Struct Mat3A

#[repr(C)]
pub struct Mat3A {
    pub x_axis: Vec3A,
    pub y_axis: Vec3A,
    pub z_axis: Vec3A,
}

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: Vec3A

y_axis: Vec3A

z_axis: Vec3A

Implementations

impl Mat3A

pub const ZERO: Mat3A = _

A 3x3 matrix with all elements set to 0.0.

pub const IDENTITY: Mat3A = _

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

pub const NAN: Mat3A = _

All NAN:s.

pub const fn from_cols(x_axis: Vec3A, y_axis: Vec3A, z_axis: Vec3A) -> Mat3A

Creates a 3x3 matrix from three column vectors.

pub const fn from_cols_array(m: &[f32; 9]) -> Mat3A

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]) -> Mat3A

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) -> Mat3A

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

pub fn from_mat4(m: Mat4) -> Mat3A

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) -> Mat3A

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) -> Mat3A

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) -> Mat3A

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) -> Mat3A

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) -> Mat3A

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

pub fn from_rotation_y(angle: f32) -> Mat3A

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

pub fn from_rotation_z(angle: f32) -> Mat3A

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

pub fn from_translation(translation: Vec2) -> Mat3A

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) -> Mat3A

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, ) -> Mat3A

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) -> Mat3A

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) -> Mat3A

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]) -> Mat3A

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) -> Vec3A

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 Vec3A

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) -> Vec3A

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) -> Mat3A

Returns the transpose of self.

pub fn determinant(&self) -> f32

Returns the determinant of self.

pub fn inverse(&self) -> Mat3A

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: &Mat3A) -> Mat3A

Multiplies two 3x3 matrices.

pub fn add_mat3(&self, rhs: &Mat3A) -> Mat3A

Adds two 3x3 matrices.

pub fn sub_mat3(&self, rhs: &Mat3A) -> Mat3A

Subtracts two 3x3 matrices.

pub fn mul_scalar(&self, rhs: f32) -> Mat3A

Multiplies a 3x3 matrix by a scalar.

pub fn div_scalar(&self, rhs: f32) -> Mat3A

Divides a 3x3 matrix by a scalar.

pub fn abs_diff_eq(&self, rhs: Mat3A, 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) -> Mat3A

Takes the absolute value of each element in self

pub fn as_dmat3(&self) -> DMat3

Trait Implementations

impl Add for Mat3A

type Output = Mat3A

The resulting type after applying the + operator.

fn add(self, rhs: Mat3A) -> <Mat3A as Add>::Output

Performs the + operation.

impl AddAssign for Mat3A

fn add_assign(&mut self, rhs: Mat3A)

Performs the += operation.

impl Clone for Mat3A

fn clone(&self) -> Mat3A

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Mat3A

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

Formats the value using the given formatter.

impl Default for Mat3A

fn default() -> Mat3A

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Mat3A

Deserialize expects a sequence of 9 values.

fn deserialize<D>( deserializer: D, ) -> Result<Mat3A, <D as Deserializer<'de>>::Error>

where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Display for Mat3A

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

Formats the value using the given formatter.

impl Div<f32> for Mat3A

type Output = Mat3A

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> <Mat3A as Div<f32>>::Output

Performs the / operation.

impl DivAssign<f32> for Mat3A

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl From<Affine2> for Mat3A

fn from(m: Affine2) -> Mat3A

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 FromReflect for Mat3A

where Mat3A: Any + Send + Sync, Vec3A: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn from_reflect(reflect: &(dyn PartialReflect + 'static)) -> Option<Mat3A>

Constructs a concrete instance of Self from a reflected value.

fn take_from_reflect( reflect: Box<dyn PartialReflect>, ) -> Result<Self, Box<dyn PartialReflect>>

Attempts to downcast the given value to Self using, constructing the value using from_reflect if that fails.

impl GetTypeRegistration for Mat3A

where Mat3A: Any + Send + Sync, Vec3A: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn get_type_registration() -> TypeRegistration

Returns the default TypeRegistration for this type.

fn register_type_dependencies(registry: &mut TypeRegistry)

Registers other types needed by this type.

impl Mul<Affine2> for Mat3A

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: Affine2) -> <Mat3A as Mul<Affine2>>::Output

Performs the * operation.

impl Mul<Mat3A> for Affine2

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: Mat3A) -> <Affine2 as Mul<Mat3A>>::Output

Performs the * operation.

impl Mul<Vec3> for Mat3A

type Output = Vec3

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3) -> Vec3

Performs the * operation.

impl Mul<Vec3A> for Mat3A

type Output = Vec3A

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3A) -> <Mat3A as Mul<Vec3A>>::Output

Performs the * operation.

impl Mul<f32> for Mat3A

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> <Mat3A as Mul<f32>>::Output

Performs the * operation.

impl Mul for Mat3A

type Output = Mat3A

The resulting type after applying the * operator.

fn mul(self, rhs: Mat3A) -> <Mat3A as Mul>::Output

Performs the * operation.

impl MulAssign<f32> for Mat3A

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl MulAssign for Mat3A

fn mul_assign(&mut self, rhs: Mat3A)

Performs the *= operation.

impl Neg for Mat3A

type Output = Mat3A

The resulting type after applying the - operator.

fn neg(self) -> <Mat3A as Neg>::Output

Performs the unary - operation.

impl PartialEq for Mat3A

fn eq(&self, rhs: &Mat3A) -> 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 PartialReflect for Mat3A

where Mat3A: Any + Send + Sync, Vec3A: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn get_represented_type_info(&self) -> Option<&'static TypeInfo>

Returns the TypeInfo of the type represented by this value.

fn clone_value(&self) -> Box<dyn PartialReflect>

Clones the value as a Reflect trait object.

fn try_apply( &mut self, value: &(dyn PartialReflect + 'static), ) -> Result<(), ApplyError>

Tries to apply a reflected value to this value.

fn reflect_kind(&self) -> ReflectKind

Returns a zero-sized enumeration of “kinds” of type.

fn reflect_ref(&self) -> ReflectRef<'_>

Returns an immutable enumeration of “kinds” of type.

fn reflect_mut(&mut self) -> ReflectMut<'_>

Returns a mutable enumeration of “kinds” of type.

fn reflect_owned(self: Box<Mat3A>) -> ReflectOwned

Returns an owned enumeration of “kinds” of type.

fn try_into_reflect( self: Box<Mat3A>, ) -> Result<Box<dyn Reflect>, Box<dyn PartialReflect>>

Attempts to cast this type to a boxed, fully-reflected value.

fn try_as_reflect(&self) -> Option<&(dyn Reflect + 'static)>

Attempts to cast this type to a fully-reflected value.

fn try_as_reflect_mut(&mut self) -> Option<&mut (dyn Reflect + 'static)>

Attempts to cast this type to a mutable, fully-reflected value.

fn into_partial_reflect(self: Box<Mat3A>) -> Box<dyn PartialReflect>

Casts this type to a boxed, reflected value.

fn as_partial_reflect(&self) -> &(dyn PartialReflect + 'static)

Casts this type to a reflected value.

fn as_partial_reflect_mut(&mut self) -> &mut (dyn PartialReflect + 'static)

Casts this type to a mutable, reflected value.

fn reflect_partial_eq( &self, value: &(dyn PartialReflect + 'static), ) -> Option<bool>

Returns a “partial equality” comparison result.

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

Debug formatter for the value.

fn apply(&mut self, value: &(dyn PartialReflect + 'static))

Applies a reflected value to this value.

fn reflect_hash(&self) -> Option<u64>

Returns a hash of the value (which includes the type).

fn serializable(&self) -> Option<Serializable<'_>>

Returns a serializable version of the value.

fn is_dynamic(&self) -> bool

Indicates whether or not this type is a dynamic type.

impl<'a> Product<&'a Mat3A> for Mat3A

fn product<I>(iter: I) -> Mat3A

where I: Iterator<Item = &'a Mat3A>,

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

impl Product for Mat3A

fn product<I>(iter: I) -> Mat3A

where I: Iterator<Item = Mat3A>,

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

impl Reflect for Mat3A

where Mat3A: Any + Send + Sync, Vec3A: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn into_any(self: Box<Mat3A>) -> Box<dyn Any>

Returns the value as a Box<dyn Any>.

fn as_any(&self) -> &(dyn Any + 'static)

Returns the value as a &dyn Any.

fn as_any_mut(&mut self) -> &mut (dyn Any + 'static)

Returns the value as a &mut dyn Any.

fn into_reflect(self: Box<Mat3A>) -> Box<dyn Reflect>

Casts this type to a boxed, fully-reflected value.

fn as_reflect(&self) -> &(dyn Reflect + 'static)

Casts this type to a fully-reflected value.

fn as_reflect_mut(&mut self) -> &mut (dyn Reflect + 'static)

Casts this type to a mutable, fully-reflected value.

fn set(&mut self, value: Box<dyn Reflect>) -> Result<(), Box<dyn Reflect>>

Performs a type-checked assignment of a reflected value to this value.

impl Serialize for Mat3A

Serialize as a sequence of 9 values.

fn serialize<S>( &self, serializer: S, ) -> Result<<S as Serializer>::Ok, <S as Serializer>::Error>

where S: Serializer,

Serialize this value into the given Serde serializer.

impl Struct for Mat3A

where Mat3A: Any + Send + Sync, Vec3A: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn field(&self, name: &str) -> Option<&(dyn PartialReflect + 'static)>

Returns a reference to the value of the field named name as a &dyn PartialReflect.

fn field_mut( &mut self, name: &str, ) -> Option<&mut (dyn PartialReflect + 'static)>

Returns a mutable reference to the value of the field named name as a &mut dyn PartialReflect.

fn field_at(&self, index: usize) -> Option<&(dyn PartialReflect + 'static)>

Returns a reference to the value of the field with index index as a &dyn PartialReflect.

fn field_at_mut( &mut self, index: usize, ) -> Option<&mut (dyn PartialReflect + 'static)>

Returns a mutable reference to the value of the field with index index as a &mut dyn PartialReflect.

fn name_at(&self, index: usize) -> Option<&str>

Returns the name of the field with index index.

fn field_len(&self) -> usize

Returns the number of fields in the struct.

fn iter_fields(&self) -> FieldIter<'_>

Returns an iterator over the values of the reflectable fields for this struct.

fn clone_dynamic(&self) -> DynamicStruct

Clones the struct into a DynamicStruct.

fn get_represented_struct_info(&self) -> Option<&'static StructInfo>

Will return None if TypeInfo is not available.

impl Sub for Mat3A

type Output = Mat3A

The resulting type after applying the - operator.

fn sub(self, rhs: Mat3A) -> <Mat3A as Sub>::Output

Performs the - operation.

impl SubAssign for Mat3A

fn sub_assign(&mut self, rhs: Mat3A)

Performs the -= operation.

impl<'a> Sum<&'a Mat3A> for Mat3A

fn sum<I>(iter: I) -> Mat3A

where I: Iterator<Item = &'a Mat3A>,

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

impl Sum for Mat3A

fn sum<I>(iter: I) -> Mat3A

where I: Iterator<Item = Mat3A>,

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

impl TypePath for Mat3A

where Mat3A: Any + Send + Sync,

fn type_path() -> &'static str

Returns the fully qualified path of the underlying type.

fn short_type_path() -> &'static str

Returns a short, pretty-print enabled path to the type.

fn type_ident() -> Option<&'static str>

Returns the name of the type, or None if it is anonymous.

fn crate_name() -> Option<&'static str>

Returns the name of the crate the type is in, or None if it is anonymous.

fn module_path() -> Option<&'static str>

Returns the path to the module the type is in, or None if it is anonymous.

impl Typed for Mat3A

where Mat3A: Any + Send + Sync, Vec3A: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn type_info() -> &'static TypeInfo

Returns the compile-time info for the underlying type.

impl Zeroable for Mat3A

fn zeroed() -> Self

Calls zeroed.

impl AnyBitPattern for Mat3A

impl Copy for Mat3A