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
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140

//! Affine transformations for n-dimensional discrete spaces.
//!
//! An affine transformation maps points to points
//! so that distances are preserved.  It can be decomposed
//! into a symmetry transformation on the underlying vectors
//! (a rotation or reflection) and a translation.

use crate::Integer;
use crate::Matrix;
use crate::Matrix2d;
use crate::Matrix3d;
use crate::Matrix4d;
use crate::MatrixOps;
use crate::Point;
use crate::Vector;

/// An affine transformation.
///
/// Transforms points to points in an n-dimensional space.
/// Consists of a linear transformation and a translation.
#[derive(Clone, Debug, Eq, PartialEq)]
pub struct AffineTransformation<S, M>
where
    S: Integer,
    M: Matrix<S>,
{
    m: M,
    t: M::V,
}
impl<S, M> AffineTransformation<S, M>
where
    S: Integer,
    M: Matrix<S>,
{
    /// Create a new affine transformation from a matrix and a translation.
    pub fn new(m: M, t: M::V) -> Self {
        AffineTransformation { m, t }
    }

    /// Creates the identity transformation.
    pub fn identity() -> Self {
        Self::new(M::unit(), M::V::zero())
    }

    /// Composes two affine transformations.
    pub fn compose<'a>(&'a self, other: &'a Self) -> Self
    where
        &'a M: MatrixOps<S, &'a M, M>,
        &'a M: MatrixOps<S, M::V, M::V>,
    {
        Self::new(&self.m * &other.m, &other.m * self.t + other.t)
    }

    /// Returns the result of applying the transformation to a point.
    pub fn apply<'a>(&'a self, p: Point<S, M::V>) -> Point<S, M::V>
    where
        &'a M: MatrixOps<S, M::V, M::V>,
    {
        Point::from(&self.m * p.to_vec() + self.t)
    }
}

impl<S, M> Default for AffineTransformation<S, M>
where
    S: Integer,
    M: Matrix<S>,
{
    /// Returns the identity transformation.
    fn default() -> Self {
        Self::identity()
    }
}

/// A 2d affine transformation.
pub type AffineTransformation2d<S> = AffineTransformation<S, Matrix2d<S>>;

/// A 3d affine transformation.
pub type AffineTransformation3d<S> = AffineTransformation<S, Matrix3d<S>>;

/// A 4d affine transformation.
pub type AffineTransformation4d<S> = AffineTransformation<S, Matrix4d<S>>;

#[cfg(test)]
mod tests {
    use crate::p2d;
    use crate::p3d;
    use crate::p4d;
    use crate::v2d;
    use crate::AffineTransformation2d as AT2d;
    use crate::AffineTransformation3d as AT3d;
    use crate::AffineTransformation4d as AT4d;
    use crate::Matrix2d;

    #[test]
    fn test_compose() {
        let at0 = AT2d::new(Matrix2d::new(0, -1, 1, 0), v2d(2, 3));
        let at1 = AT2d::new(Matrix2d::new(0, -1, 1, 0), v2d(4, 5));
        assert_eq!(
            AT2d::new(Matrix2d::new(-1, 0, 0, -1), v2d(1, 7)),
            at0.compose(&at1)
        );
    }

    #[test]
    fn test_apply() {
        let at = AT2d::new(Matrix2d::new(0, -1, 1, 0), v2d(2, 3));
        assert_eq!(p2d(-2, 6), at.apply(p2d(3, 4)));
    }

    #[test]
    fn test_compose_apply_2d() {
        let at0 = AT2d::new(Matrix2d::new(0, -1, 1, 0), v2d(2, 3));
        let at1 = AT2d::new(Matrix2d::new(0, -1, 1, 0), v2d(4, 5));
        let at = at0.compose(&at1);
        assert_eq!(at1.apply(at0.apply(p2d(1, 0))), at.apply(p2d(1, 0)));
        assert_eq!(at1.apply(at0.apply(p2d(0, 1))), at.apply(p2d(0, 1)));
    }

    #[test]
    fn test_identity_2d() {
        let at = AT2d::identity();
        assert_eq!(p2d(1, 0), at.apply(p2d(1, 0)));
        assert_eq!(p2d(0, 1), at.apply(p2d(0, 1)));
    }
    #[test]
    fn test_identity_3d() {
        let at = AT3d::identity();
        assert_eq!(p3d(1, 0, 0), at.apply(p3d(1, 0, 0)));
        assert_eq!(p3d(0, 1, 0), at.apply(p3d(0, 1, 0)));
        assert_eq!(p3d(0, 0, 1), at.apply(p3d(0, 0, 1)));
    }
    #[test]
    fn test_identity_4d() {
        let at = AT4d::identity();
        assert_eq!(p4d(1, 0, 0, 0), at.apply(p4d(1, 0, 0, 0)));
        assert_eq!(p4d(0, 1, 0, 0), at.apply(p4d(0, 1, 0, 0)));
        assert_eq!(p4d(0, 0, 1, 0), at.apply(p4d(0, 0, 1, 0)));
        assert_eq!(p4d(0, 0, 0, 1), at.apply(p4d(0, 0, 0, 1)));
    }
}