1825 lines
54 KiB
Rust
1825 lines
54 KiB
Rust
use core::num::{Zero, One};
|
||
use core::num::Zero::zero;
|
||
use core::num::One::one;
|
||
use std::cmp::{FuzzyEq, FUZZY_EPSILON};
|
||
use numeric::*;
|
||
|
||
use vec::*;
|
||
use quat::Quat;
|
||
|
||
/**
|
||
* 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.
|
||
*/
|
||
pub trait Matrix<T,V>: Index<uint, V> + Eq + Neg<Self> {
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The column vector at `i`
|
||
*/
|
||
fn col(&self, i: uint) -> V;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The row vector at `i`
|
||
*/
|
||
fn row(&self, i: uint) -> V;
|
||
|
||
/**
|
||
* Construct a diagonal matrix with the major diagonal set to `value`
|
||
*/
|
||
fn from_value(value: T) -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The identity matrix
|
||
*/
|
||
fn identity() -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* A matrix with all elements set to zero
|
||
*/
|
||
fn zero() -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The scalar multiplication of this matrix and `value`
|
||
*/
|
||
fn mul_t(&self, value: T) -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The matrix vector product of the matrix and `vec`
|
||
*/
|
||
fn mul_v(&self, vec: &V) -> V;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The matrix addition of the matrix and `other`
|
||
*/
|
||
fn add_m(&self, other: &Self) -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The difference between the matrix and `other`
|
||
*/
|
||
fn sub_m(&self, other: &Self) -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The matrix product of the matrix and `other`
|
||
*/
|
||
fn mul_m(&self, other: &Self) -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The matrix dot product of the matrix and `other`
|
||
*/
|
||
fn dot(&self, other: &Self) -> T;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The determinant of the matrix
|
||
*/
|
||
fn determinant(&self) -> T;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The sum of the main diagonal of the matrix
|
||
*/
|
||
fn trace(&self) -> T;
|
||
|
||
/**
|
||
* 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)
|
||
*/
|
||
fn inverse(&self) -> Option<Self>;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* The transposed matrix
|
||
*/
|
||
fn transpose(&self) -> Self;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* A mutable reference to the column at `i`
|
||
*/
|
||
fn col_mut(&mut self, i: uint) -> &'self mut V;
|
||
|
||
/**
|
||
* Swap two columns of the matrix in place
|
||
*/
|
||
fn swap_cols(&mut self, a: uint, b: uint);
|
||
|
||
/**
|
||
* Swap two rows of the matrix in place
|
||
*/
|
||
fn swap_rows(&mut self, a: uint, b: uint);
|
||
|
||
/**
|
||
* Sets the matrix to `other`
|
||
*/
|
||
fn set(&mut self, other: &Self);
|
||
|
||
/**
|
||
* Sets the matrix to the identity matrix
|
||
*/
|
||
fn to_identity(&mut self);
|
||
|
||
/**
|
||
* Sets each element of the matrix to zero
|
||
*/
|
||
fn to_zero(&mut self);
|
||
|
||
/**
|
||
* Multiplies the matrix by a scalar
|
||
*/
|
||
fn mul_self_t(&mut self, value: T);
|
||
|
||
/**
|
||
* Add the matrix `other` to `self`
|
||
*/
|
||
fn add_self_m(&mut self, other: &Self);
|
||
|
||
/**
|
||
* Subtract the matrix `other` from `self`
|
||
*/
|
||
fn sub_self_m(&mut self, other: &Self);
|
||
|
||
/**
|
||
* 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!
|
||
*/
|
||
fn invert_self(&mut self);
|
||
|
||
/**
|
||
* Sets the matrix to its transpose
|
||
*/
|
||
fn transpose_self(&mut self);
|
||
|
||
/**
|
||
* Check to see if the matrix is an identity matrix
|
||
*
|
||
* # Return value
|
||
*
|
||
* `true` if the matrix is approximately equal to the identity matrix
|
||
*/
|
||
fn is_identity(&self) -> bool;
|
||
|
||
/**
|
||
* Check to see if the matrix is diagonal
|
||
*
|
||
* # Return value
|
||
*
|
||
* `true` all the elements outside the main diagonal are approximately
|
||
* equal to zero.
|
||
*/
|
||
fn is_diagonal(&self) -> bool;
|
||
|
||
/**
|
||
* Check to see if the matrix is rotated
|
||
*
|
||
* # Return value
|
||
*
|
||
* `true` if the matrix is not approximately equal to the identity matrix.
|
||
*/
|
||
fn is_rotated(&self) -> bool;
|
||
|
||
/**
|
||
* Check to see if the matrix is symmetric
|
||
*
|
||
* # Return value
|
||
*
|
||
* `true` if the matrix is approximately equal to its transpose).
|
||
*/
|
||
fn is_symmetric(&self) -> bool;
|
||
|
||
/**
|
||
* Check to see if the matrix is invertable
|
||
*
|
||
* # Return value
|
||
*
|
||
* `true` if the matrix is invertable
|
||
*/
|
||
fn is_invertible(&self) -> bool;
|
||
|
||
/**
|
||
* # Return value
|
||
*
|
||
* A pointer to the first element of the matrix
|
||
*/
|
||
fn to_ptr(&self) -> *T;
|
||
}
|
||
|
||
/**
|
||
* A 2 x 2 matrix
|
||
*/
|
||
pub trait Matrix2<T,V>: Matrix<T,V> {
|
||
fn new(c0r0: T, c0r1: T,
|
||
c1r0: T, c1r1: T) -> Self;
|
||
|
||
fn from_cols(c0: V, c1: V) -> Self;
|
||
|
||
fn from_angle(radians: T) -> Self;
|
||
|
||
fn to_mat3(&self) -> Mat3<T>;
|
||
|
||
fn to_mat4(&self) -> Mat4<T>;
|
||
}
|
||
|
||
/**
|
||
* A 3 x 3 matrix
|
||
*/
|
||
pub trait Matrix3<T,V>: Matrix<T,V> {
|
||
fn new(c0r0:T, c0r1:T, c0r2:T,
|
||
c1r0:T, c1r1:T, c1r2:T,
|
||
c2r0:T, c2r1:T, c2r2:T) -> Self;
|
||
|
||
fn from_cols(c0: V, c1: V, c2: V) -> Self;
|
||
|
||
fn from_angle_x(radians: T) -> Self;
|
||
|
||
fn from_angle_y(radians: T) -> Self;
|
||
|
||
fn from_angle_z(radians: T) -> Self;
|
||
|
||
fn from_angle_xyz(radians_x: T, radians_y: T, radians_z: T) -> Self;
|
||
|
||
fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Self;
|
||
|
||
fn from_axes(x: V, y: V, z: V) -> Self;
|
||
|
||
fn look_at(dir: &Vec3<T>, up: &Vec3<T>) -> Self;
|
||
|
||
fn to_mat4(&self) -> Mat4<T>;
|
||
|
||
fn to_quat(&self) -> Quat<T>;
|
||
}
|
||
|
||
/**
|
||
* A 4 x 4 matrix
|
||
*/
|
||
pub trait Matrix4<T,V>: Matrix<T,V> {
|
||
fn new(c0r0: T, c0r1: T, c0r2: T, c0r3: T,
|
||
c1r0: T, c1r1: T, c1r2: T, c1r3: T,
|
||
c2r0: T, c2r1: T, c2r2: T, c2r3: T,
|
||
c3r0: T, c3r1: T, c3r2: T, c3r3: T) -> Self;
|
||
|
||
fn from_cols(c0: V, c1: V, c2: V, c3: V) -> Self;
|
||
}
|
||
|
||
/**
|
||
* 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
|
||
*/
|
||
#[deriving(Eq)]
|
||
pub struct Mat2<T> { x: Vec2<T>, y: Vec2<T> }
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix<T, Vec2<T>> for Mat2<T> {
|
||
#[inline(always)]
|
||
fn col(&self, i: uint) -> Vec2<T> { self[i] }
|
||
|
||
#[inline(always)]
|
||
fn row(&self, i: uint) -> Vec2<T> {
|
||
Vector2::new(self[0][i],
|
||
self[1][i])
|
||
}
|
||
|
||
/**
|
||
* 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 |
|
||
* +-----+-----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn from_value(value: T) -> Mat2<T> {
|
||
Matrix2::new(value, zero(),
|
||
zero(), value)
|
||
}
|
||
|
||
/**
|
||
* Returns the multiplicative identity matrix
|
||
* ~~~
|
||
* c0 c1
|
||
* +----+----+
|
||
* r0 | 1 | 0 |
|
||
* +----+----+
|
||
* r1 | 0 | 1 |
|
||
* +----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn identity() -> Mat2<T> {
|
||
Matrix2::new( one::<T>(), zero::<T>(),
|
||
zero::<T>(), one::<T>())
|
||
}
|
||
|
||
/**
|
||
* Returns the additive identity matrix
|
||
* ~~~
|
||
* c0 c1
|
||
* +----+----+
|
||
* r0 | 0 | 0 |
|
||
* +----+----+
|
||
* r1 | 0 | 0 |
|
||
* +----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn zero() -> Mat2<T> {
|
||
Matrix2::new(zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_t(&self, value: T) -> Mat2<T> {
|
||
Matrix2::from_cols(self[0].mul_t(value),
|
||
self[1].mul_t(value))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_v(&self, vec: &Vec2<T>) -> Vec2<T> {
|
||
Vector2::new(self.row(0).dot(vec),
|
||
self.row(1).dot(vec))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn add_m(&self, other: &Mat2<T>) -> Mat2<T> {
|
||
Matrix2::from_cols(self[0].add_v(&other[0]),
|
||
self[1].add_v(&other[1]))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_m(&self, other: &Mat2<T>) -> Mat2<T> {
|
||
Matrix2::from_cols(self[0].sub_v(&other[0]),
|
||
self[1].sub_v(&other[1]))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_m(&self, other: &Mat2<T>) -> Mat2<T> {
|
||
Matrix2::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)))
|
||
}
|
||
|
||
fn dot(&self, other: &Mat2<T>) -> T {
|
||
other.transpose().mul_m(self).trace()
|
||
}
|
||
|
||
fn determinant(&self) -> T {
|
||
self[0][0] * self[1][1] - self[1][0] * self[0][1]
|
||
}
|
||
|
||
fn trace(&self) -> T {
|
||
self[0][0] + self[1][1]
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn inverse(&self) -> Option<Mat2<T>> {
|
||
let d = self.determinant();
|
||
if d.fuzzy_eq(&zero()) {
|
||
None
|
||
} else {
|
||
Some(Matrix2::new( self[1][1]/d, -self[0][1]/d,
|
||
-self[1][0]/d, self[0][0]/d))
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn transpose(&self) -> Mat2<T> {
|
||
Matrix2::new(self[0][0], self[1][0],
|
||
self[0][1], self[1][1])
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn col_mut(&mut self, i: uint) -> &'self mut Vec2<T> {
|
||
match i {
|
||
0 => &mut self.x,
|
||
1 => &mut self.y,
|
||
_ => fail!(fmt!("index out of bounds: expected an index from 0 to 1, but found %u", i))
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn swap_cols(&mut self, a: uint, b: uint) {
|
||
*self.col_mut(a) <-> *self.col_mut(b);
|
||
}
|
||
|
||
#[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) {
|
||
(*self) = Matrix::identity();
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_zero(&mut self) {
|
||
(*self) = Matrix::zero();
|
||
}
|
||
|
||
#[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>) {
|
||
self.x.add_self_v(&other[0]);
|
||
self.y.add_self_v(&other[1]);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_self_m(&mut self, other: &Mat2<T>) {
|
||
self.x.sub_self_v(&other[0]);
|
||
self.y.sub_self_v(&other[1]);
|
||
}
|
||
|
||
#[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) {
|
||
*self.x.index_mut(1) <-> *self.y.index_mut(0);
|
||
*self.y.index_mut(0) <-> *self.x.index_mut(1);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_identity(&self) -> bool {
|
||
self.fuzzy_eq(&Matrix::identity())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_diagonal(&self) -> bool {
|
||
self[0][1].fuzzy_eq(&zero()) &&
|
||
self[1][0].fuzzy_eq(&zero())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_rotated(&self) -> bool {
|
||
!self.fuzzy_eq(&Matrix::identity())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_symmetric(&self) -> bool {
|
||
self[0][1].fuzzy_eq(&self[1][0]) &&
|
||
self[1][0].fuzzy_eq(&self[0][1])
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_invertible(&self) -> bool {
|
||
!self.determinant().fuzzy_eq(&zero())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_ptr(&self) -> *T {
|
||
unsafe { cast::transmute(self) }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix2<T, Vec2<T>> for Mat2<T> {
|
||
/**
|
||
* Construct a 2 x 2 matrix
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `c0r0`, `c0r1` - the first column of the matrix
|
||
* * `c1r0`, `c1r1` - the second column of the matrix
|
||
*
|
||
* ~~~
|
||
* c0 c1
|
||
* +------+------+
|
||
* r0 | c0r0 | c1r0 |
|
||
* +------+------+
|
||
* r1 | c0r1 | c1r1 |
|
||
* +------+------+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn new(c0r0: T, c0r1: T,
|
||
c1r0: T, c1r1: T) -> Mat2<T> {
|
||
Matrix2::from_cols(Vector2::new::<T,Vec2<T>>(c0r0, c0r1),
|
||
Vector2::new::<T,Vec2<T>>(c1r0, c1r1))
|
||
}
|
||
|
||
/**
|
||
* Construct a 2 x 2 matrix from column vectors
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `c0` - the first column vector of the matrix
|
||
* * `c1` - the second column vector of the matrix
|
||
*
|
||
* ~~~
|
||
* c0 c1
|
||
* +------+------+
|
||
* r0 | c0.x | c1.x |
|
||
* +------+------+
|
||
* r1 | c0.y | c1.y |
|
||
* +------+------+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn from_cols(c0: Vec2<T>,
|
||
c1: Vec2<T>) -> Mat2<T> {
|
||
Mat2 { x: c0, y: c1 }
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn from_angle(radians: T) -> Mat2<T> {
|
||
let cos_theta = cos(radians);
|
||
let sin_theta = sin(radians);
|
||
|
||
Matrix2::new(cos_theta, -sin_theta,
|
||
sin_theta, cos_theta)
|
||
}
|
||
|
||
/**
|
||
* Returns the the matrix with an extra row and column added
|
||
* ~~~
|
||
* c0 c1 c0 c1 c2
|
||
* +----+----+ +----+----+----+
|
||
* r0 | a | b | r0 | a | b | 0 |
|
||
* +----+----+ +----+----+----+
|
||
* r1 | c | d | => r1 | c | d | 0 |
|
||
* +----+----+ +----+----+----+
|
||
* r2 | 0 | 0 | 1 |
|
||
* +----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn to_mat3(&self) -> Mat3<T> {
|
||
Matrix3::new(self[0][0], self[0][1], zero(),
|
||
self[1][0], self[1][1], zero(),
|
||
zero(), zero(), one())
|
||
}
|
||
|
||
/**
|
||
* Returns the the matrix with an extra two rows and columns added
|
||
* ~~~
|
||
* c0 c1 c0 c1 c2 c3
|
||
* +----+----+ +----+----+----+----+
|
||
* r0 | a | b | r0 | a | b | 0 | 0 |
|
||
* +----+----+ +----+----+----+----+
|
||
* r1 | c | d | => r1 | c | d | 0 | 0 |
|
||
* +----+----+ +----+----+----+----+
|
||
* r2 | 0 | 0 | 1 | 0 |
|
||
* +----+----+----+----+
|
||
* r3 | 0 | 0 | 0 | 1 |
|
||
* +----+----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn to_mat4(&self) -> Mat4<T> {
|
||
Matrix4::new(self[0][0], self[0][1], zero(), zero(),
|
||
self[1][0], self[1][1], zero(), zero(),
|
||
zero(), zero(), one(), zero(),
|
||
zero(), zero(), zero(), one())
|
||
}
|
||
}
|
||
|
||
impl<T:Copy> Index<uint, Vec2<T>> for Mat2<T> {
|
||
#[inline(always)]
|
||
fn index(&self, i: &uint) -> Vec2<T> {
|
||
unsafe { do vec::raw::buf_as_slice(cast::transmute(self), 2) |slice| { slice[*i] } }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Neg<Mat2<T>> for Mat2<T> {
|
||
#[inline(always)]
|
||
fn neg(&self) -> Mat2<T> {
|
||
Matrix2::from_cols(-self[0], -self[1])
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T>> FuzzyEq<T> for Mat2<T> {
|
||
#[inline(always)]
|
||
fn fuzzy_eq(&self, other: &Mat2<T>) -> bool {
|
||
self.fuzzy_eq_eps(other, &num::cast(FUZZY_EPSILON))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn fuzzy_eq_eps(&self, other: &Mat2<T>, epsilon: &T) -> bool {
|
||
self[0].fuzzy_eq_eps(&other[0], epsilon) &&
|
||
self[1].fuzzy_eq_eps(&other[1], epsilon)
|
||
}
|
||
}
|
||
|
||
macro_rules! mat2_type(
|
||
($name:ident <$T:ty, $V:ty>) => (
|
||
pub impl $name {
|
||
#[inline(always)] fn new(c0r0: $T, c0r1: $T, c1r0: $T, c1r1: $T)
|
||
-> $name { Matrix2::new(c0r0, c0r1, c1r0, c1r1) }
|
||
#[inline(always)] fn from_cols(c0: $V, c1: $V)
|
||
-> $name { Matrix2::from_cols(c0, c1) }
|
||
#[inline(always)] fn from_value(v: $T) -> $name { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] fn identity() -> $name { Matrix::identity() }
|
||
#[inline(always)] fn zero() -> $name { Matrix::zero() }
|
||
|
||
#[inline(always)] fn from_angle(radians: $T) -> $name { Matrix2::from_angle(radians) }
|
||
|
||
#[inline(always)] fn dim() -> uint { 2 }
|
||
#[inline(always)] fn rows() -> uint { 2 }
|
||
#[inline(always)] fn cols() -> uint { 2 }
|
||
#[inline(always)] fn size_of() -> uint { sys::size_of::<$name>() }
|
||
}
|
||
)
|
||
)
|
||
|
||
// 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>;
|
||
|
||
mat2_type!(mat2<f32,vec2>)
|
||
mat2_type!(dmat2<f64,dvec2>)
|
||
|
||
// Rust-style type aliases
|
||
pub type Mat2f = Mat2<float>;
|
||
pub type Mat2f32 = Mat2<f32>;
|
||
pub type Mat2f64 = Mat2<f64>;
|
||
|
||
mat2_type!(Mat2f<float,Vec2f>)
|
||
mat2_type!(Mat2f32<f32,Vec2f32>)
|
||
mat2_type!(Mat2f64<f64,Vec2f64>)
|
||
|
||
/**
|
||
* 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
|
||
*/
|
||
#[deriving(Eq)]
|
||
pub struct Mat3<T> { x: Vec3<T>, y: Vec3<T>, z: Vec3<T> }
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix<T, Vec3<T>> for Mat3<T> {
|
||
#[inline(always)]
|
||
fn col(&self, i: uint) -> Vec3<T> { self[i] }
|
||
|
||
#[inline(always)]
|
||
fn row(&self, i: uint) -> Vec3<T> {
|
||
Vector3::new(self[0][i],
|
||
self[1][i],
|
||
self[2][i])
|
||
}
|
||
|
||
/**
|
||
* Construct a 3 x 3 diagonal matrix with the major diagonal set to `value`
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `value` - the value to set the major diagonal to
|
||
*
|
||
* ~~~
|
||
* c0 c1 c2
|
||
* +-----+-----+-----+
|
||
* r0 | val | 0 | 0 |
|
||
* +-----+-----+-----+
|
||
* r1 | 0 | val | 0 |
|
||
* +-----+-----+-----+
|
||
* r2 | 0 | 0 | val |
|
||
* +-----+-----+-----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn from_value(value: T) -> Mat3<T> {
|
||
Matrix3::new(value, zero(), zero(),
|
||
zero(), value, zero(),
|
||
zero(), zero(), value)
|
||
}
|
||
|
||
/**
|
||
* Returns the multiplicative identity matrix
|
||
* ~~~
|
||
* c0 c1 c2
|
||
* +----+----+----+
|
||
* r0 | 1 | 0 | 0 |
|
||
* +----+----+----+
|
||
* r1 | 0 | 1 | 0 |
|
||
* +----+----+----+
|
||
* r2 | 0 | 0 | 1 |
|
||
* +----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn identity() -> Mat3<T> {
|
||
Matrix3::new( one::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), one::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), one::<T>())
|
||
}
|
||
|
||
/**
|
||
* Returns the additive identity matrix
|
||
* ~~~
|
||
* c0 c1 c2
|
||
* +----+----+----+
|
||
* r0 | 0 | 0 | 0 |
|
||
* +----+----+----+
|
||
* r1 | 0 | 0 | 0 |
|
||
* +----+----+----+
|
||
* r2 | 0 | 0 | 0 |
|
||
* +----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn zero() -> Mat3<T> {
|
||
Matrix3::new(zero::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), zero::<T>())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_t(&self, value: T) -> Mat3<T> {
|
||
Matrix3::from_cols(self[0].mul_t(value),
|
||
self[1].mul_t(value),
|
||
self[2].mul_t(value))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T> {
|
||
Vector3::new(self.row(0).dot(vec),
|
||
self.row(1).dot(vec),
|
||
self.row(2).dot(vec))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn add_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
||
Matrix3::from_cols(self[0].add_v(&other[0]),
|
||
self[1].add_v(&other[1]),
|
||
self[2].add_v(&other[2]))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
||
Matrix3::from_cols(self[0].sub_v(&other[0]),
|
||
self[1].sub_v(&other[1]),
|
||
self[2].sub_v(&other[2]))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_m(&self, other: &Mat3<T>) -> Mat3<T> {
|
||
Matrix3::new(self.row(0).dot(&other.col(0)),
|
||
self.row(1).dot(&other.col(0)),
|
||
self.row(2).dot(&other.col(0)),
|
||
|
||
self.row(0).dot(&other.col(1)),
|
||
self.row(1).dot(&other.col(1)),
|
||
self.row(2).dot(&other.col(1)),
|
||
|
||
self.row(0).dot(&other.col(2)),
|
||
self.row(1).dot(&other.col(2)),
|
||
self.row(2).dot(&other.col(2)))
|
||
}
|
||
|
||
fn dot(&self, other: &Mat3<T>) -> T {
|
||
other.transpose().mul_m(self).trace()
|
||
}
|
||
|
||
fn determinant(&self) -> T {
|
||
self.col(0).dot(&self.col(1).cross(&self.col(2)))
|
||
}
|
||
|
||
fn trace(&self) -> T {
|
||
self[0][0] + self[1][1] + self[2][2]
|
||
}
|
||
|
||
// #[inline(always)]
|
||
fn inverse(&self) -> Option<Mat3<T>> {
|
||
let d = self.determinant();
|
||
if d.fuzzy_eq(&zero()) {
|
||
None
|
||
} else {
|
||
let m: Mat3<T> = Matrix3::from_cols(self[1].cross(&self[2]).div_t(d),
|
||
self[2].cross(&self[0]).div_t(d),
|
||
self[0].cross(&self[1]).div_t(d));
|
||
Some(m.transpose())
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn transpose(&self) -> Mat3<T> {
|
||
Matrix3::new(self[0][0], self[1][0], self[2][0],
|
||
self[0][1], self[1][1], self[2][1],
|
||
self[0][2], self[1][2], self[2][2])
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn col_mut(&mut self, i: uint) -> &'self mut Vec3<T> {
|
||
match i {
|
||
0 => &mut self.x,
|
||
1 => &mut self.y,
|
||
2 => &mut self.z,
|
||
_ => fail!(fmt!("index out of bounds: expected an index from 0 to 2, but found %u", i))
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn swap_cols(&mut self, a: uint, b: uint) {
|
||
*self.col_mut(a) <-> *self.col_mut(b);
|
||
}
|
||
|
||
#[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) {
|
||
(*self) = Matrix::identity();
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_zero(&mut self) {
|
||
(*self) = Matrix::zero();
|
||
}
|
||
|
||
#[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>) {
|
||
self.col_mut(0).add_self_v(&other[0]);
|
||
self.col_mut(1).add_self_v(&other[1]);
|
||
self.col_mut(2).add_self_v(&other[2]);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_self_m(&mut self, other: &Mat3<T>) {
|
||
self.col_mut(0).sub_self_v(&other[0]);
|
||
self.col_mut(1).sub_self_v(&other[1]);
|
||
self.col_mut(2).sub_self_v(&other[2]);
|
||
}
|
||
|
||
#[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) {
|
||
*self.col_mut(0).index_mut(1) <-> *self.col_mut(1).index_mut(0);
|
||
*self.col_mut(0).index_mut(2) <-> *self.col_mut(2).index_mut(0);
|
||
|
||
*self.col_mut(1).index_mut(0) <-> *self.col_mut(0).index_mut(1);
|
||
*self.col_mut(1).index_mut(2) <-> *self.col_mut(2).index_mut(1);
|
||
|
||
*self.col_mut(2).index_mut(0) <-> *self.col_mut(0).index_mut(2);
|
||
*self.col_mut(2).index_mut(1) <-> *self.col_mut(1).index_mut(2);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_identity(&self) -> bool {
|
||
self.fuzzy_eq(&Matrix::identity())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_diagonal(&self) -> bool {
|
||
self[0][1].fuzzy_eq(&zero()) &&
|
||
self[0][2].fuzzy_eq(&zero()) &&
|
||
|
||
self[1][0].fuzzy_eq(&zero()) &&
|
||
self[1][2].fuzzy_eq(&zero()) &&
|
||
|
||
self[2][0].fuzzy_eq(&zero()) &&
|
||
self[2][1].fuzzy_eq(&zero())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_rotated(&self) -> bool {
|
||
!self.fuzzy_eq(&Matrix::identity())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_symmetric(&self) -> bool {
|
||
self[0][1].fuzzy_eq(&self[1][0]) &&
|
||
self[0][2].fuzzy_eq(&self[2][0]) &&
|
||
|
||
self[1][0].fuzzy_eq(&self[0][1]) &&
|
||
self[1][2].fuzzy_eq(&self[2][1]) &&
|
||
|
||
self[2][0].fuzzy_eq(&self[0][2]) &&
|
||
self[2][1].fuzzy_eq(&self[1][2])
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_invertible(&self) -> bool {
|
||
!self.determinant().fuzzy_eq(&zero())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_ptr(&self) -> *T {
|
||
unsafe { cast::transmute(self) }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix3<T, Vec3<T>> for Mat3<T> {
|
||
/**
|
||
* 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 |
|
||
* +------+------+------+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn new(c0r0:T, c0r1:T, c0r2:T,
|
||
c1r0:T, c1r1:T, c1r2:T,
|
||
c2r0:T, c2r1:T, c2r2:T) -> Mat3<T> {
|
||
Matrix3::from_cols(Vector3::new::<T,Vec3<T>>(c0r0, c0r1, c0r2),
|
||
Vector3::new::<T,Vec3<T>>(c1r0, c1r1, c1r2),
|
||
Vector3::new::<T,Vec3<T>>(c2r0, c2r1, c2r2))
|
||
}
|
||
|
||
/**
|
||
* 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 |
|
||
* +------+------+------+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn from_cols(c0: Vec3<T>,
|
||
c1: Vec3<T>,
|
||
c2: Vec3<T>) -> Mat3<T> {
|
||
Mat3 { x: c0, y: c1, z: c2 }
|
||
}
|
||
|
||
/**
|
||
* Construct a matrix from an angular rotation around the `x` axis
|
||
*/
|
||
#[inline(always)]
|
||
fn from_angle_x(radians: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
||
let cos_theta = cos(radians);
|
||
let sin_theta = sin(radians);
|
||
|
||
Matrix3::new( one(), zero(), zero(),
|
||
zero(), cos_theta, sin_theta,
|
||
zero(), -sin_theta, cos_theta)
|
||
}
|
||
|
||
/**
|
||
* Construct a matrix from an angular rotation around the `y` axis
|
||
*/
|
||
#[inline(always)]
|
||
fn from_angle_y(radians: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
||
let cos_theta = cos(radians);
|
||
let sin_theta = sin(radians);
|
||
|
||
Matrix3::new(cos_theta, zero(), -sin_theta,
|
||
zero(), one(), zero(),
|
||
sin_theta, zero(), cos_theta)
|
||
}
|
||
|
||
/**
|
||
* Construct a matrix from an angular rotation around the `z` axis
|
||
*/
|
||
#[inline(always)]
|
||
fn from_angle_z(radians: T) -> Mat3<T> {
|
||
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
|
||
let cos_theta = cos(radians);
|
||
let sin_theta = sin(radians);
|
||
|
||
Matrix3::new( cos_theta, sin_theta, zero(),
|
||
-sin_theta, cos_theta, zero(),
|
||
zero(), zero(), one())
|
||
}
|
||
|
||
/**
|
||
* Construct a matrix from Euler angles
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `theta_x` - the angular rotation around the `x` axis (pitch)
|
||
* * `theta_y` - the angular rotation around the `y` axis (yaw)
|
||
* * `theta_z` - the angular rotation around the `z` axis (roll)
|
||
*/
|
||
#[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
|
||
let cx = cos(radians_x);
|
||
let sx = sin(radians_x);
|
||
let cy = cos(radians_y);
|
||
let sy = sin(radians_y);
|
||
let cz = cos(radians_z);
|
||
let sz = sin(radians_z);
|
||
|
||
Matrix3::new( cy*cz, cy*sz, -sy,
|
||
-cx*sz + sx*sy*cz, cx*cz + sx*sy*sz, sx*cy,
|
||
sx*sz + cx*sy*cz, -sx*cz + cx*sy*sz, cx*cy)
|
||
}
|
||
|
||
/**
|
||
* Construct a matrix from an axis and an angular rotation
|
||
*/
|
||
#[inline(always)]
|
||
fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Mat3<T> {
|
||
let c = cos(radians);
|
||
let s = sin(radians);
|
||
let _1_c = one::<T>() - c;
|
||
|
||
let x = axis.x;
|
||
let y = axis.y;
|
||
let z = axis.z;
|
||
|
||
Matrix3::new(_1_c*x*x + c, _1_c*x*y + s*z, _1_c*x*z - s*y,
|
||
_1_c*x*y - s*z, _1_c*y*y + c, _1_c*y*z + s*x,
|
||
_1_c*x*z + s*y, _1_c*y*z - s*x, _1_c*z*z + c)
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn from_axes(x: Vec3<T>, y: Vec3<T>, z: Vec3<T>) -> Mat3<T> {
|
||
Matrix3::from_cols(x, y, z)
|
||
}
|
||
|
||
#[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();
|
||
|
||
Matrix3::from_axes(up_, side, dir_)
|
||
}
|
||
|
||
/**
|
||
* Returns the the matrix with an extra row and column added
|
||
* ~~~
|
||
* c0 c1 c2 c0 c1 c2 c3
|
||
* +----+----+----+ +----+----+----+----+
|
||
* r0 | a | b | c | r0 | a | b | c | 0 |
|
||
* +----+----+----+ +----+----+----+----+
|
||
* r1 | d | e | f | => r1 | d | e | f | 0 |
|
||
* +----+----+----+ +----+----+----+----+
|
||
* r2 | g | h | i | r2 | g | h | i | 0 |
|
||
* +----+----+----+ +----+----+----+----+
|
||
* r3 | 0 | 0 | 0 | 1 |
|
||
* +----+----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn to_mat4(&self) -> Mat4<T> {
|
||
Matrix4::new(self[0][0], self[0][1], self[0][2], zero(),
|
||
self[1][0], self[1][1], self[1][2], zero(),
|
||
self[2][0], self[2][1], self[2][2], zero(),
|
||
zero(), zero(), zero(), one())
|
||
}
|
||
|
||
/**
|
||
* Convert the matrix to a quaternion
|
||
*/
|
||
#[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();
|
||
|
||
let _1: T = num::cast(1.0);
|
||
let half: T = num::cast(0.5);
|
||
|
||
if trace >= zero() {
|
||
s = (_1 + trace).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (self[1][2] - self[2][1]) * s;
|
||
y = (self[2][0] - self[0][2]) * s;
|
||
z = (self[0][1] - self[1][0]) * s;
|
||
} else if (self[0][0] > self[1][1]) && (self[0][0] > self[2][2]) {
|
||
s = (half + (self[0][0] - self[1][1] - self[2][2])).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (self[0][1] - self[1][0]) * s;
|
||
y = (self[2][0] - self[0][2]) * s;
|
||
z = (self[1][2] - self[2][1]) * s;
|
||
} else if self[1][1] > self[2][2] {
|
||
s = (half + (self[1][1] - self[0][0] - self[2][2])).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (self[0][1] - self[1][0]) * s;
|
||
y = (self[1][2] - self[2][1]) * s;
|
||
z = (self[2][0] - self[0][2]) * s;
|
||
} else {
|
||
s = (half + (self[2][2] - self[0][0] - self[1][1])).sqrt();
|
||
w = half * s;
|
||
s = half / s;
|
||
x = (self[2][0] - self[0][2]) * s;
|
||
y = (self[1][2] - self[2][1]) * s;
|
||
z = (self[0][1] - self[1][0]) * s;
|
||
}
|
||
|
||
Quat::new(w, x, y, z)
|
||
}
|
||
}
|
||
|
||
impl<T:Copy> Index<uint, Vec3<T>> for Mat3<T> {
|
||
#[inline(always)]
|
||
fn index(&self, i: &uint) -> Vec3<T> {
|
||
unsafe { do vec::raw::buf_as_slice(cast::transmute(self), 3) |slice| { slice[*i] } }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Neg<Mat3<T>> for Mat3<T> {
|
||
#[inline(always)]
|
||
fn neg(&self) -> Mat3<T> {
|
||
Matrix3::from_cols(-self[0], -self[1], -self[2])
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> FuzzyEq<T> for Mat3<T> {
|
||
#[inline(always)]
|
||
fn fuzzy_eq(&self, other: &Mat3<T>) -> bool {
|
||
self.fuzzy_eq_eps(other, &num::cast(FUZZY_EPSILON))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn fuzzy_eq_eps(&self, other: &Mat3<T>, epsilon: &T) -> bool {
|
||
self[0].fuzzy_eq_eps(&other[0], epsilon) &&
|
||
self[1].fuzzy_eq_eps(&other[1], epsilon) &&
|
||
self[2].fuzzy_eq_eps(&other[2], epsilon)
|
||
}
|
||
}
|
||
|
||
macro_rules! mat3_type(
|
||
($name:ident <$T:ty, $V:ty>) => (
|
||
pub impl $name {
|
||
#[inline(always)] fn new(c0r0: $T, c0r1: $T, c0r2: $T, c1r0: $T, c1r1: $T, c1r2: $T, c2r0: $T, c2r1: $T, c2r2: $T)
|
||
-> $name { Matrix3::new(c0r0, c0r1, c0r2, c1r0, c1r1, c1r2, c2r0, c2r1, c2r2) }
|
||
#[inline(always)] fn from_cols(c0: $V, c1: $V, c2: $V)
|
||
-> $name { Matrix3::from_cols(c0, c1, c2) }
|
||
#[inline(always)] fn from_value(v: $T) -> $name { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] fn identity() -> $name { Matrix::identity() }
|
||
#[inline(always)] fn zero() -> $name { Matrix::zero() }
|
||
|
||
#[inline(always)] fn from_angle_x(radians: $T) -> $name { Matrix3::from_angle_x(radians) }
|
||
#[inline(always)] fn from_angle_y(radians: $T) -> $name { Matrix3::from_angle_y(radians) }
|
||
#[inline(always)] fn from_angle_z(radians: $T) -> $name { Matrix3::from_angle_z(radians) }
|
||
#[inline(always)] fn from_angle_xyz(radians_x: $T, radians_y: $T, radians_z: $T) -> $name { Matrix3::from_angle_xyz(radians_x, radians_y, radians_z) }
|
||
#[inline(always)] fn from_angle_axis(radians: $T, axis: &$V) -> $name { Matrix3::from_angle_axis(radians, axis) }
|
||
#[inline(always)] fn from_axes(x: $V, y: $V, z: $V) -> $name { Matrix3::from_axes(x, y, z) }
|
||
#[inline(always)] fn look_at(dir: &$V, up: &$V) -> $name { Matrix3::look_at(dir, up) }
|
||
|
||
#[inline(always)] fn dim() -> uint { 3 }
|
||
#[inline(always)] fn rows() -> uint { 3 }
|
||
#[inline(always)] fn cols() -> uint { 3 }
|
||
#[inline(always)] fn size_of() -> uint { sys::size_of::<$name>() }
|
||
}
|
||
)
|
||
)
|
||
|
||
// 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>;
|
||
|
||
mat3_type!(mat3<f32,vec3>)
|
||
mat3_type!(dmat3<f64,dvec3>)
|
||
|
||
// Rust-style type aliases
|
||
pub type Mat3f = Mat3<float>;
|
||
pub type Mat3f32 = Mat3<f32>;
|
||
pub type Mat3f64 = Mat3<f64>;
|
||
|
||
mat3_type!(Mat3f<float,Vec3f>)
|
||
mat3_type!(Mat3f32<f32,Vec3f32>)
|
||
mat3_type!(Mat3f64<f64,Vec3f64>)
|
||
|
||
/**
|
||
* A 4 x 4 column major matrix
|
||
*
|
||
* # Type parameters
|
||
*
|
||
* * `T` - The type of the elements of the matrix. Should be a floating point type.
|
||
*
|
||
* # Fields
|
||
*
|
||
* * `x` - the first column vector of the matrix
|
||
* * `y` - the second column vector of the matrix
|
||
* * `z` - the third column vector of the matrix
|
||
* * `w` - the fourth column vector of the matrix
|
||
*/
|
||
#[deriving(Eq)]
|
||
pub struct Mat4<T> { x: Vec4<T>, y: Vec4<T>, z: Vec4<T>, w: Vec4<T> }
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix<T, Vec4<T>> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn col(&self, i: uint) -> Vec4<T> { self[i] }
|
||
|
||
#[inline(always)]
|
||
fn row(&self, i: uint) -> Vec4<T> {
|
||
Vector4::new(self[0][i],
|
||
self[1][i],
|
||
self[2][i],
|
||
self[3][i])
|
||
}
|
||
|
||
/**
|
||
* Construct a 4 x 4 diagonal matrix with the major diagonal set to `value`
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `value` - the value to set the major diagonal to
|
||
*
|
||
* ~~~
|
||
* c0 c1 c2 c3
|
||
* +-----+-----+-----+-----+
|
||
* r0 | val | 0 | 0 | 0 |
|
||
* +-----+-----+-----+-----+
|
||
* r1 | 0 | val | 0 | 0 |
|
||
* +-----+-----+-----+-----+
|
||
* r2 | 0 | 0 | val | 0 |
|
||
* +-----+-----+-----+-----+
|
||
* r3 | 0 | 0 | 0 | val |
|
||
* +-----+-----+-----+-----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn from_value(value: T) -> Mat4<T> {
|
||
Matrix4::new(value, zero(), zero(), zero(),
|
||
zero(), value, zero(), zero(),
|
||
zero(), zero(), value, zero(),
|
||
zero(), zero(), zero(), value)
|
||
}
|
||
|
||
/**
|
||
* Returns the multiplicative identity matrix
|
||
* ~~~
|
||
* c0 c1 c2 c3
|
||
* +----+----+----+----+
|
||
* r0 | 1 | 0 | 0 | 0 |
|
||
* +----+----+----+----+
|
||
* r1 | 0 | 1 | 0 | 0 |
|
||
* +----+----+----+----+
|
||
* r2 | 0 | 0 | 1 | 0 |
|
||
* +----+----+----+----+
|
||
* r3 | 0 | 0 | 0 | 1 |
|
||
* +----+----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn identity() -> Mat4<T> {
|
||
Matrix4::new( one::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), one::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), one::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), zero::<T>(), one::<T>())
|
||
}
|
||
|
||
/**
|
||
* Returns the additive identity matrix
|
||
* ~~~
|
||
* c0 c1 c2 c3
|
||
* +----+----+----+----+
|
||
* r0 | 0 | 0 | 0 | 0 |
|
||
* +----+----+----+----+
|
||
* r1 | 0 | 0 | 0 | 0 |
|
||
* +----+----+----+----+
|
||
* r2 | 0 | 0 | 0 | 0 |
|
||
* +----+----+----+----+
|
||
* r3 | 0 | 0 | 0 | 0 |
|
||
* +----+----+----+----+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn zero() -> Mat4<T> {
|
||
Matrix4::new(zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
|
||
zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_t(&self, value: T) -> Mat4<T> {
|
||
Matrix4::from_cols(self[0].mul_t(value),
|
||
self[1].mul_t(value),
|
||
self[2].mul_t(value),
|
||
self[3].mul_t(value))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_v(&self, vec: &Vec4<T>) -> Vec4<T> {
|
||
Vector4::new(self.row(0).dot(vec),
|
||
self.row(1).dot(vec),
|
||
self.row(2).dot(vec),
|
||
self.row(3).dot(vec))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn add_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
||
Matrix4::from_cols(self[0].add_v(&other[0]),
|
||
self[1].add_v(&other[1]),
|
||
self[2].add_v(&other[2]),
|
||
self[3].add_v(&other[3]))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
||
Matrix4::from_cols(self[0].sub_v(&other[0]),
|
||
self[1].sub_v(&other[1]),
|
||
self[2].sub_v(&other[2]),
|
||
self[3].sub_v(&other[3]))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_m(&self, other: &Mat4<T>) -> Mat4<T> {
|
||
Matrix4::new(self.row(0).dot(&other.col(0)),
|
||
self.row(1).dot(&other.col(0)),
|
||
self.row(2).dot(&other.col(0)),
|
||
self.row(3).dot(&other.col(0)),
|
||
|
||
self.row(0).dot(&other.col(1)),
|
||
self.row(1).dot(&other.col(1)),
|
||
self.row(2).dot(&other.col(1)),
|
||
self.row(3).dot(&other.col(1)),
|
||
|
||
self.row(0).dot(&other.col(2)),
|
||
self.row(1).dot(&other.col(2)),
|
||
self.row(2).dot(&other.col(2)),
|
||
self.row(3).dot(&other.col(2)),
|
||
|
||
self.row(0).dot(&other.col(3)),
|
||
self.row(1).dot(&other.col(3)),
|
||
self.row(2).dot(&other.col(3)),
|
||
self.row(3).dot(&other.col(3)))
|
||
|
||
}
|
||
|
||
fn dot(&self, other: &Mat4<T>) -> T {
|
||
other.transpose().mul_m(self).trace()
|
||
}
|
||
|
||
fn determinant(&self) -> T {
|
||
let m0: Mat3<T> = Matrix3::new(self[1][1], self[2][1], self[3][1],
|
||
self[1][2], self[2][2], self[3][2],
|
||
self[1][3], self[2][3], self[3][3]);
|
||
let m1: Mat3<T> = Matrix3::new(self[0][1], self[2][1], self[3][1],
|
||
self[0][2], self[2][2], self[3][2],
|
||
self[0][3], self[2][3], self[3][3]);
|
||
let m2: Mat3<T> = Matrix3::new(self[0][1], self[1][1], self[3][1],
|
||
self[0][2], self[1][2], self[3][2],
|
||
self[0][3], self[1][3], self[3][3]);
|
||
let m3: Mat3<T> = Matrix3::new(self[0][1], self[1][1], self[2][1],
|
||
self[0][2], self[1][2], self[2][2],
|
||
self[0][3], self[1][3], self[2][3]);
|
||
|
||
self[0][0] * m0.determinant() -
|
||
self[1][0] * m1.determinant() +
|
||
self[2][0] * m2.determinant() -
|
||
self[3][0] * m3.determinant()
|
||
}
|
||
|
||
fn trace(&self) -> T {
|
||
self[0][0] + self[1][1] + self[2][2] + self[3][3]
|
||
}
|
||
|
||
fn inverse(&self) -> Option<Mat4<T>> {
|
||
let d = self.determinant();
|
||
if d.fuzzy_eq(&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<T> = Matrix::identity();
|
||
|
||
for uint::range(0, 4) |j| {
|
||
// Find largest element in col j
|
||
let mut i1 = j;
|
||
for uint::range(j + 1, 4) |i| {
|
||
if abs(A[j][i]) > abs(A[j][i1]) {
|
||
i1 = i;
|
||
}
|
||
}
|
||
|
||
unsafe {
|
||
// 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
|
||
I.col_mut(j).div_self_t(A[j][j]);
|
||
A.col_mut(j).div_self_t(A[j][j]);
|
||
|
||
// Eliminate off-diagonal elems in col j of A,
|
||
// doing identical ops to I
|
||
for uint::range(0, 4) |i| {
|
||
if i != j {
|
||
I.col_mut(i).sub_self_v(&I[j].mul_t(A[i][j]));
|
||
A.col_mut(i).sub_self_v(&A[j].mul_t(A[i][j]));
|
||
}
|
||
}
|
||
}
|
||
}
|
||
Some(I)
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn transpose(&self) -> Mat4<T> {
|
||
Matrix4::new(self[0][0], self[1][0], self[2][0], self[3][0],
|
||
self[0][1], self[1][1], self[2][1], self[3][1],
|
||
self[0][2], self[1][2], self[2][2], self[3][2],
|
||
self[0][3], self[1][3], self[2][3], self[3][3])
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn col_mut(&mut self, i: uint) -> &'self mut Vec4<T> {
|
||
match i {
|
||
0 => &mut self.x,
|
||
1 => &mut self.y,
|
||
2 => &mut self.z,
|
||
3 => &mut self.w,
|
||
_ => fail!(fmt!("index out of bounds: expected an index from 0 to 3, but found %u", i))
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn swap_cols(&mut self, a: uint, b: uint) {
|
||
*self.col_mut(a) <-> *self.col_mut(b);
|
||
}
|
||
|
||
#[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) {
|
||
(*self) = Matrix::identity();
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_zero(&mut self) {
|
||
(*self) = Matrix::zero();
|
||
}
|
||
|
||
#[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>) {
|
||
self.col_mut(0).add_self_v(&other[0]);
|
||
self.col_mut(1).add_self_v(&other[1]);
|
||
self.col_mut(2).add_self_v(&other[2]);
|
||
self.col_mut(3).add_self_v(&other[3]);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_self_m(&mut self, other: &Mat4<T>) {
|
||
self.col_mut(0).sub_self_v(&other[0]);
|
||
self.col_mut(1).sub_self_v(&other[1]);
|
||
self.col_mut(2).sub_self_v(&other[2]);
|
||
self.col_mut(3).sub_self_v(&other[3]);
|
||
}
|
||
|
||
#[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) {
|
||
*self.col_mut(0).index_mut(1) <-> *self.col_mut(1).index_mut(0);
|
||
*self.col_mut(0).index_mut(2) <-> *self.col_mut(2).index_mut(0);
|
||
*self.col_mut(0).index_mut(3) <-> *self.col_mut(3).index_mut(0);
|
||
|
||
*self.col_mut(1).index_mut(0) <-> *self.col_mut(0).index_mut(1);
|
||
*self.col_mut(1).index_mut(2) <-> *self.col_mut(2).index_mut(1);
|
||
*self.col_mut(1).index_mut(3) <-> *self.col_mut(3).index_mut(1);
|
||
|
||
*self.col_mut(2).index_mut(0) <-> *self.col_mut(0).index_mut(2);
|
||
*self.col_mut(2).index_mut(1) <-> *self.col_mut(1).index_mut(2);
|
||
*self.col_mut(2).index_mut(3) <-> *self.col_mut(3).index_mut(2);
|
||
|
||
*self.col_mut(3).index_mut(0) <-> *self.col_mut(0).index_mut(3);
|
||
*self.col_mut(3).index_mut(1) <-> *self.col_mut(1).index_mut(3);
|
||
*self.col_mut(3).index_mut(2) <-> *self.col_mut(2).index_mut(3);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_identity(&self) -> bool {
|
||
self.fuzzy_eq(&Matrix::identity())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_diagonal(&self) -> bool {
|
||
self[0][1].fuzzy_eq(&zero()) &&
|
||
self[0][2].fuzzy_eq(&zero()) &&
|
||
self[0][3].fuzzy_eq(&zero()) &&
|
||
|
||
self[1][0].fuzzy_eq(&zero()) &&
|
||
self[1][2].fuzzy_eq(&zero()) &&
|
||
self[1][3].fuzzy_eq(&zero()) &&
|
||
|
||
self[2][0].fuzzy_eq(&zero()) &&
|
||
self[2][1].fuzzy_eq(&zero()) &&
|
||
self[2][3].fuzzy_eq(&zero()) &&
|
||
|
||
self[3][0].fuzzy_eq(&zero()) &&
|
||
self[3][1].fuzzy_eq(&zero()) &&
|
||
self[3][2].fuzzy_eq(&zero())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_rotated(&self) -> bool {
|
||
!self.fuzzy_eq(&Matrix::identity())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_symmetric(&self) -> bool {
|
||
self[0][1].fuzzy_eq(&self[1][0]) &&
|
||
self[0][2].fuzzy_eq(&self[2][0]) &&
|
||
self[0][3].fuzzy_eq(&self[3][0]) &&
|
||
|
||
self[1][0].fuzzy_eq(&self[0][1]) &&
|
||
self[1][2].fuzzy_eq(&self[2][1]) &&
|
||
self[1][3].fuzzy_eq(&self[3][1]) &&
|
||
|
||
self[2][0].fuzzy_eq(&self[0][2]) &&
|
||
self[2][1].fuzzy_eq(&self[1][2]) &&
|
||
self[2][3].fuzzy_eq(&self[3][2]) &&
|
||
|
||
self[3][0].fuzzy_eq(&self[0][3]) &&
|
||
self[3][1].fuzzy_eq(&self[1][3]) &&
|
||
self[3][2].fuzzy_eq(&self[2][3])
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn is_invertible(&self) -> bool {
|
||
!self.determinant().fuzzy_eq(&zero())
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_ptr(&self) -> *T {
|
||
unsafe { cast::transmute(self) }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix4<T, Vec4<T>> for Mat4<T> {
|
||
/**
|
||
* Construct a 4 x 4 matrix
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `c0r0`, `c0r1`, `c0r2`, `c0r3` - the first column of the matrix
|
||
* * `c1r0`, `c1r1`, `c1r2`, `c1r3` - the second column of the matrix
|
||
* * `c2r0`, `c2r1`, `c2r2`, `c2r3` - the third column of the matrix
|
||
* * `c3r0`, `c3r1`, `c3r2`, `c3r3` - the fourth column of the matrix
|
||
*
|
||
* ~~~
|
||
* c0 c1 c2 c3
|
||
* +------+------+------+------+
|
||
* r0 | c0r0 | c1r0 | c2r0 | c3r0 |
|
||
* +------+------+------+------+
|
||
* r1 | c0r1 | c1r1 | c2r1 | c3r1 |
|
||
* +------+------+------+------+
|
||
* r2 | c0r2 | c1r2 | c2r2 | c3r2 |
|
||
* +------+------+------+------+
|
||
* r3 | c0r3 | c1r3 | c2r3 | c3r3 |
|
||
* +------+------+------+------+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn new(c0r0: T, c0r1: T, c0r2: T, c0r3: T,
|
||
c1r0: T, c1r1: T, c1r2: T, c1r3: T,
|
||
c2r0: T, c2r1: T, c2r2: T, c2r3: T,
|
||
c3r0: T, c3r1: T, c3r2: T, c3r3: T) -> Mat4<T> {
|
||
Matrix4::from_cols(Vector4::new::<T,Vec4<T>>(c0r0, c0r1, c0r2, c0r3),
|
||
Vector4::new::<T,Vec4<T>>(c1r0, c1r1, c1r2, c1r3),
|
||
Vector4::new::<T,Vec4<T>>(c2r0, c2r1, c2r2, c2r3),
|
||
Vector4::new::<T,Vec4<T>>(c3r0, c3r1, c3r2, c3r3))
|
||
}
|
||
|
||
/**
|
||
* Construct a 4 x 4 matrix from column vectors
|
||
*
|
||
* # Arguments
|
||
*
|
||
* * `c0` - the first column vector of the matrix
|
||
* * `c1` - the second column vector of the matrix
|
||
* * `c2` - the third column vector of the matrix
|
||
* * `c3` - the fourth column vector of the matrix
|
||
*
|
||
* ~~~
|
||
* c0 c1 c2 c3
|
||
* +------+------+------+------+
|
||
* r0 | c0.x | c1.x | c2.x | c3.x |
|
||
* +------+------+------+------+
|
||
* r1 | c0.y | c1.y | c2.y | c3.y |
|
||
* +------+------+------+------+
|
||
* r2 | c0.z | c1.z | c2.z | c3.z |
|
||
* +------+------+------+------+
|
||
* r3 | c0.w | c1.w | c2.w | c3.w |
|
||
* +------+------+------+------+
|
||
* ~~~
|
||
*/
|
||
#[inline(always)]
|
||
fn from_cols(c0: Vec4<T>,
|
||
c1: Vec4<T>,
|
||
c2: Vec4<T>,
|
||
c3: Vec4<T>) -> Mat4<T> {
|
||
Mat4 { x: c0, y: c1, z: c2, w: c3 }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Neg<Mat4<T>> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn neg(&self) -> Mat4<T> {
|
||
Matrix4::from_cols(-self[0], -self[1], -self[2], -self[3])
|
||
}
|
||
}
|
||
|
||
impl<T:Copy> Index<uint, Vec4<T>> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn index(&self, i: &uint) -> Vec4<T> {
|
||
unsafe { do vec::raw::buf_as_slice(cast::transmute(self), 4) |slice| { slice[*i] } }
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + NumCast + Zero + One + FuzzyEq<T>> FuzzyEq<T> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn fuzzy_eq(&self, other: &Mat4<T>) -> bool {
|
||
self.fuzzy_eq_eps(other, &num::cast(FUZZY_EPSILON))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn fuzzy_eq_eps(&self, other: &Mat4<T>, epsilon: &T) -> bool {
|
||
self[0].fuzzy_eq_eps(&other[0], epsilon) &&
|
||
self[1].fuzzy_eq_eps(&other[1], epsilon) &&
|
||
self[2].fuzzy_eq_eps(&other[2], epsilon) &&
|
||
self[3].fuzzy_eq_eps(&other[3], epsilon)
|
||
}
|
||
}
|
||
|
||
macro_rules! mat4_type(
|
||
($name:ident <$T:ty, $V:ty>) => (
|
||
pub impl $name {
|
||
#[inline(always)] fn new(c0r0: $T, c0r1: $T, c0r2: $T, c0r3: $T, c1r0: $T, c1r1: $T, c1r2: $T, c1r3: $T, c2r0: $T, c2r1: $T, c2r2: $T, c2r3: $T, c3r0: $T, c3r1: $T, c3r2: $T, c3r3: $T)
|
||
-> $name { Matrix4::new(c0r0, c0r1, c0r2, c0r3, c1r0, c1r1, c1r2, c1r3, c2r0, c2r1, c2r2, c2r3, c3r0, c3r1, c3r2, c3r3) }
|
||
#[inline(always)] fn from_cols(c0: $V, c1: $V, c2: $V, c3: $V)
|
||
-> $name { Matrix4::from_cols(c0, c1, c2, c3) }
|
||
#[inline(always)] fn from_value(v: $T) -> $name { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] fn identity() -> $name { Matrix::identity() }
|
||
#[inline(always)] fn zero() -> $name { Matrix::zero() }
|
||
|
||
#[inline(always)] fn dim() -> uint { 4 }
|
||
#[inline(always)] fn rows() -> uint { 4 }
|
||
#[inline(always)] fn cols() -> uint { 4 }
|
||
#[inline(always)] fn size_of() -> uint { sys::size_of::<$name>() }
|
||
}
|
||
)
|
||
)
|
||
|
||
// 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>;
|
||
|
||
mat4_type!(mat4<f32,vec4>)
|
||
mat4_type!(dmat4<f64,dvec4>)
|
||
|
||
// Rust-style type aliases
|
||
pub type Mat4f = Mat4<float>;
|
||
pub type Mat4f32 = Mat4<f32>;
|
||
pub type Mat4f64 = Mat4<f64>;
|
||
|
||
mat4_type!(Mat4f<float,Vec4f>)
|
||
mat4_type!(Mat4f32<f32,Vec4f32>)
|
||
mat4_type!(Mat4f64<f64,Vec4f64>) |