529 lines
18 KiB
Rust
529 lines
18 KiB
Rust
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// 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 super::Mat3;
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/// A 4 x 4 column major matrix
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///
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/// # Type parameters
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///
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/// - `T` - The type of the elements of the matrix. Should be a floating point type.
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///
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/// # Fields
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///
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/// - `x`: the first column vector of the matrix
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/// - `y`: the second column vector of the matrix
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/// - `z`: the third column vector of the matrix
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/// - `w`: the fourth column vector of the matrix
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#[deriving(Eq)]
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pub struct Mat4<T> { x: Vec4<T>, y: Vec4<T>, z: Vec4<T>, w: Vec4<T> }
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impl<T> Mat4<T> {
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#[inline]
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pub fn col<'a>(&'a self, i: uint) -> &'a Vec4<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 Vec4<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 [Vec4<T>,..4] {
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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 [Vec4<T>,..4] {
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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> Mat4<T> {
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/// Construct a 4 x 4 matrix
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///
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/// # Arguments
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///
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/// - `c0r0`, `c0r1`, `c0r2`, `c0r3`: the first column of the matrix
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/// - `c1r0`, `c1r1`, `c1r2`, `c1r3`: the second column of the matrix
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/// - `c2r0`, `c2r1`, `c2r2`, `c2r3`: the third column of the matrix
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/// - `c3r0`, `c3r1`, `c3r2`, `c3r3`: the fourth column of the matrix
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///
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/// ~~~
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/// c0 c1 c2 c3
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/// +------+------+------+------+
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/// r0 | c0r0 | c1r0 | c2r0 | c3r0 |
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/// +------+------+------+------+
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/// r1 | c0r1 | c1r1 | c2r1 | c3r1 |
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/// +------+------+------+------+
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/// r2 | c0r2 | c1r2 | c2r2 | c3r2 |
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/// +------+------+------+------+
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/// r3 | c0r3 | c1r3 | c2r3 | c3r3 |
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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, c0r3: T,
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c1r0: T, c1r1: T, c1r2: T, c1r3: T,
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c2r0: T, c2r1: T, c2r2: T, c2r3: T,
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c3r0: T, c3r1: T, c3r2: T, c3r3: T) -> Mat4<T> {
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Mat4::from_cols(Vec4::new(c0r0, c0r1, c0r2, c0r3),
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Vec4::new(c1r0, c1r1, c1r2, c1r3),
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Vec4::new(c2r0, c2r1, c2r2, c2r3),
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Vec4::new(c3r0, c3r1, c3r2, c3r3))
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}
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/// Construct a 4 x 4 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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/// - `c3`: the fourth column vector of the matrix
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///
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/// ~~~
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/// c0 c1 c2 c3
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/// +------+------+------+------+
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/// r0 | c0.x | c1.x | c2.x | c3.x |
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/// +------+------+------+------+
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/// r1 | c0.y | c1.y | c2.y | c3.y |
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/// +------+------+------+------+
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/// r2 | c0.z | c1.z | c2.z | c3.z |
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/// +------+------+------+------+
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/// r3 | c0.w | c1.w | c2.w | c3.w |
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/// +------+------+------+------+
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/// ~~~
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#[inline]
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pub fn from_cols(c0: Vec4<T>,
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c1: Vec4<T>,
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c2: Vec4<T>,
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c3: Vec4<T>) -> Mat4<T> {
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Mat4 { x: c0, y: c1, z: c2, w: c3 }
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}
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#[inline]
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pub fn row(&self, i: uint) -> Vec4<T> {
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Vec4::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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*self.elem(3, 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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self.z.swap(a, b);
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self.w.swap(a, b);
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}
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#[inline]
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pub fn transpose(&self) -> Mat4<T> {
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Mat4::new(*self.elem(0, 0), *self.elem(1, 0), *self.elem(2, 0), *self.elem(3, 0),
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*self.elem(0, 1), *self.elem(1, 1), *self.elem(2, 1), *self.elem(3, 1),
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*self.elem(0, 2), *self.elem(1, 2), *self.elem(2, 2), *self.elem(3, 2),
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*self.elem(0, 3), *self.elem(1, 3), *self.elem(2, 3), *self.elem(3, 3))
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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 tmp02 = *self.elem(0, 2);
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let tmp03 = *self.elem(0, 3);
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let tmp10 = *self.elem(1, 0);
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let tmp12 = *self.elem(1, 2);
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let tmp13 = *self.elem(1, 3);
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let tmp20 = *self.elem(2, 0);
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let tmp21 = *self.elem(2, 1);
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let tmp23 = *self.elem(2, 3);
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let tmp30 = *self.elem(3, 0);
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let tmp31 = *self.elem(3, 1);
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let tmp32 = *self.elem(3, 2);
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*self.elem_mut(0, 1) = *self.elem(1, 0);
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*self.elem_mut(0, 2) = *self.elem(2, 0);
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*self.elem_mut(0, 3) = *self.elem(3, 0);
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*self.elem_mut(1, 0) = *self.elem(0, 1);
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*self.elem_mut(1, 2) = *self.elem(2, 1);
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*self.elem_mut(1, 3) = *self.elem(3, 1);
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*self.elem_mut(2, 0) = *self.elem(0, 2);
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*self.elem_mut(2, 1) = *self.elem(1, 2);
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*self.elem_mut(2, 3) = *self.elem(3, 2);
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*self.elem_mut(3, 0) = *self.elem(0, 3);
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*self.elem_mut(3, 1) = *self.elem(1, 3);
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*self.elem_mut(3, 2) = *self.elem(2, 3);
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*self.elem_mut(1, 0) = tmp01;
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*self.elem_mut(2, 0) = tmp02;
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*self.elem_mut(3, 0) = tmp03;
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*self.elem_mut(0, 1) = tmp10;
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*self.elem_mut(2, 1) = tmp12;
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*self.elem_mut(3, 1) = tmp13;
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*self.elem_mut(0, 2) = tmp20;
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*self.elem_mut(1, 2) = tmp21;
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*self.elem_mut(3, 2) = tmp23;
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*self.elem_mut(0, 3) = tmp30;
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*self.elem_mut(1, 3) = tmp31;
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*self.elem_mut(2, 3) = tmp32;
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}
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}
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impl<T:Copy + Num> Mat4<T> {
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/// Construct a 4 x 4 diagonal matrix with the major diagonal set to `value`
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///
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/// # Arguments
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///
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/// - `value`: the value to set the major diagonal to
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///
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/// ~~~
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/// c0 c1 c2 c3
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/// +-----+-----+-----+-----+
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/// r0 | val | 0 | 0 | 0 |
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/// +-----+-----+-----+-----+
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/// r1 | 0 | val | 0 | 0 |
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/// +-----+-----+-----+-----+
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/// r2 | 0 | 0 | val | 0 |
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/// +-----+-----+-----+-----+
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/// r3 | 0 | 0 | 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) -> Mat4<T> {
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Mat4::new(value, Zero::zero(), Zero::zero(), Zero::zero(),
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Zero::zero(), value, Zero::zero(), Zero::zero(),
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Zero::zero(), Zero::zero(), value, Zero::zero(),
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Zero::zero(), Zero::zero(), 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 c2 c3
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/// +----+----+----+----+
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/// r0 | 1 | 0 | 0 | 0 |
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/// +----+----+----+----+
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/// r1 | 0 | 1 | 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 identity() -> Mat4<T> {
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Mat4::new(One::one::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), One::one::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), Zero::zero::<T>(), One::one::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), Zero::zero::<T>(), 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 c2 c3
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/// +----+----+----+----+
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/// r0 | 0 | 0 | 0 | 0 |
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/// +----+----+----+----+
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/// r1 | 0 | 0 | 0 | 0 |
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/// +----+----+----+----+
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/// r2 | 0 | 0 | 0 | 0 |
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/// +----+----+----+----+
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/// r3 | 0 | 0 | 0 | 0 |
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/// +----+----+----+----+
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/// ~~~
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#[inline]
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pub fn zero() -> Mat4<T> {
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Mat4::new(Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(), Zero::zero::<T>(),
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Zero::zero::<T>(), Zero::zero::<T>(), 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) -> Mat4<T> {
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Mat4::from_cols(self.col(0).mul_t(value),
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self.col(1).mul_t(value),
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self.col(2).mul_t(value),
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self.col(3).mul_t(value))
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}
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#[inline]
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pub fn mul_v(&self, vec: &Vec4<T>) -> Vec4<T> {
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Vec4::new(self.row(0).dot(vec),
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self.row(1).dot(vec),
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self.row(2).dot(vec),
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self.row(3).dot(vec))
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}
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#[inline]
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pub fn add_m(&self, other: &Mat4<T>) -> Mat4<T> {
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Mat4::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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self.col(2).add_v(other.col(2)),
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self.col(3).add_v(other.col(3)))
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}
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#[inline]
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pub fn sub_m(&self, other: &Mat4<T>) -> Mat4<T> {
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Mat4::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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self.col(2).sub_v(other.col(2)),
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self.col(3).sub_v(other.col(3)))
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}
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#[inline]
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pub fn mul_m(&self, other: &Mat4<T>) -> Mat4<T> {
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Mat4::new(self.row(0).dot(other.col(0)),
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self.row(1).dot(other.col(0)),
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self.row(2).dot(other.col(0)),
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self.row(3).dot(other.col(0)),
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self.row(0).dot(other.col(1)),
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self.row(1).dot(other.col(1)),
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self.row(2).dot(other.col(1)),
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self.row(3).dot(other.col(1)),
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self.row(0).dot(other.col(2)),
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self.row(1).dot(other.col(2)),
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|
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)
|
||
|
|
}
|
||
|
|
}
|