Struct valence_math::Mat3

#[repr(C)]
pub struct Mat3 {
    pub x_axis: Vec3,
    pub y_axis: Vec3,
    pub z_axis: Vec3,
}

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 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.

Fields

x_axis: Vec3

y_axis: Vec3

z_axis: Vec3

Implementations

impl Mat3

pub const ZERO: Mat3 = _

A 3x3 matrix with all elements set to 0.0.

pub const IDENTITY: Mat3 = _

A 3x3 identity matrix, where all diagonal elements are 1, and all off-diagonal elements are 0.

pub const NAN: Mat3 = _

All NAN:s.

pub const fn from_cols(x_axis: Vec3, y_axis: Vec3, z_axis: Vec3) -> Mat3

Creates a 3x3 matrix from three column vectors.

pub const fn from_cols_array(m: &[f32; 9]) -> Mat3

Creates a 3x3 matrix from a [f32; 9] array stored in column major order. If your data is stored in row major you will need to transpose the returned matrix.

pub const fn to_cols_array(&self) -> [f32; 9]

Creates a [f32; 9] array storing data in column major order. If you require data in row major order transpose the matrix first.

pub const fn from_cols_array_2d(m: &[[f32; 3]; 3]) -> Mat3

Creates a 3x3 matrix from a [[f32; 3]; 3] 3D array stored in column major order. If your data is in row major order you will need to transpose the returned matrix.

pub const fn to_cols_array_2d(&self) -> [[f32; 3]; 3]

Creates a [[f32; 3]; 3] 3D array storing data in column major order. If you require data in row major order transpose the matrix first.

pub const fn from_diagonal(diagonal: Vec3) -> Mat3

Creates a 3x3 matrix with its diagonal set to diagonal and all other entries set to 0.

pub fn from_mat4(m: Mat4) -> Mat3

Creates a 3x3 matrix from a 4x4 matrix, discarding the 4th row and column.

pub fn from_mat4_minor(m: Mat4, i: usize, j: usize) -> Mat3

Creates a 3x3 matrix from the minor of the given 4x4 matrix, discarding the ith column and jth row.

Panics

Panics if i or j is greater than 3.

pub fn from_quat(rotation: Quat) -> Mat3

Creates a 3D rotation matrix from the given quaternion.

Panics

Will panic if rotation is not normalized when glam_assert is enabled.

pub fn from_axis_angle(axis: Vec3, angle: f32) -> Mat3

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.

pub fn from_euler(order: EulerRot, a: f32, b: f32, c: f32) -> Mat3

Creates a 3D rotation matrix from the given euler rotation sequence and the angles (in radians).

pub fn to_euler(&self, order: EulerRot) -> (f32, f32, f32)

Extract Euler angles with the given Euler rotation order.

Note if the input matrix contains scales, shears, or other non-rotation transformations then the resulting Euler angles will be ill-defined.

Panics

Will panic if any input matrix column is not normalized when glam_assert is enabled.

pub fn from_rotation_x(angle: f32) -> Mat3

Creates a 3D rotation matrix from angle (in radians) around the x axis.

pub fn from_rotation_y(angle: f32) -> Mat3

Creates a 3D rotation matrix from angle (in radians) around the y axis.

pub fn from_rotation_z(angle: f32) -> Mat3

Creates a 3D rotation matrix from angle (in radians) around the z axis.

pub fn from_translation(translation: Vec2) -> Mat3

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().

pub fn from_angle(angle: f32) -> Mat3

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().

pub fn from_scale_angle_translation( scale: Vec2, angle: f32, translation: Vec2, ) -> Mat3

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().

pub fn from_scale(scale: Vec2) -> Mat3

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.

pub fn from_mat2(m: Mat2) -> Mat3

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().

pub const fn from_cols_slice(slice: &[f32]) -> Mat3

Creates a 3x3 matrix from the first 9 values in slice.

Panics

Panics if slice is less than 9 elements long.

pub fn write_cols_to_slice(self, slice: &mut [f32])

Writes the columns of self to the first 9 elements in slice.

Panics

Panics if slice is less than 9 elements long.

pub fn col(&self, index: usize) -> Vec3

Returns the matrix column for the given index.

Panics

Panics if index is greater than 2.

pub fn col_mut(&mut self, index: usize) -> &mut Vec3

Returns a mutable reference to the matrix column for the given index.

Panics

Panics if index is greater than 2.

pub fn row(&self, index: usize) -> Vec3

Returns the matrix row for the given index.

Panics

Panics if index is greater than 2.

pub fn is_finite(&self) -> bool

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

pub fn is_nan(&self) -> bool

Returns true if any elements are NaN.

pub fn transpose(&self) -> Mat3

Returns the transpose of self.

pub fn determinant(&self) -> f32

Returns the determinant of self.

pub fn inverse(&self) -> Mat3

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.

pub fn transform_point2(&self, rhs: Vec2) -> Vec2

Transforms the given 2D vector as a point.

This is the equivalent of multiplying rhs as a 3D vector where z is 1.

This method assumes that self contains a valid affine transform.

Panics

Will panic if the 2nd row of self is not (0, 0, 1) when glam_assert is enabled.

pub fn transform_vector2(&self, rhs: Vec2) -> Vec2

Rotates the given 2D vector.

This is the equivalent of multiplying rhs as a 3D vector where z is 0.

This method assumes that self contains a valid affine transform.

Panics

Will panic if the 2nd row of self is not (0, 0, 1) when glam_assert is enabled.

pub fn mul_vec3(&self, rhs: Vec3) -> Vec3

Transforms a 3D vector.

pub fn mul_vec3a(&self, rhs: Vec3A) -> Vec3A

Transforms a Vec3A.

pub fn mul_mat3(&self, rhs: &Mat3) -> Mat3

Multiplies two 3x3 matrices.

pub fn add_mat3(&self, rhs: &Mat3) -> Mat3

Adds two 3x3 matrices.

pub fn sub_mat3(&self, rhs: &Mat3) -> Mat3

Subtracts two 3x3 matrices.

pub fn mul_scalar(&self, rhs: f32) -> Mat3

Multiplies a 3x3 matrix by a scalar.

pub fn div_scalar(&self, rhs: f32) -> Mat3

Divides a 3x3 matrix by a scalar.

pub fn abs_diff_eq(&self, rhs: Mat3, max_abs_diff: f32) -> bool

Returns true if the absolute difference of all elements between self and rhs 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.

pub fn abs(&self) -> Mat3

Takes the absolute value of each element in self

pub fn as_dmat3(&self) -> DMat3

Trait Implementations

impl Add for Mat3

type Output = Mat3

The resulting type after applying the + operator.

fn add(self, rhs: Mat3) -> <Mat3 as Add>::Output

Performs the + operation.

impl AddAssign for Mat3

fn add_assign(&mut self, rhs: Mat3)

Performs the += operation.

impl AsMut<[f32; 9]> for Mat3

fn as_mut(&mut self) -> &mut [f32; 9]

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

impl AsRef<[f32; 9]> for Mat3

fn as_ref(&self) -> &[f32; 9]

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

impl Clone for Mat3

fn clone(&self) -> Mat3

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Mat3

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

Formats the value using the given formatter.

impl Default for Mat3

fn default() -> Mat3

Returns the “default value” for a type.

impl Display for Mat3

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

Formats the value using the given formatter.

impl Div<f32> for Mat3

type Output = Mat3

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> <Mat3 as Div<f32>>::Output

Performs the / operation.

impl DivAssign<f32> for Mat3

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl From<Affine2> for Mat3

fn from(m: Affine2) -> Mat3

Converts to this type from the input type.

impl From<Mat3> for Mat3A

fn from(m: Mat3) -> Mat3A

Converts to this type from the input type.

impl From<Mat3A> for Mat3

fn from(m: Mat3A) -> Mat3

Converts to this type from the input type.

impl Mul<Affine2> for Mat3

type Output = Mat3

The resulting type after applying the * operator.

fn mul(self, rhs: Affine2) -> <Mat3 as Mul<Affine2>>::Output

Performs the * operation.

impl Mul<Mat3> for Affine2

type Output = Mat3

The resulting type after applying the * operator.

fn mul(self, rhs: Mat3) -> <Affine2 as Mul<Mat3>>::Output

Performs the * operation.

impl Mul<Vec3> for Mat3

type Output = Vec3

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3) -> <Mat3 as Mul<Vec3>>::Output

Performs the * operation.

impl Mul<Vec3A> for Mat3

type Output = Vec3A

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3A) -> Vec3A

Performs the * operation.

impl Mul<f32> for Mat3

type Output = Mat3

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> <Mat3 as Mul<f32>>::Output

Performs the * operation.

impl Mul for Mat3

type Output = Mat3

The resulting type after applying the * operator.

fn mul(self, rhs: Mat3) -> <Mat3 as Mul>::Output

Performs the * operation.

impl MulAssign<f32> for Mat3

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl MulAssign for Mat3

fn mul_assign(&mut self, rhs: Mat3)

Performs the *= operation.

impl Neg for Mat3

type Output = Mat3

The resulting type after applying the - operator.

fn neg(self) -> <Mat3 as Neg>::Output

Performs the unary - operation.

impl PartialEq for Mat3

fn eq(&self, rhs: &Mat3) -> 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> Product<&'a Mat3> for Mat3

fn product<I>(iter: I) -> Mat3

where I: Iterator<Item = &'a Mat3>,

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

impl Product for Mat3

fn product<I>(iter: I) -> Mat3

where I: Iterator<Item = Mat3>,

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

impl Sub for Mat3

type Output = Mat3

The resulting type after applying the - operator.

fn sub(self, rhs: Mat3) -> <Mat3 as Sub>::Output

Performs the - operation.

impl SubAssign for Mat3

fn sub_assign(&mut self, rhs: Mat3)

Performs the -= operation.

impl<'a> Sum<&'a Mat3> for Mat3

fn sum<I>(iter: I) -> Mat3

where I: Iterator<Item = &'a Mat3>,

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

impl Sum for Mat3

fn sum<I>(iter: I) -> Mat3

where I: Iterator<Item = Mat3>,

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

impl Copy for Mat3