2013-05-31 22:01:01 +00:00
|
|
|
|
// Copyright 2013 The Lmath Developers. For a full listing of the authors,
|
|
|
|
|
// refer to the AUTHORS file at the top-level directory of this distribution.
|
|
|
|
|
//
|
|
|
|
|
// Licensed under the Apache License, Version 2.0 (the "License");
|
|
|
|
|
// you may not use this file except in compliance with the License.
|
|
|
|
|
// You may obtain a copy of the License at
|
|
|
|
|
//
|
|
|
|
|
// http://www.apache.org/licenses/LICENSE-2.0
|
|
|
|
|
//
|
|
|
|
|
// Unless required by applicable law or agreed to in writing, software
|
|
|
|
|
// distributed under the License is distributed on an "AS IS" BASIS,
|
|
|
|
|
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
|
|
|
// See the License for the specific language governing permissions and
|
|
|
|
|
// limitations under the License.
|
|
|
|
|
|
2013-05-23 21:05:25 +00:00
|
|
|
|
use std::cast::transmute;
|
|
|
|
|
use std::cmp::ApproxEq;
|
2013-06-06 02:38:23 +00:00
|
|
|
|
use std::num::{Zero, One, cast};
|
|
|
|
|
use std::uint;
|
2012-12-13 13:01:42 +00:00
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
use vec::*;
|
|
|
|
|
use quat::Quat;
|
2012-11-15 02:23:39 +00:00
|
|
|
|
|
2013-05-06 03:52:22 +00:00
|
|
|
|
use num::NumAssign;
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The base square matrix trait
|
|
|
|
|
///
|
|
|
|
|
/// # Type parameters
|
|
|
|
|
///
|
|
|
|
|
/// - `T`: The type of the elements of the matrix. Should be a floating point type.
|
|
|
|
|
/// - `V`: The type of the row and column vectors. Should have components of a
|
|
|
|
|
/// floating point type and have the same number of dimensions as the
|
|
|
|
|
/// number of rows and columns in the matrix.
|
2013-05-31 11:05:43 +00:00
|
|
|
|
pub trait BaseMat<T,V>: Eq + Neg<Self> {
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The column vector at `i`
|
2013-05-31 11:05:43 +00:00
|
|
|
|
fn col<'a>(&'a self, i: uint) -> &'a V;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The row vector at `i`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn row(&self, i: uint) -> V;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The matrix element at `i`, `j`
|
2013-06-01 01:56:11 +00:00
|
|
|
|
fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T;
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a diagonal matrix with the major diagonal set to `value`
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_value(value: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The identity matrix
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn identity() -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A matrix with all elements set to zero
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn zero() -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The scalar multiplication of this matrix and `value`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn mul_t(&self, value: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The matrix vector product of the matrix and `vec`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn mul_v(&self, vec: &V) -> V;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The matrix addition of the matrix and `other`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn add_m(&self, other: &Self) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The difference between the matrix and `other`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn sub_m(&self, other: &Self) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The matrix product of the matrix and `other`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn mul_m(&self, other: &Self) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The matrix dot product of the matrix and `other`
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn dot(&self, other: &Self) -> T;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The determinant of the matrix
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn determinant(&self) -> T;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The sum of the main diagonal of the matrix
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn trace(&self) -> T;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the inverse of the matrix
|
|
|
|
|
///
|
|
|
|
|
/// # Return value
|
|
|
|
|
///
|
|
|
|
|
/// - `Some(m)`: if the inversion was successful, where `m` is the inverted matrix
|
|
|
|
|
/// - `None`: if the inversion was unsuccessful (because the matrix was not invertable)
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn inverse(&self) -> Option<Self>;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// The transposed matrix
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn transpose(&self) -> Self;
|
2013-05-07 15:00:06 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A mutable reference to the column at `i`
|
2013-04-14 20:43:21 +00:00
|
|
|
|
fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut V;
|
2013-03-29 11:51:34 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A mutable reference to the matrix element at `i`, `j`
|
2013-06-01 01:56:11 +00:00
|
|
|
|
fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T;
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Swap two columns of the matrix in place
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn swap_cols(&mut self, a: uint, b: uint);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Swap two rows of the matrix in place
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn swap_rows(&mut self, a: uint, b: uint);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Sets the matrix to `other`
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn set(&mut self, other: &Self);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Sets the matrix to the identity matrix
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn to_identity(&mut self);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Sets each element of the matrix to zero
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn to_zero(&mut self);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Multiplies the matrix by a scalar
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn mul_self_t(&mut self, value: T);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Add the matrix `other` to `self`
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn add_self_m(&mut self, other: &Self);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Subtract the matrix `other` from `self`
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn sub_self_m(&mut self, other: &Self);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Sets the matrix to its inverse
|
|
|
|
|
///
|
|
|
|
|
/// # Failure
|
|
|
|
|
///
|
|
|
|
|
/// Fails if the matrix is not invertable. Make sure you check with the
|
|
|
|
|
/// `is_invertible` method before you attempt this!
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn invert_self(&mut self);
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Sets the matrix to its transpose
|
2013-03-29 11:51:34 +00:00
|
|
|
|
fn transpose_self(&mut self);
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Check to see if the matrix is an identity matrix
|
|
|
|
|
///
|
|
|
|
|
/// # Return value
|
|
|
|
|
///
|
|
|
|
|
/// `true` if the matrix is approximately equal to the identity matrix
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn is_identity(&self) -> bool;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Check to see if the matrix is diagonal
|
|
|
|
|
///
|
|
|
|
|
/// # Return value
|
|
|
|
|
///
|
|
|
|
|
/// `true` all the elements outside the main diagonal are approximately
|
|
|
|
|
/// equal to zero.
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn is_diagonal(&self) -> bool;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Check to see if the matrix is rotated
|
|
|
|
|
///
|
|
|
|
|
/// # Return value
|
|
|
|
|
///
|
|
|
|
|
/// `true` if the matrix is not approximately equal to the identity matrix.
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn is_rotated(&self) -> bool;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Check to see if the matrix is symmetric
|
|
|
|
|
///
|
|
|
|
|
/// # Return value
|
|
|
|
|
///
|
|
|
|
|
/// `true` if the matrix is approximately equal to its transpose).
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn is_symmetric(&self) -> bool;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Check to see if the matrix is invertable
|
|
|
|
|
///
|
|
|
|
|
/// # Return value
|
|
|
|
|
///
|
|
|
|
|
/// `true` if the matrix is invertable
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn is_invertible(&self) -> bool;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A pointer to the first element of the matrix
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn to_ptr(&self) -> *T;
|
2012-11-15 02:23:39 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A 2 x 2 matrix
|
2013-04-02 05:12:13 +00:00
|
|
|
|
pub trait BaseMat2<T,V>: BaseMat<T,V> {
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn new(c0r0: T, c0r1: T,
|
2013-04-02 04:01:38 +00:00
|
|
|
|
c1r0: T, c1r1: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_cols(c0: V, c1: V) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_angle(radians: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn to_mat3(&self) -> Mat3<T>;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn to_mat4(&self) -> Mat4<T>;
|
2013-01-29 09:26:48 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A 3 x 3 matrix
|
2013-04-02 05:12:13 +00:00
|
|
|
|
pub trait BaseMat3<T,V>: BaseMat<T,V> {
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn new(c0r0:T, c0r1:T, c0r2:T,
|
2013-04-02 04:01:38 +00:00
|
|
|
|
c1r0:T, c1r1:T, c1r2:T,
|
|
|
|
|
c2r0:T, c2r1:T, c2r2:T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_cols(c0: V, c1: V, c2: V) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_angle_x(radians: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_angle_y(radians: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_angle_z(radians: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_angle_xyz(radians_x: T, radians_y: T, radians_z: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_axes(x: V, y: V, z: V) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn look_at(dir: &Vec3<T>, up: &Vec3<T>) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn to_mat4(&self) -> Mat4<T>;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:35:51 +00:00
|
|
|
|
fn to_quat(&self) -> Quat<T>;
|
2013-01-29 09:26:48 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A 4 x 4 matrix
|
2013-04-02 05:12:13 +00:00
|
|
|
|
pub trait BaseMat4<T,V>: BaseMat<T,V> {
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn new(c0r0: T, c0r1: T, c0r2: T, c0r3: T,
|
2013-04-02 04:01:38 +00:00
|
|
|
|
c1r0: T, c1r1: T, c1r2: T, c1r3: T,
|
|
|
|
|
c2r0: T, c2r1: T, c2r2: T, c2r3: T,
|
|
|
|
|
c3r0: T, c3r1: T, c3r2: T, c3r3: T) -> Self;
|
2013-03-28 09:45:43 +00:00
|
|
|
|
|
2013-03-28 10:37:25 +00:00
|
|
|
|
fn from_cols(c0: V, c1: V, c2: V, c3: V) -> Self;
|
2013-01-29 09:26:48 +00:00
|
|
|
|
}
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A 2 x 2 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
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[deriving(Eq)]
|
|
|
|
|
pub struct Mat2<T> { x: Vec2<T>, y: Vec2<T> }
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> BaseMat<T, Vec2<T>> for Mat2<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-05-31 11:05:43 +00:00
|
|
|
|
fn col<'a>(&'a self, i: uint) -> &'a Vec2<T> {
|
|
|
|
|
unsafe { &'a transmute::<&'a Mat2<T>, &'a [Vec2<T>,..2]>(self)[i] }
|
|
|
|
|
}
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn row(&self, i: uint) -> Vec2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseVec2::new(*self.col(0).index(i),
|
|
|
|
|
*self.col(1).index(i))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
|
|
|
|
|
self.col(i).index(j)
|
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a 2 x 2 diagonal matrix with the major diagonal set to `value`
|
|
|
|
|
///
|
|
|
|
|
/// # Arguments
|
|
|
|
|
///
|
|
|
|
|
/// - `value`: the value to set the major diagonal to
|
|
|
|
|
///
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1
|
|
|
|
|
/// +-----+-----+
|
|
|
|
|
/// r0 | val | 0 |
|
|
|
|
|
/// +-----+-----+
|
|
|
|
|
/// r1 | 0 | val |
|
|
|
|
|
/// +-----+-----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_value(value: T) -> Mat2<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat2::new(value, Zero::zero(),
|
|
|
|
|
Zero::zero(), value)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the multiplicative identity matrix
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1
|
|
|
|
|
/// +----+----+
|
|
|
|
|
/// r0 | 1 | 0 |
|
|
|
|
|
/// +----+----+
|
|
|
|
|
/// r1 | 0 | 1 |
|
|
|
|
|
/// +----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn identity() -> Mat2<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat2::new( One::one::<T>(), Zero::zero::<T>(),
|
|
|
|
|
Zero::zero::<T>(), One::one::<T>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the additive identity matrix
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1
|
|
|
|
|
/// +----+----+
|
|
|
|
|
/// r0 | 0 | 0 |
|
|
|
|
|
/// +----+----+
|
|
|
|
|
/// r1 | 0 | 0 |
|
|
|
|
|
/// +----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn zero() -> Mat2<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat2::new(Zero::zero::<T>(), Zero::zero::<T>(),
|
|
|
|
|
Zero::zero::<T>(), Zero::zero::<T>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_t(&self, value: T) -> Mat2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat2::from_cols(self.col(0).mul_t(value),
|
|
|
|
|
self.col(1).mul_t(value))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_v(&self, vec: &Vec2<T>) -> Vec2<T> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseVec2::new(self.row(0).dot(vec),
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.row(1).dot(vec))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn add_m(&self, other: &Mat2<T>) -> Mat2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat2::from_cols(self.col(0).add_v(other.col(0)),
|
|
|
|
|
self.col(1).add_v(other.col(1)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn sub_m(&self, other: &Mat2<T>) -> Mat2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat2::from_cols(self.col(0).sub_v(other.col(0)),
|
|
|
|
|
self.col(1).sub_v(other.col(1)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_m(&self, other: &Mat2<T>) -> Mat2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat2::new(self.row(0).dot(other.col(0)), self.row(1).dot(other.col(0)),
|
|
|
|
|
self.row(0).dot(other.col(1)), self.row(1).dot(other.col(1)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn dot(&self, other: &Mat2<T>) -> T {
|
|
|
|
|
other.transpose().mul_m(self).trace()
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn determinant(&self) -> T {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
(*self.col(0).index(0)) *
|
|
|
|
|
(*self.col(1).index(1)) -
|
|
|
|
|
(*self.col(1).index(0)) *
|
|
|
|
|
(*self.col(0).index(1))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn trace(&self) -> T {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
(*self.col(0).index(0)) +
|
|
|
|
|
(*self.col(1).index(1))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn inverse(&self) -> Option<Mat2<T>> {
|
|
|
|
|
let d = self.determinant();
|
2013-05-23 21:05:25 +00:00
|
|
|
|
if d.approx_eq(&Zero::zero()) {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
None
|
|
|
|
|
} else {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
Some(BaseMat2::new( self.elem(1, 1) / d, -self.elem(0, 1) / d,
|
|
|
|
|
-self.elem(1, 0) / d, self.elem(0, 0) / d))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn transpose(&self) -> Mat2<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseMat2::new(*self.elem(0, 0), *self.elem(1, 0),
|
|
|
|
|
*self.elem(0, 1), *self.elem(1, 1))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
2013-05-07 15:00:06 +00:00
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-04-14 20:43:21 +00:00
|
|
|
|
fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
unsafe { &'a mut transmute::<&'a mut Mat2<T>, &'a mut [Vec2<T>,..2]>(self)[i] }
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
|
|
|
|
|
self.col_mut(i).index_mut(j)
|
|
|
|
|
}
|
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn swap_cols(&mut self, a: uint, b: uint) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
let tmp = *self.col(a);
|
|
|
|
|
*self.col_mut(a) = *self.col(b);
|
2013-05-23 21:55:23 +00:00
|
|
|
|
*self.col_mut(b) = tmp;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn swap_rows(&mut self, a: uint, b: uint) {
|
|
|
|
|
self.x.swap(a, b);
|
|
|
|
|
self.y.swap(a, b);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn set(&mut self, other: &Mat2<T>) {
|
|
|
|
|
(*self) = (*other);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_identity(&mut self) {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
(*self) = BaseMat::identity();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_zero(&mut self) {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
(*self) = BaseMat::zero();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_self_t(&mut self, value: T) {
|
|
|
|
|
self.x.mul_self_t(value);
|
|
|
|
|
self.y.mul_self_t(value);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn add_self_m(&mut self, other: &Mat2<T>) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.x.add_self_v(other.col(0));
|
|
|
|
|
self.y.add_self_v(other.col(1));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn sub_self_m(&mut self, other: &Mat2<T>) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.x.sub_self_v(other.col(0));
|
|
|
|
|
self.y.sub_self_v(other.col(1));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn invert_self(&mut self) {
|
|
|
|
|
match self.inverse() {
|
|
|
|
|
Some(m) => (*self) = m,
|
|
|
|
|
None => fail!(~"Couldn't invert the matrix!")
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn transpose_self(&mut self) {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
let tmp01 = *self.elem(0, 1);
|
|
|
|
|
let tmp10 = *self.elem(1, 0);
|
2013-05-23 21:55:23 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
*self.elem_mut(0, 1) = *self.elem(1, 0);
|
|
|
|
|
*self.elem_mut(1, 0) = *self.elem(0, 1);
|
2013-05-23 21:55:23 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
*self.elem_mut(1, 0) = tmp01;
|
|
|
|
|
*self.elem_mut(0, 1) = tmp10;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_identity(&self) -> bool {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
self.approx_eq(&BaseMat::identity())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_diagonal(&self) -> bool {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(0, 1).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(1, 0).approx_eq(&Zero::zero())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_rotated(&self) -> bool {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
!self.approx_eq(&BaseMat::identity())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_symmetric(&self) -> bool {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
|
|
|
|
self.elem(1, 0).approx_eq(self.elem(0, 1))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_invertible(&self) -> bool {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
!self.determinant().approx_eq(&Zero::zero())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_ptr(&self) -> *T {
|
2013-05-22 07:01:52 +00:00
|
|
|
|
unsafe { transmute(self) }
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> BaseMat2<T, Vec2<T>> for Mat2<T> {
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a 2 x 2 matrix
|
|
|
|
|
///
|
|
|
|
|
/// # Arguments
|
|
|
|
|
///
|
|
|
|
|
/// - `c0r0`, `c0r1`: the first column of the matrix
|
|
|
|
|
/// - `c1r0`, `c1r1`: the second column of the matrix
|
|
|
|
|
///
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1
|
|
|
|
|
/// +------+------+
|
|
|
|
|
/// r0 | c0r0 | c1r0 |
|
|
|
|
|
/// +------+------+
|
|
|
|
|
/// r1 | c0r1 | c1r1 |
|
|
|
|
|
/// +------+------+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn new(c0r0: T, c0r1: T,
|
2013-04-02 04:01:38 +00:00
|
|
|
|
c1r0: T, c1r1: T) -> Mat2<T> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat2::from_cols(BaseVec2::new::<T,Vec2<T>>(c0r0, c0r1),
|
|
|
|
|
BaseVec2::new::<T,Vec2<T>>(c1r0, c1r1))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a 2 x 2 matrix from column vectors
|
|
|
|
|
///
|
|
|
|
|
/// # Arguments
|
|
|
|
|
///
|
|
|
|
|
/// - `c0`: the first column vector of the matrix
|
|
|
|
|
/// - `c1`: the second column vector of the matrix
|
|
|
|
|
///
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1
|
|
|
|
|
/// +------+------+
|
|
|
|
|
/// r0 | c0.x | c1.x |
|
|
|
|
|
/// +------+------+
|
|
|
|
|
/// r1 | c0.y | c1.y |
|
|
|
|
|
/// +------+------+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-04-02 04:01:38 +00:00
|
|
|
|
fn from_cols(c0: Vec2<T>, c1: Vec2<T>) -> Mat2<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
Mat2 { x: c0, y: c1 }
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_angle(radians: T) -> Mat2<T> {
|
2013-05-06 03:52:22 +00:00
|
|
|
|
let cos_theta = radians.cos();
|
|
|
|
|
let sin_theta = radians.sin();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat2::new(cos_theta, -sin_theta,
|
|
|
|
|
sin_theta, cos_theta)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the the matrix with an extra row and column added
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1 c0 c1 c2
|
|
|
|
|
/// +----+----+ +----+----+----+
|
|
|
|
|
/// r0 | a | b | r0 | a | b | 0 |
|
|
|
|
|
/// +----+----+ +----+----+----+
|
|
|
|
|
/// r1 | c | d | => r1 | c | d | 0 |
|
|
|
|
|
/// +----+----+ +----+----+----+
|
|
|
|
|
/// r2 | 0 | 0 | 1 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_mat3(&self) -> Mat3<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseMat3::new(*self.elem(0, 0), *self.elem(0, 1), Zero::zero(),
|
|
|
|
|
*self.elem(1, 0), *self.elem(1, 1), Zero::zero(),
|
2013-05-31 11:05:43 +00:00
|
|
|
|
Zero::zero(), Zero::zero(), One::one())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the the matrix with an extra two rows and columns added
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1 c0 c1 c2 c3
|
|
|
|
|
/// +----+----+ +----+----+----+----+
|
|
|
|
|
/// r0 | a | b | r0 | a | b | 0 | 0 |
|
|
|
|
|
/// +----+----+ +----+----+----+----+
|
|
|
|
|
/// r1 | c | d | => r1 | c | d | 0 | 0 |
|
|
|
|
|
/// +----+----+ +----+----+----+----+
|
|
|
|
|
/// r2 | 0 | 0 | 1 | 0 |
|
|
|
|
|
/// +----+----+----+----+
|
|
|
|
|
/// r3 | 0 | 0 | 0 | 1 |
|
|
|
|
|
/// +----+----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_mat4(&self) -> Mat4<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseMat4::new(*self.elem(0, 0), *self.elem(0, 1), Zero::zero(), Zero::zero(),
|
|
|
|
|
*self.elem(1, 0), *self.elem(1, 1), Zero::zero(), Zero::zero(),
|
2013-05-31 11:05:43 +00:00
|
|
|
|
Zero::zero(), Zero::zero(), One::one(), Zero::zero(),
|
|
|
|
|
Zero::zero(), Zero::zero(), Zero::zero(), One::one())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> Neg<Mat2<T>> for Mat2<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn neg(&self) -> Mat2<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat2::from_cols(-self.col(0), -self.col(1))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> ApproxEq<T> for Mat2<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-05-07 15:00:06 +00:00
|
|
|
|
fn approx_epsilon() -> T {
|
|
|
|
|
ApproxEq::approx_epsilon::<T,T>()
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
2013-05-07 15:00:06 +00:00
|
|
|
|
fn approx_eq(&self, other: &Mat2<T>) -> bool {
|
|
|
|
|
self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn approx_eq_eps(&self, other: &Mat2<T>, epsilon: &T) -> bool {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.col(0).approx_eq_eps(other.col(0), epsilon) &&
|
|
|
|
|
self.col(1).approx_eq_eps(other.col(1), epsilon)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 01:07:25 +00:00
|
|
|
|
// 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 2×2 single-precision floating-point matrix
|
|
|
|
|
pub type mat2 = Mat2<f32>;
|
|
|
|
|
// a 2×2 double-precision floating-point matrix
|
|
|
|
|
pub type dmat2 = Mat2<f64>;
|
|
|
|
|
|
|
|
|
|
// Rust-style type aliases
|
|
|
|
|
pub type Mat2f = Mat2<float>;
|
|
|
|
|
pub type Mat2f32 = Mat2<f32>;
|
|
|
|
|
pub type Mat2f64 = Mat2<f64>;
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// A 3 x 3 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
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[deriving(Eq)]
|
|
|
|
|
pub struct Mat3<T> { x: Vec3<T>, y: Vec3<T>, z: Vec3<T> }
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> BaseMat<T, Vec3<T>> for Mat3<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-05-31 11:05:43 +00:00
|
|
|
|
fn col<'a>(&'a self, i: uint) -> &'a Vec3<T> {
|
|
|
|
|
unsafe { &'a transmute::<&'a Mat3<T>, &'a [Vec3<T>,..3]>(self)[i] }
|
|
|
|
|
}
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn row(&self, i: uint) -> Vec3<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseVec3::new(*self.elem(0, i),
|
|
|
|
|
*self.elem(1, i),
|
|
|
|
|
*self.elem(2, i))
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
|
|
|
|
|
self.col(i).index(j)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +-----+-----+-----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_value(value: T) -> Mat3<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat3::new(value, Zero::zero(), Zero::zero(),
|
|
|
|
|
Zero::zero(), value, Zero::zero(),
|
|
|
|
|
Zero::zero(), Zero::zero(), value)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the multiplicative identity matrix
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1 c2
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// r0 | 1 | 0 | 0 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// r1 | 0 | 1 | 0 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// r2 | 0 | 0 | 1 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn identity() -> Mat3<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat3::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>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Returns the additive identity matrix
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1 c2
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// r0 | 0 | 0 | 0 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// r1 | 0 | 0 | 0 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// r2 | 0 | 0 | 0 |
|
|
|
|
|
/// +----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn zero() -> Mat3<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat3::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>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_t(&self, value: T) -> Mat3<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat3::from_cols(self.col(0).mul_t(value),
|
|
|
|
|
self.col(1).mul_t(value),
|
|
|
|
|
self.col(2).mul_t(value))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseVec3::new(self.row(0).dot(vec),
|
2013-05-06 03:52:22 +00:00
|
|
|
|
self.row(1).dot(vec),
|
|
|
|
|
self.row(2).dot(vec))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn add_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat3::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)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn sub_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat3::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)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat3::new(self.row(0).dot(other.col(0)),
|
|
|
|
|
self.row(1).dot(other.col(0)),
|
|
|
|
|
self.row(2).dot(other.col(0)),
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.row(0).dot(other.col(1)),
|
|
|
|
|
self.row(1).dot(other.col(1)),
|
|
|
|
|
self.row(2).dot(other.col(1)),
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.row(0).dot(other.col(2)),
|
|
|
|
|
self.row(1).dot(other.col(2)),
|
|
|
|
|
self.row(2).dot(other.col(2)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn dot(&self, other: &Mat3<T>) -> T {
|
|
|
|
|
other.transpose().mul_m(self).trace()
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn determinant(&self) -> T {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
self.col(0).dot(&self.col(1).cross(self.col(2)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn trace(&self) -> T {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
*self.elem(0, 0) +
|
|
|
|
|
*self.elem(1, 1) +
|
|
|
|
|
*self.elem(2, 2)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn inverse(&self) -> Option<Mat3<T>> {
|
|
|
|
|
let d = self.determinant();
|
2013-05-23 21:05:25 +00:00
|
|
|
|
if d.approx_eq(&Zero::zero()) {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
None
|
|
|
|
|
} else {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
let m: Mat3<T> = BaseMat3::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));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
Some(m.transpose())
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn transpose(&self) -> Mat3<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseMat3::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))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
2013-05-07 15:00:06 +00:00
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-04-14 20:43:21 +00:00
|
|
|
|
fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec3<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
unsafe { &'a mut transmute::<&'a mut Mat3<T>, &'a mut [Vec3<T>,..3]>(self)[i] }
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
|
|
|
|
|
self.col_mut(i).index_mut(j)
|
|
|
|
|
}
|
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn swap_cols(&mut self, a: uint, b: uint) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
let tmp = *self.col(a);
|
|
|
|
|
*self.col_mut(a) = *self.col(b);
|
2013-05-23 21:55:23 +00:00
|
|
|
|
*self.col_mut(b) = tmp;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
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(always)]
|
|
|
|
|
fn set(&mut self, other: &Mat3<T>) {
|
|
|
|
|
(*self) = (*other);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_identity(&mut self) {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
(*self) = BaseMat::identity();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_zero(&mut self) {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
(*self) = BaseMat::zero();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
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(always)]
|
|
|
|
|
fn add_self_m(&mut self, other: &Mat3<T>) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn sub_self_m(&mut self, other: &Mat3<T>) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn invert_self(&mut self) {
|
|
|
|
|
match self.inverse() {
|
|
|
|
|
Some(m) => (*self) = m,
|
|
|
|
|
None => fail!(~"Couldn't invert the matrix!")
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn transpose_self(&mut self) {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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);
|
2013-05-31 11:05:43 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
*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);
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
*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;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_identity(&self) -> bool {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
self.approx_eq(&BaseMat::identity())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_diagonal(&self) -> bool {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(0, 1).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(0, 2).approx_eq(&Zero::zero()) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(1, 0).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(1, 2).approx_eq(&Zero::zero()) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(2, 0).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(2, 1).approx_eq(&Zero::zero())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_rotated(&self) -> bool {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
!self.approx_eq(&BaseMat::identity())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_symmetric(&self) -> bool {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(0, 1).approx_eq(self.elem(1, 0)) &&
|
|
|
|
|
self.elem(0, 2).approx_eq(self.elem(2, 0)) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(1, 0).approx_eq(self.elem(0, 1)) &&
|
|
|
|
|
self.elem(1, 2).approx_eq(self.elem(2, 1)) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(2, 0).approx_eq(self.elem(0, 2)) &&
|
|
|
|
|
self.elem(2, 1).approx_eq(self.elem(1, 2))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_invertible(&self) -> bool {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
!self.determinant().approx_eq(&Zero::zero())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_ptr(&self) -> *T {
|
2013-05-22 07:01:52 +00:00
|
|
|
|
unsafe { transmute(self) }
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> BaseMat3<T, Vec3<T>> for Mat3<T> {
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a 3 x 3 matrix
|
|
|
|
|
///
|
|
|
|
|
/// # Arguments
|
|
|
|
|
///
|
|
|
|
|
/// - `c0r0`, `c0r1`, `c0r2`: the first column of the matrix
|
|
|
|
|
/// - `c1r0`, `c1r1`, `c1r2`: the second column of the matrix
|
|
|
|
|
/// - `c2r0`, `c2r1`, `c2r2`: the third column of the matrix
|
|
|
|
|
///
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1 c2
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// r0 | c0r0 | c1r0 | c2r0 |
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// r1 | c0r1 | c1r1 | c2r1 |
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// r2 | c0r2 | c1r2 | c2r2 |
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn new(c0r0:T, c0r1:T, c0r2:T,
|
2013-04-02 04:01:38 +00:00
|
|
|
|
c1r0:T, c1r1:T, c1r2:T,
|
|
|
|
|
c2r0:T, c2r1:T, c2r2:T) -> Mat3<T> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat3::from_cols(BaseVec3::new::<T,Vec3<T>>(c0r0, c0r1, c0r2),
|
|
|
|
|
BaseVec3::new::<T,Vec3<T>>(c1r0, c1r1, c1r2),
|
|
|
|
|
BaseVec3::new::<T,Vec3<T>>(c2r0, c2r1, c2r2))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a 3 x 3 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
|
|
|
|
|
///
|
|
|
|
|
/// ~~~
|
|
|
|
|
/// c0 c1 c2
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// r0 | c0.x | c1.x | c2.x |
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// r1 | c0.y | c1.y | c2.y |
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// r2 | c0.z | c1.z | c2.z |
|
|
|
|
|
/// +------+------+------+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-04-02 04:01:38 +00:00
|
|
|
|
fn from_cols(c0: Vec3<T>, c1: Vec3<T>, c2: Vec3<T>) -> Mat3<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
Mat3 { x: c0, y: c1, z: c2 }
|
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a matrix from an angular rotation around the `x` axis
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_angle_x(radians: T) -> Mat3<T> {
|
|
|
|
|
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
2013-05-06 03:52:22 +00:00
|
|
|
|
let cos_theta = radians.cos();
|
|
|
|
|
let sin_theta = radians.sin();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat3::new( One::one(), Zero::zero(), Zero::zero(),
|
|
|
|
|
Zero::zero(), cos_theta, sin_theta,
|
|
|
|
|
Zero::zero(), -sin_theta, cos_theta)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a matrix from an angular rotation around the `y` axis
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_angle_y(radians: T) -> Mat3<T> {
|
|
|
|
|
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
2013-05-06 03:52:22 +00:00
|
|
|
|
let cos_theta = radians.cos();
|
|
|
|
|
let sin_theta = radians.sin();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat3::new( cos_theta, Zero::zero(), -sin_theta,
|
|
|
|
|
Zero::zero(), One::one(), Zero::zero(),
|
|
|
|
|
sin_theta, Zero::zero(), cos_theta)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a matrix from an angular rotation around the `z` axis
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_angle_z(radians: T) -> Mat3<T> {
|
|
|
|
|
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
2013-05-06 03:52:22 +00:00
|
|
|
|
let cos_theta = radians.cos();
|
|
|
|
|
let sin_theta = radians.sin();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat3::new( cos_theta, sin_theta, Zero::zero(),
|
|
|
|
|
-sin_theta, cos_theta, Zero::zero(),
|
|
|
|
|
Zero::zero(), Zero::zero(), One::one())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_angle_xyz(radians_x: T, radians_y: T, radians_z: T) -> Mat3<T> {
|
|
|
|
|
// http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
|
2013-05-06 03:52:22 +00:00
|
|
|
|
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();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat3::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)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Construct a matrix from an axis and an angular rotation
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Mat3<T> {
|
2013-05-06 03:52:22 +00:00
|
|
|
|
let c = radians.cos();
|
|
|
|
|
let s = radians.sin();
|
2013-05-23 21:05:25 +00:00
|
|
|
|
let _1_c = One::one::<T>() - c;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
let x = axis.x;
|
|
|
|
|
let y = axis.y;
|
|
|
|
|
let z = axis.z;
|
|
|
|
|
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat3::new(_1_c*x*x + c, _1_c*x*y + s*z, _1_c*x*z - s*y,
|
2013-05-23 21:05:25 +00:00
|
|
|
|
_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)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_axes(x: Vec3<T>, y: Vec3<T>, z: Vec3<T>) -> Mat3<T> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat3::from_cols(x, y, z)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
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();
|
|
|
|
|
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat3::from_axes(up_, side, dir_)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +----+----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_mat4(&self) -> Mat4<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseMat4::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(),
|
2013-05-23 21:05:25 +00:00
|
|
|
|
Zero::zero(), Zero::zero(), Zero::zero(), One::one())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// Convert the matrix to a quaternion
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
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, x, y, z;
|
|
|
|
|
let trace = self.trace();
|
|
|
|
|
|
2013-06-06 02:38:23 +00:00
|
|
|
|
let _1: T = cast(1.0);
|
|
|
|
|
let half: T = cast(0.5);
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
cond! (
|
|
|
|
|
(trace >= Zero::zero()) {
|
|
|
|
|
s = (_1 + trace).sqrt();
|
|
|
|
|
w = half * s;
|
|
|
|
|
s = half / s;
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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;
|
2013-05-31 11:05:43 +00:00
|
|
|
|
}
|
2013-06-01 01:56:11 +00:00
|
|
|
|
((*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();
|
2013-05-31 11:05:43 +00:00
|
|
|
|
w = half * s;
|
|
|
|
|
s = half / s;
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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;
|
2013-05-31 11:05:43 +00:00
|
|
|
|
}
|
2013-06-01 01:56:11 +00:00
|
|
|
|
(*self.elem(1, 1) > *self.elem(2, 2)) {
|
|
|
|
|
s = (half + (*self.elem(1, 1) - *self.elem(0, 0) - *self.elem(2, 2))).sqrt();
|
2013-05-31 11:05:43 +00:00
|
|
|
|
w = half * s;
|
|
|
|
|
s = half / s;
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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;
|
2013-05-31 11:05:43 +00:00
|
|
|
|
}
|
|
|
|
|
_ {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
s = (half + (*self.elem(2, 2) - *self.elem(0, 0) - *self.elem(1, 1))).sqrt();
|
2013-05-31 11:05:43 +00:00
|
|
|
|
w = half * s;
|
|
|
|
|
s = half / s;
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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;
|
2013-05-31 11:05:43 +00:00
|
|
|
|
}
|
|
|
|
|
)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
Quat::new(w, x, y, z)
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> Neg<Mat3<T>> for Mat3<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn neg(&self) -> Mat3<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat3::from_cols(-self.col(0), -self.col(1), -self.col(2))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> ApproxEq<T> for Mat3<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-05-07 15:00:06 +00:00
|
|
|
|
fn approx_epsilon() -> T {
|
|
|
|
|
ApproxEq::approx_epsilon::<T,T>()
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
2013-05-07 15:00:06 +00:00
|
|
|
|
fn approx_eq(&self, other: &Mat3<T>) -> bool {
|
|
|
|
|
self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn approx_eq_eps(&self, other: &Mat3<T>, epsilon: &T) -> bool {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 01:07:25 +00:00
|
|
|
|
// a 3×3 single-precision floating-point matrix
|
|
|
|
|
pub type mat3 = Mat3<f32>;
|
|
|
|
|
// a 3×3 double-precision floating-point matrix
|
|
|
|
|
pub type dmat3 = Mat3<f64>;
|
|
|
|
|
|
|
|
|
|
// Rust-style type aliases
|
|
|
|
|
pub type Mat3f = Mat3<float>;
|
|
|
|
|
pub type Mat3f32 = Mat3<f32>;
|
|
|
|
|
pub type Mat3f64 = Mat3<f64>;
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[deriving(Eq)]
|
|
|
|
|
pub struct Mat4<T> { x: Vec4<T>, y: Vec4<T>, z: Vec4<T>, w: Vec4<T> }
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> BaseMat<T, Vec4<T>> for Mat4<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-05-31 11:05:43 +00:00
|
|
|
|
fn col<'a>(&'a self, i: uint) -> &'a Vec4<T> {
|
|
|
|
|
unsafe { &'a transmute::<&'a Mat4<T>, &'a [Vec4<T>,..4]>(self)[i] }
|
|
|
|
|
}
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn row(&self, i: uint) -> Vec4<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseVec4::new(*self.elem(0, i),
|
|
|
|
|
*self.elem(1, i),
|
|
|
|
|
*self.elem(2, i),
|
|
|
|
|
*self.elem(3, i))
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn elem<'a>(&'a self, i: uint, j: uint) -> &'a T {
|
|
|
|
|
self.col(i).index(j)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +-----+-----+-----+-----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn from_value(value: T) -> Mat4<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat4::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)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +----+----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn identity() -> Mat4<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat4::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>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +----+----+----+----+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn zero() -> Mat4<T> {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
BaseMat4::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>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_t(&self, value: T) -> Mat4<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat4::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))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_v(&self, vec: &Vec4<T>) -> Vec4<T> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseVec4::new(self.row(0).dot(vec),
|
|
|
|
|
self.row(1).dot(vec),
|
|
|
|
|
self.row(2).dot(vec),
|
|
|
|
|
self.row(3).dot(vec))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn add_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat4::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)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn sub_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat4::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)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn mul_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat4::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)),
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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)),
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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)),
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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)))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn dot(&self, other: &Mat4<T>) -> T {
|
|
|
|
|
other.transpose().mul_m(self).trace()
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn determinant(&self) -> T {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
let m0: Mat3<T> = BaseMat3::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<T> = BaseMat3::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<T> = BaseMat3::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<T> = BaseMat3::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()
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn trace(&self) -> T {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
*self.elem(0, 0) +
|
|
|
|
|
*self.elem(1, 1) +
|
|
|
|
|
*self.elem(2, 2) +
|
|
|
|
|
*self.elem(3, 3)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
fn inverse(&self) -> Option<Mat4<T>> {
|
|
|
|
|
let d = self.determinant();
|
2013-05-23 21:05:25 +00:00
|
|
|
|
if d.approx_eq(&Zero::zero()) {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
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;
|
2013-04-02 05:12:13 +00:00
|
|
|
|
let mut I: Mat4<T> = BaseMat::identity();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
|
|
|
|
for uint::range(0, 4) |j| {
|
|
|
|
|
// Find largest element in col j
|
|
|
|
|
let mut i1 = j;
|
|
|
|
|
for uint::range(j + 1, 4) |i| {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
if A.elem(j, i).abs() > A.elem(j, i1).abs() {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
i1 = i;
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-06 03:52:22 +00:00
|
|
|
|
// 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
|
2013-06-01 01:56:11 +00:00
|
|
|
|
let ajj = *A.elem(j, j);
|
2013-05-23 21:55:23 +00:00
|
|
|
|
I.col_mut(j).div_self_t(ajj);
|
|
|
|
|
A.col_mut(j).div_self_t(ajj);
|
2013-05-06 03:52:22 +00:00
|
|
|
|
|
|
|
|
|
// Eliminate off-diagonal elems in col j of A,
|
|
|
|
|
// doing identical ops to I
|
|
|
|
|
for uint::range(0, 4) |i| {
|
|
|
|
|
if i != j {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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));
|
2013-05-23 21:55:23 +00:00
|
|
|
|
I.col_mut(i).sub_self_v(&ij_mul_aij);
|
|
|
|
|
A.col_mut(i).sub_self_v(&aj_mul_aij);
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
Some(I)
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn transpose(&self) -> Mat4<T> {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
BaseMat4::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))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
2013-05-07 15:00:06 +00:00
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-04-14 20:43:21 +00:00
|
|
|
|
fn col_mut<'a>(&'a mut self, i: uint) -> &'a mut Vec4<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
unsafe { &'a mut transmute::<&'a mut Mat4<T>, &'a mut [Vec4<T>,..4]>(self)[i] }
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn elem_mut<'a>(&'a mut self, i: uint, j: uint) -> &'a mut T {
|
|
|
|
|
self.col_mut(i).index_mut(j)
|
|
|
|
|
}
|
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn swap_cols(&mut self, a: uint, b: uint) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
let tmp = *self.col(a);
|
|
|
|
|
*self.col_mut(a) = *self.col(b);
|
2013-05-23 21:55:23 +00:00
|
|
|
|
*self.col_mut(b) = tmp;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
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(always)]
|
|
|
|
|
fn set(&mut self, other: &Mat4<T>) {
|
|
|
|
|
(*self) = (*other);
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_identity(&mut self) {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
(*self) = BaseMat::identity();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_zero(&mut self) {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
(*self) = BaseMat::zero();
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
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(always)]
|
|
|
|
|
fn add_self_m(&mut self, other: &Mat4<T>) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn sub_self_m(&mut self, other: &Mat4<T>) {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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));
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn invert_self(&mut self) {
|
|
|
|
|
match self.inverse() {
|
|
|
|
|
Some(m) => (*self) = m,
|
|
|
|
|
None => fail!(~"Couldn't invert the matrix!")
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn transpose_self(&mut self) {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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;
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_identity(&self) -> bool {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
self.approx_eq(&BaseMat::identity())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_diagonal(&self) -> bool {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(0, 1).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(0, 2).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(0, 3).approx_eq(&Zero::zero()) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(1, 0).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(1, 2).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(1, 3).approx_eq(&Zero::zero()) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(2, 0).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(2, 1).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(2, 3).approx_eq(&Zero::zero()) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
self.elem(3, 0).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(3, 1).approx_eq(&Zero::zero()) &&
|
|
|
|
|
self.elem(3, 2).approx_eq(&Zero::zero())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_rotated(&self) -> bool {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
!self.approx_eq(&BaseMat::identity())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_symmetric(&self) -> bool {
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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)) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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)) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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)) &&
|
2013-03-31 06:27:59 +00:00
|
|
|
|
|
2013-06-01 01:56:11 +00:00
|
|
|
|
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))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn is_invertible(&self) -> bool {
|
2013-05-23 21:05:25 +00:00
|
|
|
|
!self.determinant().approx_eq(&Zero::zero())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn to_ptr(&self) -> *T {
|
2013-05-22 07:01:52 +00:00
|
|
|
|
unsafe { transmute(self) }
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> BaseMat4<T, Vec4<T>> for Mat4<T> {
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +------+------+------+------+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn new(c0r0: T, c0r1: T, c0r2: T, c0r3: T,
|
2013-04-02 04:01:38 +00:00
|
|
|
|
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> {
|
2013-04-02 05:12:13 +00:00
|
|
|
|
BaseMat4::from_cols(BaseVec4::new::<T,Vec4<T>>(c0r0, c0r1, c0r2, c0r3),
|
|
|
|
|
BaseVec4::new::<T,Vec4<T>>(c1r0, c1r1, c1r2, c1r3),
|
|
|
|
|
BaseVec4::new::<T,Vec4<T>>(c2r0, c2r1, c2r2, c2r3),
|
|
|
|
|
BaseVec4::new::<T,Vec4<T>>(c3r0, c3r1, c3r2, c3r3))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
2013-06-01 02:57:29 +00:00
|
|
|
|
/// 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 |
|
|
|
|
|
/// +------+------+------+------+
|
|
|
|
|
/// ~~~
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-04-02 04:01:38 +00:00
|
|
|
|
fn from_cols(c0: Vec4<T>, c1: Vec4<T>, c2: Vec4<T>, c3: Vec4<T>) -> Mat4<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
Mat4 { x: c0, y: c1, z: c2, w: c3 }
|
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-07 15:00:06 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> Neg<Mat4<T>> for Mat4<T> {
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn neg(&self) -> Mat4<T> {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
BaseMat4::from_cols(-self.col(0), -self.col(1), -self.col(2), -self.col(3))
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
|
|
|
|
|
2013-05-31 11:05:43 +00:00
|
|
|
|
impl<T:Copy + Float + NumAssign> ApproxEq<T> for Mat4<T> {
|
2013-05-07 15:00:06 +00:00
|
|
|
|
#[inline(always)]
|
|
|
|
|
fn approx_epsilon() -> T {
|
|
|
|
|
ApproxEq::approx_epsilon::<T,T>()
|
|
|
|
|
}
|
|
|
|
|
|
2013-03-31 06:27:59 +00:00
|
|
|
|
#[inline(always)]
|
2013-05-07 15:00:06 +00:00
|
|
|
|
fn approx_eq(&self, other: &Mat4<T>) -> bool {
|
|
|
|
|
self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
#[inline(always)]
|
2013-05-07 15:00:06 +00:00
|
|
|
|
fn approx_eq_eps(&self, other: &Mat4<T>, epsilon: &T) -> bool {
|
2013-05-31 11:05:43 +00:00
|
|
|
|
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)
|
2013-03-31 06:27:59 +00:00
|
|
|
|
}
|
|
|
|
|
}
|
2013-06-01 01:07:25 +00:00
|
|
|
|
|
|
|
|
|
// 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>;
|