cgmath/src/mat2.rs

// Copyright 2013 The Lmath Developers. For a full listing of the authors,
// refer to the AUTHORS file at the top-level directory of this distribution.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.

use std::cast::transmute;
use std::cmp::ApproxEq;
use std::num::{Zero, One};

use super::Dimensional;
use vec::Vec2;
use super::{Mat3, ToMat3};
use super::{Mat4, ToMat4};

#[deriving(Eq)]
pub struct Mat2<T> {
    x: Vec2<T>,
    y: Vec2<T>,
}

pub trait ToMat2<T> {
    pub fn to_mat2(&self) -> Mat2<T>;
}

impl<T> Mat2<T> {
    /// Construct a 2 x 2 matrix
    ///
    /// # Arguments
    ///
    /// - `c0r0`, `c0r1`: the first column of the matrix
    /// - `c1r0`, `c1r1`: the second column of the matrix
    ///
    /// ~~~
    ///        c0     c1
    ///     +------+------+
    ///  r0 | c0r0 | c1r0 |
    ///     +------+------+
    ///  r1 | c0r1 | c1r1 |
    ///     +------+------+
    /// ~~~
    #[inline]
    pub fn new(c0r0: T, c0r1: T,
               c1r0: T, c1r1: T) -> Mat2<T> {
        Mat2::from_cols(Vec2::new(c0r0, c0r1),
                        Vec2::new(c1r0, c1r1))
    }

    /// Construct a 2 x 2 matrix from column vectors
    ///
    /// # Arguments
    ///
    /// - `c0`: the first column vector of the matrix
    /// - `c1`: the second column vector of the matrix
    ///
    /// ~~~
    ///        c0     c1
    ///     +------+------+
    ///  r0 | c0.x | c1.x |
    ///     +------+------+
    ///  r1 | c0.y | c1.y |
    ///     +------+------+
    /// ~~~
    #[inline]
    pub fn from_cols(c0: Vec2<T>,
                     c1: Vec2<T>) -> Mat2<T> {
        Mat2 { x: c0, y: c1 }
    }

    #[inline]
    pub fn col<'a>(&'a self, i: uint) -> &'a Vec2<T> {
        self.index(i)
    }

    #[inline]
    pub fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec2<T> {
        self.index_mut(i)
    }

    #[inline]
    pub fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
        self.index(i).index(j)
    }

    #[inline]
    pub fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
        self.index_mut(i).index_mut(j)
    }
}

impl<T> Dimensional<Vec2<T>,[Vec2<T>,..2]> for Mat2<T> {
    #[inline]
    pub fn index<'a>(&'a self, i: uint) -> &'a Vec2<T> {
        &'a self.as_slice()[i]
    }

    #[inline]
    pub fn index_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec2<T> {
        &'a mut self.as_mut_slice()[i]
    }

    #[inline]
    pub fn as_slice<'a>(&'a self) -> &'a [Vec2<T>,..2] {
        unsafe { transmute(self) }
    }

    #[inline]
    pub fn as_mut_slice<'a>(&'a mut self) -> &'a mut [Vec2<T>,..2] {
        unsafe { transmute(self) }
    }

    #[inline(always)]
    pub fn map(&self, f: &fn(&Vec2<T>) -> Vec2<T>) -> Mat2<T> {
        Mat2::from_cols(f(self.index(0)),
                        f(self.index(1)))
    }

    #[inline(always)]
    pub fn map_mut(&mut self, f: &fn(&mut Vec2<T>)) {
        f(self.index_mut(0));
        f(self.index_mut(1));
    }
}

impl<T:Copy> Mat2<T> {
    #[inline]
    pub fn row(&self, i: uint) -> Vec2<T> {
        Vec2::new(*self.elem(0, i),
                  *self.elem(1, i))
    }

    #[inline]
    pub fn swap_cols(&mut self, a: uint, b: uint) {
        let tmp = *self.col(a);
        *self.col_mut(a) = *self.col(b);
        *self.col_mut(b) = tmp;
    }

    #[inline]
    pub fn swap_rows(&mut self, a: uint, b: uint) {
        self.x.swap(a, b);
        self.y.swap(a, b);
    }

    #[inline]
    pub fn transpose(&self) -> Mat2<T> {
        Mat2::new(*self.elem(0, 0), *self.elem(1, 0),
                  *self.elem(0, 1), *self.elem(1, 1))
    }

    #[inline]
    pub fn transpose_self(&mut self) {
        let tmp01 = *self.elem(0, 1);
        let tmp10 = *self.elem(1, 0);

        *self.elem_mut(0, 1) = *self.elem(1, 0);
        *self.elem_mut(1, 0) = *self.elem(0, 1);

        *self.elem_mut(1, 0) = tmp01;
        *self.elem_mut(0, 1) = tmp10;
    }
}

impl<T:Copy + Num> Mat2<T> {
    /// Construct a 2 x 2 diagonal matrix with the major diagonal set to `value`.
    /// ~~~
    ///        c0    c1
    ///     +-----+-----+
    ///  r0 | val |   0 |
    ///     +-----+-----+
    ///  r1 |   0 | val |
    ///     +-----+-----+
    /// ~~~
    #[inline]
    pub fn from_value(value: T) -> Mat2<T> {
        Mat2::new(value, Zero::zero(),
                  Zero::zero(), value)
    }

    /// Returns the multiplicative identity matrix
    /// ~~~
    ///       c0   c1
    ///     +----+----+
    ///  r0 |  1 |  0 |
    ///     +----+----+
    ///  r1 |  0 |  1 |
    ///     +----+----+
    /// ~~~
    #[inline]
    pub fn identity() -> Mat2<T> {
        Mat2::new(One::one::<T>(), Zero::zero::<T>(),
                  Zero::zero::<T>(), One::one::<T>())
    }

    /// Returns the additive identity matrix
    /// ~~~
    ///       c0   c1
    ///     +----+----+
    ///  r0 |  0 |  0 |
    ///     +----+----+
    ///  r1 |  0 |  0 |
    ///     +----+----+
    /// ~~~
    #[inline]
    pub fn zero() -> Mat2<T> {
        Mat2::new(Zero::zero::<T>(), Zero::zero::<T>(),
                  Zero::zero::<T>(), Zero::zero::<T>())
    }

    #[inline]
    pub fn mul_t(&self, value: T) -> Mat2<T> {
        Mat2::from_cols(self.col(0).mul_t(value),
                        self.col(1).mul_t(value))
    }

    #[inline]
    pub fn mul_v(&self, vec: &Vec2<T>) -> Vec2<T> {
        Vec2::new(self.row(0).dot(vec),
                  self.row(1).dot(vec))
    }

    #[inline]
    pub fn add_m(&self, other: &Mat2<T>) -> Mat2<T> {
        Mat2::from_cols(self.col(0).add_v(other.col(0)),
                        self.col(1).add_v(other.col(1)))
    }

    #[inline]
    pub fn sub_m(&self, other: &Mat2<T>) -> Mat2<T> {
        Mat2::from_cols(self.col(0).sub_v(other.col(0)),
                        self.col(1).sub_v(other.col(1)))
    }

    #[inline]
    pub fn mul_m(&self, other: &Mat2<T>) -> Mat2<T> {
        Mat2::new(self.row(0).dot(other.col(0)), self.row(1).dot(other.col(0)),
                  self.row(0).dot(other.col(1)), self.row(1).dot(other.col(1)))
    }

    #[inline]
    pub fn mul_self_t(&mut self, value: T) {
        self.x.mul_self_t(value);
        self.y.mul_self_t(value);
    }

    #[inline]
    pub fn add_self_m(&mut self, other: &Mat2<T>) {
        self.x.add_self_v(other.col(0));
        self.y.add_self_v(other.col(1));
    }

    #[inline]
    pub fn sub_self_m(&mut self, other: &Mat2<T>) {
        self.x.sub_self_v(other.col(0));
        self.y.sub_self_v(other.col(1));
    }

    pub fn dot(&self, other: &Mat2<T>) -> T {
        other.transpose().mul_m(self).trace()
    }

    pub fn determinant(&self) -> T {
       *self.col(0).index(0) *
       *self.col(1).index(1) -
       *self.col(1).index(0) *
       *self.col(0).index(1)
    }

    pub fn trace(&self) -> T {
        *self.col(0).index(0) +
        *self.col(1).index(1)
    }

    #[inline]
    pub fn to_identity(&mut self) {
        *self = Mat2::identity();
    }

    #[inline]
    pub fn to_zero(&mut self) {
        *self = Mat2::zero();
    }
}

impl<T:Copy + Num> ToMat3<T> for Mat2<T> {
    /// Returns the the matrix with an extra row and column added
    /// ~~~
    ///       c0   c1                 c0   c1   c2
    ///     +----+----+             +----+----+----+
    ///  r0 |  a |  b |          r0 |  a |  b |  0 |
    ///     +----+----+             +----+----+----+
    ///  r1 |  c |  d |    =>    r1 |  c |  d |  0 |
    ///     +----+----+             +----+----+----+
    ///                          r2 |  0 |  0 |  1 |
    ///                             +----+----+----+
    /// ~~~
    #[inline]
    pub fn to_mat3(&self) -> Mat3<T> {
        Mat3::new(*self.elem(0, 0), *self.elem(0, 1), Zero::zero(),
                  *self.elem(1, 0), *self.elem(1, 1), Zero::zero(),
                  Zero::zero(), Zero::zero(), One::one())
    }
}

impl<T:Copy + Num> ToMat4<T> for Mat2<T> {
    /// Returns the the matrix with an extra two rows and columns added
    /// ~~~
    ///       c0   c1                 c0   c1   c2   c3
    ///     +----+----+             +----+----+----+----+
    ///  r0 |  a |  b |          r0 |  a |  b |  0 |  0 |
    ///     +----+----+             +----+----+----+----+
    ///  r1 |  c |  d |    =>    r1 |  c |  d |  0 |  0 |
    ///     +----+----+             +----+----+----+----+
    ///                          r2 |  0 |  0 |  1 |  0 |
    ///                             +----+----+----+----+
    ///                          r3 |  0 |  0 |  0 |  1 |
    ///                             +----+----+----+----+
    /// ~~~
    #[inline]
    pub fn to_mat4(&self) -> Mat4<T> {
        Mat4::new(*self.elem(0, 0), *self.elem(0, 1), Zero::zero(), Zero::zero(),
                  *self.elem(1, 0), *self.elem(1, 1), Zero::zero(), Zero::zero(),
                  Zero::zero(), Zero::zero(), One::one(), Zero::zero(),
                  Zero::zero(), Zero::zero(), Zero::zero(), One::one())
    }
}

impl<T:Copy + Num> Neg<Mat2<T>> for Mat2<T> {
    #[inline]
    pub fn neg(&self) -> Mat2<T> {
        Mat2::from_cols(-self.col(0), -self.col(1))
    }
}

impl<T:Copy + Real> Mat2<T> {
    #[inline]
    pub fn from_angle(radians: T) -> Mat2<T> {
        let cos_theta = radians.cos();
        let sin_theta = radians.sin();

        Mat2::new(cos_theta, -sin_theta,
                  sin_theta,  cos_theta)
    }
}

impl<T:Copy + Real + ApproxEq<T>> Mat2<T> {
    #[inline]
    pub fn inverse(&self) -> Option<Mat2<T>> {
        let d = self.determinant();
        if d.approx_eq(&Zero::zero()) {
            None
        } else {
            Some(Mat2::new(self.elem(1, 1) / d, -self.elem(0, 1) / d,
                           -self.elem(1, 0) / d, self.elem(0, 0) / d))
        }
    }

    #[inline]
    pub fn invert_self(&mut self) {
        *self = self.inverse().expect("Couldn't invert the matrix!");
    }

    #[inline]
    pub fn is_identity(&self) -> bool {
        self.approx_eq(&Mat2::identity())
    }

    #[inline]
    pub fn is_diagonal(&self) -> bool {
        self.elem(0, 1).approx_eq(&Zero::zero()) &&
        self.elem(1, 0).approx_eq(&Zero::zero())
    }

    #[inline]
    pub fn is_rotated(&self) -> bool {
        !self.approx_eq(&Mat2::identity())
    }

    #[inline]
    pub fn is_symmetric(&self) -> bool {
        self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
        self.elem(1, 0).approx_eq(self.elem(0, 1))
    }

    #[inline]
    pub fn is_invertible(&self) -> bool {
        !self.determinant().approx_eq(&Zero::zero())
    }
}

impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Mat2<T> {
    #[inline]
    pub fn approx_epsilon() -> T {
        ApproxEq::approx_epsilon::<T,T>()
    }

    #[inline]
    pub fn approx_eq(&self, other: &Mat2<T>) -> bool {
        self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
    }

    #[inline]
    pub fn approx_eq_eps(&self, other: &Mat2<T>, epsilon: &T) -> bool {
        self.col(0).approx_eq_eps(other.col(0), epsilon) &&
        self.col(1).approx_eq_eps(other.col(1), epsilon)
    }
}

#[cfg(test)]
mod tests{
    use mat::*;
    use vec::*;

    #[test]
    fn test_mat2() {
        let a = Mat2 { x: Vec2 { x: 1.0, y: 3.0 },
                       y: Vec2 { x: 2.0, y: 4.0 } };
        let b = Mat2 { x: Vec2 { x: 2.0, y: 4.0 },
                       y: Vec2 { x: 3.0, y: 5.0 } };

        let v1 = Vec2::new::<float>(1.0, 2.0);
        let f1 = 0.5;

        assert_eq!(a, Mat2::new::<float>(1.0, 3.0,
                                         2.0, 4.0));

        assert_eq!(a, Mat2::from_cols::<float>(Vec2::new::<float>(1.0, 3.0),
                                               Vec2::new::<float>(2.0, 4.0)));

        assert_eq!(Mat2::from_value::<float>(4.0),
                   Mat2::new::<float>(4.0, 0.0,
                                      0.0, 4.0));

        assert_eq!(*a.col(0), Vec2::new::<float>(1.0, 3.0));
        assert_eq!(*a.col(1), Vec2::new::<float>(2.0, 4.0));

        assert_eq!(a.row(0), Vec2::new::<float>(1.0, 2.0));
        assert_eq!(a.row(1), Vec2::new::<float>(3.0, 4.0));

        assert_eq!(*a.col(0), Vec2::new::<float>(1.0, 3.0));
        assert_eq!(*a.col(1), Vec2::new::<float>(2.0, 4.0));

        assert_eq!(Mat2::identity::<float>(),
                   Mat2::new::<float>(1.0, 0.0,
                                      0.0, 1.0));

        assert_eq!(Mat2::zero::<float>(),
                   Mat2::new::<float>(0.0, 0.0,
                                      0.0, 0.0));

        assert_eq!(a.determinant(), -2.0);
        assert_eq!(a.trace(), 5.0);

        assert_eq!(a.neg(),
                   Mat2::new::<float>(-1.0, -3.0,
                                      -2.0, -4.0));
        assert_eq!(-a, a.neg());
        assert_eq!(a.mul_t(f1),
                   Mat2::new::<float>(0.5, 1.5,
                                      1.0, 2.0));
        assert_eq!(a.mul_v(&v1), Vec2::new::<float>(5.0, 11.0));
        assert_eq!(a.add_m(&b),
                   Mat2::new::<float>(3.0, 7.0,
                                      5.0, 9.0));
        assert_eq!(a.sub_m(&b),
                   Mat2::new::<float>(-1.0, -1.0,
                                      -1.0, -1.0));
        assert_eq!(a.mul_m(&b),
                   Mat2::new::<float>(10.0, 22.0,
                                      13.0, 29.0));
        assert_eq!(a.dot(&b), 40.0);

        assert_eq!(a.transpose(),
                   Mat2::new::<float>(1.0, 2.0,
                                      3.0, 4.0));

        assert_eq!(a.inverse().unwrap(),
                   Mat2::new::<float>(-2.0,  1.5,
                                      1.0, -0.5));

        assert!(Mat2::new::<float>(0.0, 2.0,
                                   0.0, 5.0).inverse().is_none());

        let ident = Mat2::identity::<float>();

        assert!(ident.is_identity());
        assert!(ident.is_symmetric());
        assert!(ident.is_diagonal());
        assert!(!ident.is_rotated());
        assert!(ident.is_invertible());

        assert!(!a.is_identity());
        assert!(!a.is_symmetric());
        assert!(!a.is_diagonal());
        assert!(a.is_rotated());
        assert!(a.is_invertible());

        let c = Mat2::new::<float>(2.0, 1.0,
                                   1.0, 2.0);
        assert!(!c.is_identity());
        assert!(c.is_symmetric());
        assert!(!c.is_diagonal());
        assert!(c.is_rotated());
        assert!(c.is_invertible());

        assert!(Mat2::from_value::<float>(6.0).is_diagonal());

        assert_eq!(a.to_mat3(),
                   Mat3::new::<float>(1.0, 3.0, 0.0,
                                      2.0, 4.0, 0.0,
                                      0.0, 0.0, 1.0));

        assert_eq!(a.to_mat4(),
                   Mat4::new::<float>(1.0, 3.0, 0.0, 0.0,
                                      2.0, 4.0, 0.0, 0.0,
                                      0.0, 0.0, 1.0, 0.0,
                                      0.0, 0.0, 0.0, 1.0));
    }

    fn test_mat2_mut() {
        let a = Mat2 { x: Vec2 { x: 1.0, y: 3.0 },
                       y: Vec2 { x: 2.0, y: 4.0 } };
        let b = Mat2 { x: Vec2 { x: 2.0, y: 4.0 },
                       y: Vec2 { x: 3.0, y: 5.0 } };

        let f1 = 0.5;

        let mut mut_a = a;

        mut_a.swap_cols(0, 1);
        assert_eq!(mut_a.col(0), a.col(1));
        assert_eq!(mut_a.col(1), a.col(0));
        mut_a = a;

        mut_a.swap_rows(0, 1);
        assert_eq!(mut_a.row(0), a.row(1));
        assert_eq!(mut_a.row(1), a.row(0));
        mut_a = a;

        mut_a.to_identity();
        assert!(mut_a.is_identity());
        mut_a = a;

        mut_a.to_zero();
        assert_eq!(mut_a, Mat2::zero::<float>());
        mut_a = a;

        mut_a.mul_self_t(f1);
        assert_eq!(mut_a, a.mul_t(f1));
        mut_a = a;

        mut_a.add_self_m(&b);
        assert_eq!(mut_a, a.add_m(&b));
        mut_a = a;

        mut_a.sub_self_m(&b);
        assert_eq!(mut_a, a.sub_m(&b));
        mut_a = a;

        mut_a.invert_self();
        assert_eq!(mut_a, a.inverse().unwrap());
        mut_a = a;

        mut_a.transpose_self();
        assert_eq!(mut_a, a.transpose());
        // mut_a = a;
    }

    #[test]
    fn test_mat2_approx_eq() {
        assert!(!Mat2::new::<float>(0.000001, 0.000001,
                           0.000001, 0.000001).approx_eq(&Mat2::zero::<float>()));
        assert!(Mat2::new::<float>(0.0000001, 0.0000001,
                          0.0000001, 0.0000001).approx_eq(&Mat2::zero::<float>()));
    }
}