Struct tri_mesh::math::Matrix4

#[repr(C)]
pub struct Matrix4<S> {
    pub x: Vector4<S>,
    pub y: Vector4<S>,
    pub z: Vector4<S>,
    pub w: Vector4<S>,
}

A 4 x 4, column major matrix

This type is marked as #[repr(C)].

Fields

x: Vector4<S>

The first column of the matrix.

y: Vector4<S>

The second column of the matrix.

z: Vector4<S>

The third column of the matrix.

w: Vector4<S>

The fourth column of the matrix.

Implementations

impl<S> Matrix4<S>

pub const 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>

Create a new matrix, providing values for each index.

pub const fn from_cols( c0: Vector4<S>, c1: Vector4<S>, c2: Vector4<S>, c3: Vector4<S>, ) -> Matrix4<S>

Create a new matrix, providing columns.

impl<S> Matrix4<S>

where S: BaseFloat,

pub fn from_translation(v: Vector3<S>) -> Matrix4<S>

Create a homogeneous transformation matrix from a translation vector.

pub fn from_scale(value: S) -> Matrix4<S>

Create a homogeneous transformation matrix from a scale value.

pub fn from_nonuniform_scale(x: S, y: S, z: S) -> Matrix4<S>

Create a homogeneous transformation matrix from a set of scale values.

pub fn look_at_dir( eye: Point3<S>, dir: Vector3<S>, up: Vector3<S>, ) -> Matrix4<S>

👎Deprecated: Use Matrix4::look_to_rh

Create a homogeneous transformation matrix that will cause a vector to point at dir, using up for orientation.

pub fn look_to_rh(eye: Point3<S>, dir: Vector3<S>, up: Vector3<S>) -> Matrix4<S>

Create a homogeneous transformation matrix that will cause a vector to point at dir, using up for orientation.

pub fn look_to_lh(eye: Point3<S>, dir: Vector3<S>, up: Vector3<S>) -> Matrix4<S>

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>

👎Deprecated: Use Matrix4::look_at_rh

Create a homogeneous transformation matrix that will cause a vector to point at center, using up for orientation.

pub fn look_at_rh( eye: Point3<S>, center: Point3<S>, up: Vector3<S>, ) -> Matrix4<S>

Create a homogeneous transformation matrix that will cause a vector to point at center, using up for orientation.

pub fn look_at_lh( eye: Point3<S>, center: Point3<S>, up: Vector3<S>, ) -> Matrix4<S>

Create a homogeneous transformation matrix that will cause a vector to point at center, using up for orientation.

pub fn from_angle_x<A>(theta: A) -> Matrix4<S>

where A: Into<Rad<S>>,

Create a homogeneous transformation matrix from a rotation around the x axis (pitch).

pub fn from_angle_y<A>(theta: A) -> Matrix4<S>

where A: Into<Rad<S>>,

Create a homogeneous transformation matrix from a rotation around the y axis (yaw).

pub fn from_angle_z<A>(theta: A) -> Matrix4<S>

where A: Into<Rad<S>>,

Create a homogeneous transformation matrix from a rotation around the z axis (roll).

pub fn from_axis_angle<A>(axis: Vector3<S>, angle: A) -> Matrix4<S>

where A: Into<Rad<S>>,

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 is_finite(&self) -> bool

Are all entries in the matrix finite.

impl<S> Matrix4<S>

where S: NumCast + Copy,

pub fn cast<T>(&self) -> Option<Matrix4<T>>

where T: NumCast,

Component-wise casting to another type

Trait Implementations

impl<S> AbsDiffEq for Matrix4<S>

where S: BaseFloat,

type Epsilon = <S as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> <S as AbsDiffEq>::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq( &self, other: &Matrix4<S>, epsilon: <S as AbsDiffEq>::Epsilon, ) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<'a, 'b, S> Add<&'a Matrix4<S>> for &'b Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the + operator.

fn add(self, other: &'a Matrix4<S>) -> Matrix4<S>

Performs the + operation.

impl<'a, S> Add<&'a Matrix4<S>> for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the + operator.

fn add(self, other: &'a Matrix4<S>) -> Matrix4<S>

Performs the + operation.

impl<'a, S> Add<Matrix4<S>> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the + operator.

fn add(self, other: Matrix4<S>) -> Matrix4<S>

Performs the + operation.

impl<S> Add for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the + operator.

fn add(self, other: Matrix4<S>) -> Matrix4<S>

Performs the + operation.

impl<S> AddAssign for Matrix4<S>

where S: BaseFloat + AddAssign,

fn add_assign(&mut self, other: Matrix4<S>)

Performs the += operation.

impl<S> AsMut<[[S; 4]; 4]> for Matrix4<S>

fn as_mut(&mut self) -> &mut [[S; 4]; 4]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<S> AsMut<[S; 16]> for Matrix4<S>

fn as_mut(&mut self) -> &mut [S; 16]

Converts this type into a mutable reference of the (usually inferred) input type.

impl<S> AsRef<[[S; 4]; 4]> for Matrix4<S>

fn as_ref(&self) -> &[[S; 4]; 4]

Converts this type into a shared reference of the (usually inferred) input type.

impl<S> AsRef<[S; 16]> for Matrix4<S>

fn as_ref(&self) -> &[S; 16]

Converts this type into a shared reference of the (usually inferred) input type.

impl<S> Clone for Matrix4<S>

where S: Clone,

fn clone(&self) -> Matrix4<S>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<S> Debug for Matrix4<S>

where S: Debug,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<'a> Div<&'a Matrix4<u32>> for u32

type Output = Matrix4<u32>

The resulting type after applying the / operator.

fn div(self, other: &'a Matrix4<u32>) -> Matrix4<u32>

Performs the / operation.

impl Div<Matrix4<u32>> for u32

type Output = Matrix4<u32>

The resulting type after applying the / operator.

fn div(self, other: Matrix4<u32>) -> Matrix4<u32>

Performs the / operation.

impl<'a, S> Div<S> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the / operator.

fn div(self, other: S) -> Matrix4<S>

Performs the / operation.

impl<S> Div<S> for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the / operator.

fn div(self, other: S) -> Matrix4<S>

Performs the / operation.

impl<S> DivAssign<S> for Matrix4<S>

where S: BaseFloat + DivAssign,

fn div_assign(&mut self, scalar: S)

Performs the /= operation.

impl<'a, S> From<&'a [[S; 4]; 4]> for &'a Matrix4<S>

fn from(m: &'a [[S; 4]; 4]) -> &'a Matrix4<S>

Converts to this type from the input type.

impl<'a, S> From<&'a [S; 16]> for &'a Matrix4<S>

fn from(m: &'a [S; 16]) -> &'a Matrix4<S>

Converts to this type from the input type.

impl<'a, S> From<&'a mut [[S; 4]; 4]> for &'a mut Matrix4<S>

fn from(m: &'a mut [[S; 4]; 4]) -> &'a mut Matrix4<S>

Converts to this type from the input type.

impl<'a, S> From<&'a mut [S; 16]> for &'a mut Matrix4<S>

fn from(m: &'a mut [S; 16]) -> &'a mut Matrix4<S>

Converts to this type from the input type.

impl<S> From<[[S; 4]; 4]> for Matrix4<S>

where S: Copy,

fn from(m: [[S; 4]; 4]) -> Matrix4<S>

Converts to this type from the input type.

impl<S, R> From<Decomposed<Vector3<S>, R>> for Matrix4<S>

where S: BaseFloat, R: Rotation3<Scalar = S>,

fn from(dec: Decomposed<Vector3<S>, R>) -> Matrix4<S>

Converts to this type from the input type.

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 as Angle>::Unitless>

Converts to this type from the input type.

impl<S> From<Matrix2<S>> for Matrix4<S>

where S: BaseFloat,

fn from(m: Matrix2<S>) -> Matrix4<S>

Clone the elements of a 2-dimensional matrix into the top-left corner of a 4-dimensional identity matrix.

impl<S> From<Matrix3<S>> for Matrix4<S>

where S: BaseFloat,

fn from(m: Matrix3<S>) -> Matrix4<S>

Clone the elements of a 3-dimensional matrix into the top-left corner of a 4-dimensional identity matrix.

impl<S> From<Ortho<S>> for Matrix4<S>

where S: BaseFloat,

fn from(ortho: Ortho<S>) -> Matrix4<S>

Converts to this type from the input type.

impl<S> From<Perspective<S>> for Matrix4<S>

where S: BaseFloat,

fn from(persp: Perspective<S>) -> Matrix4<S>

Converts to this type from the input type.

impl<S> From<PerspectiveFov<S>> for Matrix4<S>

where S: BaseFloat,

fn from(persp: PerspectiveFov<S>) -> Matrix4<S>

Converts to this type from the input type.

impl<S> From<Quaternion<S>> for Matrix4<S>

where S: BaseFloat,

fn from(quat: Quaternion<S>) -> Matrix4<S>

Convert the quaternion to a 4 x 4 rotation matrix.

impl<S> Index<usize> for Matrix4<S>

type Output = Vector4<S>

The returned type after indexing.

fn index<'a>(&'a self, i: usize) -> &'a Vector4<S>

Performs the indexing (container[index]) operation.

impl<S> IndexMut<usize> for Matrix4<S>

fn index_mut<'a>(&'a mut self, i: usize) -> &'a mut Vector4<S>

Performs the mutable indexing (container[index]) operation.

impl<S> Into<[[S; 4]; 4]> for Matrix4<S>

fn into(self) -> [[S; 4]; 4]

Converts this type into the (usually inferred) input type.

impl<S> Matrix for Matrix4<S>

where S: BaseFloat,

type Column = Vector4<S>

The column vector of the matrix.

type Row = Vector4<S>

The row vector of the matrix.

type Transpose = Matrix4<S>

The result of transposing the matrix

fn row(&self, r: usize) -> Vector4<S>

Get a row from this matrix by-value.

fn swap_rows(&mut self, a: usize, b: usize)

Swap two rows of this array.

fn swap_columns(&mut self, a: usize, b: usize)

Swap two columns of this array.

fn swap_elements(&mut self, a: (usize, usize), b: (usize, usize))

Swap the values at index a and b

fn transpose(&self) -> Matrix4<S>

Transpose this matrix, returning a new matrix.

fn as_ptr(&self) -> *const Self::Scalar

Get the pointer to the first element of the array.

fn as_mut_ptr(&mut self) -> *mut Self::Scalar

Get a mutable pointer to the first element of the array.

fn replace_col(&mut self, c: usize, src: Self::Column) -> Self::Column

Replace a column in the array.

impl<'a, 'b, S> Mul<&'a Matrix4<S>> for &'b Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Matrix4<S>) -> Matrix4<S>

Performs the * operation.

impl<'a, S> Mul<&'a Matrix4<S>> for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Matrix4<S>) -> Matrix4<S>

Performs the * operation.

impl<'a> Mul<&'a Matrix4<u32>> for u32

type Output = Matrix4<u32>

The resulting type after applying the * operator.

fn mul(self, other: &'a Matrix4<u32>) -> Matrix4<u32>

Performs the * operation.

impl<'a, 'b, S> Mul<&'a Vector4<S>> for &'b Matrix4<S>

where S: BaseFloat,

type Output = Vector4<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Vector4<S>) -> Vector4<S>

Performs the * operation.

impl<'a, S> Mul<&'a Vector4<S>> for Matrix4<S>

where S: BaseFloat,

type Output = Vector4<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Vector4<S>) -> Vector4<S>

Performs the * operation.

impl<'a, S> Mul<Matrix4<S>> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the * operator.

fn mul(self, other: Matrix4<S>) -> Matrix4<S>

Performs the * operation.

impl Mul<Matrix4<u32>> for u32

type Output = Matrix4<u32>

The resulting type after applying the * operator.

fn mul(self, other: Matrix4<u32>) -> Matrix4<u32>

Performs the * operation.

impl<'a, S> Mul<S> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the * operator.

fn mul(self, other: S) -> Matrix4<S>

Performs the * operation.

impl<S> Mul<S> for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the * operator.

fn mul(self, other: S) -> Matrix4<S>

Performs the * operation.

impl<'a, S> Mul<Vector4<S>> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Vector4<S>

The resulting type after applying the * operator.

fn mul(self, other: Vector4<S>) -> Vector4<S>

Performs the * operation.

impl<S> Mul<Vector4<S>> for Matrix4<S>

where S: BaseFloat,

type Output = Vector4<S>

The resulting type after applying the * operator.

fn mul(self, other: Vector4<S>) -> Vector4<S>

Performs the * operation.

impl<S> Mul for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the * operator.

fn mul(self, other: Matrix4<S>) -> Matrix4<S>

Performs the * operation.

impl<S> MulAssign<S> for Matrix4<S>

where S: BaseFloat + MulAssign,

fn mul_assign(&mut self, scalar: S)

Performs the *= operation.

impl<'a, S> Neg for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the - operator.

fn neg(self) -> Matrix4<S>

Performs the unary - operation.

impl<S> Neg for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the - operator.

fn neg(self) -> Matrix4<S>

Performs the unary - operation.

impl<S> One for Matrix4<S>

where S: BaseFloat,

fn one() -> Matrix4<S>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

impl<S> PartialEq for Matrix4<S>

where S: PartialEq,

fn eq(&self, other: &Matrix4<S>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<'a, S> Product<&'a Matrix4<S>> for Matrix4<S>

where S: 'a + BaseFloat,

fn product<I>(iter: I) -> Matrix4<S>

where I: Iterator<Item = &'a Matrix4<S>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<S> Product for Matrix4<S>

where S: BaseFloat,

fn product<I>(iter: I) -> Matrix4<S>

where I: Iterator<Item = Matrix4<S>>,

Takes an iterator and generates Self from the elements by multiplying the items.

impl<S> RelativeEq for Matrix4<S>

where S: BaseFloat,

fn default_max_relative() -> <S as AbsDiffEq>::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq( &self, other: &Matrix4<S>, epsilon: <S as AbsDiffEq>::Epsilon, max_relative: <S as AbsDiffEq>::Epsilon, ) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon, ) -> bool

The inverse of RelativeEq::relative_eq.

impl<'a> Rem<&'a Matrix4<u32>> for u32

type Output = Matrix4<u32>

The resulting type after applying the % operator.

fn rem(self, other: &'a Matrix4<u32>) -> Matrix4<u32>

Performs the % operation.

impl Rem<Matrix4<u32>> for u32

type Output = Matrix4<u32>

The resulting type after applying the % operator.

fn rem(self, other: Matrix4<u32>) -> Matrix4<u32>

Performs the % operation.

impl<'a, S> Rem<S> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the % operator.

fn rem(self, other: S) -> Matrix4<S>

Performs the % operation.

impl<S> Rem<S> for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the % operator.

fn rem(self, other: S) -> Matrix4<S>

Performs the % operation.

impl<S> RemAssign<S> for Matrix4<S>

where S: BaseFloat + RemAssign,

fn rem_assign(&mut self, scalar: S)

Performs the %= operation.

impl<S> SquareMatrix for Matrix4<S>

where S: BaseFloat,

type ColumnRow = Vector4<S>

The row/column vector of the matrix.

fn from_value(value: S) -> Matrix4<S>

Create a new diagonal matrix using the supplied value.

fn from_diagonal(value: Vector4<S>) -> Matrix4<S>

Create a matrix from a non-uniform scale

fn transpose_self(&mut self)

Transpose this matrix in-place.

fn determinant(&self) -> S

Take the determinant of this matrix.

fn diagonal(&self) -> Vector4<S>

Return a vector containing the diagonal of this matrix.

fn invert(&self) -> Option<Matrix4<S>>

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 is_diagonal(&self) -> bool

Test if this is a diagonal matrix. That is, every element outside of the diagonal is 0.

fn is_symmetric(&self) -> bool

Test if this matrix is symmetric. That is, it is equal to its transpose.

fn identity() -> Self

The identity matrix. Multiplying this matrix with another should have no effect.

fn trace(&self) -> Self::Scalar

Return the trace of this matrix. That is, the sum of the diagonal.

fn is_identity(&self) -> bool

where Self: UlpsEq,

Test if this matrix is the identity matrix. That is, it is diagonal and every element in the diagonal is one.

impl<'a, 'b, S> Sub<&'a Matrix4<S>> for &'b Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the - operator.

fn sub(self, other: &'a Matrix4<S>) -> Matrix4<S>

Performs the - operation.

impl<'a, S> Sub<&'a Matrix4<S>> for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the - operator.

fn sub(self, other: &'a Matrix4<S>) -> Matrix4<S>

Performs the - operation.

impl<'a, S> Sub<Matrix4<S>> for &'a Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the - operator.

fn sub(self, other: Matrix4<S>) -> Matrix4<S>

Performs the - operation.

impl<S> Sub for Matrix4<S>

where S: BaseFloat,

type Output = Matrix4<S>

The resulting type after applying the - operator.

fn sub(self, other: Matrix4<S>) -> Matrix4<S>

Performs the - operation.

impl<S> SubAssign for Matrix4<S>

where S: BaseFloat + SubAssign,

fn sub_assign(&mut self, other: Matrix4<S>)

Performs the -= operation.

impl<'a, S> Sum<&'a Matrix4<S>> for Matrix4<S>

where S: 'a + BaseFloat,

fn sum<I>(iter: I) -> Matrix4<S>

where I: Iterator<Item = &'a Matrix4<S>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<S> Sum for Matrix4<S>

where S: BaseFloat,

fn sum<I>(iter: I) -> Matrix4<S>

where I: Iterator<Item = Matrix4<S>>,

Takes an iterator and generates Self from the elements by “summing up” the items.

impl<S> Transform<Point3<S>> for Matrix4<S>

where S: BaseFloat,

fn look_at(eye: Point3<S>, center: Point3<S>, up: Vector3<S>) -> Matrix4<S>

👎Deprecated: Use look_at_rh or look_at_lh

Create a transformation that rotates a vector to look at center from eye, using up for orientation.

fn look_at_lh(eye: Point3<S>, center: Point3<S>, up: Vector3<S>) -> Matrix4<S>

Create a transformation that rotates a vector to look at center from eye, using up for orientation.

fn look_at_rh(eye: Point3<S>, center: Point3<S>, up: Vector3<S>) -> Matrix4<S>

Create a transformation that rotates a vector to look at center from eye, using up for orientation.

fn transform_vector(&self, vec: Vector3<S>) -> Vector3<S>

Transform a vector using this transform.

fn transform_point(&self, point: Point3<S>) -> Point3<S>

Transform a point using this transform.

fn concat(&self, other: &Matrix4<S>) -> Matrix4<S>

Combine this transform with another, yielding a new transformation which has the effects of both.

fn inverse_transform(&self) -> Option<Matrix4<S>>

Create a transform that “un-does” this one.

fn inverse_transform_vector( &self, vec: <P as EuclideanSpace>::Diff, ) -> Option<<P as EuclideanSpace>::Diff>

Inverse transform a vector using this transform

fn concat_self(&mut self, other: &Self)

Combine this transform with another, in-place.

impl<S> Transform3 for Matrix4<S>

where S: BaseFloat,

type Scalar = S

impl<S> UlpsEq for Matrix4<S>

where S: BaseFloat,

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq( &self, other: &Matrix4<S>, epsilon: <S as AbsDiffEq>::Epsilon, max_ulps: u32, ) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.

impl<S> VectorSpace for Matrix4<S>

where S: BaseFloat,

type Scalar = S

The associated scalar.

fn lerp(self, other: Self, amount: Self::Scalar) -> Self

Returns the result of linearly interpolating the vector towards other by the specified amount.

impl<S> Zero for Matrix4<S>

where S: BaseFloat,

fn zero() -> Matrix4<S>

Returns the additive identity element of Self, 0.

fn is_zero(&self) -> bool

Returns true if self is equal to the additive identity.

fn set_zero(&mut self)

Sets self to the additive identity element of Self, 0.

impl<S> Copy for Matrix4<S>

where S: Copy,

impl<S> StructuralPartialEq for Matrix4<S>