// 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 vec::*;
use super::{Mat3, Mat4};
#[deriving(Eq)]
pub struct Mat2<T> { x: Vec2<T>, y: Vec2<T> }
impl<T> Mat2<T> {
#[inline]
pub fn col<'a>(&'a self, i: uint) -> &'a Vec2<T> {
&'a self.as_slice()[i]
}
#[inline]
pub fn col_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]
pub fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
self.col(i).index(j)
}
#[inline]
pub fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
self.col_mut(i).index_mut(j)
}
}
impl<T:Copy> 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 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();
}
/// 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())
}
/// 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)
}
}