Struct SymmetricMat4 

pub struct SymmetricMat4 {
    pub m00: f32,
    pub m01: f32,
    pub m02: f32,
    pub m03: f32,
    pub m11: f32,
    pub m12: f32,
    pub m13: f32,
    pub m22: f32,
    pub m23: f32,
    pub m33: f32,
}

The bottom left triangle (including the diagonal) of a symmetric 4x4 column-major matrix.

This is useful for storing a symmetric 4x4 matrix in a more compact form and performing some matrix operations more efficiently.

Some defining properties of symmetric matrices include:

• The matrix is equal to its transpose.
• The matrix has real eigenvalues.
• The eigenvectors corresponding to the eigenvalues are orthogonal.
• The matrix is always diagonalizable.

The sum and difference of two symmetric matrices is always symmetric. However, the product of two symmetric matrices is only symmetric if the matrices are commutable, meaning that AB = BA.

Fields

m00: f32

The first element of the first column.

m01: f32

The second element of the first column.

m02: f32

The third element of the first column.

m03: f32

The fourth element of the first column.

m11: f32

The second element of the second column.

m12: f32

The third element of the second column.

m13: f32

The fourth element of the second column.

m22: f32

The third element of the third column.

m23: f32

The fourth element of the third column.

m33: f32

The fourth element of the fourth column.

Implementations

impl SymmetricMat4

pub const ZERO: Self

A symmetric 4x4 matrix with all elements set to 0.0.

pub const IDENTITY: Self

A symmetric 4x4 identity matrix, where all diagonal elements are 1.0, and all off-diagonal elements are 0.0.

pub const NAN: Self

All NaNs.

pub const fn new( m00: f32, m01: f32, m02: f32, m03: f32, m11: f32, m12: f32, m13: f32, m22: f32, m23: f32, m33: f32, ) -> Self

Creates a new symmetric 4x4 matrix from its bottom left triangle, including diagonal elements.

The elements are in column-major order mCR, where C is the column index and R is the row index.

pub fn from_cols_unchecked( x_axis: Vec4, y_axis: Vec4, z_axis: Vec4, w_axis: Vec4, ) -> Self

Creates a symmetric 4x4 matrix from four column vectors.

Only the lower left triangle of the matrix is used. No check is performed to ensure that the given columns truly produce a symmetric matrix.

pub const fn from_cols_array_unchecked(m: &[f32; 16]) -> Self

Creates a symmetric 4x4 matrix from an array stored in column major order.

Only the lower left triangle of the matrix is used. No check is performed to ensure that the given columns truly produce a symmetric matrix.

pub const fn to_cols_array(&self) -> [f32; 16]

Creates an array storing data in column major order.

pub fn from_cols_array_2d_unchecked(m: &[[f32; 4]; 4]) -> Self

Creates a symmetric 4x4 matrix from a 2D array stored in column major order.

Only the lower left triangle of the matrix is used. No check is performed to ensure that the given columns truly produce a symmetric matrix.

pub const fn to_cols_array_2d(&self) -> [[f32; 4]; 4]

Creates a 2D array storing data in column major order.

pub const fn from_cols_slice(slice: &[f32]) -> Self

Creates a 4x4 matrix from the first 16 values in slice.

Only the lower left triangle of the matrix is used. No check is performed to ensure that the given columns truly produce a symmetric matrix.

Panics

Panics if slice is less than 16 elements long.

pub fn from_diagonal(diagonal: Vec4) -> Self

Creates a symmetric 4x4 matrix with its diagonal set to diagonal and all other entries set to 0.0.

pub fn try_from_mat4(mat: Mat4) -> Result<Self, MatConversionError>

Tries to create a symmetric 4x4 matrix from a 4x4 matrix.

Errors

Returns a MatConversionError if the given matrix is not symmetric.

pub fn from_mat4_unchecked(mat: Mat4) -> Self

Creates a symmetric 4x4 matrix from a 4x4 matrix.

Only the lower left triangle of the matrix is used. No check is performed to ensure that the given matrix is truly symmetric.

pub const fn to_mat4(&self) -> Mat4

Creates a 4x4 matrix from the symmetric 4x4 matrix in self.

pub fn from_outer_product(v: Vec4) -> Self

Creates a new symmetric 4x4 matrix from the outer product v * v^T.

pub const fn col(&self, index: usize) -> Vec4

Returns the matrix column for the given index.

Panics

Panics if index is greater than 3.

pub const fn row(&self, index: usize) -> Vec4

Returns the matrix row for the given index.

Panics

Panics if index is greater than 3.

pub fn diagonal(&self) -> Vec4

Returns the diagonal of the matrix.

pub fn is_finite(&self) -> bool

Returns true if, and only if, all elements are finite. If any element is either NaN or positive or negative infinity, this will return false.

pub fn is_nan(&self) -> bool

Returns true if any elements are NaN.

pub fn determinant(&self) -> f32

Returns the determinant of self.

pub fn inverse(&self) -> Self

Returns the inverse of self.

If the matrix is not invertible the returned matrix will be invalid.

pub fn inverse_or_zero(&self) -> Self

Returns the inverse of self, or a zero matrix if the matrix is not invertible.

pub fn abs(&self) -> Self

Takes the absolute value of each element in self.

pub fn mul_vec4(&self, rhs: Vec4) -> Vec4

Transforms a 4D vector.

pub fn mul_mat4(&self, rhs: &Mat4) -> Mat4

Multiplies two 4x4 matrices.

pub fn add_mat4(&self, rhs: &Mat4) -> Mat4

Adds two 4x4 matrices.

pub fn sub_mat4(&self, rhs: &Mat4) -> Mat4

Subtracts two 4x4 matrices.

pub fn mul_symmetric_mat4(&self, rhs: &Self) -> Mat4

Multiplies two symmetric 4x4 matrices.

pub fn add_symmetric_mat4(&self, rhs: &Self) -> Self

Adds two symmetric 4x4 matrices.

pub fn sub_symmetric_mat4(&self, rhs: &Self) -> Self

Subtracts two symmetric 4x4 matrices.

pub fn mul_scalar(&self, rhs: f32) -> Self

Multiplies a 4x4 matrix by a scalar.

pub fn div_scalar(&self, rhs: f32) -> Self

Divides a 4x4 matrix by a scalar.

impl SymmetricMat4

pub fn as_symmetric_dmat4(&self) -> SymmetricDMat4

Returns the double precision version of self.

Trait Implementations

impl Add<&&SymmetricMat4> for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl Add<&Mat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: &Mat4) -> Self::Output

Performs the + operation.

impl Add<&Mat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: &Mat4) -> Self::Output

Performs the + operation.

impl Add<&SymmetricMat4> for &Mat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: &SymmetricMat4) -> Self::Output

Performs the + operation.

impl Add<&SymmetricMat4> for Mat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: &SymmetricMat4) -> Self::Output

Performs the + operation.

impl Add<&SymmetricMat4> for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the + operator.

fn add(self, rhs: &Self) -> Self::Output

Performs the + operation.

impl Add<Mat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: Mat4) -> Self::Output

Performs the + operation.

impl Add<Mat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: Mat4) -> Self::Output

Performs the + operation.

impl Add<SymmetricMat4> for Mat4

type Output = Mat4

The resulting type after applying the + operator.

fn add(self, rhs: SymmetricMat4) -> Self::Output

Performs the + operation.

impl Add for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl Add for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self::Output

Performs the + operation.

impl AddAssign<&SymmetricMat4> for Mat4

fn add_assign(&mut self, rhs: &SymmetricMat4)

Performs the += operation.

impl AddAssign<&SymmetricMat4> for SymmetricMat4

fn add_assign(&mut self, rhs: &Self)

Performs the += operation.

impl AddAssign<SymmetricMat4> for Mat4

fn add_assign(&mut self, rhs: SymmetricMat4)

Performs the += operation.

impl AddAssign for SymmetricMat4

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for SymmetricMat4

fn clone(&self) -> SymmetricMat4

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for SymmetricMat4

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

Formats the value using the given formatter.

impl Default for SymmetricMat4

fn default() -> Self

Returns the “default value” for a type.

impl Display for SymmetricMat4

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

Formats the value using the given formatter.

impl Div<&SymmetricMat4> for &f32

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: &SymmetricMat4) -> Self::Output

Performs the / operation.

impl Div<&SymmetricMat4> for f32

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: &SymmetricMat4) -> Self::Output

Performs the / operation.

impl Div<&f32> for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: &f32) -> Self::Output

Performs the / operation.

impl Div<&f32> for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: &f32) -> Self::Output

Performs the / operation.

impl Div<SymmetricMat4> for &f32

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: SymmetricMat4) -> Self::Output

Performs the / operation.

impl Div<SymmetricMat4> for f32

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: SymmetricMat4) -> Self::Output

Performs the / operation.

impl Div<f32> for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> Self::Output

Performs the / operation.

impl Div<f32> for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> Self::Output

Performs the / operation.

impl DivAssign<&f32> for SymmetricMat4

fn div_assign(&mut self, rhs: &f32)

Performs the /= operation.

impl DivAssign<f32> for SymmetricMat4

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl From<SymmetricMat4> for Mat4

fn from(mat: SymmetricMat4) -> Self

Converts to this type from the input type.

impl Mul<&&SymmetricMat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: &Self) -> Self::Output

Performs the * operation.

impl Mul<&Mat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: &Mat4) -> Self::Output

Performs the * operation.

impl Mul<&Mat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: &Mat4) -> Self::Output

Performs the * operation.

impl Mul<&SymmetricMat4> for &Mat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: &SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<&SymmetricMat4> for &f32

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: &SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<&SymmetricMat4> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: &SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<&SymmetricMat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: &Self) -> Self::Output

Performs the * operation.

impl Mul<&SymmetricMat4> for f32

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: &SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<&Vec4> for &SymmetricMat4

type Output = Vec4

The resulting type after applying the * operator.

fn mul(self, rhs: &Vec4) -> Self::Output

Performs the * operation.

impl Mul<&Vec4> for SymmetricMat4

type Output = Vec4

The resulting type after applying the * operator.

fn mul(self, rhs: &Vec4) -> Self::Output

Performs the * operation.

impl Mul<&f32> for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: &f32) -> Self::Output

Performs the * operation.

impl Mul<&f32> for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: &f32) -> Self::Output

Performs the * operation.

impl Mul<Mat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: Mat4) -> Self::Output

Performs the * operation.

impl Mul<Mat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: Mat4) -> Self::Output

Performs the * operation.

impl Mul<SymmetricMat4> for &Mat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<SymmetricMat4> for &f32

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<SymmetricMat4> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<SymmetricMat4> for f32

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: SymmetricMat4) -> Self::Output

Performs the * operation.

impl Mul<Vec4> for &SymmetricMat4

type Output = Vec4

The resulting type after applying the * operator.

fn mul(self, rhs: Vec4) -> Self::Output

Performs the * operation.

impl Mul<Vec4> for SymmetricMat4

type Output = Vec4

The resulting type after applying the * operator.

fn mul(self, rhs: Vec4) -> Self::Output

Performs the * operation.

impl Mul<f32> for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> Self::Output

Performs the * operation.

impl Mul<f32> for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> Self::Output

Performs the * operation.

impl Mul for &SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl Mul for SymmetricMat4

type Output = Mat4

The resulting type after applying the * operator.

fn mul(self, rhs: Self) -> Self::Output

Performs the * operation.

impl MulAssign<&SymmetricMat4> for Mat4

fn mul_assign(&mut self, rhs: &SymmetricMat4)

Performs the *= operation.

impl MulAssign<&f32> for SymmetricMat4

fn mul_assign(&mut self, rhs: &f32)

Performs the *= operation.

impl MulAssign<SymmetricMat4> for Mat4

fn mul_assign(&mut self, rhs: SymmetricMat4)

Performs the *= operation.

impl MulAssign<f32> for SymmetricMat4

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl Neg for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl Neg for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the - operator.

fn neg(self) -> Self::Output

Performs the unary - operation.

impl PartialEq for SymmetricMat4

fn eq(&self, other: &SymmetricMat4) -> 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 Sub<&&SymmetricMat4> for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl Sub<&Mat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: &Mat4) -> Self::Output

Performs the - operation.

impl Sub<&Mat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: &Mat4) -> Self::Output

Performs the - operation.

impl Sub<&SymmetricMat4> for &Mat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: &SymmetricMat4) -> Self::Output

Performs the - operation.

impl Sub<&SymmetricMat4> for Mat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: &SymmetricMat4) -> Self::Output

Performs the - operation.

impl Sub<&SymmetricMat4> for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the - operator.

fn sub(self, rhs: &Self) -> Self::Output

Performs the - operation.

impl Sub<Mat4> for &SymmetricMat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: Mat4) -> Self::Output

Performs the - operation.

impl Sub<Mat4> for SymmetricMat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: Mat4) -> Self::Output

Performs the - operation.

impl Sub<SymmetricMat4> for Mat4

type Output = Mat4

The resulting type after applying the - operator.

fn sub(self, rhs: SymmetricMat4) -> Self::Output

Performs the - operation.

impl Sub for &SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl Sub for SymmetricMat4

type Output = SymmetricMat4

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self::Output

Performs the - operation.

impl SubAssign<&SymmetricMat4> for Mat4

fn sub_assign(&mut self, rhs: &SymmetricMat4)

Performs the -= operation.

impl SubAssign<&SymmetricMat4> for SymmetricMat4

fn sub_assign(&mut self, rhs: &Self)

Performs the -= operation.

impl SubAssign<SymmetricMat4> for Mat4

fn sub_assign(&mut self, rhs: SymmetricMat4)

Performs the -= operation.

impl SubAssign for SymmetricMat4

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl<'a> Sum<&'a SymmetricMat4> for SymmetricMat4

fn sum<I: Iterator<Item = &'a SymmetricMat4>>(iter: I) -> Self

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

impl Sum for SymmetricMat4

fn sum<I: Iterator<Item = SymmetricMat4>>(iter: I) -> Self

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

impl TryFrom<Mat4> for SymmetricMat4

type Error = MatConversionError

The type returned in the event of a conversion error.

fn try_from(mat: Mat4) -> Result<Self, Self::Error>

Performs the conversion.

impl Copy for SymmetricMat4

impl StructuralPartialEq for SymmetricMat4