      1
      2
      3
      4
      5
      6
      7
      8
      9
     10
     11
     12
     13
     14
     15
     16
     17
     18
     19
     20
     21
     22
     23
     24
     25
     26
     27
     28
     29
     30
     31
     32
     33
     34
     35
     36
     37
     38
     39
     40
     41
     42
     43
     44
     45
     46
     47
     48
     49
     50
     51
     52
     53
     54
     55
     56
     57
     58
     59
     60
     61
     62
     63
     64
     65
     66
     67
     68
     69
     70
     71
     72
     73
     74
     75
     76
     77
     78
     79
     80
     81
     82
     83
     84
     85
     86
     87
     88
     89
     90
     91
     92
     93
     94
     95
     96
     97
     98
     99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121

    use alga::general::ComplexField;
    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};

    use crate::geometry::Point;

    /// A reflection wrt. a plane.
    pub struct Reflection<N: Scalar, D: Dim, S: Storage<N, D>> {
        axis: Vector<N, D, S>,
        bias: N,
    }

    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,
            }
        }

        /// Creates a new reflection wrt. the plane orthogonal to the given axis and that contains the
        /// point `pt`.
        pub fn new_containing_point(
            axis: Unit<Vector<N, D, S>>,
            pt: &Point<N, D>,
        ) -> Self
        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
        }

        // FIXME: 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>)
        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.
                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());
            }
        }

        // FIXME: naming convention: reflect_to, reflect_assign ?
        /// 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)
            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.
                let m_two = sign.scale(crate::convert(-2.0f64));
                let factor = (self.axis.dotc(&rhs.column(i)) - self.bias) * m_two;
                rhs.column_mut(i).axpy(factor, &self.axis, sign);
            }
        }

        /// Applies the reflection to the rows of `lhs`.
        pub fn reflect_rows<R2: Dim, C2: Dim, S2, S3>(
            &self,
            lhs: &mut Matrix<N, R2, C2, S2>,
            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>,
        {
            lhs.mul_to(&self.axis, work);

            if !self.bias.is_zero() {
                work.add_scalar_mut(-self.bias);
            }

            let m_two: N = crate::convert(-2.0f64);
            lhs.gerc(m_two, &work, &self.axis, N::one());
        }

        /// 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);
            }

            let m_two = sign.scale(crate::convert(-2.0f64));
            lhs.gerc(m_two, &work, &self.axis, sign);
        }
    }

# Help

## Keyboard Shortcuts

`?`
  Show this help dialog
`S`
  Focus the search field
`↑`
  Move up in search results
`↓`
  Move down in search results
`↹`
  Switch tab
`⏎`
  Go to active search result
`+`
  Expand all sections
`-`
  Collapse all sections

## Search Tricks

Prefix searches with a type followed by a colon (e.g., `fn:`) to restrict the search to a given type.

Accepted types are: `fn`, `mod`, `struct`, `enum`, `trait`, `type`, `macro`, and `const`.

Search functions by type signature (e.g., `vec -> usize` or `* -> vec`)

Search multiple things at once by splitting your query with comma (e.g., `str,u8` or `String,struct:Vec,test`)