585 lines
17 KiB
Rust
585 lines
17 KiB
Rust
// Copyright 2013 The Lmath Developers. For a full listing of the authors,
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// refer to the AUTHORS file at the top-level directory of this distribution.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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use std::cast::transmute;
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use std::cmp::ApproxEq;
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use std::num::{Zero, One};
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use super::Dimensional;
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use vec::Vec2;
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use super::{Mat3, ToMat3};
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use super::{Mat4, ToMat4};
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#[deriving(Eq)]
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pub struct Mat2<T> {
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x: Vec2<T>,
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y: Vec2<T>,
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}
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pub trait ToMat2<T> {
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pub fn to_mat2(&self) -> Mat2<T>;
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}
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impl<T> Mat2<T> {
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/// Construct a 2 x 2 matrix
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///
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/// # Arguments
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///
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/// - `c0r0`, `c0r1`: the first column of the matrix
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/// - `c1r0`, `c1r1`: the second column of the matrix
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///
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/// ~~~
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/// c0 c1
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/// +------+------+
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/// r0 | c0r0 | c1r0 |
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/// +------+------+
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/// r1 | c0r1 | c1r1 |
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/// +------+------+
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/// ~~~
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#[inline]
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pub fn new(c0r0: T, c0r1: T,
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c1r0: T, c1r1: T) -> Mat2<T> {
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Mat2::from_cols(Vec2::new(c0r0, c0r1),
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Vec2::new(c1r0, c1r1))
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}
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/// Construct a 2 x 2 matrix from column vectors
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///
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/// # Arguments
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///
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/// - `c0`: the first column vector of the matrix
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/// - `c1`: the second column vector of the matrix
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///
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/// ~~~
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/// c0 c1
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/// +------+------+
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/// r0 | c0.x | c1.x |
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/// +------+------+
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/// r1 | c0.y | c1.y |
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/// +------+------+
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/// ~~~
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#[inline]
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pub fn from_cols(c0: Vec2<T>,
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c1: Vec2<T>) -> Mat2<T> {
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Mat2 { x: c0, y: c1 }
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}
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#[inline]
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pub fn col<'a>(&'a self, i: uint) -> &'a Vec2<T> {
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self.index(i)
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}
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#[inline]
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pub fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec2<T> {
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self.index_mut(i)
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}
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#[inline]
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pub fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
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self.index(i).index(j)
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}
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#[inline]
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pub fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
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self.index_mut(i).index_mut(j)
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}
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}
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impl<T> Dimensional<Vec2<T>,[Vec2<T>,..2]> for Mat2<T> {
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#[inline]
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pub fn index<'a>(&'a self, i: uint) -> &'a Vec2<T> {
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&'a self.as_slice()[i]
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}
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#[inline]
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pub fn index_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec2<T> {
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&'a mut self.as_mut_slice()[i]
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}
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#[inline]
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pub fn as_slice<'a>(&'a self) -> &'a [Vec2<T>,..2] {
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unsafe { transmute(self) }
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}
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#[inline]
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pub fn as_mut_slice<'a>(&'a mut self) -> &'a mut [Vec2<T>,..2] {
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unsafe { transmute(self) }
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}
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#[inline(always)]
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pub fn map(&self, f: &fn(&Vec2<T>) -> Vec2<T>) -> Mat2<T> {
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Mat2::from_cols(f(self.index(0)),
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f(self.index(1)))
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}
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#[inline(always)]
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pub fn map_mut(&mut self, f: &fn(&mut Vec2<T>)) {
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f(self.index_mut(0));
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f(self.index_mut(1));
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}
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}
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impl<T:Copy> Mat2<T> {
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#[inline]
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pub fn row(&self, i: uint) -> Vec2<T> {
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Vec2::new(*self.elem(0, i),
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*self.elem(1, i))
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}
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#[inline]
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pub fn swap_cols(&mut self, a: uint, b: uint) {
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let tmp = *self.col(a);
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*self.col_mut(a) = *self.col(b);
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*self.col_mut(b) = tmp;
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}
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#[inline]
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pub fn swap_rows(&mut self, a: uint, b: uint) {
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self.x.swap(a, b);
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self.y.swap(a, b);
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}
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#[inline]
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pub fn transpose(&self) -> Mat2<T> {
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Mat2::new(*self.elem(0, 0), *self.elem(1, 0),
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*self.elem(0, 1), *self.elem(1, 1))
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}
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#[inline]
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pub fn transpose_self(&mut self) {
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let tmp01 = *self.elem(0, 1);
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let tmp10 = *self.elem(1, 0);
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*self.elem_mut(0, 1) = *self.elem(1, 0);
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*self.elem_mut(1, 0) = *self.elem(0, 1);
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*self.elem_mut(1, 0) = tmp01;
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*self.elem_mut(0, 1) = tmp10;
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}
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}
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impl<T:Copy + Num> Mat2<T> {
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/// Construct a 2 x 2 diagonal matrix with the major diagonal set to `value`.
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/// ~~~
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/// c0 c1
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/// +-----+-----+
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/// r0 | val | 0 |
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/// +-----+-----+
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/// r1 | 0 | val |
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/// +-----+-----+
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/// ~~~
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#[inline]
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pub fn from_value(value: T) -> Mat2<T> {
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Mat2::new(value, Zero::zero(),
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Zero::zero(), value)
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}
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/// Returns the multiplicative identity matrix
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/// ~~~
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/// c0 c1
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/// +----+----+
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/// r0 | 1 | 0 |
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/// +----+----+
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/// r1 | 0 | 1 |
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/// +----+----+
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/// ~~~
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#[inline]
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pub fn identity() -> Mat2<T> {
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Mat2::new(One::one::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), One::one::<T>())
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}
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/// Returns the additive identity matrix
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/// ~~~
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/// c0 c1
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/// +----+----+
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/// r0 | 0 | 0 |
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/// +----+----+
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/// r1 | 0 | 0 |
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/// +----+----+
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/// ~~~
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#[inline]
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pub fn zero() -> Mat2<T> {
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Mat2::new(Zero::zero::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), Zero::zero::<T>())
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}
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#[inline]
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pub fn mul_t(&self, value: T) -> Mat2<T> {
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Mat2::from_cols(self.col(0).mul_t(value),
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self.col(1).mul_t(value))
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}
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#[inline]
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pub fn mul_v(&self, vec: &Vec2<T>) -> Vec2<T> {
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Vec2::new(self.row(0).dot(vec),
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self.row(1).dot(vec))
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}
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#[inline]
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pub fn add_m(&self, other: &Mat2<T>) -> Mat2<T> {
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Mat2::from_cols(self.col(0).add_v(other.col(0)),
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self.col(1).add_v(other.col(1)))
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}
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#[inline]
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pub fn sub_m(&self, other: &Mat2<T>) -> Mat2<T> {
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Mat2::from_cols(self.col(0).sub_v(other.col(0)),
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self.col(1).sub_v(other.col(1)))
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}
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#[inline]
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pub fn mul_m(&self, other: &Mat2<T>) -> Mat2<T> {
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Mat2::new(self.row(0).dot(other.col(0)), self.row(1).dot(other.col(0)),
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self.row(0).dot(other.col(1)), self.row(1).dot(other.col(1)))
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}
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#[inline]
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pub fn mul_self_t(&mut self, value: T) {
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self.x.mul_self_t(value);
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self.y.mul_self_t(value);
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}
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#[inline]
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pub fn add_self_m(&mut self, other: &Mat2<T>) {
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self.x.add_self_v(other.col(0));
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self.y.add_self_v(other.col(1));
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}
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#[inline]
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pub fn sub_self_m(&mut self, other: &Mat2<T>) {
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self.x.sub_self_v(other.col(0));
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self.y.sub_self_v(other.col(1));
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}
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pub fn dot(&self, other: &Mat2<T>) -> T {
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other.transpose().mul_m(self).trace()
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}
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pub fn determinant(&self) -> T {
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*self.col(0).index(0) *
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*self.col(1).index(1) -
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*self.col(1).index(0) *
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*self.col(0).index(1)
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}
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pub fn trace(&self) -> T {
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*self.col(0).index(0) +
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*self.col(1).index(1)
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}
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#[inline]
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pub fn to_identity(&mut self) {
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*self = Mat2::identity();
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}
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#[inline]
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pub fn to_zero(&mut self) {
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*self = Mat2::zero();
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}
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}
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impl<T:Copy + Num> ToMat3<T> for Mat2<T> {
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/// Returns the the matrix with an extra row and column added
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/// ~~~
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/// c0 c1 c0 c1 c2
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/// +----+----+ +----+----+----+
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/// r0 | a | b | r0 | a | b | 0 |
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/// +----+----+ +----+----+----+
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/// r1 | c | d | => r1 | c | d | 0 |
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/// +----+----+ +----+----+----+
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/// r2 | 0 | 0 | 1 |
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/// +----+----+----+
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/// ~~~
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#[inline]
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pub fn to_mat3(&self) -> Mat3<T> {
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Mat3::new(*self.elem(0, 0), *self.elem(0, 1), Zero::zero(),
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*self.elem(1, 0), *self.elem(1, 1), Zero::zero(),
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Zero::zero(), Zero::zero(), One::one())
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}
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}
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impl<T:Copy + Num> ToMat4<T> for Mat2<T> {
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/// Returns the the matrix with an extra two rows and columns added
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/// ~~~
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/// c0 c1 c0 c1 c2 c3
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/// +----+----+ +----+----+----+----+
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/// r0 | a | b | r0 | a | b | 0 | 0 |
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/// +----+----+ +----+----+----+----+
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/// r1 | c | d | => r1 | c | d | 0 | 0 |
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/// +----+----+ +----+----+----+----+
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/// r2 | 0 | 0 | 1 | 0 |
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/// +----+----+----+----+
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/// r3 | 0 | 0 | 0 | 1 |
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/// +----+----+----+----+
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/// ~~~
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#[inline]
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pub fn to_mat4(&self) -> Mat4<T> {
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Mat4::new(*self.elem(0, 0), *self.elem(0, 1), Zero::zero(), Zero::zero(),
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*self.elem(1, 0), *self.elem(1, 1), Zero::zero(), Zero::zero(),
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Zero::zero(), Zero::zero(), One::one(), Zero::zero(),
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Zero::zero(), Zero::zero(), Zero::zero(), One::one())
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}
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}
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impl<T:Copy + Num> Neg<Mat2<T>> for Mat2<T> {
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#[inline]
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pub fn neg(&self) -> Mat2<T> {
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Mat2::from_cols(-self.col(0), -self.col(1))
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}
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}
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impl<T:Copy + Real> Mat2<T> {
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#[inline]
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pub fn from_angle(radians: T) -> Mat2<T> {
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let cos_theta = radians.cos();
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let sin_theta = radians.sin();
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Mat2::new(cos_theta, -sin_theta,
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sin_theta, cos_theta)
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}
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}
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impl<T:Copy + Real + ApproxEq<T>> Mat2<T> {
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#[inline]
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pub fn inverse(&self) -> Option<Mat2<T>> {
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let d = self.determinant();
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if d.approx_eq(&Zero::zero()) {
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None
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} else {
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Some(Mat2::new(self.elem(1, 1) / d, -self.elem(0, 1) / d,
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-self.elem(1, 0) / d, self.elem(0, 0) / d))
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}
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}
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#[inline]
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pub fn invert_self(&mut self) {
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*self = self.inverse().expect("Couldn't invert the matrix!");
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}
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#[inline]
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pub fn is_identity(&self) -> bool {
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self.approx_eq(&Mat2::identity())
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}
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#[inline]
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pub fn is_diagonal(&self) -> bool {
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self.elem(0, 1).approx_eq(&Zero::zero()) &&
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self.elem(1, 0).approx_eq(&Zero::zero())
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}
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#[inline]
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pub fn is_rotated(&self) -> bool {
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!self.approx_eq(&Mat2::identity())
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}
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#[inline]
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pub fn is_symmetric(&self) -> bool {
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self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
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self.elem(1, 0).approx_eq(self.elem(0, 1))
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}
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#[inline]
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pub fn is_invertible(&self) -> bool {
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!self.determinant().approx_eq(&Zero::zero())
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}
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}
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impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Mat2<T> {
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#[inline]
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pub fn approx_epsilon() -> T {
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ApproxEq::approx_epsilon::<T,T>()
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}
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#[inline]
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pub fn approx_eq(&self, other: &Mat2<T>) -> bool {
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self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
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}
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#[inline]
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pub fn approx_eq_eps(&self, other: &Mat2<T>, epsilon: &T) -> bool {
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self.col(0).approx_eq_eps(other.col(0), epsilon) &&
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self.col(1).approx_eq_eps(other.col(1), epsilon)
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}
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}
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#[cfg(test)]
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mod tests{
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use mat::*;
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use vec::*;
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#[test]
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fn test_mat2() {
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let a = Mat2 { x: Vec2 { x: 1.0, y: 3.0 },
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y: Vec2 { x: 2.0, y: 4.0 } };
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let b = Mat2 { x: Vec2 { x: 2.0, y: 4.0 },
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y: Vec2 { x: 3.0, y: 5.0 } };
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let v1 = Vec2::new::<float>(1.0, 2.0);
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let f1 = 0.5;
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assert_eq!(a, Mat2::new::<float>(1.0, 3.0,
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2.0, 4.0));
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assert_eq!(a, Mat2::from_cols::<float>(Vec2::new::<float>(1.0, 3.0),
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Vec2::new::<float>(2.0, 4.0)));
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assert_eq!(Mat2::from_value::<float>(4.0),
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Mat2::new::<float>(4.0, 0.0,
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0.0, 4.0));
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assert_eq!(*a.col(0), Vec2::new::<float>(1.0, 3.0));
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assert_eq!(*a.col(1), Vec2::new::<float>(2.0, 4.0));
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assert_eq!(a.row(0), Vec2::new::<float>(1.0, 2.0));
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assert_eq!(a.row(1), Vec2::new::<float>(3.0, 4.0));
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assert_eq!(*a.col(0), Vec2::new::<float>(1.0, 3.0));
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assert_eq!(*a.col(1), Vec2::new::<float>(2.0, 4.0));
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assert_eq!(Mat2::identity::<float>(),
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Mat2::new::<float>(1.0, 0.0,
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0.0, 1.0));
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assert_eq!(Mat2::zero::<float>(),
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Mat2::new::<float>(0.0, 0.0,
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0.0, 0.0));
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assert_eq!(a.determinant(), -2.0);
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assert_eq!(a.trace(), 5.0);
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assert_eq!(a.neg(),
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Mat2::new::<float>(-1.0, -3.0,
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-2.0, -4.0));
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assert_eq!(-a, a.neg());
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assert_eq!(a.mul_t(f1),
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Mat2::new::<float>(0.5, 1.5,
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1.0, 2.0));
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assert_eq!(a.mul_v(&v1), Vec2::new::<float>(5.0, 11.0));
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assert_eq!(a.add_m(&b),
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Mat2::new::<float>(3.0, 7.0,
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5.0, 9.0));
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assert_eq!(a.sub_m(&b),
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Mat2::new::<float>(-1.0, -1.0,
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-1.0, -1.0));
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assert_eq!(a.mul_m(&b),
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Mat2::new::<float>(10.0, 22.0,
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13.0, 29.0));
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assert_eq!(a.dot(&b), 40.0);
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assert_eq!(a.transpose(),
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Mat2::new::<float>(1.0, 2.0,
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3.0, 4.0));
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assert_eq!(a.inverse().unwrap(),
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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>()));
|
|
}
|
|
}
|