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cgmath/src/matrix.rs
Brendan Zabarauskas 7147180936 Merge pull request #359 from jminer/rotation-fixes 
Rotation fixes
2016-05-18 00:19:43 +10:00

1246 lines
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// Copyright 2013-2014 The CGMath Developers. For a full listing of the authors,
// refer to the Cargo.toml 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.
use rand::{Rand, Rng};
use num_traits::cast;
use std::fmt;
use std::mem;
use std::ops::*;
use std::ptr;
use structure::*;
use angle::Rad;
use approx::ApproxEq;
use euler::Euler;
use num::BaseFloat;
use point::{Point2, Point3};
use quaternion::Quaternion;
use transform::{Transform, Transform2, Transform3};
use vector::{Vector2, Vector3, Vector4};
/// A 2 x 2, column major matrix
///
/// This type is marked as `#[repr(C, packed)]`.
#[repr(C, packed)]
#[derive(Copy, Clone, PartialEq)]
#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))]
#[cfg_attr(feature = "eders", derive(Serialize, Deserialize))]
pub struct Matrix2<S> {
/// The first column of the matrix.
pub x: Vector2<S>,
/// The second column of the matrix.
pub y: Vector2<S>,
}
/// A 3 x 3, column major matrix
///
/// This type is marked as `#[repr(C, packed)]`.
#[repr(C, packed)]
#[derive(Copy, Clone, PartialEq)]
#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))]
#[cfg_attr(feature = "eders", derive(Serialize, Deserialize))]
pub struct Matrix3<S> {
/// The first column of the matrix.
pub x: Vector3<S>,
/// The second column of the matrix.
pub y: Vector3<S>,
/// The third column of the matrix.
pub z: Vector3<S>,
}
/// A 4 x 4, column major matrix
///
/// This type is marked as `#[repr(C, packed)]`.
#[repr(C, packed)]
#[derive(Copy, Clone, PartialEq)]
#[cfg_attr(feature = "rustc-serialize", derive(RustcEncodable, RustcDecodable))]
#[cfg_attr(feature = "eders", derive(Serialize, Deserialize))]
pub struct Matrix4<S> {
/// The first column of the matrix.
pub x: Vector4<S>,
/// The second column of the matrix.
pub y: Vector4<S>,
/// The third column of the matrix.
pub z: Vector4<S>,
/// The fourth column of the matrix.
pub w: Vector4<S>,
}
impl<S: BaseFloat> 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 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, dir).transpose()
}
#[inline]
pub fn from_angle(theta: Rad<S>) -> Matrix2<S> {
let cos_theta = Rad::cos(theta);
let sin_theta = Rad::sin(theta);
Matrix2::new(cos_theta, sin_theta,
-sin_theta, cos_theta)
}
}
impl<S: BaseFloat> 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 rotation 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 rotation 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) = Rad::sin_cos(theta);
Matrix3::new(S::one(), S::zero(), S::zero(),
S::zero(), c, s,
S::zero(), -s, c)
}
/// Create a rotation 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) = Rad::sin_cos(theta);
Matrix3::new(c, S::zero(), -s,
S::zero(), S::one(), S::zero(),
s, S::zero(), c)
}
/// Create a rotation 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) = Rad::sin_cos(theta);
Matrix3::new( c, s, S::zero(),
-s, c, S::zero(),
S::zero(), S::zero(), S::one())
}
/// Create a rotation matrix from an angle around an arbitrary axis.
///
/// The specified axis **must be normalized**, or it represents an invalid rotation.
pub fn from_axis_angle(axis: Vector3<S>, angle: Rad<S>) -> Matrix3<S> {
let (s, c) = Rad::sin_cos(angle);
let _1subc = S::one() - 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)
}
}
impl<S: BaseFloat> 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 homogeneous transformation matrix from a translation vector.
#[inline]
pub fn from_translation(v: Vector3<S>) -> Matrix4<S> {
Matrix4::new(S::one(), S::zero(), S::zero(), S::zero(),
S::zero(), S::one(), S::zero(), S::zero(),
S::zero(), S::zero(), S::one(), S::zero(),
v.x, v.y, v.z, S::one())
}
/// Create a homogeneous transformation matrix from a scale value.
#[inline]
pub fn from_scale(value: S) -> Matrix4<S> {
Matrix4::from_nonuniform_scale(value, value, value)
}
/// Create a homogeneous transformation matrix from a set of scale values.
#[inline]
pub fn from_nonuniform_scale(x: S, y: S, z: S) -> Matrix4<S> {
Matrix4::new(x, S::zero(), S::zero(), S::zero(),
S::zero(), y, S::zero(), S::zero(),
S::zero(), S::zero(), z, S::zero(),
S::zero(), S::zero(), S::zero(), S::one())
}
/// Create a homogeneous 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 - eye).normalize();
let s = f.cross(up).normalize();
let u = s.cross(f);
Matrix4::new(s.x.clone(), u.x.clone(), -f.x.clone(), S::zero(),
s.y.clone(), u.y.clone(), -f.y.clone(), S::zero(),
s.z.clone(), u.z.clone(), -f.z.clone(), S::zero(),
-eye.dot(s), -eye.dot(u), eye.dot(f), S::one())
}
/// Create a homogeneous transformation matrix from a rotation around the `x` axis (pitch).
pub fn from_angle_x(theta: Rad<S>) -> Matrix4<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
let (s, c) = Rad::sin_cos(theta);
Matrix4::new(S::one(), S::zero(), S::zero(), S::zero(),
S::zero(), c, s, S::zero(),
S::zero(), -s, c, S::zero(),
S::zero(), S::zero(), S::zero(), S::one())
}
/// Create a homogeneous transformation matrix from a rotation around the `y` axis (yaw).
pub fn from_angle_y(theta: Rad<S>) -> Matrix4<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
let (s, c) = Rad::sin_cos(theta);
Matrix4::new(c, S::zero(), -s, S::zero(),
S::zero(), S::one(), S::zero(), S::zero(),
s, S::zero(), c, S::zero(),
S::zero(), S::zero(), S::zero(), S::one())
}
/// Create a homogeneous transformation matrix from a rotation around the `z` axis (roll).
pub fn from_angle_z(theta: Rad<S>) -> Matrix4<S> {
// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
let (s, c) = Rad::sin_cos(theta);
Matrix4::new( c, s, S::zero(), S::zero(),
-s, c, S::zero(), S::zero(),
S::zero(), S::zero(), S::one(), S::zero(),
S::zero(), S::zero(), S::zero(), S::one())
}
/// Create a homogeneous transformation matrix from an angle around an arbitrary axis.
///
/// The specified axis **must be normalized**, or it represents an invalid rotation.
pub fn from_axis_angle(axis: Vector3<S>, angle: Rad<S>) -> Matrix4<S> {
let (s, c) = Rad::sin_cos(angle);
let _1subc = S::one() - c;
Matrix4::new(_1subc * axis.x * axis.x + c,
_1subc * axis.x * axis.y + s * axis.z,
_1subc * axis.x * axis.z - s * axis.y,
S::zero(),
_1subc * axis.x * axis.y - s * axis.z,
_1subc * axis.y * axis.y + c,
_1subc * axis.y * axis.z + s * axis.x,
S::zero(),
_1subc * axis.x * axis.z + s * axis.y,
_1subc * axis.y * axis.z - s * axis.x,
_1subc * axis.z * axis.z + c,
S::zero(),
S::zero(),
S::zero(),
S::zero(),
S::one())
}
}
impl<S: BaseFloat> Zero for Matrix2<S> {
#[inline]
fn zero() -> Matrix2<S> {
Matrix2::new(S::zero(), S::zero(),
S::zero(), S::zero())
}
#[inline]
fn is_zero(&self) -> bool {
Matrix2::approx_eq(self, &Matrix2::zero())
}
}
impl<S: BaseFloat> Zero for Matrix3<S> {
#[inline]
fn zero() -> Matrix3<S> {
Matrix3::new(S::zero(), S::zero(), S::zero(),
S::zero(), S::zero(), S::zero(),
S::zero(), S::zero(), S::zero())
}
#[inline]
fn is_zero(&self) -> bool {
Matrix3::approx_eq(self, &Matrix3::zero())
}
}
impl<S: BaseFloat> Zero for Matrix4<S> {
#[inline]
fn zero() -> Matrix4<S> {
Matrix4::new(S::zero(), S::zero(), S::zero(), S::zero(),
S::zero(), S::zero(), S::zero(), S::zero(),
S::zero(), S::zero(), S::zero(), S::zero(),
S::zero(), S::zero(), S::zero(), S::zero())
}
#[inline]
fn is_zero(&self) -> bool {
Matrix4::approx_eq(self, &Matrix4::zero())
}
}
impl<S: BaseFloat> One for Matrix2<S> {
#[inline]
fn one() -> Matrix2<S> {
Matrix2::from_value(S::one())
}
}
impl<S: BaseFloat> One for Matrix3<S> {
#[inline]
fn one() -> Matrix3<S> {
Matrix3::from_value(S::one())
}
}
impl<S: BaseFloat> One for Matrix4<S> {
#[inline]
fn one() -> Matrix4<S> {
Matrix4::from_value(S::one())
}
}
impl<S: BaseFloat> VectorSpace for Matrix2<S> {
type Scalar = S;
}
impl<S: BaseFloat> VectorSpace for Matrix3<S> {
type Scalar = S;
}
impl<S: BaseFloat> VectorSpace for Matrix4<S> {
type Scalar = S;
}
impl<S: BaseFloat> Matrix for Matrix2<S> {
type Column = Vector2<S>;
type Row = Vector2<S>;
type Transpose = Matrix2<S>;
#[inline]
fn row(&self, r: usize) -> Vector2<S> {
Vector2::new(self[0][r],
self[1][r])
}
#[inline]
fn swap_rows(&mut self, a: usize, b: usize) {
self[0].swap_elements(a, b);
self[1].swap_elements(a, b);
}
#[inline]
fn swap_columns(&mut self, a: usize, b: usize) {
unsafe { ptr::swap(&mut self[a], &mut self[b]) };
}
#[inline]
fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)) {
let (ac, ar) = a;
let (bc, br) = b;
unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
}
fn transpose(&self) -> Matrix2<S> {
Matrix2::new(self[0][0], self[1][0],
self[0][1], self[1][1])
}
}
impl<S: BaseFloat> SquareMatrix for Matrix2<S> {
type ColumnRow = Vector2<S>;
#[inline]
fn from_value(value: S) -> Matrix2<S> {
Matrix2::new(value, S::zero(),
S::zero(), value)
}
#[inline]
fn from_diagonal(value: Vector2<S>) -> Matrix2<S> {
Matrix2::new(value.x, S::zero(),
S::zero(), value.y)
}
#[inline]
fn transpose_self(&mut self) {
self.swap_elements((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(&S::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(&S::zero()) &&
self[1][0].approx_eq(&S::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> Matrix for Matrix3<S> {
type Column = Vector3<S>;
type Row = Vector3<S>;
type Transpose = Matrix3<S>;
#[inline]
fn row(&self, r: usize) -> Vector3<S> {
Vector3::new(self[0][r],
self[1][r],
self[2][r])
}
#[inline]
fn swap_rows(&mut self, a: usize, b: usize) {
self[0].swap_elements(a, b);
self[1].swap_elements(a, b);
self[2].swap_elements(a, b);
}
#[inline]
fn swap_columns(&mut self, a: usize, b: usize) {
unsafe { ptr::swap(&mut self[a], &mut self[b]) };
}
#[inline]
fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)) {
let (ac, ar) = a;
let (bc, br) = b;
unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
}
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])
}
}
impl<S: BaseFloat> SquareMatrix for Matrix3<S> {
type ColumnRow = Vector3<S>;
#[inline]
fn from_value(value: S) -> Matrix3<S> {
Matrix3::new(value, S::zero(), S::zero(),
S::zero(), value, S::zero(),
S::zero(), S::zero(), value)
}
#[inline]
fn from_diagonal(value: Vector3<S>) -> Matrix3<S> {
Matrix3::new(value.x, S::zero(), S::zero(),
S::zero(), value.y, S::zero(),
S::zero(), S::zero(), value.z)
}
#[inline]
fn transpose_self(&mut self) {
self.swap_elements((0, 1), (1, 0));
self.swap_elements((0, 2), (2, 0));
self.swap_elements((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(&S::zero()) { None } else {
Some(Matrix3::from_cols(self[1].cross(self[2]) / det,
self[2].cross(self[0]) / det,
self[0].cross(self[1]) / det).transpose())
}
}
fn is_diagonal(&self) -> bool {
self[0][1].approx_eq(&S::zero()) &&
self[0][2].approx_eq(&S::zero()) &&
self[1][0].approx_eq(&S::zero()) &&
self[1][2].approx_eq(&S::zero()) &&
self[2][0].approx_eq(&S::zero()) &&
self[2][1].approx_eq(&S::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])
}
}
impl<S: BaseFloat> Matrix for Matrix4<S> {
type Column = Vector4<S>;
type Row = Vector4<S>;
type Transpose = Matrix4<S>;
#[inline]
fn row(&self, r: usize) -> Vector4<S> {
Vector4::new(self[0][r],
self[1][r],
self[2][r],
self[3][r])
}
#[inline]
fn swap_rows(&mut self, a: usize, b: usize) {
self[0].swap_elements(a, b);
self[1].swap_elements(a, b);
self[2].swap_elements(a, b);
self[3].swap_elements(a, b);
}
#[inline]
fn swap_columns(&mut self, a: usize, b: usize) {
unsafe { ptr::swap(&mut self[a], &mut self[b]) };
}
#[inline]
fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize)) {
let (ac, ar) = a;
let (bc, br) = b;
unsafe { ptr::swap(&mut self[ac][ar], &mut self[bc][br]) };
}
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])
}
}
impl<S: BaseFloat> SquareMatrix for Matrix4<S> {
type ColumnRow = Vector4<S>;
#[inline]
fn from_value(value: S) -> Matrix4<S> {
Matrix4::new(value, S::zero(), S::zero(), S::zero(),
S::zero(), value, S::zero(), S::zero(),
S::zero(), S::zero(), value, S::zero(),
S::zero(), S::zero(), S::zero(), value)
}
#[inline]
fn from_diagonal(value: Vector4<S>) -> Matrix4<S> {
Matrix4::new(value.x, S::zero(), S::zero(), S::zero(),
S::zero(), value.y, S::zero(), S::zero(),
S::zero(), S::zero(), value.z, S::zero(),
S::zero(), S::zero(), S::zero(), value.w)
}
fn transpose_self(&mut self) {
self.swap_elements((0, 1), (1, 0));
self.swap_elements((0, 2), (2, 0));
self.swap_elements((0, 3), (3, 0));
self.swap_elements((1, 2), (2, 1));
self.swap_elements((1, 3), (3, 1));
self.swap_elements((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(&S::zero()) { None } else {
let inv_det = S::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)),
_ => panic!("out of range"),
};
let sign = if (i + j) & 1 == 1 { -S::one() } else { S::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)))
}
}
fn is_diagonal(&self) -> bool {
self[0][1].approx_eq(&S::zero()) &&
self[0][2].approx_eq(&S::zero()) &&
self[0][3].approx_eq(&S::zero()) &&
self[1][0].approx_eq(&S::zero()) &&
self[1][2].approx_eq(&S::zero()) &&
self[1][3].approx_eq(&S::zero()) &&
self[2][0].approx_eq(&S::zero()) &&
self[2][1].approx_eq(&S::zero()) &&
self[2][3].approx_eq(&S::zero()) &&
self[3][0].approx_eq(&S::zero()) &&
self[3][1].approx_eq(&S::zero()) &&
self[3][2].approx_eq(&S::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 for Matrix2<S> {
type Epsilon = 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 for Matrix3<S> {
type Epsilon = 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 for Matrix4<S> {
type Epsilon = 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)
}
}
impl<S: BaseFloat> Transform<Point2<S>> for Matrix3<S> {
fn one() -> Matrix3<S> {
One::one()
}
fn look_at(eye: Point2<S>, center: Point2<S>, up: Vector2<S>) -> Matrix3<S> {
let dir = center - eye;
Matrix3::from(Matrix2::look_at(dir, up))
}
fn transform_vector(&self, vec: Vector2<S>) -> Vector2<S> {
(self * vec.extend(S::zero())).truncate()
}
fn transform_point(&self, point: Point2<S>) -> Point2<S> {
Point2::from_vec((self * Point3::new(point.x, point.y, S::one()).to_vec()).truncate())
}
fn concat(&self, other: &Matrix3<S>) -> Matrix3<S> {
self * other
}
fn inverse_transform(&self) -> Option<Matrix3<S>> {
SquareMatrix::invert(self)
}
}
impl<S: BaseFloat> Transform<Point3<S>> for Matrix3<S> {
fn one() -> Matrix3<S> {
One::one()
}
fn look_at(eye: Point3<S>, center: Point3<S>, up: Vector3<S>) -> Matrix3<S> {
let dir = center - eye;
Matrix3::look_at(dir, up)
}
fn transform_vector(&self, vec: Vector3<S>) -> Vector3<S> {
self * vec
}
fn transform_point(&self, point: Point3<S>) -> Point3<S> {
Point3::from_vec(self * point.to_vec())
}
fn concat(&self, other: &Matrix3<S>) -> Matrix3<S> {
self * other
}
fn inverse_transform(&self) -> Option<Matrix3<S>> {
SquareMatrix::invert(self)
}
}
impl<S: BaseFloat> Transform<Point3<S>> for Matrix4<S> {
fn one() -> Matrix4<S> {
One::one()
}
fn look_at(eye: Point3<S>, center: Point3<S>, up: Vector3<S>) -> Matrix4<S> {
Matrix4::look_at(eye, center, up)
}
fn transform_vector(&self, vec: Vector3<S>) -> Vector3<S> {
(self * vec.extend(S::zero())).truncate()
}
fn transform_point(&self, point: Point3<S>) -> Point3<S> {
Point3::from_homogeneous(self * point.to_homogeneous())
}
fn concat(&self, other: &Matrix4<S>) -> Matrix4<S> {
self * other
}
fn inverse_transform(&self) -> Option<Matrix4<S>> {
SquareMatrix::invert(self)
}
}
impl<S: BaseFloat> Transform2<S> for Matrix3<S> {}
impl<S: BaseFloat> Transform3<S> for Matrix3<S> {}
impl<S: BaseFloat> Transform3<S> for Matrix4<S> {}
macro_rules! impl_operators {
($MatrixN:ident, $VectorN:ident { $($field:ident : $row_index:expr),+ }) => {
impl_operator!(<S: BaseFloat> Neg for $MatrixN<S> {
fn neg(matrix) -> $MatrixN<S> { $MatrixN { $($field: -matrix.$field),+ } }
});
impl_operator!(<S: BaseFloat> Mul<S> for $MatrixN<S> {
fn mul(matrix, scalar) -> $MatrixN<S> { $MatrixN { $($field: matrix.$field * scalar),+ } }
});
impl_operator!(<S: BaseFloat> Div<S> for $MatrixN<S> {
fn div(matrix, scalar) -> $MatrixN<S> { $MatrixN { $($field: matrix.$field / scalar),+ } }
});
impl_operator!(<S: BaseFloat> Rem<S> for $MatrixN<S> {
fn rem(matrix, scalar) -> $MatrixN<S> { $MatrixN { $($field: matrix.$field % scalar),+ } }
});
impl_assignment_operator!(<S: BaseFloat> MulAssign<S> for $MatrixN<S> {
fn mul_assign(&mut self, scalar) { $(self.$field *= scalar);+ }
});
impl_assignment_operator!(<S: BaseFloat> DivAssign<S> for $MatrixN<S> {
fn div_assign(&mut self, scalar) { $(self.$field /= scalar);+ }
});
impl_assignment_operator!(<S: BaseFloat> RemAssign<S> for $MatrixN<S> {
fn rem_assign(&mut self, scalar) { $(self.$field %= scalar);+ }
});
impl_operator!(<S: BaseFloat> Add<$MatrixN<S> > for $MatrixN<S> {
fn add(lhs, rhs) -> $MatrixN<S> { $MatrixN { $($field: lhs.$field + rhs.$field),+ } }
});
impl_operator!(<S: BaseFloat> Sub<$MatrixN<S> > for $MatrixN<S> {
fn sub(lhs, rhs) -> $MatrixN<S> { $MatrixN { $($field: lhs.$field - rhs.$field),+ } }
});
impl<S: BaseFloat + AddAssign<S>> AddAssign<$MatrixN<S>> for $MatrixN<S> {
fn add_assign(&mut self, other: $MatrixN<S>) { $(self.$field += other.$field);+ }
}
impl<S: BaseFloat + SubAssign<S>> SubAssign<$MatrixN<S>> for $MatrixN<S> {
fn sub_assign(&mut self, other: $MatrixN<S>) { $(self.$field -= other.$field);+ }
}
impl_operator!(<S: BaseFloat> Mul<$VectorN<S> > for $MatrixN<S> {
fn mul(matrix, vector) -> $VectorN<S> { $VectorN::new($(matrix.row($row_index).dot(vector.clone())),+) }
});
impl_scalar_ops!($MatrixN<usize> { $($field),+ });
impl_scalar_ops!($MatrixN<u8> { $($field),+ });
impl_scalar_ops!($MatrixN<u16> { $($field),+ });
impl_scalar_ops!($MatrixN<u32> { $($field),+ });
impl_scalar_ops!($MatrixN<u64> { $($field),+ });
impl_scalar_ops!($MatrixN<isize> { $($field),+ });
impl_scalar_ops!($MatrixN<i8> { $($field),+ });
impl_scalar_ops!($MatrixN<i16> { $($field),+ });
impl_scalar_ops!($MatrixN<i32> { $($field),+ });
impl_scalar_ops!($MatrixN<i64> { $($field),+ });
impl_scalar_ops!($MatrixN<f32> { $($field),+ });
impl_scalar_ops!($MatrixN<f64> { $($field),+ });
}
}
macro_rules! impl_scalar_ops {
($MatrixN:ident<$S:ident> { $($field:ident),+ }) => {
impl_operator!(Mul<$MatrixN<$S>> for $S {
fn mul(scalar, matrix) -> $MatrixN<$S> { $MatrixN { $($field: scalar * matrix.$field),+ } }
});
impl_operator!(Div<$MatrixN<$S>> for $S {
fn div(scalar, matrix) -> $MatrixN<$S> { $MatrixN { $($field: scalar / matrix.$field),+ } }
});
impl_operator!(Rem<$MatrixN<$S>> for $S {
fn rem(scalar, matrix) -> $MatrixN<$S> { $MatrixN { $($field: scalar % matrix.$field),+ } }
});
};
}
impl_operators!(Matrix2, Vector2 { x: 0, y: 1 });
impl_operators!(Matrix3, Vector3 { x: 0, y: 1, z: 2 });
impl_operators!(Matrix4, Vector4 { x: 0, y: 1, z: 2, w: 3 });
impl_operator!(<S: BaseFloat> Mul<Matrix2<S> > for Matrix2<S> {
fn mul(lhs, rhs) -> Matrix2<S> {
Matrix2::new(lhs.row(0).dot(rhs[0]), lhs.row(1).dot(rhs[0]),
lhs.row(0).dot(rhs[1]), lhs.row(1).dot(rhs[1]))
}
});
impl_operator!(<S: BaseFloat> Mul<Matrix3<S> > for Matrix3<S> {
fn mul(lhs, rhs) -> Matrix3<S> {
Matrix3::new(lhs.row(0).dot(rhs[0]), lhs.row(1).dot(rhs[0]), lhs.row(2).dot(rhs[0]),
lhs.row(0).dot(rhs[1]), lhs.row(1).dot(rhs[1]), lhs.row(2).dot(rhs[1]),
lhs.row(0).dot(rhs[2]), lhs.row(1).dot(rhs[2]), lhs.row(2).dot(rhs[2]))
}
});
// Using self.row(0).dot(other[0]) like the other matrix multiplies
// causes the LLVM to miss identical loads and multiplies. This optimization
// causes the code to be auto vectorized properly increasing the performance
// around ~4 times.
macro_rules! dot_matrix4 {
($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[$J][3])
};
}
impl_operator!(<S: BaseFloat> Mul<Matrix4<S> > for Matrix4<S> {
fn mul(lhs, rhs) -> Matrix4<S> {
Matrix4::new(dot_matrix4!(lhs, rhs, 0, 0), dot_matrix4!(lhs, rhs, 1, 0), dot_matrix4!(lhs, rhs, 2, 0), dot_matrix4!(lhs, rhs, 3, 0),
dot_matrix4!(lhs, rhs, 0, 1), dot_matrix4!(lhs, rhs, 1, 1), dot_matrix4!(lhs, rhs, 2, 1), dot_matrix4!(lhs, rhs, 3, 1),
dot_matrix4!(lhs, rhs, 0, 2), dot_matrix4!(lhs, rhs, 1, 2), dot_matrix4!(lhs, rhs, 2, 2), dot_matrix4!(lhs, rhs, 3, 2),
dot_matrix4!(lhs, rhs, 0, 3), dot_matrix4!(lhs, rhs, 1, 3), dot_matrix4!(lhs, rhs, 2, 3), dot_matrix4!(lhs, rhs, 3, 3))
}
});
macro_rules! index_operators {
($MatrixN:ident<$S:ident>, $n:expr, $Output:ty, $I:ty) => {
impl<$S> Index<$I> for $MatrixN<$S> {
type Output = $Output;
#[inline]
fn index<'a>(&'a self, i: $I) -> &'a $Output {
let v: &[[$S; $n]; $n] = self.as_ref();
From::from(&v[i])
}
}
impl<$S> IndexMut<$I> for $MatrixN<$S> {
#[inline]
fn index_mut<'a>(&'a mut self, i: $I) -> &'a mut $Output {
let v: &mut [[$S; $n]; $n] = self.as_mut();
From::from(&mut v[i])
}
}
}
}
index_operators!(Matrix2<S>, 2, Vector2<S>, usize);
index_operators!(Matrix3<S>, 3, Vector3<S>, usize);
index_operators!(Matrix4<S>, 4, Vector4<S>, usize);
// index_operators!(Matrix2<S>, 2, [Vector2<S>], Range<usize>);
// index_operators!(Matrix3<S>, 3, [Vector3<S>], Range<usize>);
// index_operators!(Matrix4<S>, 4, [Vector4<S>], Range<usize>);
// index_operators!(Matrix2<S>, 2, [Vector2<S>], RangeTo<usize>);
// index_operators!(Matrix3<S>, 3, [Vector3<S>], RangeTo<usize>);
// index_operators!(Matrix4<S>, 4, [Vector4<S>], RangeTo<usize>);
// index_operators!(Matrix2<S>, 2, [Vector2<S>], RangeFrom<usize>);
// index_operators!(Matrix3<S>, 3, [Vector3<S>], RangeFrom<usize>);
// index_operators!(Matrix4<S>, 4, [Vector4<S>], RangeFrom<usize>);
// index_operators!(Matrix2<S>, 2, [Vector2<S>], RangeFull);
// index_operators!(Matrix3<S>, 3, [Vector3<S>], RangeFull);
// index_operators!(Matrix4<S>, 4, [Vector4<S>], RangeFull);
impl<A> From<Euler<A>> for Matrix3<<A as Angle>::Unitless> where
A: Angle + Into<Rad<<A as Angle>::Unitless>>,
{
fn from(src: Euler<A>) -> Matrix3<A::Unitless> {
// Page A-2: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf
let (sx, cx) = Rad::sin_cos(src.x.into());
let (sy, cy) = Rad::sin_cos(src.y.into());
let (sz, cz) = Rad::sin_cos(src.z.into());
Matrix3::new(cy * cz, cx * sz + sx * sy * cz, sx * sz - cx * sy * cz,
-cy * sz, cx * cz - sx * sy * sz, sx * cz + cx * sy * sz,
sy, -sx * cy, cx * cy)
}
}
impl<A> From<Euler<A>> for Matrix4<<A as Angle>::Unitless> where
A: Angle + Into<Rad<<A as Angle>::Unitless>>,
{
fn from(src: Euler<A>) -> Matrix4<A::Unitless> {
// Page A-2: http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770024290.pdf
let (sx, cx) = Rad::sin_cos(src.x.into());
let (sy, cy) = Rad::sin_cos(src.y.into());
let (sz, cz) = Rad::sin_cos(src.z.into());
Matrix4::new(cy * cz, cx * sz + sx * sy * cz, sx * sz - cx * sy * cz, A::Unitless::zero(),
-cy * sz, cx * cz - sx * sy * sz, sx * cz + cx * sy * sz, A::Unitless::zero(),
sy, -sx * cy, cx * cy, A::Unitless::zero(),
A::Unitless::zero(), A::Unitless::zero(), A::Unitless::zero(), A::Unitless::one())
}
}
macro_rules! fixed_array_conversions {
($MatrixN:ident <$S:ident> { $($field:ident : $index:expr),+ }, $n:expr) => {
impl<$S> Into<[[$S; $n]; $n]> for $MatrixN<$S> {
#[inline]
fn into(self) -> [[$S; $n]; $n] {
match self { $MatrixN { $($field),+ } => [$($field.into()),+] }
}
}
impl<$S> AsRef<[[$S; $n]; $n]> for $MatrixN<$S> {
#[inline]
fn as_ref(&self) -> &[[$S; $n]; $n] {
unsafe { mem::transmute(self) }
}
}
impl<$S> AsMut<[[$S; $n]; $n]> for $MatrixN<$S> {
#[inline]
fn as_mut(&mut self) -> &mut [[$S; $n]; $n] {
unsafe { mem::transmute(self) }
}
}
impl<$S: Copy> From<[[$S; $n]; $n]> for $MatrixN<$S> {
#[inline]
fn from(m: [[$S; $n]; $n]) -> $MatrixN<$S> {
// We need to use a copy here because we can't pattern match on arrays yet
$MatrixN { $($field: From::from(m[$index])),+ }
}
}
impl<'a, $S> From<&'a [[$S; $n]; $n]> for &'a $MatrixN<$S> {
#[inline]
fn from(m: &'a [[$S; $n]; $n]) -> &'a $MatrixN<$S> {
unsafe { mem::transmute(m) }
}
}
impl<'a, $S> From<&'a mut [[$S; $n]; $n]> for &'a mut $MatrixN<$S> {
#[inline]
fn from(m: &'a mut [[$S; $n]; $n]) -> &'a mut $MatrixN<$S> {
unsafe { mem::transmute(m) }
}
}
// impl<$S> Into<[$S; ($n * $n)]> for $MatrixN<$S> {
// #[inline]
// fn into(self) -> [[$S; $n]; $n] {
// // TODO: Not sure how to implement this...
// unimplemented!()
// }
// }
impl<$S> AsRef<[$S; ($n * $n)]> for $MatrixN<$S> {
#[inline]
fn as_ref(&self) -> &[$S; ($n * $n)] {
unsafe { mem::transmute(self) }
}
}
impl<$S> AsMut<[$S; ($n * $n)]> for $MatrixN<$S> {
#[inline]
fn as_mut(&mut self) -> &mut [$S; ($n * $n)] {
unsafe { mem::transmute(self) }
}
}
// impl<$S> From<[$S; ($n * $n)]> for $MatrixN<$S> {
// #[inline]
// fn from(m: [$S; ($n * $n)]) -> $MatrixN<$S> {
// // TODO: Not sure how to implement this...
// unimplemented!()
// }
// }
impl<'a, $S> From<&'a [$S; ($n * $n)]> for &'a $MatrixN<$S> {
#[inline]
fn from(m: &'a [$S; ($n * $n)]) -> &'a $MatrixN<$S> {
unsafe { mem::transmute(m) }
}
}
impl<'a, $S> From<&'a mut [$S; ($n * $n)]> for &'a mut $MatrixN<$S> {
#[inline]
fn from(m: &'a mut [$S; ($n * $n)]) -> &'a mut $MatrixN<$S> {
unsafe { mem::transmute(m) }
}
}
}
}
fixed_array_conversions!(Matrix2<S> { x:0, y:1 }, 2);
fixed_array_conversions!(Matrix3<S> { x:0, y:1, z:2 }, 3);
fixed_array_conversions!(Matrix4<S> { x:0, y:1, z:2, w:3 }, 4);
impl<S: BaseFloat> From<Matrix2<S>> for Matrix3<S> {
/// Clone the elements of a 2-dimensional matrix into the top-left corner
/// of a 3-dimensional identity matrix.
fn from(m: Matrix2<S>) -> Matrix3<S> {
Matrix3::new(m[0][0], m[0][1], S::zero(),
m[1][0], m[1][1], S::zero(),
S::zero(), S::zero(), S::one())
}
}
impl<S: BaseFloat> From<Matrix2<S>> for Matrix4<S> {
/// Clone the elements of a 2-dimensional matrix into the top-left corner
/// of a 4-dimensional identity matrix.
fn from(m: Matrix2<S>) -> Matrix4<S> {
Matrix4::new(m[0][0], m[0][1], S::zero(), S::zero(),
m[1][0], m[1][1], S::zero(), S::zero(),
S::zero(), S::zero(), S::one(), S::zero(),
S::zero(), S::zero(), S::zero(), S::one())
}
}
impl<S: BaseFloat> From<Matrix3<S>> for Matrix4<S> {
/// Clone the elements of a 3-dimensional matrix into the top-left corner
/// of a 4-dimensional identity matrix.
fn from(m: Matrix3<S>) -> Matrix4<S> {
Matrix4::new(m[0][0], m[0][1], m[0][2], S::zero(),
m[1][0], m[1][1], m[1][2], S::zero(),
m[2][0], m[2][1], m[2][2], S::zero(),
S::zero(), S::zero(), S::zero(), S::one())
}
}
impl<S: BaseFloat> From<Matrix3<S>> for Quaternion<S> {
/// Convert the matrix to a quaternion
fn from(mat: Matrix3<S>) -> Quaternion<S> {
// http://www.cs.ucr.edu/~vbz/resources/quatut.pdf
let trace = mat.trace();
let half: S = cast(0.5f64).unwrap();
if trace >= S::zero() {
let s = (S::one() + trace).sqrt();
let w = half * s;
let s = half / s;
let x = (mat[1][2] - mat[2][1]) * s;
let y = (mat[2][0] - mat[0][2]) * s;
let z = (mat[0][1] - mat[1][0]) * s;
Quaternion::new(w, x, y, z)
} else if (mat[0][0] > mat[1][1]) && (mat[0][0] > mat[2][2]) {
let s = ((mat[0][0] - mat[1][1] - mat[2][2]) + S::one()).sqrt();
let x = half * s;
let s = half / s;
let y = (mat[1][0] + mat[0][1]) * s;
let z = (mat[0][2] + mat[2][0]) * s;
let w = (mat[1][2] - mat[2][1]) * s;
Quaternion::new(w, x, y, z)
} else if mat[1][1] > mat[2][2] {
let s = ((mat[1][1] - mat[0][0] - mat[2][2]) + S::one()).sqrt();
let y = half * s;
let s = half / s;
let z = (mat[2][1] + mat[1][2]) * s;
let x = (mat[1][0] + mat[0][1]) * s;
let w = (mat[2][0] - mat[0][2]) * s;
Quaternion::new(w, x, y, z)
} else {
let s = ((mat[2][2] - mat[0][0] - mat[1][1]) + S::one()).sqrt();
let z = half * s;
let s = half / s;
let x = (mat[0][2] + mat[2][0]) * s;
let y = (mat[2][1] + mat[1][2]) * s;
let w = (mat[0][1] - mat[1][0]) * s;
Quaternion::new(w, x, y, z)
}
}
}
impl<S: fmt::Debug> fmt::Debug for Matrix2<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
try!(write!(f, "Matrix2 "));
<[[S; 2]; 2] as fmt::Debug>::fmt(self.as_ref(), f)
}
}
impl<S: fmt::Debug> fmt::Debug for Matrix3<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
try!(write!(f, "Matrix3 "));
<[[S; 3]; 3] as fmt::Debug>::fmt(self.as_ref(), f)
}
}
impl<S: fmt::Debug> fmt::Debug for Matrix4<S> {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
try!(write!(f, "Matrix4 "));
<[[S; 4]; 4] as fmt::Debug>::fmt(self.as_ref(), f)
}
}
impl<S: BaseFloat + Rand> Rand for Matrix2<S> {
#[inline]
fn rand<R: Rng>(rng: &mut R) -> Matrix2<S> {
Matrix2{ x: rng.gen(), y: rng.gen() }
}
}
impl<S: BaseFloat + Rand> Rand for Matrix3<S> {
#[inline]
fn rand<R: Rng>(rng: &mut R) -> Matrix3<S> {
Matrix3{ x: rng.gen(), y: rng.gen(), z: rng.gen() }
}
}
impl<S: BaseFloat + Rand> Rand for Matrix4<S> {
#[inline]
fn rand<R: Rng>(rng: &mut R) -> Matrix4<S> {
Matrix4{ x: rng.gen(), y: rng.gen(), z: rng.gen(), w: rng.gen() }
}
}
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