nalgebra/src/geometry/similarity_conversion.rs

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use num::Zero;
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use simba::scalar::{RealField, SubsetOf, SupersetOf};
use simba::simd::{PrimitiveSimdValue, SimdRealField, SimdValue};
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use crate::base::allocator::Allocator;
use crate::base::dimension::{DimMin, DimName, DimNameAdd, DimNameSum, U1};
use crate::base::{DefaultAllocator, MatrixN, Scalar};
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use crate::geometry::{
AbstractRotation, Isometry, Similarity, SuperTCategoryOf, TAffine, Transform, Translation,
};
/*
* This file provides the following conversions:
* =============================================
*
* Similarity -> Similarity
* Similarity -> Transform
* Similarity -> Matrix (homogeneous)
*/
impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<N1, D, R1>
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where
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N1: RealField + SubsetOf<N2>,
N2: RealField + SupersetOf<N1>,
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R1: AbstractRotation<N1, D> + SubsetOf<R2>,
R2: AbstractRotation<N2, D>,
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DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,
{
#[inline]
fn to_superset(&self) -> Similarity<N2, D, R2> {
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Similarity::from_isometry(self.isometry.to_superset(), self.scaling().to_superset())
}
#[inline]
fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool {
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crate::is_convertible::<_, Isometry<N1, D, R1>>(&sim.isometry)
&& crate::is_convertible::<_, N1>(&sim.scaling())
}
#[inline]
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fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self {
Similarity::from_isometry(
sim.isometry.to_subset_unchecked(),
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sim.scaling().to_subset_unchecked(),
)
}
}
impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Similarity<N1, D, R>
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where
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N1: RealField,
N2: RealField + SupersetOf<N1>,
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C: SuperTCategoryOf<TAffine>,
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R: AbstractRotation<N1, D>
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+ SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
+ SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .determinant()
DefaultAllocator: Allocator<N1, D>
+ Allocator<N1, D, D>
+ Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<(usize, usize), D>
+ Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<N2, D, D>
+ Allocator<N2, D>,
{
#[inline]
fn to_superset(&self) -> Transform<N2, D, C> {
Transform::from_matrix_unchecked(self.to_homogeneous().to_superset())
}
#[inline]
fn is_in_subset(t: &Transform<N2, D, C>) -> bool {
<Self as SubsetOf<_>>::is_in_subset(t.matrix())
}
#[inline]
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fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self {
Self::from_superset_unchecked(t.matrix())
}
}
impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Similarity<N1, D, R>
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where
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N1: RealField,
N2: RealField + SupersetOf<N1>,
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R: AbstractRotation<N1, D>
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+ SubsetOf<MatrixN<N1, DimNameSum<D, U1>>>
+ SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
D: DimNameAdd<U1> + DimMin<D, Output = D>, // needed by .determinant()
DefaultAllocator: Allocator<N1, D>
+ Allocator<N1, D, D>
+ Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<(usize, usize), D>
+ Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>
+ Allocator<N2, D, D>
+ Allocator<N2, D>,
{
#[inline]
fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>> {
self.to_homogeneous().to_superset()
}
#[inline]
fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool {
let mut rot = m.fixed_slice::<D, D>(0, 0).clone_owned();
if rot
.fixed_columns_mut::<U1>(0)
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.try_normalize_mut(N2::zero())
.is_some()
&& rot
.fixed_columns_mut::<U1>(1)
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.try_normalize_mut(N2::zero())
.is_some()
&& rot
.fixed_columns_mut::<U1>(2)
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.try_normalize_mut(N2::zero())
.is_some()
{
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// TODO: could we avoid explicit the computation of the determinant?
// (its sign is needed to see if the scaling factor is negative).
if rot.determinant() < N2::zero() {
rot.fixed_columns_mut::<U1>(0).neg_mut();
rot.fixed_columns_mut::<U1>(1).neg_mut();
rot.fixed_columns_mut::<U1>(2).neg_mut();
}
let bottom = m.fixed_slice::<U1, D>(D::dim(), 0);
// Scalar types agree.
m.iter().all(|e| SupersetOf::<N1>::is_in_subset(e)) &&
// The normalized block part is a rotation.
// rot.is_special_orthogonal(N2::default_epsilon().sqrt()) &&
// The bottom row is (0, 0, ..., 1)
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bottom.iter().all(|e| e.is_zero()) && m[(D::dim(), D::dim())] == N2::one()
} else {
false
}
}
#[inline]
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fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self {
let mut mm = m.clone_owned();
let na = mm.fixed_slice_mut::<D, U1>(0, 0).normalize_mut();
let nb = mm.fixed_slice_mut::<D, U1>(0, 1).normalize_mut();
let nc = mm.fixed_slice_mut::<D, U1>(0, 2).normalize_mut();
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let mut scale = (na + nb + nc) / crate::convert(3.0); // We take the mean, for robustness.
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// TODO: could we avoid the explicit computation of the determinant?
// (its sign is needed to see if the scaling factor is negative).
if mm.fixed_slice::<D, D>(0, 0).determinant() < N2::zero() {
mm.fixed_slice_mut::<D, U1>(0, 0).neg_mut();
mm.fixed_slice_mut::<D, U1>(0, 1).neg_mut();
mm.fixed_slice_mut::<D, U1>(0, 2).neg_mut();
scale = -scale;
}
let t = m.fixed_slice::<D, U1>(0, D::dim()).into_owned();
let t = Translation {
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vector: crate::convert_unchecked(t),
};
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Self::from_parts(
t,
crate::convert_unchecked(mm),
crate::convert_unchecked(scale),
)
}
}
impl<N: SimdRealField, D: DimName, R> From<Similarity<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>
where
D: DimNameAdd<U1>,
R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
{
#[inline]
fn from(sim: Similarity<N, D, R>) -> Self {
sim.to_homogeneous()
}
}
impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
From<[Similarity<N::Element, D, R::Element>; 2]> for Similarity<N, D, R>
where
N: From<[<N as SimdValue>::Element; 2]>,
R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 2]>,
R::Element: AbstractRotation<N::Element, D>,
N::Element: Scalar + Zero + Copy,
R::Element: Scalar + Zero + Copy,
DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
{
#[inline]
fn from(arr: [Similarity<N::Element, D, R::Element>; 2]) -> Self {
let iso = Isometry::from([arr[0].isometry.clone(), arr[1].isometry.clone()]);
let scale = N::from([arr[0].scaling(), arr[1].scaling()]);
Self::from_isometry(iso, scale)
}
}
impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
From<[Similarity<N::Element, D, R::Element>; 4]> for Similarity<N, D, R>
where
N: From<[<N as SimdValue>::Element; 4]>,
R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 4]>,
R::Element: AbstractRotation<N::Element, D>,
N::Element: Scalar + Zero + Copy,
R::Element: Scalar + Zero + Copy,
DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
{
#[inline]
fn from(arr: [Similarity<N::Element, D, R::Element>; 4]) -> Self {
let iso = Isometry::from([
arr[0].isometry.clone(),
arr[1].isometry.clone(),
arr[2].isometry.clone(),
arr[3].isometry.clone(),
]);
let scale = N::from([
arr[0].scaling(),
arr[1].scaling(),
arr[2].scaling(),
arr[3].scaling(),
]);
Self::from_isometry(iso, scale)
}
}
impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
From<[Similarity<N::Element, D, R::Element>; 8]> for Similarity<N, D, R>
where
N: From<[<N as SimdValue>::Element; 8]>,
R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 8]>,
R::Element: AbstractRotation<N::Element, D>,
N::Element: Scalar + Zero + Copy,
R::Element: Scalar + Zero + Copy,
DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
{
#[inline]
fn from(arr: [Similarity<N::Element, D, R::Element>; 8]) -> Self {
let iso = Isometry::from([
arr[0].isometry.clone(),
arr[1].isometry.clone(),
arr[2].isometry.clone(),
arr[3].isometry.clone(),
arr[4].isometry.clone(),
arr[5].isometry.clone(),
arr[6].isometry.clone(),
arr[7].isometry.clone(),
]);
let scale = N::from([
arr[0].scaling(),
arr[1].scaling(),
arr[2].scaling(),
arr[3].scaling(),
arr[4].scaling(),
arr[5].scaling(),
arr[6].scaling(),
arr[7].scaling(),
]);
Self::from_isometry(iso, scale)
}
}
impl<N: Scalar + Zero + PrimitiveSimdValue, D: DimName, R>
From<[Similarity<N::Element, D, R::Element>; 16]> for Similarity<N, D, R>
where
N: From<[<N as SimdValue>::Element; 16]>,
R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 16]>,
R::Element: AbstractRotation<N::Element, D>,
N::Element: Scalar + Zero + Copy,
R::Element: Scalar + Zero + Copy,
DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>,
{
#[inline]
fn from(arr: [Similarity<N::Element, D, R::Element>; 16]) -> Self {
let iso = Isometry::from([
arr[0].isometry.clone(),
arr[1].isometry.clone(),
arr[2].isometry.clone(),
arr[3].isometry.clone(),
arr[4].isometry.clone(),
arr[5].isometry.clone(),
arr[6].isometry.clone(),
arr[7].isometry.clone(),
arr[8].isometry.clone(),
arr[9].isometry.clone(),
arr[10].isometry.clone(),
arr[11].isometry.clone(),
arr[12].isometry.clone(),
arr[13].isometry.clone(),
arr[14].isometry.clone(),
arr[15].isometry.clone(),
]);
let scale = N::from([
arr[0].scaling(),
arr[1].scaling(),
arr[2].scaling(),
arr[3].scaling(),
arr[4].scaling(),
arr[5].scaling(),
arr[6].scaling(),
arr[7].scaling(),
arr[8].scaling(),
arr[9].scaling(),
arr[10].scaling(),
arr[11].scaling(),
arr[12].scaling(),
arr[13].scaling(),
arr[14].scaling(),
arr[15].scaling(),
]);
Self::from_isometry(iso, scale)
}
}