1446 lines
45 KiB
Rust
1446 lines
45 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 std::uint;
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use vec::*;
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use quat::Quat;
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#[deriving(Eq)]
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pub struct Mat2<T> { x: Vec2<T>, y: Vec2<T> }
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impl<T> Mat2<T> {
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#[inline]
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pub fn col<'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 col_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]
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pub fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
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self.col(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.col_mut(i).index_mut(j)
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}
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}
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impl<T:Copy> 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 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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/// 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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/// 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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// GLSL-style type aliases
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pub type mat2 = Mat2<f32>;
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pub type dmat2 = Mat2<f64>;
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// Rust-style type aliases
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pub type Mat2f = Mat2<float>;
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pub type Mat2f32 = Mat2<f32>;
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pub type Mat2f64 = Mat2<f64>;
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#[deriving(Eq)]
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pub struct Mat3<T> { x: Vec3<T>, y: Vec3<T>, z: Vec3<T> }
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impl<T> Mat3<T> {
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#[inline]
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pub fn col<'a>(&'a self, i: uint) -> &'a Vec3<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 col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec3<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 [Vec3<T>,..3] {
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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 [Vec3<T>,..3] {
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unsafe { transmute(self) }
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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.col(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.col_mut(i).index_mut(j)
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}
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}
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impl<T:Copy> Mat3<T> {
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/// Construct a 3 x 3 matrix
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///
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/// # Arguments
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///
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/// - `c0r0`, `c0r1`, `c0r2`: the first column of the matrix
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/// - `c1r0`, `c1r1`, `c1r2`: the second column of the matrix
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/// - `c2r0`, `c2r1`, `c2r2`: the third column of the matrix
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///
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/// ~~~
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/// c0 c1 c2
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/// +------+------+------+
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/// r0 | c0r0 | c1r0 | c2r0 |
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/// +------+------+------+
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/// r1 | c0r1 | c1r1 | c2r1 |
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/// +------+------+------+
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/// r2 | c0r2 | c1r2 | c2r2 |
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/// +------+------+------+
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/// ~~~
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#[inline]
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pub fn new(c0r0:T, c0r1:T, c0r2:T,
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c1r0:T, c1r1:T, c1r2:T,
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c2r0:T, c2r1:T, c2r2:T) -> Mat3<T> {
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Mat3::from_cols(Vec3::new(c0r0, c0r1, c0r2),
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Vec3::new(c1r0, c1r1, c1r2),
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Vec3::new(c2r0, c2r1, c2r2))
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}
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/// Construct a 3 x 3 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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/// - `c2`: the third column vector of the matrix
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///
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/// ~~~
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/// c0 c1 c2
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/// +------+------+------+
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/// r0 | c0.x | c1.x | c2.x |
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/// +------+------+------+
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/// r1 | c0.y | c1.y | c2.y |
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/// +------+------+------+
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/// r2 | c0.z | c1.z | c2.z |
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/// +------+------+------+
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/// ~~~
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#[inline]
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pub fn from_cols(c0: Vec3<T>,
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c1: Vec3<T>,
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c2: Vec3<T>) -> Mat3<T> {
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Mat3 { x: c0, y: c1, z: c2 }
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}
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#[inline]
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pub fn row(&self, i: uint) -> Vec3<T> {
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Vec3::new(*self.elem(0, i),
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*self.elem(1, i),
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*self.elem(2, 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);
|
||
*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);
|
||
self.z.swap(a, b);
|
||
}
|
||
|
||
#[inline]
|
||
pub fn transpose(&self) -> Mat3<T> {
|
||
Mat3::new(*self.elem(0, 0), *self.elem(1, 0), *self.elem(2, 0),
|
||
*self.elem(0, 1), *self.elem(1, 1), *self.elem(2, 1),
|
||
*self.elem(0, 2), *self.elem(1, 2), *self.elem(2, 2))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn transpose_self(&mut self) {
|
||
let tmp01 = *self.elem(0, 1);
|
||
let tmp02 = *self.elem(0, 2);
|
||
let tmp10 = *self.elem(1, 0);
|
||
let tmp12 = *self.elem(1, 2);
|
||
let tmp20 = *self.elem(2, 0);
|
||
let tmp21 = *self.elem(2, 1);
|
||
|
||
*self.elem_mut(0, 1) = *self.elem(1, 0);
|
||
*self.elem_mut(0, 2) = *self.elem(2, 0);
|
||
*self.elem_mut(1, 0) = *self.elem(0, 1);
|
||
*self.elem_mut(1, 2) = *self.elem(2, 1);
|
||
*self.elem_mut(2, 0) = *self.elem(0, 2);
|
||
*self.elem_mut(2, 1) = *self.elem(1, 2);
|
||
|
||
*self.elem_mut(1, 0) = tmp01;
|
||
*self.elem_mut(2, 0) = tmp02;
|
||
*self.elem_mut(0, 1) = tmp10;
|
||
*self.elem_mut(2, 1) = tmp12;
|
||
*self.elem_mut(0, 2) = tmp20;
|
||
*self.elem_mut(1, 2) = tmp21;
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Num> Mat3<T> {
|
||
/// Construct a 3 x 3 diagonal matrix with the major diagonal set to `value`
|
||
///
|
||
/// # Arguments
|
||
///
|
||
/// - `value`: the value to set the major diagonal to
|
||
///
|
||
/// ~~~
|
||
/// c0 c1 c2
|
||
/// +-----+-----+-----+
|
||
/// r0 | val | 0 | 0 |
|
||
/// +-----+-----+-----+
|
||
/// r1 | 0 | val | 0 |
|
||
/// +-----+-----+-----+
|
||
/// r2 | 0 | 0 | val |
|
||
/// +-----+-----+-----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn from_value(value: T) -> Mat3<T> {
|
||
Mat3::new(value, Zero::zero(), Zero::zero(),
|
||
Zero::zero(), value, Zero::zero(),
|
||
Zero::zero(), Zero::zero(), value)
|
||
}
|
||
|
||
/// Returns the multiplicative identity matrix
|
||
/// ~~~
|
||
/// c0 c1 c2
|
||
/// +----+----+----+
|
||
/// r0 | 1 | 0 | 0 |
|
||
/// +----+----+----+
|
||
/// r1 | 0 | 1 | 0 |
|
||
/// +----+----+----+
|
||
/// r2 | 0 | 0 | 1 |
|
||
/// +----+----+----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn identity() -> Mat3<T> {
|
||
Mat3::new(One::one::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), One::one::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), One::one::<T>())
|
||
}
|
||
|
||
/// Returns the additive identity matrix
|
||
/// ~~~
|
||
/// c0 c1 c2
|
||
/// +----+----+----+
|
||
/// r0 | 0 | 0 | 0 |
|
||
/// +----+----+----+
|
||
/// r1 | 0 | 0 | 0 |
|
||
/// +----+----+----+
|
||
/// r2 | 0 | 0 | 0 |
|
||
/// +----+----+----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn zero() -> Mat3<T> {
|
||
Mat3::new(Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_t(&self, value: T) -> Mat3<T> {
|
||
Mat3::from_cols(self.col(0).mul_t(value),
|
||
self.col(1).mul_t(value),
|
||
self.col(2).mul_t(value))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T> {
|
||
Vec3::new(self.row(0).dot(vec),
|
||
self.row(1).dot(vec),
|
||
self.row(2).dot(vec))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn add_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
||
Mat3::from_cols(self.col(0).add_v(other.col(0)),
|
||
self.col(1).add_v(other.col(1)),
|
||
self.col(2).add_v(other.col(2)))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn sub_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
||
Mat3::from_cols(self.col(0).sub_v(other.col(0)),
|
||
self.col(1).sub_v(other.col(1)),
|
||
self.col(2).sub_v(other.col(2)))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
||
Mat3::new(self.row(0).dot(other.col(0)),
|
||
self.row(1).dot(other.col(0)),
|
||
self.row(2).dot(other.col(0)),
|
||
|
||
self.row(0).dot(other.col(1)),
|
||
self.row(1).dot(other.col(1)),
|
||
self.row(2).dot(other.col(1)),
|
||
|
||
self.row(0).dot(other.col(2)),
|
||
self.row(1).dot(other.col(2)),
|
||
self.row(2).dot(other.col(2)))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_self_t(&mut self, value: T) {
|
||
self.col_mut(0).mul_self_t(value);
|
||
self.col_mut(1).mul_self_t(value);
|
||
self.col_mut(2).mul_self_t(value);
|
||
}
|
||
|
||
#[inline]
|
||
pub fn add_self_m(&mut self, other: &Mat3<T>) {
|
||
self.col_mut(0).add_self_v(other.col(0));
|
||
self.col_mut(1).add_self_v(other.col(1));
|
||
self.col_mut(2).add_self_v(other.col(2));
|
||
}
|
||
|
||
#[inline]
|
||
pub fn sub_self_m(&mut self, other: &Mat3<T>) {
|
||
self.col_mut(0).sub_self_v(other.col(0));
|
||
self.col_mut(1).sub_self_v(other.col(1));
|
||
self.col_mut(2).sub_self_v(other.col(2));
|
||
}
|
||
|
||
pub fn dot(&self, other: &Mat3<T>) -> T {
|
||
other.transpose().mul_m(self).trace()
|
||
}
|
||
|
||
pub fn determinant(&self) -> T {
|
||
self.col(0).dot(&self.col(1).cross(self.col(2)))
|
||
}
|
||
|
||
pub fn trace(&self) -> T {
|
||
*self.elem(0, 0) +
|
||
*self.elem(1, 1) +
|
||
*self.elem(2, 2)
|
||
}
|
||
|
||
#[inline]
|
||
pub fn to_identity(&mut self) {
|
||
*self = Mat3::identity();
|
||
}
|
||
|
||
#[inline]
|
||
pub fn to_zero(&mut self) {
|
||
*self = Mat3::zero();
|
||
}
|
||
|
||
/// Returns the the matrix with an extra row and column added
|
||
/// ~~~
|
||
/// c0 c1 c2 c0 c1 c2 c3
|
||
/// +----+----+----+ +----+----+----+----+
|
||
/// r0 | a | b | c | r0 | a | b | c | 0 |
|
||
/// +----+----+----+ +----+----+----+----+
|
||
/// r1 | d | e | f | => r1 | d | e | f | 0 |
|
||
/// +----+----+----+ +----+----+----+----+
|
||
/// r2 | g | h | i | r2 | g | h | i | 0 |
|
||
/// +----+----+----+ +----+----+----+----+
|
||
/// r3 | 0 | 0 | 0 | 1 |
|
||
/// +----+----+----+----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn to_mat4(&self) -> Mat4<T> {
|
||
Mat4::new(*self.elem(0, 0), *self.elem(0, 1), *self.elem(0, 2), Zero::zero(),
|
||
*self.elem(1, 0), *self.elem(1, 1), *self.elem(1, 2), Zero::zero(),
|
||
*self.elem(2, 0), *self.elem(2, 1), *self.elem(2, 2), Zero::zero(),
|
||
Zero::zero(), Zero::zero(), Zero::zero(), One::one())
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Num> Neg<Mat3<T>> for Mat3<T> {
|
||
#[inline]
|
||
pub fn neg(&self) -> Mat3<T> {
|
||
Mat3::from_cols(-self.col(0), -self.col(1), -self.col(2))
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Real> Mat3<T> {
|
||
/// Construct a matrix from an angular rotation around the `x` axis
|
||
pub fn from_angle_x(radians: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
||
let cos_theta = radians.cos();
|
||
let sin_theta = radians.sin();
|
||
|
||
Mat3::new(One::one(), Zero::zero(), Zero::zero(),
|
||
Zero::zero(), cos_theta, sin_theta,
|
||
Zero::zero(), -sin_theta, cos_theta)
|
||
}
|
||
|
||
/// Construct a matrix from an angular rotation around the `y` axis
|
||
pub fn from_angle_y(radians: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
||
let cos_theta = radians.cos();
|
||
let sin_theta = radians.sin();
|
||
|
||
Mat3::new(cos_theta, Zero::zero(), -sin_theta,
|
||
Zero::zero(), One::one(), Zero::zero(),
|
||
sin_theta, Zero::zero(), cos_theta)
|
||
}
|
||
|
||
/// Construct a matrix from an angular rotation around the `z` axis
|
||
pub fn from_angle_z(radians: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
||
let cos_theta = radians.cos();
|
||
let sin_theta = radians.sin();
|
||
|
||
Mat3::new(cos_theta, sin_theta, Zero::zero(),
|
||
-sin_theta, cos_theta, Zero::zero(),
|
||
Zero::zero(), Zero::zero(), One::one())
|
||
}
|
||
|
||
/// Construct a matrix from Euler angles
|
||
///
|
||
/// # Arguments
|
||
///
|
||
/// - `theta_x`: the angular rotation around the `x` axis (pitch)
|
||
/// - `theta_y`: the angular rotation around the `y` axis (yaw)
|
||
/// - `theta_z`: the angular rotation around the `z` axis (roll)
|
||
pub fn from_angle_xyz(radians_x: T, radians_y: T, radians_z: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
|
||
let cx = radians_x.cos();
|
||
let sx = radians_x.sin();
|
||
let cy = radians_y.cos();
|
||
let sy = radians_y.sin();
|
||
let cz = radians_z.cos();
|
||
let sz = radians_z.sin();
|
||
|
||
Mat3::new(cy*cz, cy*sz, -sy,
|
||
-cx*sz + sx*sy*cz, cx*cz + sx*sy*sz, sx*cy,
|
||
sx*sz + cx*sy*cz, -sx*cz + cx*sy*sz, cx*cy)
|
||
}
|
||
|
||
/// Construct a matrix from an axis and an angular rotation
|
||
pub fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Mat3<T> {
|
||
let c = radians.cos();
|
||
let s = radians.sin();
|
||
let _1_c = One::one::<T>() - c;
|
||
|
||
let x = axis.x;
|
||
let y = axis.y;
|
||
let z = axis.z;
|
||
|
||
Mat3::new(_1_c*x*x + c, _1_c*x*y + s*z, _1_c*x*z - s*y,
|
||
_1_c*x*y - s*z, _1_c*y*y + c, _1_c*y*z + s*x,
|
||
_1_c*x*z + s*y, _1_c*y*z - s*x, _1_c*z*z + c)
|
||
}
|
||
|
||
#[inline]
|
||
pub fn from_axes(x: Vec3<T>, y: Vec3<T>, z: Vec3<T>) -> Mat3<T> {
|
||
Mat3::from_cols(x, y, z)
|
||
}
|
||
|
||
pub fn look_at(dir: &Vec3<T>, up: &Vec3<T>) -> Mat3<T> {
|
||
let dir_ = dir.normalize();
|
||
let side = dir_.cross(&up.normalize());
|
||
let up_ = side.cross(&dir_).normalize();
|
||
|
||
Mat3::from_axes(up_, side, dir_)
|
||
}
|
||
|
||
/// Convert the matrix to a quaternion
|
||
pub fn to_quat(&self) -> Quat<T> {
|
||
// Implemented using a mix of ideas from jMonkeyEngine and Ken Shoemake's
|
||
// paper on Quaternions: http://www.cs.ucr.edu/~vbz/resources/Quatut.pdf
|
||
|
||
let mut s;
|
||
let w; let x; let y; let z;
|
||
let trace = self.trace();
|
||
|
||
// FIXME: We don't have any numeric conversions in std yet :P
|
||
let half = One::one::<T>() / (One::one::<T>() + One::one::<T>());
|
||
|
||
cond! (
|
||
(trace >= Zero::zero()) {
|
||
s = (One::one::<T>() + trace).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (*self.elem(1, 2) - *self.elem(2, 1)) * s;
|
||
y = (*self.elem(2, 0) - *self.elem(0, 2)) * s;
|
||
z = (*self.elem(0, 1) - *self.elem(1, 0)) * s;
|
||
}
|
||
((*self.elem(0, 0) > *self.elem(1, 1))
|
||
&& (*self.elem(0, 0) > *self.elem(2, 2))) {
|
||
s = (half + (*self.elem(0, 0) - *self.elem(1, 1) - *self.elem(2, 2))).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (*self.elem(0, 1) - *self.elem(1, 0)) * s;
|
||
y = (*self.elem(2, 0) - *self.elem(0, 2)) * s;
|
||
z = (*self.elem(1, 2) - *self.elem(2, 1)) * s;
|
||
}
|
||
(*self.elem(1, 1) > *self.elem(2, 2)) {
|
||
s = (half + (*self.elem(1, 1) - *self.elem(0, 0) - *self.elem(2, 2))).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (*self.elem(0, 1) - *self.elem(1, 0)) * s;
|
||
y = (*self.elem(1, 2) - *self.elem(2, 1)) * s;
|
||
z = (*self.elem(2, 0) - *self.elem(0, 2)) * s;
|
||
}
|
||
_ {
|
||
s = (half + (*self.elem(2, 2) - *self.elem(0, 0) - *self.elem(1, 1))).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (*self.elem(2, 0) - *self.elem(0, 2)) * s;
|
||
y = (*self.elem(1, 2) - *self.elem(2, 1)) * s;
|
||
z = (*self.elem(0, 1) - *self.elem(1, 0)) * s;
|
||
}
|
||
)
|
||
Quat::new(w, x, y, z)
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Real + ApproxEq<T>> Mat3<T> {
|
||
pub fn inverse(&self) -> Option<Mat3<T>> {
|
||
let d = self.determinant();
|
||
if d.approx_eq(&Zero::zero()) {
|
||
None
|
||
} else {
|
||
Some(Mat3::from_cols(self.col(1).cross(self.col(2)).div_t(d),
|
||
self.col(2).cross(self.col(0)).div_t(d),
|
||
self.col(0).cross(self.col(1)).div_t(d)).transpose())
|
||
}
|
||
}
|
||
|
||
#[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(&Mat3::identity())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_diagonal(&self) -> bool {
|
||
self.elem(0, 1).approx_eq(&Zero::zero()) &&
|
||
self.elem(0, 2).approx_eq(&Zero::zero()) &&
|
||
|
||
self.elem(1, 0).approx_eq(&Zero::zero()) &&
|
||
self.elem(1, 2).approx_eq(&Zero::zero()) &&
|
||
|
||
self.elem(2, 0).approx_eq(&Zero::zero()) &&
|
||
self.elem(2, 1).approx_eq(&Zero::zero())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_rotated(&self) -> bool {
|
||
!self.approx_eq(&Mat3::identity())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_symmetric(&self) -> bool {
|
||
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
||
self.elem(0, 2).approx_eq(self.elem(2, 0)) &&
|
||
|
||
self.elem(1, 0).approx_eq(self.elem(0, 1)) &&
|
||
self.elem(1, 2).approx_eq(self.elem(2, 1)) &&
|
||
|
||
self.elem(2, 0).approx_eq(self.elem(0, 2)) &&
|
||
self.elem(2, 1).approx_eq(self.elem(1, 2))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_invertible(&self) -> bool {
|
||
!self.determinant().approx_eq(&Zero::zero())
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Mat3<T> {
|
||
#[inline]
|
||
pub fn approx_epsilon() -> T {
|
||
ApproxEq::approx_epsilon::<T,T>()
|
||
}
|
||
|
||
#[inline]
|
||
pub fn approx_eq(&self, other: &Mat3<T>) -> bool {
|
||
self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn approx_eq_eps(&self, other: &Mat3<T>, epsilon: &T) -> bool {
|
||
self.col(0).approx_eq_eps(other.col(0), epsilon) &&
|
||
self.col(1).approx_eq_eps(other.col(1), epsilon) &&
|
||
self.col(2).approx_eq_eps(other.col(2), epsilon)
|
||
}
|
||
}
|
||
|
||
// GLSL-style type aliases
|
||
pub type mat3 = Mat3<f32>;
|
||
pub type dmat3 = Mat3<f64>;
|
||
|
||
// Rust-style type aliases
|
||
pub type Mat3f = Mat3<float>;
|
||
pub type Mat3f32 = Mat3<f32>;
|
||
pub type Mat3f64 = Mat3<f64>;
|
||
|
||
/// A 4 x 4 column major matrix
|
||
///
|
||
/// # Type parameters
|
||
///
|
||
/// - `T` - The type of the elements of the matrix. Should be a floating point type.
|
||
///
|
||
/// # Fields
|
||
///
|
||
/// - `x`: the first column vector of the matrix
|
||
/// - `y`: the second column vector of the matrix
|
||
/// - `z`: the third column vector of the matrix
|
||
/// - `w`: the fourth column vector of the matrix
|
||
#[deriving(Eq)]
|
||
pub struct Mat4<T> { x: Vec4<T>, y: Vec4<T>, z: Vec4<T>, w: Vec4<T> }
|
||
|
||
impl<T> Mat4<T> {
|
||
#[inline]
|
||
pub fn col<'a>(&'a self, i: uint) -> &'a Vec4<T> {
|
||
&'a self.as_slice()[i]
|
||
}
|
||
|
||
#[inline]
|
||
pub fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec4<T> {
|
||
&'a mut self.as_mut_slice()[i]
|
||
}
|
||
|
||
#[inline]
|
||
pub fn as_slice<'a>(&'a self) -> &'a [Vec4<T>,..4] {
|
||
unsafe { transmute(self) }
|
||
}
|
||
|
||
#[inline]
|
||
pub fn as_mut_slice<'a>(&'a mut self) -> &'a mut [Vec4<T>,..4] {
|
||
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> Mat4<T> {
|
||
/// Construct a 4 x 4 matrix
|
||
///
|
||
/// # Arguments
|
||
///
|
||
/// - `c0r0`, `c0r1`, `c0r2`, `c0r3`: the first column of the matrix
|
||
/// - `c1r0`, `c1r1`, `c1r2`, `c1r3`: the second column of the matrix
|
||
/// - `c2r0`, `c2r1`, `c2r2`, `c2r3`: the third column of the matrix
|
||
/// - `c3r0`, `c3r1`, `c3r2`, `c3r3`: the fourth column of the matrix
|
||
///
|
||
/// ~~~
|
||
/// c0 c1 c2 c3
|
||
/// +------+------+------+------+
|
||
/// r0 | c0r0 | c1r0 | c2r0 | c3r0 |
|
||
/// +------+------+------+------+
|
||
/// r1 | c0r1 | c1r1 | c2r1 | c3r1 |
|
||
/// +------+------+------+------+
|
||
/// r2 | c0r2 | c1r2 | c2r2 | c3r2 |
|
||
/// +------+------+------+------+
|
||
/// r3 | c0r3 | c1r3 | c2r3 | c3r3 |
|
||
/// +------+------+------+------+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn new(c0r0: T, c0r1: T, c0r2: T, c0r3: T,
|
||
c1r0: T, c1r1: T, c1r2: T, c1r3: T,
|
||
c2r0: T, c2r1: T, c2r2: T, c2r3: T,
|
||
c3r0: T, c3r1: T, c3r2: T, c3r3: T) -> Mat4<T> {
|
||
Mat4::from_cols(Vec4::new(c0r0, c0r1, c0r2, c0r3),
|
||
Vec4::new(c1r0, c1r1, c1r2, c1r3),
|
||
Vec4::new(c2r0, c2r1, c2r2, c2r3),
|
||
Vec4::new(c3r0, c3r1, c3r2, c3r3))
|
||
}
|
||
|
||
/// Construct a 4 x 4 matrix from column vectors
|
||
///
|
||
/// # Arguments
|
||
///
|
||
/// - `c0`: the first column vector of the matrix
|
||
/// - `c1`: the second column vector of the matrix
|
||
/// - `c2`: the third column vector of the matrix
|
||
/// - `c3`: the fourth column vector of the matrix
|
||
///
|
||
/// ~~~
|
||
/// c0 c1 c2 c3
|
||
/// +------+------+------+------+
|
||
/// r0 | c0.x | c1.x | c2.x | c3.x |
|
||
/// +------+------+------+------+
|
||
/// r1 | c0.y | c1.y | c2.y | c3.y |
|
||
/// +------+------+------+------+
|
||
/// r2 | c0.z | c1.z | c2.z | c3.z |
|
||
/// +------+------+------+------+
|
||
/// r3 | c0.w | c1.w | c2.w | c3.w |
|
||
/// +------+------+------+------+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn from_cols(c0: Vec4<T>,
|
||
c1: Vec4<T>,
|
||
c2: Vec4<T>,
|
||
c3: Vec4<T>) -> Mat4<T> {
|
||
Mat4 { x: c0, y: c1, z: c2, w: c3 }
|
||
}
|
||
|
||
#[inline]
|
||
pub fn row(&self, i: uint) -> Vec4<T> {
|
||
Vec4::new(*self.elem(0, i),
|
||
*self.elem(1, i),
|
||
*self.elem(2, i),
|
||
*self.elem(3, 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);
|
||
self.z.swap(a, b);
|
||
self.w.swap(a, b);
|
||
}
|
||
|
||
#[inline]
|
||
pub fn transpose(&self) -> Mat4<T> {
|
||
Mat4::new(*self.elem(0, 0), *self.elem(1, 0), *self.elem(2, 0), *self.elem(3, 0),
|
||
*self.elem(0, 1), *self.elem(1, 1), *self.elem(2, 1), *self.elem(3, 1),
|
||
*self.elem(0, 2), *self.elem(1, 2), *self.elem(2, 2), *self.elem(3, 2),
|
||
*self.elem(0, 3), *self.elem(1, 3), *self.elem(2, 3), *self.elem(3, 3))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn transpose_self(&mut self) {
|
||
let tmp01 = *self.elem(0, 1);
|
||
let tmp02 = *self.elem(0, 2);
|
||
let tmp03 = *self.elem(0, 3);
|
||
let tmp10 = *self.elem(1, 0);
|
||
let tmp12 = *self.elem(1, 2);
|
||
let tmp13 = *self.elem(1, 3);
|
||
let tmp20 = *self.elem(2, 0);
|
||
let tmp21 = *self.elem(2, 1);
|
||
let tmp23 = *self.elem(2, 3);
|
||
let tmp30 = *self.elem(3, 0);
|
||
let tmp31 = *self.elem(3, 1);
|
||
let tmp32 = *self.elem(3, 2);
|
||
|
||
*self.elem_mut(0, 1) = *self.elem(1, 0);
|
||
*self.elem_mut(0, 2) = *self.elem(2, 0);
|
||
*self.elem_mut(0, 3) = *self.elem(3, 0);
|
||
*self.elem_mut(1, 0) = *self.elem(0, 1);
|
||
*self.elem_mut(1, 2) = *self.elem(2, 1);
|
||
*self.elem_mut(1, 3) = *self.elem(3, 1);
|
||
*self.elem_mut(2, 0) = *self.elem(0, 2);
|
||
*self.elem_mut(2, 1) = *self.elem(1, 2);
|
||
*self.elem_mut(2, 3) = *self.elem(3, 2);
|
||
*self.elem_mut(3, 0) = *self.elem(0, 3);
|
||
*self.elem_mut(3, 1) = *self.elem(1, 3);
|
||
*self.elem_mut(3, 2) = *self.elem(2, 3);
|
||
|
||
*self.elem_mut(1, 0) = tmp01;
|
||
*self.elem_mut(2, 0) = tmp02;
|
||
*self.elem_mut(3, 0) = tmp03;
|
||
*self.elem_mut(0, 1) = tmp10;
|
||
*self.elem_mut(2, 1) = tmp12;
|
||
*self.elem_mut(3, 1) = tmp13;
|
||
*self.elem_mut(0, 2) = tmp20;
|
||
*self.elem_mut(1, 2) = tmp21;
|
||
*self.elem_mut(3, 2) = tmp23;
|
||
*self.elem_mut(0, 3) = tmp30;
|
||
*self.elem_mut(1, 3) = tmp31;
|
||
*self.elem_mut(2, 3) = tmp32;
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Num> Mat4<T> {
|
||
/// Construct a 4 x 4 diagonal matrix with the major diagonal set to `value`
|
||
///
|
||
/// # Arguments
|
||
///
|
||
/// - `value`: the value to set the major diagonal to
|
||
///
|
||
/// ~~~
|
||
/// c0 c1 c2 c3
|
||
/// +-----+-----+-----+-----+
|
||
/// r0 | val | 0 | 0 | 0 |
|
||
/// +-----+-----+-----+-----+
|
||
/// r1 | 0 | val | 0 | 0 |
|
||
/// +-----+-----+-----+-----+
|
||
/// r2 | 0 | 0 | val | 0 |
|
||
/// +-----+-----+-----+-----+
|
||
/// r3 | 0 | 0 | 0 | val |
|
||
/// +-----+-----+-----+-----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn from_value(value: T) -> Mat4<T> {
|
||
Mat4::new(value, Zero::zero(), Zero::zero(), Zero::zero(),
|
||
Zero::zero(), value, Zero::zero(), Zero::zero(),
|
||
Zero::zero(), Zero::zero(), value, Zero::zero(),
|
||
Zero::zero(), Zero::zero(), Zero::zero(), value)
|
||
}
|
||
|
||
/// Returns the multiplicative identity matrix
|
||
/// ~~~
|
||
/// c0 c1 c2 c3
|
||
/// +----+----+----+----+
|
||
/// r0 | 1 | 0 | 0 | 0 |
|
||
/// +----+----+----+----+
|
||
/// r1 | 0 | 1 | 0 | 0 |
|
||
/// +----+----+----+----+
|
||
/// r2 | 0 | 0 | 1 | 0 |
|
||
/// +----+----+----+----+
|
||
/// r3 | 0 | 0 | 0 | 1 |
|
||
/// +----+----+----+----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn identity() -> Mat4<T> {
|
||
Mat4::new(One::one::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), One::one::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), One::one::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), One::one::<T>())
|
||
}
|
||
|
||
/// Returns the additive identity matrix
|
||
/// ~~~
|
||
/// c0 c1 c2 c3
|
||
/// +----+----+----+----+
|
||
/// r0 | 0 | 0 | 0 | 0 |
|
||
/// +----+----+----+----+
|
||
/// r1 | 0 | 0 | 0 | 0 |
|
||
/// +----+----+----+----+
|
||
/// r2 | 0 | 0 | 0 | 0 |
|
||
/// +----+----+----+----+
|
||
/// r3 | 0 | 0 | 0 | 0 |
|
||
/// +----+----+----+----+
|
||
/// ~~~
|
||
#[inline]
|
||
pub fn zero() -> Mat4<T> {
|
||
Mat4::new(Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
|
||
Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_t(&self, value: T) -> Mat4<T> {
|
||
Mat4::from_cols(self.col(0).mul_t(value),
|
||
self.col(1).mul_t(value),
|
||
self.col(2).mul_t(value),
|
||
self.col(3).mul_t(value))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_v(&self, vec: &Vec4<T>) -> Vec4<T> {
|
||
Vec4::new(self.row(0).dot(vec),
|
||
self.row(1).dot(vec),
|
||
self.row(2).dot(vec),
|
||
self.row(3).dot(vec))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn add_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
||
Mat4::from_cols(self.col(0).add_v(other.col(0)),
|
||
self.col(1).add_v(other.col(1)),
|
||
self.col(2).add_v(other.col(2)),
|
||
self.col(3).add_v(other.col(3)))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn sub_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
||
Mat4::from_cols(self.col(0).sub_v(other.col(0)),
|
||
self.col(1).sub_v(other.col(1)),
|
||
self.col(2).sub_v(other.col(2)),
|
||
self.col(3).sub_v(other.col(3)))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
||
Mat4::new(self.row(0).dot(other.col(0)),
|
||
self.row(1).dot(other.col(0)),
|
||
self.row(2).dot(other.col(0)),
|
||
self.row(3).dot(other.col(0)),
|
||
|
||
self.row(0).dot(other.col(1)),
|
||
self.row(1).dot(other.col(1)),
|
||
self.row(2).dot(other.col(1)),
|
||
self.row(3).dot(other.col(1)),
|
||
|
||
self.row(0).dot(other.col(2)),
|
||
self.row(1).dot(other.col(2)),
|
||
self.row(2).dot(other.col(2)),
|
||
self.row(3).dot(other.col(2)),
|
||
|
||
self.row(0).dot(other.col(3)),
|
||
self.row(1).dot(other.col(3)),
|
||
self.row(2).dot(other.col(3)),
|
||
self.row(3).dot(other.col(3)))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn mul_self_t(&mut self, value: T) {
|
||
self.col_mut(0).mul_self_t(value);
|
||
self.col_mut(1).mul_self_t(value);
|
||
self.col_mut(2).mul_self_t(value);
|
||
self.col_mut(3).mul_self_t(value);
|
||
}
|
||
|
||
#[inline]
|
||
pub fn add_self_m(&mut self, other: &Mat4<T>) {
|
||
self.col_mut(0).add_self_v(other.col(0));
|
||
self.col_mut(1).add_self_v(other.col(1));
|
||
self.col_mut(2).add_self_v(other.col(2));
|
||
self.col_mut(3).add_self_v(other.col(3));
|
||
}
|
||
|
||
#[inline]
|
||
pub fn sub_self_m(&mut self, other: &Mat4<T>) {
|
||
self.col_mut(0).sub_self_v(other.col(0));
|
||
self.col_mut(1).sub_self_v(other.col(1));
|
||
self.col_mut(2).sub_self_v(other.col(2));
|
||
self.col_mut(3).sub_self_v(other.col(3));
|
||
}
|
||
|
||
pub fn dot(&self, other: &Mat4<T>) -> T {
|
||
other.transpose().mul_m(self).trace()
|
||
}
|
||
|
||
pub fn determinant(&self) -> T {
|
||
let m0 = Mat3::new(*self.elem(1, 1), *self.elem(2, 1), *self.elem(3, 1),
|
||
*self.elem(1, 2), *self.elem(2, 2), *self.elem(3, 2),
|
||
*self.elem(1, 3), *self.elem(2, 3), *self.elem(3, 3));
|
||
let m1 = Mat3::new(*self.elem(0, 1), *self.elem(2, 1), *self.elem(3, 1),
|
||
*self.elem(0, 2), *self.elem(2, 2), *self.elem(3, 2),
|
||
*self.elem(0, 3), *self.elem(2, 3), *self.elem(3, 3));
|
||
let m2 = Mat3::new(*self.elem(0, 1), *self.elem(1, 1), *self.elem(3, 1),
|
||
*self.elem(0, 2), *self.elem(1, 2), *self.elem(3, 2),
|
||
*self.elem(0, 3), *self.elem(1, 3), *self.elem(3, 3));
|
||
let m3 = Mat3::new(*self.elem(0, 1), *self.elem(1, 1), *self.elem(2, 1),
|
||
*self.elem(0, 2), *self.elem(1, 2), *self.elem(2, 2),
|
||
*self.elem(0, 3), *self.elem(1, 3), *self.elem(2, 3));
|
||
|
||
self.elem(0, 0) * m0.determinant() -
|
||
self.elem(1, 0) * m1.determinant() +
|
||
self.elem(2, 0) * m2.determinant() -
|
||
self.elem(3, 0) * m3.determinant()
|
||
}
|
||
|
||
pub fn trace(&self) -> T {
|
||
*self.elem(0, 0) +
|
||
*self.elem(1, 1) +
|
||
*self.elem(2, 2) +
|
||
*self.elem(3, 3)
|
||
}
|
||
|
||
#[inline]
|
||
pub fn to_identity(&mut self) {
|
||
*self = Mat4::identity();
|
||
}
|
||
|
||
#[inline]
|
||
pub fn to_zero(&mut self) {
|
||
*self = Mat4::zero();
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Num> Neg<Mat4<T>> for Mat4<T> {
|
||
#[inline]
|
||
pub fn neg(&self) -> Mat4<T> {
|
||
Mat4::from_cols(-self.col(0), -self.col(1), -self.col(2), -self.col(3))
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Real + ApproxEq<T>> Mat4<T> {
|
||
pub fn inverse(&self) -> Option<Mat4<T>> {
|
||
let d = self.determinant();
|
||
if d.approx_eq(&Zero::zero()) {
|
||
None
|
||
} else {
|
||
// Gauss Jordan Elimination with partial pivoting
|
||
// So take this matrix, A, augmented with the identity
|
||
// and essentially reduce [A|I]
|
||
|
||
let mut A = *self;
|
||
let mut I = Mat4::identity::<T>();
|
||
|
||
for uint::range(0, 4) |j| {
|
||
// Find largest element in col j
|
||
let mut i1 = j;
|
||
for uint::range(j + 1, 4) |i| {
|
||
if A.elem(j, i).abs() > A.elem(j, i1).abs() {
|
||
i1 = i;
|
||
}
|
||
}
|
||
|
||
// Swap columns i1 and j in A and I to
|
||
// put pivot on diagonal
|
||
A.swap_cols(i1, j);
|
||
I.swap_cols(i1, j);
|
||
|
||
// Scale col j to have a unit diagonal
|
||
let ajj = *A.elem(j, j);
|
||
I.col_mut(j).div_self_t(ajj);
|
||
A.col_mut(j).div_self_t(ajj);
|
||
|
||
// Eliminate off-diagonal elems in col j of A,
|
||
// doing identical ops to I
|
||
for uint::range(0, 4) |i| {
|
||
if i != j {
|
||
let ij_mul_aij = I.col(j).mul_t(*A.elem(i, j));
|
||
let aj_mul_aij = A.col(j).mul_t(*A.elem(i, j));
|
||
I.col_mut(i).sub_self_v(&ij_mul_aij);
|
||
A.col_mut(i).sub_self_v(&aj_mul_aij);
|
||
}
|
||
}
|
||
}
|
||
Some(I)
|
||
}
|
||
}
|
||
|
||
#[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(&Mat4::identity())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_diagonal(&self) -> bool {
|
||
self.elem(0, 1).approx_eq(&Zero::zero()) &&
|
||
self.elem(0, 2).approx_eq(&Zero::zero()) &&
|
||
self.elem(0, 3).approx_eq(&Zero::zero()) &&
|
||
|
||
self.elem(1, 0).approx_eq(&Zero::zero()) &&
|
||
self.elem(1, 2).approx_eq(&Zero::zero()) &&
|
||
self.elem(1, 3).approx_eq(&Zero::zero()) &&
|
||
|
||
self.elem(2, 0).approx_eq(&Zero::zero()) &&
|
||
self.elem(2, 1).approx_eq(&Zero::zero()) &&
|
||
self.elem(2, 3).approx_eq(&Zero::zero()) &&
|
||
|
||
self.elem(3, 0).approx_eq(&Zero::zero()) &&
|
||
self.elem(3, 1).approx_eq(&Zero::zero()) &&
|
||
self.elem(3, 2).approx_eq(&Zero::zero())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_rotated(&self) -> bool {
|
||
!self.approx_eq(&Mat4::identity())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_symmetric(&self) -> bool {
|
||
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
||
self.elem(0, 2).approx_eq(self.elem(2, 0)) &&
|
||
self.elem(0, 3).approx_eq(self.elem(3, 0)) &&
|
||
|
||
self.elem(1, 0).approx_eq(self.elem(0, 1)) &&
|
||
self.elem(1, 2).approx_eq(self.elem(2, 1)) &&
|
||
self.elem(1, 3).approx_eq(self.elem(3, 1)) &&
|
||
|
||
self.elem(2, 0).approx_eq(self.elem(0, 2)) &&
|
||
self.elem(2, 1).approx_eq(self.elem(1, 2)) &&
|
||
self.elem(2, 3).approx_eq(self.elem(3, 2)) &&
|
||
|
||
self.elem(3, 0).approx_eq(self.elem(0, 3)) &&
|
||
self.elem(3, 1).approx_eq(self.elem(1, 3)) &&
|
||
self.elem(3, 2).approx_eq(self.elem(2, 3))
|
||
}
|
||
|
||
#[inline]
|
||
pub fn is_invertible(&self) -> bool {
|
||
!self.determinant().approx_eq(&Zero::zero())
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Eq + ApproxEq<T>> ApproxEq<T> for Mat4<T> {
|
||
#[inline]
|
||
pub fn approx_epsilon() -> T {
|
||
ApproxEq::approx_epsilon::<T,T>()
|
||
}
|
||
|
||
#[inline]
|
||
pub fn approx_eq(&self, other: &Mat4<T>) -> bool {
|
||
self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
|
||
}
|
||
|
||
#[inline]
|
||
pub fn approx_eq_eps(&self, other: &Mat4<T>, epsilon: &T) -> bool {
|
||
self.col(0).approx_eq_eps(other.col(0), epsilon) &&
|
||
self.col(1).approx_eq_eps(other.col(1), epsilon) &&
|
||
self.col(2).approx_eq_eps(other.col(2), epsilon) &&
|
||
self.col(3).approx_eq_eps(other.col(3), epsilon)
|
||
}
|
||
}
|
||
|
||
// GLSL-style type aliases, corresponding to Section 4.1.6 of the [GLSL 4.30.6 specification]
|
||
// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).
|
||
|
||
// a 4×4 single-precision floating-point matrix
|
||
pub type mat4 = Mat4<f32>;
|
||
// a 4×4 double-precision floating-point matrix
|
||
pub type dmat4 = Mat4<f64>;
|
||
|
||
// Rust-style type aliases
|
||
pub type Mat4f = Mat4<float>;
|
||
pub type Mat4f32 = Mat4<f32>;
|
||
pub type Mat4f64 = Mat4<f64>;
|