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use crate::core::{
storage::{Columns3, XYZ},
traits::matrix::{FloatMatrix3x3, Matrix3x3, MatrixConst},
};
use crate::{DMat2, DMat4, DQuat, DVec2, DVec3, EulerRot, Mat2, Mat4, Quat, Vec2, Vec3, Vec3A};
#[cfg(not(target_arch = "spirv"))]
use core::fmt;
use core::ops::{Add, AddAssign, Deref, DerefMut, Mul, MulAssign, Sub, SubAssign};
#[cfg(all(
target_arch = "x86",
target_feature = "sse2",
not(feature = "scalar-math")
))]
use core::arch::x86::*;
#[cfg(all(
target_arch = "x86_64",
target_feature = "sse2",
not(feature = "scalar-math")
))]
use core::arch::x86_64::*;
#[cfg(feature = "std")]
use std::iter::{Product, Sum};
macro_rules! define_mat3_struct {
($mat3:ident, $inner:ident) => {
/// A 3x3 column major matrix.
///
/// This 3x3 matrix type features convenience methods for creating and using linear and
/// affine transformations. If you are primarily dealing with 2D affine transformations the
/// [`Affine2`][crate::Affine2] type is much faster and more space efficient than using a
/// 3x3 matrix.
///
/// Linear transformations including 3D rotation and scale can be created using methods
/// such as [`Self::from_diagonal()`], [`Self::from_quat()`], [`Self::from_axis_angle()`],
/// [`Self::from_rotation_x()`], [`Self::from_rotation_y()`], or
/// [`Self::from_rotation_z()`].
///
/// The resulting matrices can be use to transform 3D vectors using regular vector
/// multiplication.
///
/// Affine transformations including 2D translation, rotation and scale can be created
/// using methods such as [`Self::from_translation()`], [`Self::from_angle()`],
/// [`Self::from_scale()`] and [`Self::from_scale_angle_translation()`].
///
/// The [`Self::transform_point2()`] and [`Self::transform_vector2()`] convenience methods
/// are provided for performing affine transforms on 2D vectors and points. These multiply
/// 2D inputs as 3D vectors with an implicit `z` value of `1` for points and `0` for
/// vectors respectively. These methods assume that `Self` contains a valid affine
/// transform.
#[derive(Clone, Copy)]
#[cfg_attr(not(target_arch = "spirv"), repr(C))]
pub struct $mat3(pub(crate) $inner);
};
}
macro_rules! impl_mat3_methods {
($t:ty, $vec3:ident, $vec3a:ident, $vec2:ident, $quat:ident, $mat2:ident, $mat4:ident, $inner:ident) => {
/// A 3x3 matrix with all elements set to `0.0`.
pub const ZERO: Self = Self($inner::ZERO);
/// A 3x3 identity matrix, where all diagonal elements are `1`, and all off-diagonal
/// elements are `0`.
pub const IDENTITY: Self = Self($inner::IDENTITY);
/// Creates a 3x3 matrix from three column vectors.
#[inline(always)]
pub fn from_cols(x_axis: $vec3a, y_axis: $vec3a, z_axis: $vec3a) -> Self {
Self(Matrix3x3::from_cols(x_axis.0, y_axis.0, z_axis.0))
}
/// Creates a 3x3 matrix from a `[S; 9]` array stored in column major order.
/// If your data is stored in row major you will need to `transpose` the returned
/// matrix.
#[inline(always)]
pub fn from_cols_array(m: &[$t; 9]) -> Self {
Self(Matrix3x3::from_cols_array(m))
}
/// Creates a `[S; 9]` array storing data in column major order.
/// If you require data in row major order `transpose` the matrix first.
#[inline(always)]
pub fn to_cols_array(&self) -> [$t; 9] {
self.0.to_cols_array()
}
/// Creates a 3x3 matrix from a `[[S; 3]; 3]` 2D array stored in column major order.
/// If your data is in row major order you will need to `transpose` the returned
/// matrix.
#[inline(always)]
pub fn from_cols_array_2d(m: &[[$t; 3]; 3]) -> Self {
Self(Matrix3x3::from_cols_array_2d(m))
}
/// Creates a `[[S; 3]; 3]` 2D array storing data in column major order.
/// If you require data in row major order `transpose` the matrix first.
#[inline(always)]
pub fn to_cols_array_2d(&self) -> [[$t; 3]; 3] {
self.0.to_cols_array_2d()
}
/// Creates a 3x3 matrix with its diagonal set to `diagonal` and all other entries set to 0.
/// The resulting matrix is a 3D scale transfom.
#[cfg_attr(docsrs, doc(alias = "scale"))]
#[inline(always)]
pub fn from_diagonal(diagonal: $vec3) -> Self {
Self($inner::from_diagonal(diagonal.0))
}
/// Creates a 3x3 matrix from a 4x4 matrix, discarding the 3rd row and column.
pub fn from_mat4(m: $mat4) -> Self {
Self::from_cols(m.x_axis.into(), m.y_axis.into(), m.z_axis.into())
}
/// Creates a 3D rotation matrix from the given quaternion.
///
/// # Panics
///
/// Will panic if `rotation` is not normalized when `glam_assert` is enabled.
#[inline(always)]
pub fn from_quat(rotation: $quat) -> Self {
// TODO: SIMD?
Self($inner::from_quaternion(rotation.0.into()))
}
/// Creates a 3D rotation matrix from a normalized rotation `axis` and `angle` (in
/// radians).
///
/// # Panics
///
/// Will panic if `axis` is not normalized when `glam_assert` is enabled.
#[inline(always)]
pub fn from_axis_angle(axis: $vec3, angle: $t) -> Self {
Self(FloatMatrix3x3::from_axis_angle(axis.0, angle))
}
#[inline(always)]
/// Creates a 3D rotation matrix from the given euler rotation sequence and the angles (in
/// radians).
pub fn from_euler(order: EulerRot, a: $t, b: $t, c: $t) -> Self {
let quat = $quat::from_euler(order, a, b, c);
Self::from_quat(quat)
}
/// Creates a 3D rotation matrix from `angle` (in radians) around the x axis.
#[inline(always)]
pub fn from_rotation_x(angle: $t) -> Self {
Self($inner::from_rotation_x(angle))
}
/// Creates a 3D rotation matrix from `angle` (in radians) around the y axis.
#[inline(always)]
pub fn from_rotation_y(angle: $t) -> Self {
Self($inner::from_rotation_y(angle))
}
/// Creates a 3D rotation matrix from `angle` (in radians) around the z axis.
#[inline(always)]
pub fn from_rotation_z(angle: $t) -> Self {
Self($inner::from_rotation_z(angle))
}
/// Creates an affine transformation matrix from the given 2D `translation`.
///
/// The resulting matrix can be used to transform 2D points and vectors. See
/// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
#[inline(always)]
pub fn from_translation(translation: $vec2) -> Self {
Self(Matrix3x3::from_translation(translation.0))
}
/// Creates an affine transformation matrix from the given 2D rotation `angle` (in
/// radians).
///
/// The resulting matrix can be used to transform 2D points and vectors. See
/// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
#[inline(always)]
pub fn from_angle(angle: $t) -> Self {
Self(FloatMatrix3x3::from_angle(angle))
}
/// Creates an affine transformation matrix from the given 2D `scale`, rotation `angle` (in
/// radians) and `translation`.
///
/// The resulting matrix can be used to transform 2D points and vectors. See
/// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
#[inline(always)]
pub fn from_scale_angle_translation(scale: $vec2, angle: $t, translation: $vec2) -> Self {
Self(FloatMatrix3x3::from_scale_angle_translation(
scale.0,
angle,
translation.0,
))
}
/// Creates an affine transformation matrix from the given non-uniform 2D `scale`.
///
/// The resulting matrix can be used to transform 2D points and vectors. See
/// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
///
/// # Panics
///
/// Will panic if all elements of `scale` are zero when `glam_assert` is enabled.
#[inline(always)]
pub fn from_scale(scale: $vec2) -> Self {
Self(Matrix3x3::from_scale(scale.0))
}
/// Creates an affine transformation matrix from the given 2x2 matrix.
///
/// The resulting matrix can be used to transform 2D points and vectors. See
/// [`Self::transform_point2()`] and [`Self::transform_vector2()`].
#[inline(always)]
pub fn from_mat2(m: $mat2) -> Self {
Self::from_cols((m.x_axis, 0.0).into(), (m.y_axis, 0.0).into(), $vec3a::Z)
}
/// Creates a 3x3 matrix from the first 9 values in `slice`.
///
/// # Panics
///
/// Panics if `slice` is less than 9 elements long.
#[inline(always)]
pub fn from_cols_slice(slice: &[$t]) -> Self {
Self(Matrix3x3::from_cols_slice(slice))
}
/// Writes the columns of `self` to the first 9 elements in `slice`.
///
/// # Panics
///
/// Panics if `slice` is less than 9 elements long.
#[inline(always)]
pub fn write_cols_to_slice(self, slice: &mut [$t]) {
Matrix3x3::write_cols_to_slice(&self.0, slice)
}
/// Returns the matrix column for the given `index`.
///
/// # Panics
///
/// Panics if `index` is greater than 2.
#[inline]
pub fn col(&self, index: usize) -> $vec3a {
match index {
0 => self.x_axis,
1 => self.y_axis,
2 => self.z_axis,
_ => panic!("index out of bounds"),
}
}
/// Returns a mutable reference to the matrix column for the given `index`.
///
/// # Panics
///
/// Panics if `index` is greater than 2.
#[inline]
pub fn col_mut(&mut self, index: usize) -> &mut $vec3a {
match index {
0 => &mut self.x_axis,
1 => &mut self.y_axis,
2 => &mut self.z_axis,
_ => panic!("index out of bounds"),
}
}
/// Returns the matrix row for the given `index`.
///
/// # Panics
///
/// Panics if `index` is greater than 2.
#[inline]
pub fn row(&self, index: usize) -> $vec3a {
match index {
0 => $vec3a::new(self.x_axis.x, self.y_axis.x, self.z_axis.x),
1 => $vec3a::new(self.x_axis.y, self.y_axis.y, self.z_axis.y),
2 => $vec3a::new(self.x_axis.z, self.y_axis.z, self.z_axis.z),
_ => panic!("index out of bounds"),
}
}
/// Returns `true` if, and only if, all elements are finite.
/// If any element is either `NaN`, positive or negative infinity, this will return `false`.
#[inline]
pub fn is_finite(&self) -> bool {
self.x_axis.is_finite() && self.y_axis.is_finite() && self.z_axis.is_finite()
}
/// Returns `true` if any elements are `NaN`.
#[inline]
pub fn is_nan(&self) -> bool {
self.x_axis.is_nan() || self.y_axis.is_nan() || self.z_axis.is_nan()
}
/// Returns the transpose of `self`.
#[must_use]
#[inline(always)]
pub fn transpose(&self) -> Self {
Self(self.0.transpose())
}
/// Returns the determinant of `self`.
#[inline(always)]
pub fn determinant(&self) -> $t {
self.0.determinant()
}
/// Returns the inverse of `self`.
///
/// If the matrix is not invertible the returned matrix will be invalid.
///
/// # Panics
///
/// Will panic if the determinant of `self` is zero when `glam_assert` is enabled.
#[must_use]
#[inline(always)]
pub fn inverse(&self) -> Self {
Self(self.0.inverse())
}
/// Transforms a 3D vector.
#[inline(always)]
pub fn mul_vec3(&self, other: $vec3) -> $vec3 {
$vec3(self.0.mul_vector(other.0.into()).into())
}
/// Multiplies two 3x3 matrices.
#[inline]
pub fn mul_mat3(&self, other: &Self) -> Self {
Self(self.0.mul_matrix(&other.0))
}
/// Adds two 3x3 matrices.
#[inline(always)]
pub fn add_mat3(&self, other: &Self) -> Self {
Self(self.0.add_matrix(&other.0))
}
/// Subtracts two 3x3 matrices.
#[inline(always)]
pub fn sub_mat3(&self, other: &Self) -> Self {
Self(self.0.sub_matrix(&other.0))
}
/// Multiplies a 3x3 matrix by a scalar.
#[inline(always)]
pub fn mul_scalar(&self, other: $t) -> Self {
Self(self.0.mul_scalar(other))
}
/// Transforms the given 2D vector as a point.
///
/// This is the equivalent of multiplying `other` as a 3D vector where `z` is `1`.
///
/// This method assumes that `self` contains a valid affine transform.
#[inline(always)]
pub fn transform_point2(&self, other: $vec2) -> $vec2 {
$mat2::from_cols(self.x_axis.into(), self.y_axis.into()) * other
+ $vec2::from(self.z_axis)
}
/// Rotates the given 2D vector.
///
/// This is the equivalent of multiplying `other` as a 3D vector where `z` is `0`.
///
/// This method assumes that `self` contains a valid affine transform.
#[inline(always)]
pub fn transform_vector2(&self, other: $vec2) -> $vec2 {
$mat2::from_cols(self.x_axis.into(), self.y_axis.into()) * other
}
/// Returns true if the absolute difference of all elements between `self` and `other`
/// is less than or equal to `max_abs_diff`.
///
/// This can be used to compare if two matrices contain similar elements. It works best
/// when comparing with a known value. The `max_abs_diff` that should be used used
/// depends on the values being compared against.
///
/// For more see
/// [comparing floating point numbers](https://randomascii.wordpress.com/2012/02/25/comparing-floating-point-numbers-2012-edition/).
#[inline(always)]
pub fn abs_diff_eq(&self, other: Self, max_abs_diff: $t) -> bool {
self.0.abs_diff_eq(&other.0, max_abs_diff)
}
};
}
macro_rules! impl_mat3_traits {
($t:ty, $new:ident, $mat3:ident, $vec3:ident, $vec3a:ident) => {
/// Creates a 3x3 matrix from three column vectors.
#[inline(always)]
pub fn $new(x_axis: $vec3a, y_axis: $vec3a, z_axis: $vec3a) -> $mat3 {
$mat3::from_cols(x_axis, y_axis, z_axis)
}
impl_matn_common_traits!($t, $mat3, $vec3a);
impl PartialEq for $mat3 {
#[inline]
fn eq(&self, other: &Self) -> bool {
self.x_axis.eq(&other.x_axis)
&& self.y_axis.eq(&other.y_axis)
&& self.z_axis.eq(&other.z_axis)
}
}
impl Deref for $mat3 {
type Target = Columns3<$vec3a>;
#[inline(always)]
fn deref(&self) -> &Self::Target {
unsafe { &*(self as *const Self as *const Self::Target) }
}
}
impl DerefMut for $mat3 {
#[inline(always)]
fn deref_mut(&mut self) -> &mut Self::Target {
unsafe { &mut *(self as *mut Self as *mut Self::Target) }
}
}
#[cfg(not(target_arch = "spirv"))]
impl fmt::Display for $mat3 {
fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
write!(f, "[{}, {}, {}]", self.x_axis, self.y_axis, self.z_axis)
}
}
#[cfg(not(target_arch = "spirv"))]
impl fmt::Debug for $mat3 {
fn fmt(&self, fmt: &mut fmt::Formatter) -> fmt::Result {
fmt.debug_struct("$mat3")
.field("x_axis", &self.x_axis)
.field("y_axis", &self.y_axis)
.field("z_axis", &self.z_axis)
.finish()
}
}
};
}
macro_rules! impl_mat3_traits_unsafe {
($t:ty, $mat3:ident) => {
#[cfg(not(target_arch = "spriv"))]
impl AsRef<[$t; 9]> for $mat3 {
#[inline(always)]
fn as_ref(&self) -> &[$t; 9] {
unsafe { &*(self as *const Self as *const [$t; 9]) }
}
}
#[cfg(not(target_arch = "spriv"))]
impl AsMut<[$t; 9]> for $mat3 {
#[inline(always)]
fn as_mut(&mut self) -> &mut [$t; 9] {
unsafe { &mut *(self as *mut Self as *mut [$t; 9]) }
}
}
};
}
type InnerF32 = Columns3<XYZ<f32>>;
define_mat3_struct!(Mat3, InnerF32);
impl Mat3 {
impl_mat3_methods!(f32, Vec3, Vec3, Vec2, Quat, Mat2, Mat4, InnerF32);
/// Transforms a `Vec3A`.
#[inline]
pub fn mul_vec3a(&self, other: Vec3A) -> Vec3A {
self.mul_vec3(other.into()).into()
}
#[inline(always)]
pub fn as_f64(&self) -> DMat3 {
DMat3::from_cols(
self.x_axis.as_f64(),
self.y_axis.as_f64(),
self.z_axis.as_f64(),
)
}
}
impl_mat3_traits!(f32, mat3, Mat3, Vec3, Vec3);
impl_mat3_traits_unsafe!(f32, Mat3);
impl Mul<Vec3A> for Mat3 {
type Output = Vec3A;
#[inline(always)]
fn mul(self, other: Vec3A) -> Vec3A {
self.mul_vec3a(other)
}
}
#[cfg(all(target_feature = "sse2", not(feature = "scalar-math")))]
type InnerF32A = Columns3<__m128>;
#[cfg(any(not(target_feature = "sse2"), feature = "scalar-math"))]
type InnerF32A = Columns3<crate::core::storage::XYZF32A16>;
define_mat3_struct!(Mat3A, InnerF32A);
impl Mat3A {
impl_mat3_methods!(f32, Vec3, Vec3A, Vec2, Quat, Mat2, Mat4, InnerF32A);
/// Transforms a `Vec3A`.
#[inline]
pub fn mul_vec3a(&self, other: Vec3A) -> Vec3A {
Vec3A(self.0.mul_vector(other.0))
}
#[inline(always)]
pub fn as_f64(&self) -> DMat3 {
DMat3::from_cols(
self.x_axis.as_f64(),
self.y_axis.as_f64(),
self.z_axis.as_f64(),
)
}
}
impl_mat3_traits!(f32, mat3a, Mat3A, Vec3, Vec3A);
impl Mul<Vec3> for Mat3A {
type Output = Vec3;
#[inline(always)]
fn mul(self, other: Vec3) -> Vec3 {
self.mul_vec3(other)
}
}
impl From<Mat3> for Mat3A {
#[inline(always)]
fn from(m: Mat3) -> Self {
Self(m.0.into())
}
}
impl From<Mat3A> for Mat3 {
#[inline(always)]
fn from(m: Mat3A) -> Self {
Self(m.0.into())
}
}
type InnerF64 = Columns3<XYZ<f64>>;
define_mat3_struct!(DMat3, InnerF64);
impl DMat3 {
impl_mat3_methods!(f64, DVec3, DVec3, DVec2, DQuat, DMat2, DMat4, InnerF64);
#[inline(always)]
pub fn as_f32(&self) -> Mat3 {
Mat3::from_cols(
self.x_axis.as_f32(),
self.y_axis.as_f32(),
self.z_axis.as_f32(),
)
}
}
impl_mat3_traits!(f64, dmat3, DMat3, DVec3, DVec3);
impl_mat3_traits_unsafe!(f64, DMat3);
mod const_test_mat3 {
const_assert_eq!(
core::mem::align_of::<f32>(),
core::mem::align_of::<super::Mat3>()
);
const_assert_eq!(36, core::mem::size_of::<super::Mat3>());
}
mod const_test_mat3a {
const_assert_eq!(16, core::mem::align_of::<super::Mat3A>());
const_assert_eq!(48, core::mem::size_of::<super::Mat3A>());
}
mod const_test_dmat3 {
const_assert_eq!(
core::mem::align_of::<f64>(),
core::mem::align_of::<super::DMat3>()
);
const_assert_eq!(72, core::mem::size_of::<super::DMat3>());
}