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Re-add all the alga trait impls behind a feature.

This commit is contained in:
sebcrozet 2020-04-05 17:53:27 +02:00
parent 4103da4bc1
commit c5dad7f960
13 changed files with 2142 additions and 15 deletions
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4
Cargo.toml
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@ -40,7 +40,7 @@ num-complex = { version = "0.2", default-features = false }
num-rational = { version = "0.2", default-features = false }
approx = { version = "0.3", default-features = false }
simba = { version = "0.1", default-features = false }
#alga = { version = "0.9", default-features = false }
alga = { version = "0.9", default-features = false, optional = true }
rand_distr = { version = "0.2", optional = true }
matrixmultiply = { version = "0.2", optional = true }
serde = { version = "1.0", optional = true }
@ -73,4 +73,4 @@ path = "benches/lib.rs"
lto = true
#[patch.crates-io]
#alga = { path = "../alga/alga" }
#simba = { path = "../simba" }

452
src/base/matrix_alga.rs Normal file
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@ -0,0 +1,452 @@
#[cfg(all(feature = "alloc", not(feature = "std")))]
use alloc::vec::Vec;
use num::{One, Zero};
use alga::general::{
AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, ClosedAdd, ClosedMul,
ClosedNeg, ComplexField, Field, Identity, JoinSemilattice, Lattice, MeetSemilattice, Module,
Multiplicative, RingCommutative, TwoSidedInverse,
};
use alga::linear::{
FiniteDimInnerSpace, FiniteDimVectorSpace, InnerSpace, NormedSpace, VectorSpace,
};
use crate::base::allocator::Allocator;
use crate::base::dimension::{Dim, DimName};
use crate::base::storage::{Storage, StorageMut};
use crate::base::{DefaultAllocator, MatrixMN, MatrixN, Scalar};
/*
*
* Additive structures.
*
*/
impl<N, R: DimName, C: DimName> Identity<Additive> for MatrixMN<N, R, C>
where
N: Scalar + Zero,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn identity() -> Self {
Self::from_element(N::zero())
}
}
impl<N, R: DimName, C: DimName> AbstractMagma<Additive> for MatrixMN<N, R, C>
where
N: Scalar + ClosedAdd,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn operate(&self, other: &Self) -> Self {
self + other
}
}
impl<N, R: DimName, C: DimName> TwoSidedInverse<Additive> for MatrixMN<N, R, C>
where
N: Scalar + ClosedNeg,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
-self
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
*self = -self.clone()
}
}
macro_rules! inherit_additive_structure(
($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
impl<N, R: DimName, C: DimName> $marker<$operator> for MatrixMN<N, R, C>
where N: Scalar + $marker<$operator> $(+ $bounds)*,
DefaultAllocator: Allocator<N, R, C> { }
)*}
);
inherit_additive_structure!(
AbstractSemigroup<Additive> + ClosedAdd,
AbstractMonoid<Additive> + Zero + ClosedAdd,
AbstractQuasigroup<Additive> + ClosedAdd + ClosedNeg,
AbstractLoop<Additive> + Zero + ClosedAdd + ClosedNeg,
AbstractGroup<Additive> + Zero + ClosedAdd + ClosedNeg,
AbstractGroupAbelian<Additive> + Zero + ClosedAdd + ClosedNeg
);
impl<N, R: DimName, C: DimName> AbstractModule for MatrixMN<N, R, C>
where
N: Scalar + RingCommutative,
DefaultAllocator: Allocator<N, R, C>,
{
type AbstractRing = N;
#[inline]
fn multiply_by(&self, n: N) -> Self {
self * n
}
}
impl<N, R: DimName, C: DimName> Module for MatrixMN<N, R, C>
where
N: Scalar + RingCommutative,
DefaultAllocator: Allocator<N, R, C>,
{
type Ring = N;
}
impl<N, R: DimName, C: DimName> VectorSpace for MatrixMN<N, R, C>
where
N: Scalar + Field,
DefaultAllocator: Allocator<N, R, C>,
{
type Field = N;
}
impl<N, R: DimName, C: DimName> FiniteDimVectorSpace for MatrixMN<N, R, C>
where
N: Scalar + Field,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn dimension() -> usize {
R::dim() * C::dim()
}
#[inline]
fn canonical_basis_element(i: usize) -> Self {
assert!(i < Self::dimension(), "Index out of bound.");
let mut res = Self::zero();
unsafe {
*res.data.get_unchecked_linear_mut(i) = N::one();
}
res
}
#[inline]
fn dot(&self, other: &Self) -> N {
self.dot(other)
}
#[inline]
unsafe fn component_unchecked(&self, i: usize) -> &N {
self.data.get_unchecked_linear(i)
}
#[inline]
unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
self.data.get_unchecked_linear_mut(i)
}
}
impl<
N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
R: DimName,
C: DimName,
> NormedSpace for MatrixMN<N, R, C>
where
<N as ComplexField>::RealField: simba::scalar::RealField,
DefaultAllocator: Allocator<N, R, C>,
{
type RealField = <N as ComplexField>::RealField;
type ComplexField = N;
#[inline]
fn norm_squared(&self) -> <N as ComplexField>::RealField {
self.norm_squared()
}
#[inline]
fn norm(&self) -> <N as ComplexField>::RealField {
self.norm()
}
#[inline]
#[must_use = "Did you mean to use normalize_mut()?"]
fn normalize(&self) -> Self {
self.normalize()
}
#[inline]
fn normalize_mut(&mut self) -> <N as ComplexField>::RealField {
self.normalize_mut()
}
#[inline]
#[must_use = "Did you mean to use try_normalize_mut()?"]
fn try_normalize(&self, min_norm: <N as ComplexField>::RealField) -> Option<Self> {
self.try_normalize(min_norm)
}
#[inline]
fn try_normalize_mut(
&mut self,
min_norm: <N as ComplexField>::RealField,
) -> Option<<N as ComplexField>::RealField> {
self.try_normalize_mut(min_norm)
}
}
impl<
N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
R: DimName,
C: DimName,
> InnerSpace for MatrixMN<N, R, C>
where
<N as ComplexField>::RealField: simba::scalar::RealField,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn angle(&self, other: &Self) -> <N as ComplexField>::RealField {
self.angle(other)
}
#[inline]
fn inner_product(&self, other: &Self) -> N {
self.dotc(other)
}
}
// FIXME: specialization will greatly simplify this implementation in the future.
// In particular:
// − use `x()` instead of `::canonical_basis_element`
// − use `::new(x, y, z)` instead of `::from_slice`
impl<
N: ComplexField + simba::scalar::ComplexField<RealField = <N as ComplexField>::RealField>,
R: DimName,
C: DimName,
> FiniteDimInnerSpace for MatrixMN<N, R, C>
where
<N as ComplexField>::RealField: simba::scalar::RealField,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn orthonormalize(vs: &mut [Self]) -> usize {
let mut nbasis_elements = 0;
for i in 0..vs.len() {
{
let (elt, basis) = vs[..i + 1].split_last_mut().unwrap();
for basis_element in &basis[..nbasis_elements] {
*elt -= &*basis_element * elt.dot(basis_element)
}
}
if vs[i]
.try_normalize_mut(<N as ComplexField>::RealField::zero())
.is_some()
{
// FIXME: this will be efficient on dynamically-allocated vectors but for
// statically-allocated ones, `.clone_from` would be better.
vs.swap(nbasis_elements, i);
nbasis_elements += 1;
// All the other vectors will be dependent.
if nbasis_elements == Self::dimension() {
break;
}
}
}
nbasis_elements
}
#[inline]
fn orthonormal_subspace_basis<F>(vs: &[Self], mut f: F)
where
F: FnMut(&Self) -> bool,
{
// FIXME: is this necessary?
assert!(
vs.len() <= Self::dimension(),
"The given set of vectors has no chance of being a free family."
);
match Self::dimension() {
1 => {
if vs.len() == 0 {
let _ = f(&Self::canonical_basis_element(0));
}
}
2 => {
if vs.len() == 0 {
let _ = f(&Self::canonical_basis_element(0))
&& f(&Self::canonical_basis_element(1));
} else if vs.len() == 1 {
let v = &vs[0];
let res = Self::from_column_slice(&[-v[1], v[0]]);
let _ = f(&res.normalize());
}
// Otherwise, nothing.
}
3 => {
if vs.len() == 0 {
let _ = f(&Self::canonical_basis_element(0))
&& f(&Self::canonical_basis_element(1))
&& f(&Self::canonical_basis_element(2));
} else if vs.len() == 1 {
let v = &vs[0];
let mut a;
if ComplexField::norm1(v[0]) > ComplexField::norm1(v[1]) {
a = Self::from_column_slice(&[v[2], N::zero(), -v[0]]);
} else {
a = Self::from_column_slice(&[N::zero(), -v[2], v[1]]);
};
let _ = a.normalize_mut();
if f(&a.cross(v)) {
let _ = f(&a);
}
} else if vs.len() == 2 {
let _ = f(&vs[0].cross(&vs[1]).normalize());
}
}
_ => {
#[cfg(any(feature = "std", feature = "alloc"))]
{
// XXX: use a GenericArray instead.
let mut known_basis = Vec::new();
for v in vs.iter() {
known_basis.push(v.normalize())
}
for i in 0..Self::dimension() - vs.len() {
let mut elt = Self::canonical_basis_element(i);
for v in &known_basis {
elt -= v * elt.dot(v)
}
if let Some(subsp_elt) =
elt.try_normalize(<N as ComplexField>::RealField::zero())
{
if !f(&subsp_elt) {
return;
};
known_basis.push(subsp_elt);
}
}
}
#[cfg(all(not(feature = "std"), not(feature = "alloc")))]
{
panic!("Cannot compute the orthogonal subspace basis of a vector with a dimension greater than 3 \
if #![no_std] is enabled and the 'alloc' feature is not enabled.")
}
}
}
}
}
/*
*
*
* Multiplicative structures.
*
*
*/
impl<N, D: DimName> Identity<Multiplicative> for MatrixN<N, D>
where
N: Scalar + Zero + One,
DefaultAllocator: Allocator<N, D, D>,
{
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N, D: DimName> AbstractMagma<Multiplicative> for MatrixN<N, D>
where
N: Scalar + Zero + One + ClosedAdd + ClosedMul,
DefaultAllocator: Allocator<N, D, D>,
{
#[inline]
fn operate(&self, other: &Self) -> Self {
self * other
}
}
macro_rules! impl_multiplicative_structure(
($($marker: ident<$operator: ident> $(+ $bounds: ident)*),* $(,)*) => {$(
impl<N, D: DimName> $marker<$operator> for MatrixN<N, D>
where N: Scalar + Zero + One + ClosedAdd + ClosedMul + $marker<$operator> $(+ $bounds)*,
DefaultAllocator: Allocator<N, D, D> { }
)*}
);
impl_multiplicative_structure!(
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative> + One
);
/*
*
* Ordering
*
*/
impl<N, R: Dim, C: Dim> MeetSemilattice for MatrixMN<N, R, C>
where
N: Scalar + MeetSemilattice,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn meet(&self, other: &Self) -> Self {
self.zip_map(other, |a, b| a.meet(&b))
}
}
impl<N, R: Dim, C: Dim> JoinSemilattice for MatrixMN<N, R, C>
where
N: Scalar + JoinSemilattice,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn join(&self, other: &Self) -> Self {
self.zip_map(other, |a, b| a.join(&b))
}
}
impl<N, R: Dim, C: Dim> Lattice for MatrixMN<N, R, C>
where
N: Scalar + Lattice,
DefaultAllocator: Allocator<N, R, C>,
{
#[inline]
fn meet_join(&self, other: &Self) -> (Self, Self) {
let shape = self.data.shape();
assert!(
shape == other.data.shape(),
"Matrix meet/join error: mismatched dimensions."
);
let mut mres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
let mut jres = unsafe { Self::new_uninitialized_generic(shape.0, shape.1) };
for i in 0..shape.0.value() * shape.1.value() {
unsafe {
let mj = self
.data
.get_unchecked_linear(i)
.meet_join(other.data.get_unchecked_linear(i));
*mres.data.get_unchecked_linear_mut(i) = mj.0;
*jres.data.get_unchecked_linear_mut(i) = mj.1;
}
}
(mres, jres)
}
}

2
src/base/mod.rs
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@ -21,6 +21,8 @@ mod conversion;
mod edition;
pub mod indexing;
mod matrix;
#[cfg(feature = "alga")]
mod matrix_alga;
mod matrix_simba;
mod matrix_slice;
mod norm;

210
src/geometry/isometry_alga.rs Executable file
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@ -0,0 +1,210 @@
use alga::general::{
AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::Isometry as AlgaIsometry;
use alga::linear::{
AffineTransformation, DirectIsometry, ProjectiveTransformation, Rotation, Similarity,
Transformation,
};
use crate::base::allocator::Allocator;
use crate::base::dimension::DimName;
use crate::base::{DefaultAllocator, VectorN};
use crate::geometry::{AbstractRotation, Isometry, Point, Translation};
/*
*
* Algebraic structures.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName, R> Identity<Multiplicative>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
self.inverse()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.inverse_mut()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
macro_rules! impl_multiplicative_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName, R> $marker<$operator> for Isometry<N, D, R>
where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D> { }
)*}
);
impl_multiplicative_structures!(
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractQuasigroup<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
/*
*
* Transformation groups.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.inverse_transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> AffineTransformation<Point<N, D>>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
type Rotation = R;
type NonUniformScaling = Id;
type Translation = Translation<N, D>;
#[inline]
fn decompose(&self) -> (Self::Translation, R, Id, R) {
(
self.translation.clone(),
self.rotation.clone(),
Id::new(),
<R as AbstractRotation<N, D>>::identity(),
)
}
#[inline]
fn append_translation(&self, t: &Self::Translation) -> Self {
t * self
}
#[inline]
fn prepend_translation(&self, t: &Self::Translation) -> Self {
self * t
}
#[inline]
fn append_rotation(&self, r: &Self::Rotation) -> Self {
let shift = Transformation::transform_vector(r, &self.translation.vector);
Isometry::from_parts(Translation::from(shift), r.clone() * self.rotation.clone())
}
#[inline]
fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
Isometry::from_parts(self.translation.clone(), self.rotation.prepend_rotation(r))
}
#[inline]
fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
#[inline]
fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
#[inline]
fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
let mut res = self.clone();
res.append_rotation_wrt_point_mut(r, p);
Some(res)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> Similarity<Point<N, D>>
for Isometry<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
type Scaling = Id;
#[inline]
fn translation(&self) -> Translation<N, D> {
self.translation.clone()
}
#[inline]
fn rotation(&self) -> R {
self.rotation.clone()
}
#[inline]
fn scaling(&self) -> Id {
Id::new()
}
}
macro_rules! marker_impl(
($($Trait: ident),*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName, R> $Trait<Point<N, D>> for Isometry<N, D, R>
where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D> { }
)*}
);
marker_impl!(AlgaIsometry, DirectIsometry);

16
src/geometry/mod.rs
View File

@ -6,6 +6,8 @@ mod op_macros;
mod abstract_rotation;
mod point;
#[cfg(feature = "alga")]
mod point_alga;
mod point_alias;
mod point_construction;
mod point_conversion;
@ -14,6 +16,8 @@ mod point_ops;
mod point_simba;
mod rotation;
#[cfg(feature = "alga")]
mod rotation_alga;
mod rotation_alias;
mod rotation_construction;
mod rotation_conversion;
@ -22,6 +26,8 @@ mod rotation_simba; // FIXME: implement Rotation methods.
mod rotation_specialization;
mod quaternion;
#[cfg(feature = "alga")]
mod quaternion_alga;
mod quaternion_construction;
mod quaternion_conversion;
mod quaternion_coordinates;
@ -29,12 +35,16 @@ mod quaternion_ops;
mod quaternion_simba;
mod unit_complex;
#[cfg(feature = "alga")]
mod unit_complex_alga;
mod unit_complex_construction;
mod unit_complex_conversion;
mod unit_complex_ops;
mod unit_complex_simba;
mod translation;
#[cfg(feature = "alga")]
mod translation_alga;
mod translation_alias;
mod translation_construction;
mod translation_conversion;
@ -43,6 +53,8 @@ mod translation_ops;
mod translation_simba;
mod isometry;
#[cfg(feature = "alga")]
mod isometry_alga;
mod isometry_alias;
mod isometry_construction;
mod isometry_conversion;
@ -50,6 +62,8 @@ mod isometry_ops;
mod isometry_simba;
mod similarity;
#[cfg(feature = "alga")]
mod similarity_alga;
mod similarity_alias;
mod similarity_construction;
mod similarity_conversion;
@ -59,6 +73,8 @@ mod similarity_simba;
mod swizzle;
mod transform;
#[cfg(feature = "alga")]
mod transform_alga;
mod transform_alias;
mod transform_construction;
mod transform_conversion;

84
src/geometry/point_alga.rs Normal file
View File

@ -0,0 +1,84 @@
use alga::general::{Field, JoinSemilattice, Lattice, MeetSemilattice, RealField};
use alga::linear::{AffineSpace, EuclideanSpace};
use crate::base::allocator::Allocator;
use crate::base::dimension::DimName;
use crate::base::{DefaultAllocator, Scalar, VectorN};
use crate::geometry::Point;
impl<N: Scalar + Field, D: DimName> AffineSpace for Point<N, D>
where
N: Scalar + Field,
DefaultAllocator: Allocator<N, D>,
{
type Translation = VectorN<N, D>;
}
impl<N: RealField + simba::scalar::RealField, D: DimName> EuclideanSpace for Point<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
type Coordinates = VectorN<N, D>;
type RealField = N;
#[inline]
fn origin() -> Self {
Self::origin()
}
#[inline]
fn coordinates(&self) -> Self::Coordinates {
self.coords.clone()
}
#[inline]
fn from_coordinates(coords: Self::Coordinates) -> Self {
Self::from(coords)
}
#[inline]
fn scale_by(&self, n: N) -> Self {
self * n
}
}
/*
*
* Ordering
*
*/
impl<N, D: DimName> MeetSemilattice for Point<N, D>
where
N: Scalar + MeetSemilattice,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn meet(&self, other: &Self) -> Self {
Self::from(self.coords.meet(&other.coords))
}
}
impl<N, D: DimName> JoinSemilattice for Point<N, D>
where
N: Scalar + JoinSemilattice,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn join(&self, other: &Self) -> Self {
Self::from(self.coords.join(&other.coords))
}
}
impl<N, D: DimName> Lattice for Point<N, D>
where
N: Scalar + Lattice,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn meet_join(&self, other: &Self) -> (Self, Self) {
let (meet, join) = self.coords.meet_join(&other.coords);
(Self::from(meet), Self::from(join))
}
}

313
src/geometry/quaternion_alga.rs Executable file
View File

@ -0,0 +1,313 @@
use num::Zero;
use alga::general::{
AbstractGroup, AbstractGroupAbelian, AbstractLoop, AbstractMagma, AbstractModule,
AbstractMonoid, AbstractQuasigroup, AbstractSemigroup, Additive, Id, Identity, Module,
Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::{
AffineTransformation, DirectIsometry, FiniteDimVectorSpace, Isometry, NormedSpace,
OrthogonalTransformation, ProjectiveTransformation, Rotation, Similarity, Transformation,
VectorSpace,
};
use crate::base::{Vector3, Vector4};
use crate::geometry::{Point3, Quaternion, UnitQuaternion};
impl<N: RealField + simba::scalar::RealField> Identity<Multiplicative> for Quaternion<N> {
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField> Identity<Additive> for Quaternion<N> {
#[inline]
fn identity() -> Self {
Self::zero()
}
}
impl<N: RealField + simba::scalar::RealField> AbstractMagma<Multiplicative> for Quaternion<N> {
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
impl<N: RealField + simba::scalar::RealField> AbstractMagma<Additive> for Quaternion<N> {
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self + rhs
}
}
impl<N: RealField + simba::scalar::RealField> TwoSidedInverse<Additive> for Quaternion<N> {
#[inline]
fn two_sided_inverse(&self) -> Self {
-self
}
}
macro_rules! impl_structures(
($Quaternion: ident; $($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField> $marker<$operator> for $Quaternion<N> { }
)*}
);
impl_structures!(
Quaternion;
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractSemigroup<Additive>,
AbstractQuasigroup<Additive>,
AbstractMonoid<Additive>,
AbstractLoop<Additive>,
AbstractGroup<Additive>,
AbstractGroupAbelian<Additive>
);
/*
*
* Vector space.
*
*/
impl<N: RealField + simba::scalar::RealField> AbstractModule for Quaternion<N> {
type AbstractRing = N;
#[inline]
fn multiply_by(&self, n: N) -> Self {
self * n
}
}
impl<N: RealField + simba::scalar::RealField> Module for Quaternion<N> {
type Ring = N;
}
impl<N: RealField + simba::scalar::RealField> VectorSpace for Quaternion<N> {
type Field = N;
}
impl<N: RealField + simba::scalar::RealField> FiniteDimVectorSpace for Quaternion<N> {
#[inline]
fn dimension() -> usize {
4
}
#[inline]
fn canonical_basis_element(i: usize) -> Self {
Self::from(Vector4::canonical_basis_element(i))
}
#[inline]
fn dot(&self, other: &Self) -> N {
self.coords.dot(&other.coords)
}
#[inline]
unsafe fn component_unchecked(&self, i: usize) -> &N {
self.coords.component_unchecked(i)
}
#[inline]
unsafe fn component_unchecked_mut(&mut self, i: usize) -> &mut N {
self.coords.component_unchecked_mut(i)
}
}
impl<N: RealField + simba::scalar::RealField> NormedSpace for Quaternion<N> {
type RealField = N;
type ComplexField = N;
#[inline]
fn norm_squared(&self) -> N {
self.coords.norm_squared()
}
#[inline]
fn norm(&self) -> N {
self.as_vector().norm()
}
#[inline]
fn normalize(&self) -> Self {
let v = self.coords.normalize();
Self::from(v)
}
#[inline]
fn normalize_mut(&mut self) -> N {
self.coords.normalize_mut()
}
#[inline]
fn try_normalize(&self, min_norm: N) -> Option<Self> {
if let Some(v) = self.coords.try_normalize(min_norm) {
Some(Self::from(v))
} else {
None
}
}
#[inline]
fn try_normalize_mut(&mut self, min_norm: N) -> Option<N> {
self.coords.try_normalize_mut(min_norm)
}
}
/*
*
* Implementations for UnitQuaternion.
*
*/
impl<N: RealField + simba::scalar::RealField> Identity<Multiplicative> for UnitQuaternion<N> {
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField> AbstractMagma<Multiplicative> for UnitQuaternion<N> {
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
impl<N: RealField + simba::scalar::RealField> TwoSidedInverse<Multiplicative>
for UnitQuaternion<N>
{
#[inline]
fn two_sided_inverse(&self) -> Self {
self.inverse()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.inverse_mut()
}
}
impl_structures!(
UnitQuaternion;
AbstractSemigroup<Multiplicative>,
AbstractQuasigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
impl<N: RealField + simba::scalar::RealField> Transformation<Point3<N>> for UnitQuaternion<N> {
#[inline]
fn transform_point(&self, pt: &Point3<N>) -> Point3<N> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
self.transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField> ProjectiveTransformation<Point3<N>>
for UnitQuaternion<N>
{
#[inline]
fn inverse_transform_point(&self, pt: &Point3<N>) -> Point3<N> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &Vector3<N>) -> Vector3<N> {
self.inverse_transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField> AffineTransformation<Point3<N>>
for UnitQuaternion<N>
{
type Rotation = Self;
type NonUniformScaling = Id;
type Translation = Id;
#[inline]
fn decompose(&self) -> (Id, Self, Id, Self) {
(Id::new(), self.clone(), Id::new(), Self::identity())
}
#[inline]
fn append_translation(&self, _: &Self::Translation) -> Self {
self.clone()
}
#[inline]
fn prepend_translation(&self, _: &Self::Translation) -> Self {
self.clone()
}
#[inline]
fn append_rotation(&self, r: &Self::Rotation) -> Self {
r * self
}
#[inline]
fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
self * r
}
#[inline]
fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
#[inline]
fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
}
impl<N: RealField + simba::scalar::RealField> Similarity<Point3<N>> for UnitQuaternion<N> {
type Scaling = Id;
#[inline]
fn translation(&self) -> Id {
Id::new()
}
#[inline]
fn rotation(&self) -> Self {
self.clone()
}
#[inline]
fn scaling(&self) -> Id {
Id::new()
}
}
macro_rules! marker_impl(
($($Trait: ident),*) => {$(
impl<N: RealField + simba::scalar::RealField> $Trait<Point3<N>> for UnitQuaternion<N> { }
)*}
);
marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
impl<N: RealField + simba::scalar::RealField> Rotation<Point3<N>> for UnitQuaternion<N> {
#[inline]
fn powf(&self, n: N) -> Option<Self> {
Some(self.powf(n))
}
#[inline]
fn rotation_between(a: &Vector3<N>, b: &Vector3<N>) -> Option<Self> {
Self::rotation_between(a, b)
}
#[inline]
fn scaled_rotation_between(a: &Vector3<N>, b: &Vector3<N>, s: N) -> Option<Self> {
Self::scaled_rotation_between(a, b, s)
}
}

291
src/geometry/rotation_alga.rs Executable file
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use alga::general::{
AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::{
self, AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
ProjectiveTransformation, Similarity, Transformation,
};
use crate::base::allocator::Allocator;
use crate::base::dimension::DimName;
use crate::base::{DefaultAllocator, VectorN};
use crate::geometry::{Point, Rotation};
/*
*
* Algebraic structures.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName> Identity<Multiplicative>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D>,
{
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> TwoSidedInverse<Multiplicative>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D>,
{
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
self.transpose()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.transpose_mut()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> AbstractMagma<Multiplicative>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D>,
{
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
macro_rules! impl_multiplicative_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName> $marker<$operator> for Rotation<N, D>
where DefaultAllocator: Allocator<N, D, D> { }
)*}
);
impl_multiplicative_structures!(
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractQuasigroup<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
/*
*
* Transformation groups.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName> Transformation<Point<N, D>>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
#[inline]
fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> ProjectiveTransformation<Point<N, D>>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
#[inline]
fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.inverse_transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> AffineTransformation<Point<N, D>>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
type Rotation = Self;
type NonUniformScaling = Id;
type Translation = Id;
#[inline]
fn decompose(&self) -> (Id, Self, Id, Self) {
(Id::new(), self.clone(), Id::new(), Self::identity())
}
#[inline]
fn append_translation(&self, _: &Self::Translation) -> Self {
self.clone()
}
#[inline]
fn prepend_translation(&self, _: &Self::Translation) -> Self {
self.clone()
}
#[inline]
fn append_rotation(&self, r: &Self::Rotation) -> Self {
r * self
}
#[inline]
fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
self * r
}
#[inline]
fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
#[inline]
fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> Similarity<Point<N, D>> for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
type Scaling = Id;
#[inline]
fn translation(&self) -> Id {
Id::new()
}
#[inline]
fn rotation(&self) -> Self {
self.clone()
}
#[inline]
fn scaling(&self) -> Id {
Id::new()
}
}
macro_rules! marker_impl(
($($Trait: ident),*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName> $Trait<Point<N, D>> for Rotation<N, D>
where DefaultAllocator: Allocator<N, D, D> +
Allocator<N, D> { }
)*}
);
marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
/// Subgroups of the n-dimensional rotation group `SO(n)`.
impl<N: RealField + simba::scalar::RealField, D: DimName> linear::Rotation<Point<N, D>>
for Rotation<N, D>
where
DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>,
{
#[inline]
fn powf(&self, _: N) -> Option<Self> {
// XXX: Add the general case.
// XXX: Use specialization for 2D and 3D.
unimplemented!()
}
#[inline]
fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self> {
// XXX: Add the general case.
// XXX: Use specialization for 2D and 3D.
unimplemented!()
}
#[inline]
fn scaled_rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>, _: N) -> Option<Self> {
// XXX: Add the general case.
// XXX: Use specialization for 2D and 3D.
unimplemented!()
}
}
/*
impl<N: RealField + simba::scalar::RealField> Matrix for Rotation<N> {
type Field = N;
type Row = Matrix<N>;
type Column = Matrix<N>;
type Transpose = Self;
#[inline]
fn nrows(&self) -> usize {
self.submatrix.nrows()
}
#[inline]
fn ncolumns(&self) -> usize {
self.submatrix.ncolumns()
}
#[inline]
fn row(&self, i: usize) -> Self::Row {
self.submatrix.row(i)
}
#[inline]
fn column(&self, i: usize) -> Self::Column {
self.submatrix.column(i)
}
#[inline]
fn get(&self, i: usize, j: usize) -> Self::Field {
self.submatrix[(i, j)]
}
#[inline]
unsafe fn get_unchecked(&self, i: usize, j: usize) -> Self::Field {
self.submatrix.at_fast(i, j)
}
#[inline]
fn transpose(&self) -> Self::Transpose {
Rotation::from_matrix_unchecked(self.submatrix.transpose())
}
}
impl<N: RealField + simba::scalar::RealField> SquareMatrix for Rotation<N> {
type Vector = Matrix<N>;
#[inline]
fn diagonal(&self) -> Self::Coordinates {
self.submatrix.diagonal()
}
#[inline]
fn determinant(&self) -> Self::Field {
crate::one()
}
#[inline]
fn try_inverse(&self) -> Option<Self> {
Some(::transpose(self))
}
#[inline]
fn try_inverse_mut(&mut self) -> bool {
self.transpose_mut();
true
}
#[inline]
fn transpose_mut(&mut self) {
self.submatrix.transpose_mut()
}
}
impl<N: RealField + simba::scalar::RealField> InversibleSquareMatrix for Rotation<N> { }
*/

196
src/geometry/similarity_alga.rs Executable file
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use alga::general::{
AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
AbstractSemigroup, Identity, Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::Similarity as AlgaSimilarity;
use alga::linear::{AffineTransformation, ProjectiveTransformation, Rotation, Transformation};
use crate::base::allocator::Allocator;
use crate::base::dimension::DimName;
use crate::base::{DefaultAllocator, VectorN};
use crate::geometry::{AbstractRotation, Point, Similarity, Translation};
/*
*
* Algebraic structures.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName, R> Identity<Multiplicative>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> TwoSidedInverse<Multiplicative>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
self.inverse()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.inverse_mut()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> AbstractMagma<Multiplicative>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
macro_rules! impl_multiplicative_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName, R> $marker<$operator> for Similarity<N, D, R>
where R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D> { }
)*}
);
impl_multiplicative_structures!(
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractQuasigroup<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
/*
*
* Transformation groups.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName, R> Transformation<Point<N, D>>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> ProjectiveTransformation<Point<N, D>>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.inverse_transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> AffineTransformation<Point<N, D>>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
type NonUniformScaling = N;
type Rotation = R;
type Translation = Translation<N, D>;
#[inline]
fn decompose(&self) -> (Translation<N, D>, R, N, R) {
(
self.isometry.translation.clone(),
self.isometry.rotation.clone(),
self.scaling(),
<R as AbstractRotation<N, D>>::identity(),
)
}
#[inline]
fn append_translation(&self, t: &Self::Translation) -> Self {
t * self
}
#[inline]
fn prepend_translation(&self, t: &Self::Translation) -> Self {
self * t
}
#[inline]
fn append_rotation(&self, r: &Self::Rotation) -> Self {
Similarity::from_isometry(self.isometry.append_rotation(r), self.scaling())
}
#[inline]
fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
Similarity::from_isometry(self.isometry.prepend_rotation(r), self.scaling())
}
#[inline]
fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self {
self.append_scaling(*s)
}
#[inline]
fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self {
self.prepend_scaling(*s)
}
#[inline]
fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &Point<N, D>) -> Option<Self> {
let mut res = self.clone();
res.append_rotation_wrt_point_mut(r, p);
Some(res)
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName, R> AlgaSimilarity<Point<N, D>>
for Similarity<N, D, R>
where
R: Rotation<Point<N, D>> + AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
type Scaling = N;
#[inline]
fn translation(&self) -> Translation<N, D> {
self.isometry.translation()
}
#[inline]
fn rotation(&self) -> R {
self.isometry.rotation()
}
#[inline]
fn scaling(&self) -> N {
self.scaling()
}
}

149
src/geometry/transform_alga.rs Executable file
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use alga::general::{
AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
AbstractSemigroup, Identity, Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::{ProjectiveTransformation, Transformation};
use crate::base::allocator::Allocator;
use crate::base::dimension::{DimNameAdd, DimNameSum, U1};
use crate::base::{DefaultAllocator, VectorN};
use crate::geometry::{Point, SubTCategoryOf, TCategory, TProjective, Transform};
/*
*
* Algebraic structures.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> Identity<Multiplicative>
for Transform<N, D, C>
where
C: TCategory,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative>
for Transform<N, D, C>
where
C: SubTCategoryOf<TProjective>,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
self.clone().inverse()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.inverse_mut()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative>
for Transform<N, D, C>
where
C: TCategory,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
macro_rules! impl_multiplicative_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
where C: TCategory,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
)*}
);
macro_rules! impl_inversible_multiplicative_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimNameAdd<U1>, C> $marker<$operator> for Transform<N, D, C>
where C: SubTCategoryOf<TProjective>,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> { }
)*}
);
impl_multiplicative_structures!(
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
);
impl_inversible_multiplicative_structures!(
AbstractQuasigroup<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
/*
*
* Transformation groups.
*
*/
impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C>
where
N: RealField + simba::scalar::RealField,
C: TCategory,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<N, DimNameSum<D, U1>>
+ Allocator<N, D, D>
+ Allocator<N, D>,
{
#[inline]
fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.transform_vector(v)
}
}
impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C>
where
N: RealField + simba::scalar::RealField,
C: SubTCategoryOf<TProjective>,
DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<N, DimNameSum<D, U1>>
+ Allocator<N, D, D>
+ Allocator<N, D>,
{
#[inline]
fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
self.inverse_transform_vector(v)
}
}
// FIXME: we need to implement an SVD for this.
//
// impl<N, D: DimNameAdd<U1>, C> AffineTransformation<Point<N, D>> for Transform<N, D, C>
// where N: RealField,
// C: SubTCategoryOf<TAffine>,
// DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> +
// Allocator<N, D, D> +
// Allocator<N, D> {
// type PreRotation = Rotation<N, D>;
// type NonUniformScaling = VectorN<N, D>;
// type PostRotation = Rotation<N, D>;
// type Translation = Translation<N, D>;
//
// #[inline]
// fn decompose(&self) -> (Self::Translation, Self::PostRotation, Self::NonUniformScaling, Self::PreRotation) {
// unimplemented!()
// }
// }

215
src/geometry/translation_alga.rs Executable file
View File

@ -0,0 +1,215 @@
use alga::general::{
AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::Translation as AlgaTranslation;
use alga::linear::{
AffineTransformation, DirectIsometry, Isometry, ProjectiveTransformation, Similarity,
Transformation,
};
use crate::base::allocator::Allocator;
use crate::base::dimension::DimName;
use crate::base::{DefaultAllocator, VectorN};
use crate::geometry::{Point, Translation};
/*
*
* Algebraic structures.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName> Identity<Multiplicative>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> TwoSidedInverse<Multiplicative>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
self.inverse()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.inverse_mut()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> AbstractMagma<Multiplicative>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
macro_rules! impl_multiplicative_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName> $marker<$operator> for Translation<N, D>
where DefaultAllocator: Allocator<N, D> { }
)*}
);
impl_multiplicative_structures!(
AbstractSemigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractQuasigroup<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
/*
*
* Transformation groups.
*
*/
impl<N: RealField + simba::scalar::RealField, D: DimName> Transformation<Point<N, D>>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
v.clone()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> ProjectiveTransformation<Point<N, D>>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> {
v.clone()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> AffineTransformation<Point<N, D>>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
type Rotation = Id;
type NonUniformScaling = Id;
type Translation = Self;
#[inline]
fn decompose(&self) -> (Self, Id, Id, Id) {
(self.clone(), Id::new(), Id::new(), Id::new())
}
#[inline]
fn append_translation(&self, t: &Self::Translation) -> Self {
t * self
}
#[inline]
fn prepend_translation(&self, t: &Self::Translation) -> Self {
self * t
}
#[inline]
fn append_rotation(&self, _: &Self::Rotation) -> Self {
self.clone()
}
#[inline]
fn prepend_rotation(&self, _: &Self::Rotation) -> Self {
self.clone()
}
#[inline]
fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
#[inline]
fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
}
impl<N: RealField + simba::scalar::RealField, D: DimName> Similarity<Point<N, D>>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
type Scaling = Id;
#[inline]
fn translation(&self) -> Self {
self.clone()
}
#[inline]
fn rotation(&self) -> Id {
Id::new()
}
#[inline]
fn scaling(&self) -> Id {
Id::new()
}
}
macro_rules! marker_impl(
($($Trait: ident),*) => {$(
impl<N: RealField + simba::scalar::RealField, D: DimName> $Trait<Point<N, D>> for Translation<N, D>
where DefaultAllocator: Allocator<N, D> { }
)*}
);
marker_impl!(Isometry, DirectIsometry);
/// Subgroups of the n-dimensional translation group `T(n)`.
impl<N: RealField + simba::scalar::RealField, D: DimName> AlgaTranslation<Point<N, D>>
for Translation<N, D>
where
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn to_vector(&self) -> VectorN<N, D> {
self.vector.clone()
}
#[inline]
fn from_vector(v: VectorN<N, D>) -> Option<Self> {
Some(Self::from(v))
}
#[inline]
fn powf(&self, n: N) -> Option<Self> {
Some(Self::from(&self.vector * n))
}
#[inline]
fn translation_between(a: &Point<N, D>, b: &Point<N, D>) -> Option<Self> {
Some(Self::from(b - a))
}
}

185
src/geometry/unit_complex_alga.rs Executable file
View File

@ -0,0 +1,185 @@
use alga::general::{
AbstractGroup, AbstractLoop, AbstractMagma, AbstractMonoid, AbstractQuasigroup,
AbstractSemigroup, Id, Identity, Multiplicative, RealField, TwoSidedInverse,
};
use alga::linear::{
AffineTransformation, DirectIsometry, Isometry, OrthogonalTransformation,
ProjectiveTransformation, Rotation, Similarity, Transformation,
};
use crate::base::allocator::Allocator;
use crate::base::dimension::U2;
use crate::base::{DefaultAllocator, Vector2};
use crate::geometry::{Point2, UnitComplex};
/*
*
* Implementations for UnitComplex.
*
*/
impl<N: RealField + simba::scalar::RealField> Identity<Multiplicative> for UnitComplex<N> {
#[inline]
fn identity() -> Self {
Self::identity()
}
}
impl<N: RealField + simba::scalar::RealField> AbstractMagma<Multiplicative> for UnitComplex<N> {
#[inline]
fn operate(&self, rhs: &Self) -> Self {
self * rhs
}
}
impl<N: RealField + simba::scalar::RealField> TwoSidedInverse<Multiplicative> for UnitComplex<N> {
#[inline]
#[must_use = "Did you mean to use two_sided_inverse_mut()?"]
fn two_sided_inverse(&self) -> Self {
self.inverse()
}
#[inline]
fn two_sided_inverse_mut(&mut self) {
self.inverse_mut()
}
}
macro_rules! impl_structures(
($($marker: ident<$operator: ident>),* $(,)*) => {$(
impl<N: RealField + simba::scalar::RealField> $marker<$operator> for UnitComplex<N> {
}
)*}
);
impl_structures!(
AbstractSemigroup<Multiplicative>,
AbstractQuasigroup<Multiplicative>,
AbstractMonoid<Multiplicative>,
AbstractLoop<Multiplicative>,
AbstractGroup<Multiplicative>
);
impl<N: RealField + simba::scalar::RealField> Transformation<Point2<N>> for UnitComplex<N>
where
DefaultAllocator: Allocator<N, U2>,
{
#[inline]
fn transform_point(&self, pt: &Point2<N>) -> Point2<N> {
self.transform_point(pt)
}
#[inline]
fn transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
self.transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField> ProjectiveTransformation<Point2<N>> for UnitComplex<N>
where
DefaultAllocator: Allocator<N, U2>,
{
#[inline]
fn inverse_transform_point(&self, pt: &Point2<N>) -> Point2<N> {
self.inverse_transform_point(pt)
}
#[inline]
fn inverse_transform_vector(&self, v: &Vector2<N>) -> Vector2<N> {
self.inverse_transform_vector(v)
}
}
impl<N: RealField + simba::scalar::RealField> AffineTransformation<Point2<N>> for UnitComplex<N>
where
DefaultAllocator: Allocator<N, U2>,
{
type Rotation = Self;
type NonUniformScaling = Id;
type Translation = Id;
#[inline]
fn decompose(&self) -> (Id, Self, Id, Self) {
(Id::new(), self.clone(), Id::new(), Self::identity())
}
#[inline]
fn append_translation(&self, _: &Self::Translation) -> Self {
self.clone()
}
#[inline]
fn prepend_translation(&self, _: &Self::Translation) -> Self {
self.clone()
}
#[inline]
fn append_rotation(&self, r: &Self::Rotation) -> Self {
r * self
}
#[inline]
fn prepend_rotation(&self, r: &Self::Rotation) -> Self {
self * r
}
#[inline]
fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
#[inline]
fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self {
self.clone()
}
}
impl<N: RealField + simba::scalar::RealField> Similarity<Point2<N>> for UnitComplex<N>
where
DefaultAllocator: Allocator<N, U2>,
{
type Scaling = Id;
#[inline]
fn translation(&self) -> Id {
Id::new()
}
#[inline]
fn rotation(&self) -> Self {
self.clone()
}
#[inline]
fn scaling(&self) -> Id {
Id::new()
}
}
macro_rules! marker_impl(
($($Trait: ident),*) => {$(
impl<N: RealField + simba::scalar::RealField> $Trait<Point2<N>> for UnitComplex<N>
where DefaultAllocator: Allocator<N, U2> { }
)*}
);
marker_impl!(Isometry, DirectIsometry, OrthogonalTransformation);
impl<N: RealField + simba::scalar::RealField> Rotation<Point2<N>> for UnitComplex<N>
where
DefaultAllocator: Allocator<N, U2>,
{
#[inline]
fn powf(&self, n: N) -> Option<Self> {
Some(self.powf(n))
}
#[inline]
fn rotation_between(a: &Vector2<N>, b: &Vector2<N>) -> Option<Self> {
Some(Self::rotation_between(a, b))
}
#[inline]
fn scaled_rotation_between(a: &Vector2<N>, b: &Vector2<N>, s: N) -> Option<Self> {
Some(Self::scaled_rotation_between(a, b, s))
}
}

40
src/sparse/cs_matrix.rs
View File

@ -55,7 +55,6 @@ pub trait CsStorageIter<'a, N, R, C = U1> {
/// Iterates through all the row indices of the j-th column.
fn column_row_indices(&'a self, j: usize) -> Self::ColumnRowIndices;
#[inline(always)]
/// Iterates through all the entries of the j-th column.
fn column_entries(&'a self, j: usize) -> Self::ColumnEntries;
}
@ -106,7 +105,8 @@ pub trait CsStorageMut<N, R, C = U1>:
/// A storage of column-compressed sparse matrix based on a Vec.
#[derive(Clone, Debug, PartialEq)]
pub struct CsVecStorage<N: Scalar, R: Dim, C: Dim>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
pub(crate) shape: (R, C),
pub(crate) p: VectorN<usize, C>,
@ -115,7 +115,8 @@ where DefaultAllocator: Allocator<usize, C>
}
impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
/// The value buffer of this storage.
pub fn values(&self) -> &[N] {
@ -136,7 +137,8 @@ where DefaultAllocator: Allocator<usize, C>
impl<N: Scalar, R: Dim, C: Dim> CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C> {}
impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIter<'a, N, R, C> for CsVecStorage<N, R, C>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
type ColumnEntries = ColumnEntries<'a, N>;
type ColumnRowIndices = iter::Cloned<slice::Iter<'a, usize>>;
@ -155,7 +157,8 @@ where DefaultAllocator: Allocator<usize, C>
}
impl<N: Scalar, R: Dim, C: Dim> CsStorage<N, R, C> for CsVecStorage<N, R, C>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
#[inline]
fn shape(&self) -> (R, C) {
@ -200,7 +203,8 @@ where DefaultAllocator: Allocator<usize, C>
}
impl<'a, N: Scalar, R: Dim, C: Dim> CsStorageIterMut<'a, N, R, C> for CsVecStorage<N, R, C>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
type ValuesMut = slice::IterMut<'a, N>;
type ColumnEntriesMut = iter::Zip<iter::Cloned<slice::Iter<'a, usize>>, slice::IterMut<'a, N>>;
@ -220,8 +224,10 @@ where DefaultAllocator: Allocator<usize, C>
}
}
impl<N: Scalar, R: Dim, C: Dim> CsStorageMut<N, R, C> for CsVecStorage<N, R, C> where DefaultAllocator: Allocator<usize, C>
{}
impl<N: Scalar, R: Dim, C: Dim> CsStorageMut<N, R, C> for CsVecStorage<N, R, C> where
DefaultAllocator: Allocator<usize, C>
{
}
/*
pub struct CsSliceStorage<'a, N: Scalar, R: Dim, C: DimAdd<U1>> {
@ -247,7 +253,8 @@ pub struct CsMatrix<
pub type CsVector<N, R = Dynamic, S = CsVecStorage<N, R, U1>> = CsMatrix<N, R, U1, S>;
impl<N: Scalar, R: Dim, C: Dim> CsMatrix<N, R, C>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
/// Creates a new compressed sparse column matrix with the specified dimension and
/// `nvals` possible non-zero values.
@ -403,7 +410,9 @@ impl<N: Scalar, R: Dim, C: Dim, S: CsStorage<N, R, C>> CsMatrix<N, R, C, S> {
/// Computes the transpose of this sparse matrix.
pub fn transpose(&self) -> CsMatrix<N, C, R>
where DefaultAllocator: Allocator<usize, R> {
where
DefaultAllocator: Allocator<usize, R>,
{
let (nrows, ncols) = self.data.shape();
let nvals = self.len();
@ -442,10 +451,13 @@ impl<N: Scalar, R: Dim, C: Dim, S: CsStorageMut<N, R, C>> CsMatrix<N, R, C, S> {
}
impl<N: Scalar, R: Dim, C: Dim> CsMatrix<N, R, C>
where DefaultAllocator: Allocator<usize, C>
where
DefaultAllocator: Allocator<usize, C>,
{
pub(crate) fn sort(&mut self)
where DefaultAllocator: Allocator<N, R> {
where
DefaultAllocator: Allocator<N, R>,
{
// Size = R
let nrows = self.data.shape().0;
let mut workspace = unsafe { VectorN::new_uninitialized_generic(nrows, U1) };
@ -477,7 +489,9 @@ where DefaultAllocator: Allocator<usize, C>
// Remove dupliate entries on a sorted CsMatrix.
pub(crate) fn dedup(&mut self)
where N: Zero + ClosedAdd {
where
N: Zero + ClosedAdd,
{
let mut curr_i = 0;
for j in 0..self.ncols() {