nalgebra/src/geometry/similarity_ops.rs

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use num::{One, Zero};
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use std::ops::{Div, DivAssign, Mul, MulAssign};
use simba::scalar::{ClosedAdd, ClosedMul};
use simba::simd::SimdRealField;
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use crate::base::allocator::Allocator;
use crate::base::dimension::{DimName, U1, U2, U3, U4};
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use crate::base::{DefaultAllocator, Scalar, VectorN};
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use crate::geometry::{
AbstractRotation, Isometry, Point, Rotation, Similarity, Translation, UnitComplex,
UnitQuaternion,
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};
// FIXME: there are several cloning of rotations that we could probably get rid of (but we didn't
// yet because that would require to add a bound like `where for<'a, 'b> &'a R: Mul<&'b R, Output = R>`
// which is quite ugly.
/*
*
* In this file, we provide:
* =========================
*
*
* (Operators)
*
* Similarity × Similarity
* Similarity × R
* Similarity × Isometry
*
* Isometry × Similarity
* Isometry ÷ Similarity
*
*
* Similarity ÷ Similarity
* Similarity ÷ R
* Similarity ÷ Isometry
*
* Similarity × Point
* Similarity × Vector
*
*
* Similarity × Translation
* Translation × Similarity
*
* NOTE: The following are provided explicitly because we can't have R × Similarity.
* Rotation × Similarity<Rotation>
* UnitQuaternion × Similarity<UnitQuaternion>
*
* Rotation ÷ Similarity<Rotation>
* UnitQuaternion ÷ Similarity<UnitQuaternion>
*
* (Assignment Operators)
*
* Similarity ×= Translation
*
* Similarity ×= Similarity
* Similarity ×= Isometry
* Similarity ×= R
*
* Similarity ÷= Similarity
* Similarity ÷= Isometry
* Similarity ÷= R
*
*/
// XXX: code duplication: those macros are the same as for the isometry.
macro_rules! similarity_binop_impl(
($Op: ident, $op: ident;
$lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
$action: expr; $($lives: tt),*) => {
impl<$($lives ,)* N: SimdRealField, D: DimName, R> $Op<$Rhs> for $Lhs
where N::Element: SimdRealField,
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D> {
type Output = $Output;
#[inline]
fn $op($lhs, $rhs: $Rhs) -> Self::Output {
$action
}
}
}
);
macro_rules! similarity_binop_impl_all(
($Op: ident, $op: ident;
$lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
[val val] => $action_val_val: expr;
[ref val] => $action_ref_val: expr;
[val ref] => $action_val_ref: expr;
[ref ref] => $action_ref_ref: expr;) => {
similarity_binop_impl!(
$Op, $op;
$lhs: $Lhs, $rhs: $Rhs, Output = $Output;
$action_val_val; );
similarity_binop_impl!(
$Op, $op;
$lhs: &'a $Lhs, $rhs: $Rhs, Output = $Output;
$action_ref_val; 'a);
similarity_binop_impl!(
$Op, $op;
$lhs: $Lhs, $rhs: &'b $Rhs, Output = $Output;
$action_val_ref; 'b);
similarity_binop_impl!(
$Op, $op;
$lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Output;
$action_ref_ref; 'a, 'b);
}
);
macro_rules! similarity_binop_assign_impl_all(
($OpAssign: ident, $op_assign: ident;
$lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty;
[val] => $action_val: expr;
[ref] => $action_ref: expr;) => {
impl<N: SimdRealField, D: DimName, R> $OpAssign<$Rhs> for $Lhs
where N::Element: SimdRealField,
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D> {
#[inline]
fn $op_assign(&mut $lhs, $rhs: $Rhs) {
$action_val
}
}
impl<'b, N: SimdRealField, D: DimName, R> $OpAssign<&'b $Rhs> for $Lhs
where N::Element: SimdRealField,
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D> {
#[inline]
fn $op_assign(&mut $lhs, $rhs: &'b $Rhs) {
$action_ref
}
}
}
);
// Similarity × Similarity
// Similarity ÷ Similarity
similarity_binop_impl_all!(
Mul, mul;
self: Similarity<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
[val val] => &self * &rhs;
[ref val] => self * &rhs;
[val ref] => &self * rhs;
[ref ref] => {
let mut res = self * &rhs.isometry;
res.prepend_scaling_mut(rhs.scaling());
res
};
);
similarity_binop_impl_all!(
Div, div;
self: Similarity<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
[val val] => self * rhs.inverse();
[ref val] => self * rhs.inverse();
[val ref] => self * rhs.inverse();
[ref ref] => self * rhs.inverse();
);
// Similarity ×= Translation
similarity_binop_assign_impl_all!(
MulAssign, mul_assign;
self: Similarity<N, D, R>, rhs: Translation<N, D>;
[val] => *self *= &rhs;
[ref] => {
let shift = self.isometry.rotation.transform_vector(&rhs.vector) * self.scaling();
self.isometry.translation.vector += shift;
};
);
// Similarity ×= Similarity
// Similarity ÷= Similarity
similarity_binop_assign_impl_all!(
MulAssign, mul_assign;
self: Similarity<N, D, R>, rhs: Similarity<N, D, R>;
[val] => *self *= &rhs;
[ref] => {
*self *= &rhs.isometry;
self.prepend_scaling_mut(rhs.scaling());
};
);
similarity_binop_assign_impl_all!(
DivAssign, div_assign;
self: Similarity<N, D, R>, rhs: Similarity<N, D, R>;
[val] => *self /= &rhs;
// FIXME: don't invert explicitly.
[ref] => *self *= rhs.inverse();
);
// Similarity ×= Isometry
// Similarity ÷= Isometry
similarity_binop_assign_impl_all!(
MulAssign, mul_assign;
self: Similarity<N, D, R>, rhs: Isometry<N, D, R>;
[val] => *self *= &rhs;
[ref] => {
let shift = self.isometry.rotation.transform_vector(&rhs.translation.vector) * self.scaling();
self.isometry.translation.vector += shift;
self.isometry.rotation *= rhs.rotation.clone();
};
);
similarity_binop_assign_impl_all!(
DivAssign, div_assign;
self: Similarity<N, D, R>, rhs: Isometry<N, D, R>;
[val] => *self /= &rhs;
// FIXME: don't invert explicitly.
[ref] => *self *= rhs.inverse();
);
// Similarity ×= R
// Similarity ÷= R
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md_assign_impl_all!(
MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
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(D, U1), (D, D) for D: DimName;
self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
[val] => self.isometry.rotation *= rhs;
[ref] => self.isometry.rotation *= rhs.clone();
);
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md_assign_impl_all!(
DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
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(D, U1), (D, D) for D: DimName;
self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>;
// FIXME: don't invert explicitly?
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[val] => *self *= rhs.inverse();
[ref] => *self *= rhs.inverse();
);
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md_assign_impl_all!(
MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
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(U3, U3), (U3, U3) for;
self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
[val] => self.isometry.rotation *= rhs;
[ref] => self.isometry.rotation *= rhs.clone();
);
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md_assign_impl_all!(
DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
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(U3, U3), (U3, U3) for;
self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>;
// FIXME: don't invert explicitly?
[val] => *self *= rhs.inverse();
[ref] => *self *= rhs.inverse();
);
md_assign_impl_all!(
MulAssign, mul_assign where N: SimdRealField for N::Element: SimdRealField;
(U2, U2), (U2, U2) for;
self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
[val] => self.isometry.rotation *= rhs;
[ref] => self.isometry.rotation *= rhs.clone();
);
md_assign_impl_all!(
DivAssign, div_assign where N: SimdRealField for N::Element: SimdRealField;
(U2, U2), (U2, U2) for;
self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>;
// FIXME: don't invert explicitly?
[val] => *self *= rhs.inverse();
[ref] => *self *= rhs.inverse();
);
// Similarity × Isometry
// Similarity ÷ Isometry
similarity_binop_impl_all!(
Mul, mul;
self: Similarity<N, D, R>, rhs: Isometry<N, D, R>, Output = Similarity<N, D, R>;
[val val] => &self * &rhs;
[ref val] => self * &rhs;
[val ref] => &self * rhs;
[ref ref] => {
let shift = self.isometry.rotation.transform_vector(&rhs.translation.vector) * self.scaling();
Similarity::from_parts(
Translation::from(&self.isometry.translation.vector + shift),
self.isometry.rotation.clone() * rhs.rotation.clone(),
self.scaling())
};
);
similarity_binop_impl_all!(
Div, div;
self: Similarity<N, D, R>, rhs: Isometry<N, D, R>, Output = Similarity<N, D, R>;
[val val] => self * rhs.inverse();
[ref val] => self * rhs.inverse();
[val ref] => self * rhs.inverse();
[ref ref] => self * rhs.inverse();
);
// Isometry × Similarity
// Isometry ÷ Similarity
similarity_binop_impl_all!(
Mul, mul;
self: Isometry<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
[val val] => {
let scaling = rhs.scaling();
Similarity::from_isometry(self * rhs.isometry, scaling)
};
[ref val] => {
let scaling = rhs.scaling();
Similarity::from_isometry(self * rhs.isometry, scaling)
};
[val ref] => {
let scaling = rhs.scaling();
Similarity::from_isometry(self * &rhs.isometry, scaling)
};
[ref ref] => {
let scaling = rhs.scaling();
Similarity::from_isometry(self * &rhs.isometry, scaling)
};
);
similarity_binop_impl_all!(
Div, div;
self: Isometry<N, D, R>, rhs: Similarity<N, D, R>, Output = Similarity<N, D, R>;
[val val] => self * rhs.inverse();
[ref val] => self * rhs.inverse();
[val ref] => self * rhs.inverse();
[ref ref] => self * rhs.inverse();
);
// Similarity × Point
similarity_binop_impl_all!(
Mul, mul;
self: Similarity<N, D, R>, right: Point<N, D>, Output = Point<N, D>;
[val val] => {
let scaling = self.scaling();
self.isometry.translation * (self.isometry.rotation.transform_point(&right) * scaling)
};
[ref val] => &self.isometry.translation * (self.isometry.rotation.transform_point(&right) * self.scaling());
[val ref] => {
let scaling = self.scaling();
self.isometry.translation * (self.isometry.rotation.transform_point(right) * scaling)
};
[ref ref] => &self.isometry.translation * (self.isometry.rotation.transform_point(right) * self.scaling());
);
// Similarity × Vector
similarity_binop_impl_all!(
Mul, mul;
self: Similarity<N, D, R>, right: VectorN<N, D>, Output = VectorN<N, D>;
[val val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
[ref val] => self.isometry.rotation.transform_vector(&right) * self.scaling();
[val ref] => self.isometry.rotation.transform_vector(right) * self.scaling();
[ref ref] => self.isometry.rotation.transform_vector(right) * self.scaling();
);
// Similarity × Translation
similarity_binop_impl_all!(
Mul, mul;
self: Similarity<N, D, R>, right: Translation<N, D>, Output = Similarity<N, D, R>;
[val val] => &self * &right;
[ref val] => self * &right;
[val ref] => &self * right;
[ref ref] => {
let shift = self.isometry.rotation.transform_vector(&right.vector) * self.scaling();
Similarity::from_parts(
Translation::from(&self.isometry.translation.vector + shift),
self.isometry.rotation.clone(),
self.scaling())
};
);
// Translation × Similarity
similarity_binop_impl_all!(
Mul, mul;
self: Translation<N, D>, right: Similarity<N, D, R>, Output = Similarity<N, D, R>;
[val val] => {
let scaling = right.scaling();
Similarity::from_isometry(self * right.isometry, scaling)
};
[ref val] => {
let scaling = right.scaling();
Similarity::from_isometry(self * right.isometry, scaling)
};
[val ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
[ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
);
macro_rules! similarity_from_composition_impl(
($Op: ident, $op: ident;
($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
$lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
$action: expr; $($lives: tt),*) => {
impl<$($lives ,)* N: SimdRealField $(, $Dims: $DimsBound)*> $Op<$Rhs> for $Lhs
where N::Element: SimdRealField,
DefaultAllocator: Allocator<N, $R1, $C1> +
Allocator<N, $R2, $C2> {
type Output = $Output;
#[inline]
fn $op($lhs, $rhs: $Rhs) -> Self::Output {
$action
}
}
}
);
macro_rules! similarity_from_composition_impl_all(
($Op: ident, $op: ident;
($R1: ty, $C1: ty),($R2: ty, $C2: ty) $(for $Dims: ident: $DimsBound: ident),*;
$lhs: ident: $Lhs: ty, $rhs: ident: $Rhs: ty, Output = $Output: ty;
[val val] => $action_val_val: expr;
[ref val] => $action_ref_val: expr;
[val ref] => $action_val_ref: expr;
[ref ref] => $action_ref_ref: expr;) => {
similarity_from_composition_impl!(
$Op, $op;
($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
$lhs: $Lhs, $rhs: $Rhs, Output = $Output;
$action_val_val; );
similarity_from_composition_impl!(
$Op, $op;
($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
$lhs: &'a $Lhs, $rhs: $Rhs, Output = $Output;
$action_ref_val; 'a);
similarity_from_composition_impl!(
$Op, $op;
($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
$lhs: $Lhs, $rhs: &'b $Rhs, Output = $Output;
$action_val_ref; 'b);
similarity_from_composition_impl!(
$Op, $op;
($R1, $C1),($R2, $C2) $(for $Dims: $DimsBound),*;
$lhs: &'a $Lhs, $rhs: &'b $Rhs, Output = $Output;
$action_ref_ref; 'a, 'b);
}
);
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// Similarity × Rotation
similarity_from_composition_impl_all!(
Mul, mul;
(D, D), (D, U1) for D: DimName;
self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
Output = Similarity<N, D, Rotation<N, D>>;
[val val] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry * rhs, scaling)
};
[ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
[val ref] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry * rhs, scaling)
};
[ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
);
// Rotation × Similarity
similarity_from_composition_impl_all!(
Mul, mul;
(D, D), (D, U1) for D: DimName;
self: Rotation<N, D>, right: Similarity<N, D, Rotation<N, D>>,
Output = Similarity<N, D, Rotation<N, D>>;
[val val] => &self * &right;
[ref val] => self * &right;
[val ref] => &self * right;
[ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
);
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// Similarity ÷ Rotation
similarity_from_composition_impl_all!(
Div, div;
(D, D), (D, U1) for D: DimName;
self: Similarity<N, D, Rotation<N, D>>, rhs: Rotation<N, D>,
Output = Similarity<N, D, Rotation<N, D>>;
[val val] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry / rhs, scaling)
};
[ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
[val ref] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry / rhs, scaling)
};
[ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
);
// Rotation ÷ Similarity
similarity_from_composition_impl_all!(
Div, div;
(D, D), (D, U1) for D: DimName;
self: Rotation<N, D>, right: Similarity<N, D, Rotation<N, D>>,
Output = Similarity<N, D, Rotation<N, D>>;
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// FIXME: don't call inverse explicitly?
[val val] => self * right.inverse();
[ref val] => self * right.inverse();
[val ref] => self * right.inverse();
[ref ref] => self * right.inverse();
);
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// Similarity × UnitQuaternion
similarity_from_composition_impl_all!(
Mul, mul;
(U4, U1), (U3, U1);
self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
Output = Similarity<N, U3, UnitQuaternion<N>>;
[val val] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry * rhs, scaling)
};
[ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
[val ref] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry * rhs, scaling)
};
[ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
);
// UnitQuaternion × Similarity
similarity_from_composition_impl_all!(
Mul, mul;
(U4, U1), (U3, U1);
self: UnitQuaternion<N>, right: Similarity<N, U3, UnitQuaternion<N>>,
Output = Similarity<N, U3, UnitQuaternion<N>>;
[val val] => &self * &right;
[ref val] => self * &right;
[val ref] => &self * right;
[ref ref] => Similarity::from_isometry(self * &right.isometry, right.scaling());
);
// Similarity ÷ UnitQuaternion
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similarity_from_composition_impl_all!(
Div, div;
(U4, U1), (U3, U1);
self: Similarity<N, U3, UnitQuaternion<N>>, rhs: UnitQuaternion<N>,
Output = Similarity<N, U3, UnitQuaternion<N>>;
[val val] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry / rhs, scaling)
};
[ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
[val ref] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry / rhs, scaling)
};
[ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
);
// UnitQuaternion ÷ Similarity
similarity_from_composition_impl_all!(
Div, div;
(U4, U1), (U3, U1);
self: UnitQuaternion<N>, right: Similarity<N, U3, UnitQuaternion<N>>,
Output = Similarity<N, U3, UnitQuaternion<N>>;
// FIXME: don't call inverse explicitly?
[val val] => self * right.inverse();
[ref val] => self * right.inverse();
[val ref] => self * right.inverse();
[ref ref] => self * right.inverse();
);
// Similarity × UnitComplex
similarity_from_composition_impl_all!(
Mul, mul;
(U2, U1), (U2, U1);
self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
Output = Similarity<N, U2, UnitComplex<N>>;
[val val] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry * rhs, scaling)
};
[ref val] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
[val ref] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry * rhs, scaling)
};
[ref ref] => Similarity::from_isometry(&self.isometry * rhs, self.scaling());
);
// Similarity ÷ UnitComplex
similarity_from_composition_impl_all!(
Div, div;
(U2, U1), (U2, U1);
self: Similarity<N, U2, UnitComplex<N>>, rhs: UnitComplex<N>,
Output = Similarity<N, U2, UnitComplex<N>>;
[val val] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry / rhs, scaling)
};
[ref val] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
[val ref] => {
let scaling = self.scaling();
Similarity::from_isometry(self.isometry / rhs, scaling)
};
[ref ref] => Similarity::from_isometry(&self.isometry / rhs, self.scaling());
);