self.inv_principal_inertia_sqrt);
if self.inv_mass != 0.0 {
let mass = 1.0 / self.inv_mass;
i + shift.norm_squared() * mass
} else {
i
}
}
#[cfg(feature = "dim3")]
pub(crate) fn construct_shifted_inertia_matrix(&self, shift: Vector<f32>) -> Matrix3<f32> {
let matrix = self.reconstruct_inertia_matrix();
if self.inv_mass != 0.0 {
let mass = 1.0 / self.inv_mass;
let diag = shift.norm_squared();
let diagm = Matrix3::from_diagonal_element(diag);
matrix + (diagm + shift * shift.transpose()) * mass
} else {
matrix
}
}
pub fn transform_by(&self, m: &Isometry<f32>) -> Self {
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 {
fn zero() -> Self {
Self {
inv_mass: 0.0,
inv_principal_inertia_sqrt: na::zero(),
#[cfg(feature = "dim3")]
principal_inertia_local_frame: Rotation::identity(),
local_com: Point::origin(),
}
}
fn is_zero(&self) -> bool {
*self == Self::zero()
}
}
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;
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;
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;
#[cfg(feature = "dim2")]
fn add(self, other: MassProperties) -> Self {
if self.is_zero() {
return other;
} else if 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 inv_principal_inertia_sqrt = utils::inv(inertia.sqrt());
Self {
local_com,
inv_mass,
inv_principal_inertia_sqrt,
}
}
#[cfg(feature = "dim3")]
fn add(self, other: MassProperties) -> Self {
if self.is_zero() {
return other;
} else if 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;
let inv_principal_inertia_sqrt = principal_inertia.map(|e| utils::inv(e.sqrt()));
Self {
local_com,
inv_mass,
inv_principal_inertia_sqrt,
principal_inertia_local_frame,
}
}
}
impl AddAssign<MassProperties> for MassProperties {
fn add_assign(&mut self, rhs: 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 crate::math::{Point, Rotation, Vector};
use approx::assert_relative_eq;
use num::Zero;
#[test]
fn mass_properties_add_partial_zero() {
let m1 = MassProperties {
local_com: Point::origin(),
inv_mass: 2.0,
inv_principal_inertia_sqrt: na::zero(),
#[cfg(feature = "dim3")]
principal_inertia_local_frame: Rotation::identity(),
};
let m2 = MassProperties {
local_com: Point::origin(),
inv_mass: 0.0,
#[cfg(feature = "dim2")]
inv_principal_inertia_sqrt: 1.0,
#[cfg(feature = "dim3")]
inv_principal_inertia_sqrt: Vector::new(1.0, 2.0, 3.0),
#[cfg(feature = "dim3")]
principal_inertia_local_frame: Rotation::identity(),
};
let result = MassProperties {
local_com: Point::origin(),
inv_mass: 2.0,
#[cfg(feature = "dim2")]
inv_principal_inertia_sqrt: 1.0,
#[cfg(feature = "dim3")]
inv_principal_inertia_sqrt: Vector::new(1.0, 2.0, 3.0),
#[cfg(feature = "dim3")]
principal_inertia_local_frame: Rotation::identity(),
};
assert_eq!(m1 + m2, result);
assert_eq!(m2 + m1, result);
}
#[test]
fn mass_properties_add_sub() {
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
);
}
}