nalgebra/src/geometry/reflection.rs

119 lines
4.1 KiB
Rust
Raw Normal View History

2019-03-23 21:29:07 +08:00
use crate::base::allocator::Allocator;
use crate::base::constraint::{AreMultipliable, DimEq, SameNumberOfRows, ShapeConstraint};
use crate::base::{DefaultAllocator, Matrix, Scalar, Unit, Vector};
use crate::dimension::{Dim, DimName, U1};
use crate::storage::{Storage, StorageMut};
2020-03-21 19:16:46 +08:00
use simba::scalar::ComplexField;
2019-03-23 21:29:07 +08:00
use crate::geometry::Point;
/// A reflection wrt. a plane.
pub struct Reflection<N: Scalar, D: Dim, S: Storage<N, D>> {
2018-02-02 19:26:35 +08:00
axis: Vector<N, D, S>,
bias: N,
}
2019-03-25 18:19:36 +08:00
impl<N: ComplexField, D: Dim, S: Storage<N, D>> Reflection<N, D, S> {
/// Creates a new reflection wrt the plane orthogonal to the given axis and bias.
///
/// The bias is the position of the plane on the axis. In particular, a bias equal to zero
/// represents a plane that passes through the origin.
pub fn new(axis: Unit<Vector<N, D, S>>, bias: N) -> Self {
Self {
axis: axis.into_inner(),
bias,
2018-02-02 19:26:35 +08:00
}
}
/// Creates a new reflection wrt. the plane orthogonal to the given axis and that contains the
/// point `pt`.
2020-03-21 19:16:46 +08:00
pub fn new_containing_point(axis: Unit<Vector<N, D, S>>, pt: &Point<N, D>) -> Self
2018-02-02 19:26:35 +08:00
where
D: DimName,
DefaultAllocator: Allocator<N, D>,
{
let bias = axis.dotc(&pt.coords);
Self::new(axis, bias)
}
/// The reflexion axis.
pub fn axis(&self) -> &Vector<N, D, S> {
&self.axis
}
2020-11-15 23:57:49 +08:00
// TODO: naming convention: reflect_to, reflect_assign ?
/// Applies the reflection to the columns of `rhs`.
pub fn reflect<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<N, R2, C2, S2>)
2018-02-02 19:26:35 +08:00
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
{
for i in 0..rhs.ncols() {
// NOTE: we borrow the column twice here. First it is borrowed immutably for the
// dot product, and then mutably. Somehow, this allows significantly
// better optimizations of the dot product from the compiler.
2019-03-23 21:29:07 +08:00
let m_two: N = crate::convert(-2.0f64);
let factor = (self.axis.dotc(&rhs.column(i)) - self.bias) * m_two;
rhs.column_mut(i).axpy(factor, &self.axis, N::one());
}
}
2020-11-15 23:57:49 +08:00
// TODO: naming convention: reflect_to, reflect_assign ?
2019-03-19 19:00:10 +08:00
/// Applies the reflection to the columns of `rhs`.
pub fn reflect_with_sign<R2: Dim, C2: Dim, S2>(&self, rhs: &mut Matrix<N, R2, C2, S2>, sign: N)
2020-03-21 19:16:46 +08:00
where
S2: StorageMut<N, R2, C2>,
ShapeConstraint: SameNumberOfRows<R2, D>,
2019-03-19 19:00:10 +08:00
{
for i in 0..rhs.ncols() {
// NOTE: we borrow the column twice here. First it is borrowed immutably for the
// dot product, and then mutably. Somehow, this allows significantly
// better optimizations of the dot product from the compiler.
2019-03-23 21:29:07 +08:00
let m_two = sign.scale(crate::convert(-2.0f64));
let factor = (self.axis.dotc(&rhs.column(i)) - self.bias) * m_two;
2019-03-19 19:00:10 +08:00
rhs.column_mut(i).axpy(factor, &self.axis, sign);
}
}
2019-03-18 18:23:19 +08:00
/// Applies the reflection to the rows of `lhs`.
2018-02-02 19:26:35 +08:00
pub fn reflect_rows<R2: Dim, C2: Dim, S2, S3>(
&self,
2019-03-18 18:23:19 +08:00
lhs: &mut Matrix<N, R2, C2, S2>,
2018-02-02 19:26:35 +08:00
work: &mut Vector<N, R2, S3>,
) where
S2: StorageMut<N, R2, C2>,
S3: StorageMut<N, R2>,
ShapeConstraint: DimEq<C2, D> + AreMultipliable<R2, C2, D, U1>,
{
2019-03-18 18:23:19 +08:00
lhs.mul_to(&self.axis, work);
if !self.bias.is_zero() {
work.add_scalar_mut(-self.bias);
}
2019-03-23 21:29:07 +08:00
let m_two: N = crate::convert(-2.0f64);
lhs.gerc(m_two, &work, &self.axis, N::one());
}
2019-03-19 19:00:10 +08:00
/// Applies the reflection to the rows of `lhs`.
pub fn reflect_rows_with_sign<R2: Dim, C2: Dim, S2, S3>(
&self,
lhs: &mut Matrix<N, R2, C2, S2>,
work: &mut Vector<N, R2, S3>,
sign: N,
) where
S2: StorageMut<N, R2, C2>,
S3: StorageMut<N, R2>,
ShapeConstraint: DimEq<C2, D> + AreMultipliable<R2, C2, D, U1>,
{
lhs.mul_to(&self.axis, work);
if !self.bias.is_zero() {
work.add_scalar_mut(-self.bias);
}
2019-03-23 21:29:07 +08:00
let m_two = sign.scale(crate::convert(-2.0f64));
lhs.gerc(m_two, &work, &self.axis, sign);
2019-03-19 19:00:10 +08:00
}
}