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cgmath/src/matrix.rs

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// Copyright 2013-2014 The CGMath 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.
//! Column major, square matrix types and traits.
use std::fmt;
use std::mem;
use std::num::{Zero, zero, One, one, cast};
use angle::{Rad, sin, cos, sin_cos};
use approx::ApproxEq;
use array::{Array1, Array2, FixedArray};
use num::{BaseFloat, BaseNum};
use point::{Point, Point3};
use quaternion::{Quaternion, ToQuaternion};
use vector::{Vector, EuclideanVector};
use vector::{Vector2, Vector3, Vector4};
/// A 2 x 2, column major matrix
#[deriving(Clone, PartialEq, Encodable, Decodable)]
pub struct Matrix2<S> { pub x: Vector2<S>, pub y: Vector2<S> }
/// A 3 x 3, column major matrix
#[deriving(Clone, PartialEq, Encodable, Decodable)]
pub struct Matrix3<S> { pub x: Vector3<S>, pub y: Vector3<S>, pub z: Vector3<S> }
/// A 4 x 4, column major matrix
#[deriving(Clone, PartialEq, Encodable, Decodable)]
pub struct Matrix4<S> { pub x: Vector4<S>, pub y: Vector4<S>, pub z: Vector4<S>, pub w: Vector4<S> }
impl<S: BaseNum> Matrix2<S> {
/// Create a new matrix, providing values for each index.
#[inline]
pub fn new(c0r0: S, c0r1: S,
c1r0: S, c1r1: S) -> Matrix2<S> {
Matrix2::from_cols(Vector2::new(c0r0, c0r1),
Vector2::new(c1r0, c1r1))
}
/// Create a new matrix, providing columns.
#[inline]
pub fn from_cols(c0: Vector2<S>, c1: Vector2<S>) -> Matrix2<S> {
Matrix2 { x: c0, y: c1 }
}
/// Create a new diagonal matrix, providing a single value to use for each
/// non-zero index.
#[inline]
pub fn from_value(value: S) -> Matrix2<S> {
Matrix2::new(value.clone(), zero(),
zero(), value.clone())
}
/// Create a zero matrix (all zeros).
#[inline]
pub fn zero() -> Matrix2<S> {
Matrix2::from_value(zero())
}
/// Create an identity matrix (diagonal matrix of ones).
#[inline]
pub fn identity() -> Matrix2<S> {
Matrix2::from_value(one())
}
}
impl<S: BaseFloat + 'static> Matrix2<S> {
/// Create a transformation matrix that will cause a vector to point at
/// `dir`, using `up` for orientation.
pub fn look_at(dir: &Vector2<S>, up: &Vector2<S>) -> Matrix2<S> {
//TODO: verify look_at 2D
Matrix2::from_cols(up.clone(), dir.clone()).transpose()
}
#[inline]
pub fn from_angle(theta: Rad<S>) -> Matrix2<S> {
let cos_theta = cos(theta.clone());
let sin_theta = sin(theta.clone());
Matrix2::new(cos_theta.clone(), sin_theta.clone(),
-sin_theta.clone(), cos_theta.clone())
}
}
impl<S: BaseNum> Matrix3<S> {
/// Create a new matrix, providing values for each index.
#[inline]
pub fn new(c0r0:S, c0r1:S, c0r2:S,
c1r0:S, c1r1:S, c1r2:S,
c2r0:S, c2r1:S, c2r2:S) -> Matrix3<S> {
Matrix3::from_cols(Vector3::new(c0r0, c0r1, c0r2),
Vector3::new(c1r0, c1r1, c1r2),
Vector3::new(c2r0, c2r1, c2r2))
}
/// Create a new matrix, providing columns.
#[inline]
pub fn from_cols(c0: Vector3<S>, c1: Vector3<S>, c2: Vector3<S>) -> Matrix3<S> {
Matrix3 { x: c0, y: c1, z: c2 }
}
/// Create a new diagonal matrix, providing a single value to use for each
/// non-zero index.
#[inline]
pub fn from_value(value: S) -> Matrix3<S> {
Matrix3::new(value.clone(), zero(), zero(),
zero(), value.clone(), zero(),
zero(), zero(), value.clone())
}
/// Create a zero matrix (all zeros).
#[inline]
pub fn zero() -> Matrix3<S> {
Matrix3::from_value(zero())
}
/// Create an identity matrix (diagonal matrix of ones).
#[inline]
pub fn identity() -> Matrix3<S> {
Matrix3::from_value(one())
}
}
impl<S: BaseFloat + 'static>
Matrix3<S> {
/// Create a transformation matrix that will cause a vector to point at
/// `dir`, using `up` for orientation.
pub fn look_at(dir: &Vector3<S>, up: &Vector3<S>) -> Matrix3<S> {
let dir = dir.normalize();
let side = up.cross(&dir).normalize();
let up = dir.cross(&side).normalize();
Matrix3::from_cols(side, up, dir).transpose()
}
/// Create a matrix from a rotation around the `x` axis (pitch).
pub fn from_angle_x(theta: Rad<S>) -> Matrix3<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
let (s, c) = sin_cos(theta);
Matrix3::new( one(), zero(), zero(),
zero(), c.clone(), s.clone(),
zero(), -s.clone(), c.clone())
}
/// Create a matrix from a rotation around the `y` axis (yaw).
pub fn from_angle_y(theta: Rad<S>) -> Matrix3<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
let (s, c) = sin_cos(theta);
Matrix3::new(c.clone(), zero(), -s.clone(),
zero(), one(), zero(),
s.clone(), zero(), c.clone())
}
/// Create a matrix from a rotation around the `z` axis (roll).
pub fn from_angle_z(theta: Rad<S>) -> Matrix3<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
let (s, c) = sin_cos(theta);
Matrix3::new( c.clone(), s.clone(), zero(),
-s.clone(), c.clone(), zero(),
zero(), zero(), one())
}
/// Create a matrix from a set of euler angles.
///
/// # Parameters
///
/// - `x`: the angular rotation around the `x` axis (pitch).
/// - `y`: the angular rotation around the `y` axis (yaw).
/// - `z`: the angular rotation around the `z` axis (roll).
pub fn from_euler(x: Rad<S>, y: Rad<S>, z: Rad<S>) -> Matrix3<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
let (sx, cx) = sin_cos(x);
let (sy, cy) = sin_cos(y);
let (sz, cz) = sin_cos(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)
}
/// Create a matrix from a rotation around an arbitrary axis
pub fn from_axis_angle(axis: &Vector3<S>, angle: Rad<S>) -> Matrix3<S> {
let (s, c) = sin_cos(angle);
let _1subc = one::<S>() - c;
Matrix3::new(_1subc * axis.x * axis.x + c,
_1subc * axis.x * axis.y + s * axis.z,
_1subc * axis.x * axis.z - s * axis.y,
_1subc * axis.x * axis.y - s * axis.z,
_1subc * axis.y * axis.y + c,
_1subc * axis.y * axis.z + s * axis.x,
_1subc * axis.x * axis.z + s * axis.y,
_1subc * axis.y * axis.z - s * axis.x,
_1subc * axis.z * axis.z + c)
}
/// Create a matrix from a non-uniform scale
pub fn from_diagonal(value: &Vector3<S>) -> Matrix3<S> {
Matrix3::new(value.x, zero(), zero(),
zero(), value.y, zero(),
zero(), zero(), value.z)
}
}
impl<S: BaseNum> Matrix4<S> {
/// Create a new matrix, providing values for each index.
#[inline]
pub fn new(c0r0: S, c0r1: S, c0r2: S, c0r3: S,
c1r0: S, c1r1: S, c1r2: S, c1r3: S,
c2r0: S, c2r1: S, c2r2: S, c2r3: S,
c3r0: S, c3r1: S, c3r2: S, c3r3: S) -> Matrix4<S> {
Matrix4::from_cols(Vector4::new(c0r0, c0r1, c0r2, c0r3),
Vector4::new(c1r0, c1r1, c1r2, c1r3),
Vector4::new(c2r0, c2r1, c2r2, c2r3),
Vector4::new(c3r0, c3r1, c3r2, c3r3))
}
/// Create a new matrix, providing columns.
#[inline]
pub fn from_cols(c0: Vector4<S>, c1: Vector4<S>, c2: Vector4<S>, c3: Vector4<S>) -> Matrix4<S> {
Matrix4 { x: c0, y: c1, z: c2, w: c3 }
}
/// Create a new diagonal matrix, providing a single value to use for each
/// non-zero index.
#[inline]
pub fn from_value(value: S) -> Matrix4<S> {
Matrix4::new(value.clone(), zero(), zero(), zero(),
zero(), value.clone(), zero(), zero(),
zero(), zero(), value.clone(), zero(),
zero(), zero(), zero(), value.clone())
}
/// Create a zero matrix (all zeros).
#[inline]
pub fn zero() -> Matrix4<S> {
Matrix4::from_value(zero())
}
/// Create an identity matrix (diagonal matrix of ones).
#[inline]
pub fn identity() -> Matrix4<S> {
Matrix4::from_value(one())
}
/// Create a translation matrix from a Vector3
#[inline]
pub fn from_translation(v: &Vector3<S>) -> Matrix4<S> {
Matrix4::new(one(), zero(), zero(), zero(),
zero(), one(), zero(), zero(),
zero(), zero(), one(), zero(),
v.x, v.y, v.z, one())
}
}
impl<S: BaseFloat>
Matrix4<S> {
/// Create a transformation matrix that will cause a vector to point at
/// `dir`, using `up` for orientation.
pub fn look_at(eye: &Point3<S>, center: &Point3<S>, up: &Vector3<S>) -> Matrix4<S> {
let f = center.sub_p(eye).normalize();
let s = f.cross(up).normalize();
let u = s.cross(&f);
Matrix4::new( s.x.clone(), u.x.clone(), -f.x.clone(), zero(),
s.y.clone(), u.y.clone(), -f.y.clone(), zero(),
s.z.clone(), u.z.clone(), -f.z.clone(), zero(),
-eye.dot(&s), -eye.dot(&u), eye.dot(&f), one())
}
}
pub trait Matrix<S: BaseFloat, V: Clone + Vector<S>>: Array2<V, V, S>
+ Neg<Self>
+ Zero + One
+ ApproxEq<S> {
/// Multiply this matrix by a scalar, returning the new matrix.
fn mul_s(&self, s: S) -> Self;
/// Divide this matrix by a scalar, returning the new matrix.
fn div_s(&self, s: S) -> Self;
/// Take the remainder of this matrix by a scalar, returning the new
/// matrix.
fn rem_s(&self, s: S) -> Self;
/// Add this matrix with another matrix, returning the new metrix.
fn add_m(&self, m: &Self) -> Self;
/// Subtract another matrix from this matrix, returning the new matrix.
fn sub_m(&self, m: &Self) -> Self;
/// Multiplay a vector by this matrix, returning a new vector.
fn mul_v(&self, v: &V) -> V;
/// Multiply this matrix by another matrix, returning the new matrix.
fn mul_m(&self, m: &Self) -> Self;
/// Negate this matrix in-place (multiply by scalar -1).
fn neg_self(&mut self);
/// Multiply this matrix by a scalar, in-place.
fn mul_self_s(&mut self, s: S);
/// Divide this matrix by a scalar, in-place.
fn div_self_s(&mut self, s: S);
/// Take the remainder of this matrix, in-place.
fn rem_self_s(&mut self, s: S);
/// Add this matrix with another matrix, in-place.
fn add_self_m(&mut self, m: &Self);
/// Subtract another matrix from this matrix, in-place.
fn sub_self_m(&mut self, m: &Self);
/// Multiply this matrix by another matrix, in-place.
#[inline]
fn mul_self_m(&mut self, m: &Self) { *self = self.mul_m(m); }
/// Transpose this matrix, returning a new matrix.
fn transpose(&self) -> Self;
/// Transpose this matrix in-place.
fn transpose_self(&mut self);
/// Take the determinant of this matrix.
fn determinant(&self) -> S;
/// Return a vector containing the diagonal of this matrix.
fn diagonal(&self) -> V;
/// Return the trace of this matrix. That is, the sum of the diagonal.
#[inline]
fn trace(&self) -> S { self.diagonal().comp_add() }
/// Invert this matrix, returning a new matrix. `m.mul_m(m.invert())` is
/// the identity matrix. Returns `None` if this matrix is not invertible
/// (has a determinant of zero).
fn invert(&self) -> Option<Self>;
/// Invert this matrix in-place.
#[inline]
fn invert_self(&mut self) {
*self = self.invert().expect("Attempted to invert a matrix with zero determinant.");
}
/// Test if this matrix is invertible.
#[inline]
fn is_invertible(&self) -> bool { !self.determinant().approx_eq(&zero()) }
/// Test if this matrix is the identity matrix. That is, it is diagonal
/// and every element in the diagonal is one.
#[inline]
fn is_identity(&self) -> bool { self.approx_eq(&one()) }
/// Test if this is a diagonal matrix. That is, every element outside of
/// the diagonal is 0.
fn is_diagonal(&self) -> bool;
/// Test if this matrix is symmetric. That is, it is equal to its
/// transpose.
fn is_symmetric(&self) -> bool;
}
impl<S: BaseFloat + 'static> Add<Matrix2<S>, Matrix2<S>> for Matrix2<S> { #[inline] fn add(&self, other: &Matrix2<S>) -> Matrix2<S> { self.add_m(other) } }
impl<S: BaseFloat + 'static> Add<Matrix3<S>, Matrix3<S>> for Matrix3<S> { #[inline] fn add(&self, other: &Matrix3<S>) -> Matrix3<S> { self.add_m(other) } }
impl<S: BaseFloat + 'static> Add<Matrix4<S>, Matrix4<S>> for Matrix4<S> { #[inline] fn add(&self, other: &Matrix4<S>) -> Matrix4<S> { self.add_m(other) } }
impl<S: BaseFloat + 'static> Sub<Matrix2<S>, Matrix2<S>> for Matrix2<S> { #[inline] fn sub(&self, other: &Matrix2<S>) -> Matrix2<S> { self.sub_m(other) } }
impl<S: BaseFloat + 'static> Sub<Matrix3<S>, Matrix3<S>> for Matrix3<S> { #[inline] fn sub(&self, other: &Matrix3<S>) -> Matrix3<S> { self.sub_m(other) } }
impl<S: BaseFloat + 'static> Sub<Matrix4<S>, Matrix4<S>> for Matrix4<S> { #[inline] fn sub(&self, other: &Matrix4<S>) -> Matrix4<S> { self.sub_m(other) } }
impl<S: BaseFloat> Neg<Matrix2<S>> for Matrix2<S> { #[inline] fn neg(&self) -> Matrix2<S> { Matrix2::from_cols(self[0].neg(), self[1].neg()) } }
impl<S: BaseFloat> Neg<Matrix3<S>> for Matrix3<S> { #[inline] fn neg(&self) -> Matrix3<S> { Matrix3::from_cols(self[0].neg(), self[1].neg(), self[2].neg()) } }
impl<S: BaseFloat> Neg<Matrix4<S>> for Matrix4<S> { #[inline] fn neg(&self) -> Matrix4<S> { Matrix4::from_cols(self[0].neg(), self[1].neg(), self[2].neg(), self[3].neg()) } }
impl<S: BaseFloat> Zero for Matrix2<S> { #[inline] fn zero() -> Matrix2<S> { Matrix2::zero() } #[inline] fn is_zero(&self) -> bool { *self == zero() } }
impl<S: BaseFloat> Zero for Matrix3<S> { #[inline] fn zero() -> Matrix3<S> { Matrix3::zero() } #[inline] fn is_zero(&self) -> bool { *self == zero() } }
impl<S: BaseFloat> Zero for Matrix4<S> { #[inline] fn zero() -> Matrix4<S> { Matrix4::zero() } #[inline] fn is_zero(&self) -> bool { *self == zero() } }
impl<S: BaseFloat + 'static> Mul<Matrix2<S>, Matrix2<S>> for Matrix2<S> { #[inline] fn mul(&self, other: &Matrix2<S>) -> Matrix2<S> { self.mul_m(other) } }
impl<S: BaseFloat + 'static> Mul<Matrix3<S>, Matrix3<S>> for Matrix3<S> { #[inline] fn mul(&self, other: &Matrix3<S>) -> Matrix3<S> { self.mul_m(other) } }
impl<S: BaseFloat + 'static> Mul<Matrix4<S>, Matrix4<S>> for Matrix4<S> { #[inline] fn mul(&self, other: &Matrix4<S>) -> Matrix4<S> { self.mul_m(other) } }
impl<S: BaseFloat> One for Matrix2<S> { #[inline] fn one() -> Matrix2<S> { Matrix2::identity() } }
impl<S: BaseFloat> One for Matrix3<S> { #[inline] fn one() -> Matrix3<S> { Matrix3::identity() } }
impl<S: BaseFloat> One for Matrix4<S> { #[inline] fn one() -> Matrix4<S> { Matrix4::identity() } }
impl<S> FixedArray<[[S, ..2], ..2]> for Matrix2<S> {
#[inline]
fn into_fixed(self) -> [[S, ..2], ..2] {
match self {
Matrix2 { x, y } => [
x.into_fixed(),
y.into_fixed(),
],
}
}
#[inline]
fn as_fixed<'a>(&'a self) -> &'a [[S, ..2], ..2] {
unsafe { mem::transmute(self) }
}
#[inline]
fn as_mut_fixed<'a>(&'a mut self) -> &'a mut [[S, ..2], ..2] {
unsafe { mem::transmute(self) }
}
#[inline]
fn from_fixed(_v: [[S, ..2], ..2]) -> Matrix2<S> {
// match v {
// [x, y] => Matrix2 {
// x: FixedArray::from_fixed(x),
// y: FixedArray::from_fixed(y),
// },
// }
fail!("Unimplemented, pending a fix for rust-lang/rust#16418")
}
#[inline]
fn from_fixed_ref<'a>(v: &'a [[S, ..2], ..2]) -> &'a Matrix2<S> {
unsafe { mem::transmute(v) }
}
#[inline]
fn from_fixed_mut<'a>(v: &'a mut [[S, ..2], ..2]) -> &'a mut Matrix2<S> {
unsafe { mem::transmute(v) }
}
}
impl<S> Index<uint, Vector2<S>> for Matrix2<S> {
#[inline]
fn index<'a>(&'a self, i: &uint) -> &'a Vector2<S> {
FixedArray::from_fixed_ref(&self.as_fixed()[*i])
}
}
impl<S> IndexMut<uint, Vector2<S>> for Matrix2<S> {
#[inline]
fn index_mut<'a>(&'a mut self, i: &uint) -> &'a mut Vector2<S> {
FixedArray::from_fixed_mut(&mut self.as_mut_fixed()[*i])
}
}
impl<S: Copy + 'static> Array2<Vector2<S>, Vector2<S>, S> for Matrix2<S> {
#[inline]
fn row(&self, r: uint) -> Vector2<S> {
Vector2::new(self[0][r],
self[1][r])
}
#[inline]
fn swap_rows(&mut self, a: uint, b: uint) {
(&mut self[0]).swap_elems(a, b);
(&mut self[1]).swap_elems(a, b);
}
#[inline]
fn map(&mut self, op: |&Vector2<S>| -> Vector2<S>) -> Matrix2<S> {
self.x = op(&self.x);
self.y = op(&self.y);
*self
}
}
impl<S> FixedArray<[[S, ..3], ..3]> for Matrix3<S> {
#[inline]
fn into_fixed(self) -> [[S, ..3], ..3] {
match self {
Matrix3 { x, y, z } => [
x.into_fixed(),
y.into_fixed(),
z.into_fixed(),
],
}
}
#[inline]
fn as_fixed<'a>(&'a self) -> &'a [[S, ..3], ..3] {
unsafe { mem::transmute(self) }
}
#[inline]
fn as_mut_fixed<'a>(&'a mut self) -> &'a mut [[S, ..3], ..3] {
unsafe { mem::transmute(self) }
}
#[inline]
fn from_fixed(_v: [[S, ..3], ..3]) -> Matrix3<S> {
// match v {
// [x, y, z] => Matrix3 {
// x: FixedArray::from_fixed(x),
// y: FixedArray::from_fixed(y),
// z: FixedArray::from_fixed(z),
// },
// }
fail!("Unimplemented, pending a fix for rust-lang/rust#16418")
}
#[inline]
fn from_fixed_ref<'a>(v: &'a [[S, ..3], ..3]) -> &'a Matrix3<S> {
unsafe { mem::transmute(v) }
}
#[inline]
fn from_fixed_mut<'a>(v: &'a mut [[S, ..3], ..3]) -> &'a mut Matrix3<S> {
unsafe { mem::transmute(v) }
}
}
impl<S> Index<uint, Vector3<S>> for Matrix3<S> {
#[inline]
fn index<'a>(&'a self, i: &uint) -> &'a Vector3<S> {
FixedArray::from_fixed_ref(&self.as_fixed()[*i])
}
}
impl<S> IndexMut<uint, Vector3<S>> for Matrix3<S> {
#[inline]
fn index_mut<'a>(&'a mut self, i: &uint) -> &'a mut Vector3<S> {
FixedArray::from_fixed_mut(&mut self.as_mut_fixed()[*i])
}
}
impl<S: Copy + 'static> Array2<Vector3<S>, Vector3<S>, S> for Matrix3<S> {
#[inline]
fn row(&self, r: uint) -> Vector3<S> {
Vector3::new(self[0][r],
self[1][r],
self[2][r])
}
#[inline]
fn swap_rows(&mut self, a: uint, b: uint) {
(&mut self[0]).swap_elems(a, b);
(&mut self[1]).swap_elems(a, b);
(&mut self[2]).swap_elems(a, b);
}
#[inline]
fn map(&mut self, op: |&Vector3<S>| -> Vector3<S>) -> Matrix3<S> {
self.x = op(&self.x);
self.y = op(&self.y);
self.z = op(&self.z);
*self
}
}
impl<S> FixedArray<[[S, ..4], ..4]> for Matrix4<S> {
#[inline]
fn into_fixed(self) -> [[S, ..4], ..4] {
match self {
Matrix4 { x, y, z, w } => [
x.into_fixed(),
y.into_fixed(),
z.into_fixed(),
w.into_fixed(),
],
}
}
#[inline]
fn as_fixed<'a>(&'a self) -> &'a [[S, ..4], ..4] {
unsafe { mem::transmute(self) }
}
#[inline]
fn as_mut_fixed<'a>(&'a mut self) -> &'a mut [[S, ..4], ..4] {
unsafe { mem::transmute(self) }
}
#[inline]
fn from_fixed(_v: [[S, ..4], ..4]) -> Matrix4<S> {
// match v {
// [x, y, z, w] => Matrix4 {
// x: FixedArray::from_fixed(x),
// y: FixedArray::from_fixed(y),
// z: FixedArray::from_fixed(z),
// w: FixedArray::from_fixed(w),
// },
// }
fail!("Unimplemented, pending a fix for rust-lang/rust#16418")
}
#[inline]
fn from_fixed_ref<'a>(v: &'a [[S, ..4], ..4]) -> &'a Matrix4<S> {
unsafe { mem::transmute(v) }
}
#[inline]
fn from_fixed_mut<'a>(v: &'a mut [[S, ..4], ..4]) -> &'a mut Matrix4<S> {
unsafe { mem::transmute(v) }
}
}
impl<S> Index<uint, Vector4<S>> for Matrix4<S> {
#[inline]
fn index<'a>(&'a self, i: &uint) -> &'a Vector4<S> {
FixedArray::from_fixed_ref(&self.as_fixed()[*i])
}
}
impl<S> IndexMut<uint, Vector4<S>> for Matrix4<S> {
#[inline]
fn index_mut<'a>(&'a mut self, i: &uint) -> &'a mut Vector4<S> {
FixedArray::from_fixed_mut(&mut self.as_mut_fixed()[*i])
}
}
impl<S: Copy + 'static> Array2<Vector4<S>, Vector4<S>, S> for Matrix4<S> {
#[inline]
fn row(&self, r: uint) -> Vector4<S> {
Vector4::new(self[0][r],
self[1][r],
self[2][r],
self[3][r])
}
#[inline]
fn swap_rows(&mut self, a: uint, b: uint) {
(&mut self[0]).swap_elems(a, b);
(&mut self[1]).swap_elems(a, b);
(&mut self[2]).swap_elems(a, b);
(&mut self[3]).swap_elems(a, b);
}
#[inline]
fn map(&mut self, op: |&Vector4<S>| -> Vector4<S>) -> Matrix4<S> {
self.x = op(&self.x);
self.y = op(&self.y);
self.z = op(&self.z);
self.w = op(&self.w);
*self
}
}
impl<S: BaseFloat + 'static> Matrix<S, Vector2<S>> for Matrix2<S> {
#[inline]
fn mul_s(&self, s: S) -> Matrix2<S> {
Matrix2::from_cols(self[0].mul_s(s),
self[1].mul_s(s))
}
#[inline]
fn div_s(&self, s: S) -> Matrix2<S> {
Matrix2::from_cols(self[0].div_s(s),
self[1].div_s(s))
}
#[inline]
fn rem_s(&self, s: S) -> Matrix2<S> {
Matrix2::from_cols(self[0].rem_s(s),
self[1].rem_s(s))
}
#[inline]
fn add_m(&self, m: &Matrix2<S>) -> Matrix2<S> {
Matrix2::from_cols(self[0].add_v(&m[0]),
self[1].add_v(&m[1]))
}
#[inline]
fn sub_m(&self, m: &Matrix2<S>) -> Matrix2<S> {
Matrix2::from_cols(self[0].sub_v(&m[0]),
self[1].sub_v(&m[1]))
}
#[inline]
fn mul_v(&self, v: &Vector2<S>) -> Vector2<S> {
Vector2::new(self.row(0).dot(v),
self.row(1).dot(v))
}
fn mul_m(&self, other: &Matrix2<S>) -> Matrix2<S> {
Matrix2::new(self.row(0).dot(&other[0]), self.row(1).dot(&other[0]),
self.row(0).dot(&other[1]), self.row(1).dot(&other[1]))
}
#[inline]
fn neg_self(&mut self) {
(&mut self[0]).neg_self();
(&mut self[1]).neg_self();
}
#[inline]
fn mul_self_s(&mut self, s: S) {
(&mut self[0]).mul_self_s(s);
(&mut self[1]).mul_self_s(s);
}
#[inline]
fn div_self_s(&mut self, s: S) {
(&mut self[0]).div_self_s(s);
(&mut self[1]).div_self_s(s);
}
#[inline]
fn rem_self_s(&mut self, s: S) {
(&mut self[0]).rem_self_s(s);
(&mut self[1]).rem_self_s(s);
}
#[inline]
fn add_self_m(&mut self, m: &Matrix2<S>) {
(&mut self[0]).add_self_v(&m[0]);
(&mut self[1]).add_self_v(&m[1]);
}
#[inline]
fn sub_self_m(&mut self, m: &Matrix2<S>) {
(&mut self[0]).sub_self_v(&m[0]);
(&mut self[1]).sub_self_v(&m[1]);
}
fn transpose(&self) -> Matrix2<S> {
Matrix2::new(self[0][0], self[1][0],
self[0][1], self[1][1])
}
#[inline]
fn transpose_self(&mut self) {
self.swap_elems((0, 1), (1, 0));
}
#[inline]
fn determinant(&self) -> S {
self[0][0] * self[1][1] - self[1][0] * self[0][1]
}
#[inline]
fn diagonal(&self) -> Vector2<S> {
Vector2::new(self[0][0],
self[1][1])
}
#[inline]
fn invert(&self) -> Option<Matrix2<S>> {
let det = self.determinant();
if det.approx_eq(&zero()) {
None
} else {
Some(Matrix2::new( self[1][1] / det, -self[0][1] / det,
-self[1][0] / det, self[0][0] / det))
}
}
#[inline]
fn is_diagonal(&self) -> bool {
(&self[0][1]).approx_eq(&zero()) &&
(&self[1][0]).approx_eq(&zero())
}
#[inline]
fn is_symmetric(&self) -> bool {
(&self[0][1]).approx_eq(&self[1][0]) &&
(&self[1][0]).approx_eq(&self[0][1])
}
}
impl<S: BaseFloat + 'static> Matrix<S, Vector3<S>> for Matrix3<S> {
#[inline]
fn mul_s(&self, s: S) -> Matrix3<S> {
Matrix3::from_cols(self[0].mul_s(s),
self[1].mul_s(s),
self[2].mul_s(s))
}
#[inline]
fn div_s(&self, s: S) -> Matrix3<S> {
Matrix3::from_cols(self[0].div_s(s),
self[1].div_s(s),
self[2].div_s(s))
}
#[inline]
fn rem_s(&self, s: S) -> Matrix3<S> {
Matrix3::from_cols(self[0].rem_s(s),
self[1].rem_s(s),
self[2].rem_s(s))
}
#[inline]
fn add_m(&self, m: &Matrix3<S>) -> Matrix3<S> {
Matrix3::from_cols(self[0].add_v(&m[0]),
self[1].add_v(&m[1]),
self[2].add_v(&m[2]))
}
#[inline]
fn sub_m(&self, m: &Matrix3<S>) -> Matrix3<S> {
Matrix3::from_cols(self[0].sub_v(&m[0]),
self[1].sub_v(&m[1]),
self[2].sub_v(&m[2]))
}
#[inline]
fn mul_v(&self, v: &Vector3<S>) -> Vector3<S> {
Vector3::new(self.row(0).dot(v),
self.row(1).dot(v),
self.row(2).dot(v))
}
fn mul_m(&self, other: &Matrix3<S>) -> Matrix3<S> {
Matrix3::new(self.row(0).dot(&other[0]),self.row(1).dot(&other[0]),self.row(2).dot(&other[0]),
self.row(0).dot(&other[1]),self.row(1).dot(&other[1]),self.row(2).dot(&other[1]),
self.row(0).dot(&other[2]),self.row(1).dot(&other[2]),self.row(2).dot(&other[2]))
}
#[inline]
fn neg_self(&mut self) {
(&mut self[0]).neg_self();
(&mut self[1]).neg_self();
(&mut self[2]).neg_self();
}
#[inline]
fn mul_self_s(&mut self, s: S) {
(&mut self[0]).mul_self_s(s);
(&mut self[1]).mul_self_s(s);
(&mut self[2]).mul_self_s(s);
}
#[inline]
fn div_self_s(&mut self, s: S) {
(&mut self[0]).div_self_s(s);
(&mut self[1]).div_self_s(s);
(&mut self[2]).div_self_s(s);
}
#[inline]
fn rem_self_s(&mut self, s: S) {
(&mut self[0]).rem_self_s(s);
(&mut self[1]).rem_self_s(s);
(&mut self[2]).rem_self_s(s);
}
#[inline]
fn add_self_m(&mut self, m: &Matrix3<S>) {
(&mut self[0]).add_self_v(&m[0]);
(&mut self[1]).add_self_v(&m[1]);
(&mut self[2]).add_self_v(&m[2]);
}
#[inline]
fn sub_self_m(&mut self, m: &Matrix3<S>) {
(&mut self[0]).sub_self_v(&m[0]);
(&mut self[1]).sub_self_v(&m[1]);
(&mut self[2]).sub_self_v(&m[2]);
}
fn transpose(&self) -> Matrix3<S> {
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]
fn transpose_self(&mut self) {
self.swap_elems((0, 1), (1, 0));
self.swap_elems((0, 2), (2, 0));
self.swap_elems((1, 2), (2, 1));
}
fn determinant(&self) -> S {
self[0][0] * (self[1][1] * self[2][2] - self[2][1] * self[1][2]) -
self[1][0] * (self[0][1] * self[2][2] - self[2][1] * self[0][2]) +
self[2][0] * (self[0][1] * self[1][2] - self[1][1] * self[0][2])
}
#[inline]
fn diagonal(&self) -> Vector3<S> {
Vector3::new(self[0][0],
self[1][1],
self[2][2])
}
fn invert(&self) -> Option<Matrix3<S>> {
let det = self.determinant();
if det.approx_eq(&zero()) { None } else {
Some(Matrix3::from_cols(self[1].cross(&self[2]).div_s(det),
self[2].cross(&self[0]).div_s(det),
self[0].cross(&self[1]).div_s(det)).transpose())
}
}
fn is_diagonal(&self) -> bool {
(&self[0][1]).approx_eq(&zero()) &&
(&self[0][2]).approx_eq(&zero()) &&
(&self[1][0]).approx_eq(&zero()) &&
(&self[1][2]).approx_eq(&zero()) &&
(&self[2][0]).approx_eq(&zero()) &&
(&self[2][1]).approx_eq(&zero())
}
fn is_symmetric(&self) -> bool {
(&self[0][1]).approx_eq(&self[1][0]) &&
(&self[0][2]).approx_eq(&self[2][0]) &&
(&self[1][0]).approx_eq(&self[0][1]) &&
(&self[1][2]).approx_eq(&self[2][1]) &&
(&self[2][0]).approx_eq(&self[0][2]) &&
(&self[2][1]).approx_eq(&self[1][2])
}
}
// Using self.row(0).dot(other[0]) like the other matrix multiplies
// causes the LLVM to miss identical loads and multiplies. This optimization
// causes the code to be auto vectorized properly increasing the performance
// around ~4 times.
macro_rules! dot_matrix4(
($A:expr, $B:expr, $I:expr, $J:expr) => (
($A[0][$I]) * ($B[$J][0]) +
($A[1][$I]) * ($B[$J][1]) +
($A[2][$I]) * ($B[$J][2]) +
($A[3][$I]) * ($B[$J][3])
))
impl<S: BaseFloat + 'static> Matrix<S, Vector4<S>> for Matrix4<S> {
#[inline]
fn mul_s(&self, s: S) -> Matrix4<S> {
Matrix4::from_cols(self[0].mul_s(s),
self[1].mul_s(s),
self[2].mul_s(s),
self[3].mul_s(s))
}
#[inline]
fn div_s(&self, s: S) -> Matrix4<S> {
Matrix4::from_cols(self[0].div_s(s),
self[1].div_s(s),
self[2].div_s(s),
self[3].div_s(s))
}
#[inline]
fn rem_s(&self, s: S) -> Matrix4<S> {
Matrix4::from_cols(self[0].rem_s(s),
self[1].rem_s(s),
self[2].rem_s(s),
self[3].rem_s(s))
}
#[inline]
fn add_m(&self, m: &Matrix4<S>) -> Matrix4<S> {
Matrix4::from_cols(self[0].add_v(&m[0]),
self[1].add_v(&m[1]),
self[2].add_v(&m[2]),
self[3].add_v(&m[3]))
}
#[inline]
fn sub_m(&self, m: &Matrix4<S>) -> Matrix4<S> {
Matrix4::from_cols(self[0].sub_v(&m[0]),
self[1].sub_v(&m[1]),
self[2].sub_v(&m[2]),
self[3].sub_v(&m[3]))
}
#[inline]
fn mul_v(&self, v: &Vector4<S>) -> Vector4<S> {
Vector4::new(self.row(0).dot(v),
self.row(1).dot(v),
self.row(2).dot(v),
self.row(3).dot(v))
}
fn mul_m(&self, other: &Matrix4<S>) -> Matrix4<S> {
Matrix4::new(dot_matrix4!(self, other, 0, 0), dot_matrix4!(self, other, 1, 0), dot_matrix4!(self, other, 2, 0), dot_matrix4!(self, other, 3, 0),
dot_matrix4!(self, other, 0, 1), dot_matrix4!(self, other, 1, 1), dot_matrix4!(self, other, 2, 1), dot_matrix4!(self, other, 3, 1),
dot_matrix4!(self, other, 0, 2), dot_matrix4!(self, other, 1, 2), dot_matrix4!(self, other, 2, 2), dot_matrix4!(self, other, 3, 2),
dot_matrix4!(self, other, 0, 3), dot_matrix4!(self, other, 1, 3), dot_matrix4!(self, other, 2, 3), dot_matrix4!(self, other, 3, 3))
}
#[inline]
fn neg_self(&mut self) {
(&mut self[0]).neg_self();
(&mut self[1]).neg_self();
(&mut self[2]).neg_self();
(&mut self[3]).neg_self();
}
#[inline]
fn mul_self_s(&mut self, s: S) {
(&mut self[0]).mul_self_s(s);
(&mut self[1]).mul_self_s(s);
(&mut self[2]).mul_self_s(s);
(&mut self[3]).mul_self_s(s);
}
#[inline]
fn div_self_s(&mut self, s: S) {
(&mut self[0]).div_self_s(s);
(&mut self[1]).div_self_s(s);
(&mut self[2]).div_self_s(s);
(&mut self[3]).div_self_s(s);
}
#[inline]
fn rem_self_s(&mut self, s: S) {
(&mut self[0]).rem_self_s(s);
(&mut self[1]).rem_self_s(s);
(&mut self[2]).rem_self_s(s);
(&mut self[3]).rem_self_s(s);
}
#[inline]
fn add_self_m(&mut self, m: &Matrix4<S>) {
(&mut self[0]).add_self_v(&m[0]);
(&mut self[1]).add_self_v(&m[1]);
(&mut self[2]).add_self_v(&m[2]);
(&mut self[3]).add_self_v(&m[3]);
}
#[inline]
fn sub_self_m(&mut self, m: &Matrix4<S>) {
(&mut self[0]).sub_self_v(&m[0]);
(&mut self[1]).sub_self_v(&m[1]);
(&mut self[2]).sub_self_v(&m[2]);
(&mut self[3]).sub_self_v(&m[3]);
}
fn transpose(&self) -> Matrix4<S> {
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])
}
fn transpose_self(&mut self) {
self.swap_elems((0, 1), (1, 0));
self.swap_elems((0, 2), (2, 0));
self.swap_elems((0, 3), (3, 0));
self.swap_elems((1, 2), (2, 1));
self.swap_elems((1, 3), (3, 1));
self.swap_elems((2, 3), (3, 2));
}
fn determinant(&self) -> S {
let m0 = 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 = 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 = 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 = 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()
}
#[inline]
fn diagonal(&self) -> Vector4<S> {
Vector4::new(self[0][0],
self[1][1],
self[2][2],
self[3][3])
}
fn invert(&self) -> Option<Matrix4<S>> {
let det = self.determinant();
if !det.approx_eq(&zero()) {
let one: S = one();
let inv_det = one / det;
let t = self.transpose();
let cf = |i, j| {
let mat = match i {
0 => Matrix3::from_cols(t.y.truncate_n(j),
t.z.truncate_n(j),
t.w.truncate_n(j)),
1 => Matrix3::from_cols(t.x.truncate_n(j),
t.z.truncate_n(j),
t.w.truncate_n(j)),
2 => Matrix3::from_cols(t.x.truncate_n(j),
t.y.truncate_n(j),
t.w.truncate_n(j)),
3 => Matrix3::from_cols(t.x.truncate_n(j),
t.y.truncate_n(j),
t.z.truncate_n(j)),
_ => fail!("out of range")
};
let sign = if (i+j) & 1 == 1 {-one} else {one};
mat.determinant() * sign * inv_det
};
Some(Matrix4::new(cf(0, 0), cf(0, 1), cf(0, 2), cf(0, 3),
cf(1, 0), cf(1, 1), cf(1, 2), cf(1, 3),
cf(2, 0), cf(2, 1), cf(2, 2), cf(2, 3),
cf(3, 0), cf(3, 1), cf(3, 2), cf(3, 3)))
} else {
None
}
}
fn is_diagonal(&self) -> bool {
(&self[0][1]).approx_eq(&zero()) &&
(&self[0][2]).approx_eq(&zero()) &&
(&self[0][3]).approx_eq(&zero()) &&
(&self[1][0]).approx_eq(&zero()) &&
(&self[1][2]).approx_eq(&zero()) &&
(&self[1][3]).approx_eq(&zero()) &&
(&self[2][0]).approx_eq(&zero()) &&
(&self[2][1]).approx_eq(&zero()) &&
(&self[2][3]).approx_eq(&zero()) &&
(&self[3][0]).approx_eq(&zero()) &&
(&self[3][1]).approx_eq(&zero()) &&
(&self[3][2]).approx_eq(&zero())
}
fn is_symmetric(&self) -> bool {
(&self[0][1]).approx_eq(&self[1][0]) &&
(&self[0][2]).approx_eq(&self[2][0]) &&
(&self[0][3]).approx_eq(&self[3][0]) &&
(&self[1][0]).approx_eq(&self[0][1]) &&
(&self[1][2]).approx_eq(&self[2][1]) &&
(&self[1][3]).approx_eq(&self[3][1]) &&
(&self[2][0]).approx_eq(&self[0][2]) &&
(&self[2][1]).approx_eq(&self[1][2]) &&
(&self[2][3]).approx_eq(&self[3][2]) &&
(&self[3][0]).approx_eq(&self[0][3]) &&
(&self[3][1]).approx_eq(&self[1][3]) &&
(&self[3][2]).approx_eq(&self[2][3])
}
}
impl<S: BaseFloat> ApproxEq<S> for Matrix2<S> {
#[inline]
fn approx_eq_eps(&self, other: &Matrix2<S>, epsilon: &S) -> bool {
self[0].approx_eq_eps(&other[0], epsilon) &&
self[1].approx_eq_eps(&other[1], epsilon)
}
}
impl<S: BaseFloat> ApproxEq<S> for Matrix3<S> {
#[inline]
fn approx_eq_eps(&self, other: &Matrix3<S>, epsilon: &S) -> bool {
self[0].approx_eq_eps(&other[0], epsilon) &&
self[1].approx_eq_eps(&other[1], epsilon) &&
self[2].approx_eq_eps(&other[2], epsilon)
}
}
impl<S: BaseFloat> ApproxEq<S> for Matrix4<S> {
#[inline]
fn approx_eq_eps(&self, other: &Matrix4<S>, epsilon: &S) -> bool {
self[0].approx_eq_eps(&other[0], epsilon) &&
self[1].approx_eq_eps(&other[1], epsilon) &&
self[2].approx_eq_eps(&other[2], epsilon) &&
self[3].approx_eq_eps(&other[3], epsilon)
}
}
// Conversion traits
/// Represents types which can be converted to a Matrix2
pub trait ToMatrix2<S: BaseNum> {
/// Convert this value to a Matrix2
fn to_matrix2(&self) -> Matrix2<S>;
}
/// Represents types which can be converted to a Matrix3
pub trait ToMatrix3<S: BaseNum> {
/// Convert this value to a Matrix3
fn to_matrix3(&self) -> Matrix3<S>;
}
/// Represents types which can be converted to a Matrix4
pub trait ToMatrix4<S: BaseNum> {
/// Convert this value to a Matrix4
fn to_matrix4(&self) -> Matrix4<S>;
}
impl<S: BaseFloat> ToMatrix3<S> for Matrix2<S> {
/// Clone the elements of a 2-dimensional matrix into the top-left corner
/// of a 3-dimensional identity matrix.
fn to_matrix3(&self) -> Matrix3<S> {
Matrix3::new(self[0][0], self[0][1], zero(),
self[1][0], self[1][1], zero(),
zero(), zero(), one())
}
}
impl<S: BaseFloat> ToMatrix4<S> for Matrix2<S> {
/// Clone the elements of a 2-dimensional matrix into the top-left corner
/// of a 4-dimensional identity matrix.
fn to_matrix4(&self) -> Matrix4<S> {
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<S: BaseFloat> ToMatrix4<S> for Matrix3<S> {
/// Clone the elements of a 3-dimensional matrix into the top-left corner
/// of a 4-dimensional identity matrix.
fn to_matrix4(&self) -> Matrix4<S> {
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())
}
}
impl<S: BaseFloat + 'static> ToQuaternion<S> for Matrix3<S> {
/// Convert the matrix to a quaternion
fn to_quaternion(&self) -> Quaternion<S> {
// http://www.cs.ucr.edu/~vbz/resources/quatut.pdf
let trace = self.trace();
let half: S = cast(0.5f64).unwrap();
match () {
() if trace >= zero::<S>() => {
let s = (one::<S>() + trace).sqrt();
let w = half * s;
let s = half / s;
let x = (self[1][2] - self[2][1]) * s;
let y = (self[2][0] - self[0][2]) * s;
let z = (self[0][1] - self[1][0]) * s;
Quaternion::new(w, x, y, z)
}
() if (self[0][0] > self[1][1]) && (self[0][0] > self[2][2]) => {
let s = (half + (self[0][0] - self[1][1] - self[2][2])).sqrt();
let w = half * s;
let s = half / s;
let x = (self[0][1] - self[1][0]) * s;
let y = (self[2][0] - self[0][2]) * s;
let z = (self[1][2] - self[2][1]) * s;
Quaternion::new(w, x, y, z)
}
() if self[1][1] > self[2][2] => {
let s = (half + (self[1][1] - self[0][0] - self[2][2])).sqrt();
let w = half * s;
let s = half / s;
let x = (self[0][1] - self[1][0]) * s;
let y = (self[1][2] - self[2][1]) * s;
let z = (self[2][0] - self[0][2]) * s;
Quaternion::new(w, x, y, z)
}
() => {
let s = (half + (self[2][2] - self[0][0] - self[1][1])).sqrt();
let w = half * s;
let s = half / s;
let x = (self[2][0] - self[0][2]) * s;
let y = (self[1][2] - self[2][1]) * s;
let z = (self[0][1] - self[1][0]) * s;
Quaternion::new(w, x, y, z)
}
}
}
}
impl<S: BaseNum> fmt::Show for Matrix2<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "[[{}, {}], [{}, {}]]",
self[0][0], self[0][1],
self[1][0], self[1][1])
}
}
impl<S: BaseNum> fmt::Show for Matrix3<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "[[{}, {}, {}], [{}, {}, {}], [{}, {}, {}]]",
self[0][0], self[0][1], self[0][2],
self[1][0], self[1][1], self[1][2],
self[2][0], self[2][1], self[2][2])
}
}
impl<S: BaseNum> fmt::Show for Matrix4<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "[[{}, {}, {}, {}], [{}, {}, {}, {}], [{}, {}, {}, {}], [{}, {}, {}, {}]]",
self[0][0], self[0][1], self[0][2], self[0][3],
self[1][0], self[1][1], self[1][2], self[1][3],
self[2][0], self[2][1], self[2][2], self[2][3],
self[3][0], self[3][1], self[3][2], self[3][3])
}
}
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