Struct nannou::prelude::Mat4

#[repr(align(16))]
pub struct Mat4(_);

A 4x4 column major matrix.

This 4x4 matrix type features convenience methods for creating and using affine transforms and perspective projections. If you are primarily dealing with 3D affine transformations condidering using Affine3A which is faster tha a 4x4 matrix for some affine operations.

Affine transformations including 3D translation, rotation and scale can be created using methods such as Self::from_translation(), Self::from_quat(), Self::from_scale() and Self::from_scale_rotation_translation().

Othographic projections can be created using the methods Self::orthographic_lh() for left-handed coordinate systems and Self::orthographic_rh() for right-handed systems. The resulting matrix is also an affine transformation.

The Self::transform_point3() and Self::transform_vector3() convenience methods are provided for performing affine transformations on 3D vectors and points. These multiply 3D inputs as 4D vectors with an implicit w value of 1 for points and 0 for vectors respectively. These methods assume that Self contains a valid affine transform.

Perspective projections can be created using methods such as Self::perspective_lh(), Self::perspective_infinite_lh() and Self::perspective_infinite_reverse_lh() for left-handed co-ordinate systems and Self::perspective_rh(), Self::perspective_infinite_rh() and Self::perspective_infinite_reverse_rh() for right-handed co-ordinate systems.

The resulting perspective project can be use to transform 3D vectors as points with perspective correction using the Self::project_point3() convenience method.

Implementations

impl Mat4

pub const ZERO: Mat4

A 4x4 matrix with all elements set to 0.0.

pub const IDENTITY: Mat4

A 4x4 identity matrix, where all diagonal elements are 1, and all off-diagonal elements are 0.

pub fn from_cols(x_axis: Vec4, y_axis: Vec4, z_axis: Vec4, w_axis: Vec4) -> Mat4

Creates a 4x4 matrix from four column vectors.

pub fn from_cols_array(m: &[f32; 16]) -> Mat4

Creates a 4x4 matrix from a [S; 16] array stored in column major order. If your data is stored in row major you will need to transpose the returned matrix.

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

Creates a [S; 16] array storing data in column major order. If you require data in row major order transpose the matrix first.

pub fn from_cols_array_2d(m: &[[f32; 4]; 4]) -> Mat4

Creates a 4x4 matrix from a [[S; 4]; 4] 2D array stored in column major order. If your data is in row major order you will need to transpose the returned matrix.

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

Creates a [[S; 4]; 4] 2D array storing data in column major order. If you require data in row major order transpose the matrix first.

pub fn from_diagonal(diagonal: Vec4) -> Mat4

Creates a 4x4 matrix with its diagonal set to diagonal and all other entries set to 0.

pub fn from_scale_rotation_translation(
    scale: Vec3,
    rotation: Quat,
    translation: Vec3
) -> Mat4

Creates an affine transformation matrix from the given 3D scale, rotation and translation.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_translation(rotation: Quat, translation: Vec3) -> Mat4

Creates an affine transformation matrix from the given 3D translation.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn to_scale_rotation_translation(&self) -> (Vec3, Quat, Vec3)

Extracts scale, rotation and translation from self. The input matrix is expected to be a 3D affine transformation matrix otherwise the output will be invalid.

pub fn from_quat(rotation: Quat) -> Mat4

Creates an affine transformation matrix from the given rotation quaternion.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_translation(translation: Vec3) -> Mat4

Creates an affine transformation matrix from the given 3D translation.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_axis_angle(axis: Vec3, angle: f32) -> Mat4

Creates an affine transformation matrix containing a 3D rotation around a normalized rotation axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_ypr(yaw: f32, pitch: f32, roll: f32) -> Mat4

👎 Deprecated since 0.15.0:

Please use from_euler(EulerRot::YXZ, yaw, pitch, roll) instead

pub fn from_euler(order: EulerRot, a: f32, b: f32, c: f32) -> Mat4

Creates a affine transformation matrix containing a rotation from the given euler rotation sequence and angles (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_x(angle: f32) -> Mat4

Creates an affine transformation matrix containing a 3D rotation around the x axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_y(angle: f32) -> Mat4

Creates an affine transformation matrix containing a 3D rotation around the y axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_rotation_z(angle: f32) -> Mat4

Creates an affine transformation matrix containing a 3D rotation around the z axis of angle (in radians).

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_scale(scale: Vec3) -> Mat4

Creates an affine transformation matrix containing the given 3D non-uniform scale.

The resulting matrix can be used to transform 3D points and vectors. See Self::transform_point3() and Self::transform_vector3().

pub fn from_cols_slice(slice: &[f32]) -> Mat4

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

Panics

Panics if slice is less than 16 elements long.

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

Writes the columns of self to the first 16 elements in slice.

Panics

Panics if slice is less than 16 elements long.

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

Returns the matrix column for the given index.

Panics

Panics if index is greater than 3.

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

Returns the matrix row for the given index.

Panics

Panics if index is greater than 3.

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) -> Mat4

Returns the transpose of self.

pub fn determinant(&self) -> f32

Returns the determinant of self.

pub fn inverse(&self) -> Mat4

Returns the inverse of self.

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

pub fn look_at_lh(eye: Vec3, center: Vec3, up: Vec3) -> Mat4

Creates a left-handed view matrix using a camera position, an up direction, and a focal point. For a view coordinate system with +X=right, +Y=up and +Z=forward.

pub fn look_at_rh(eye: Vec3, center: Vec3, up: Vec3) -> Mat4

Creates a right-handed view matrix using a camera position, an up direction, and a focal point. For a view coordinate system with +X=right, +Y=up and +Z=back.

pub fn perspective_rh_gl(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32,
    z_far: f32
) -> Mat4

Creates a right-handed perspective projection matrix with [-1,1] depth range. This is the same as the OpenGL gluPerspective function. See https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml

pub fn perspective_lh(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32,
    z_far: f32
) -> Mat4

Creates a left-handed perspective projection matrix with [0,1] depth range.

pub fn perspective_rh(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32,
    z_far: f32
) -> Mat4

Creates a right-handed perspective projection matrix with [0,1] depth range.

pub fn perspective_infinite_lh(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32
) -> Mat4

Creates an infinite left-handed perspective projection matrix with [0,1] depth range.

pub fn perspective_infinite_reverse_lh(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32
) -> Mat4

Creates an infinite left-handed perspective projection matrix with [0,1] depth range.

pub fn perspective_infinite_rh(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32
) -> Mat4

Creates an infinite right-handed perspective projection matrix with [0,1] depth range.

pub fn perspective_infinite_reverse_rh(
    fov_y_radians: f32,
    aspect_ratio: f32,
    z_near: f32
) -> Mat4

Creates an infinite reverse right-handed perspective projection matrix with [0,1] depth range.

pub fn orthographic_rh_gl(
    left: f32,
    right: f32,
    bottom: f32,
    top: f32,
    near: f32,
    far: f32
) -> Mat4

Creates a right-handed orthographic projection matrix with [-1,1] depth range. This is the same as the OpenGL glOrtho function in OpenGL. See https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/glOrtho.xml

pub fn orthographic_lh(
    left: f32,
    right: f32,
    bottom: f32,
    top: f32,
    near: f32,
    far: f32
) -> Mat4

Creates a left-handed orthographic projection matrix with [0,1] depth range.

pub fn orthographic_rh(
    left: f32,
    right: f32,
    bottom: f32,
    top: f32,
    near: f32,
    far: f32
) -> Mat4

Creates a right-handed orthographic projection matrix with [0,1] depth range.

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

Transforms a 4D vector.

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

Multiplies two 4x4 matrices.

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

Adds two 4x4 matrices.

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

Subtracts two 4x4 matrices.

pub fn mul_scalar(&self, other: f32) -> Mat4

Multiplies this matrix by a scalar value.

pub fn project_point3(&self, other: Vec3) -> Vec3

Transforms the given 3D vector as a point, applying perspective correction.

This is the equivalent of multiplying the 3D vector as a 4D vector where w is 1.0. The perspective divide is performed meaning the resulting 3D vector is divided by w.

This method assumes that self contains a projective transform.

pub fn transform_point3(&self, other: Vec3) -> Vec3

Transforms the given 3D vector as a point.

This is the equivalent of multiplying the 3D vector as a 4D vector where w is 1.0.

This method assumes that self contains a valid affine transform. It does not perform a persective divide, if self contains a perspective transform, or if you are unsure, the Self::project_point3() method should be used instead.

pub fn transform_vector3(&self, other: Vec3) -> Vec3

Transforms the give 3D vector as a direction.

This is the equivalent of multiplying the 3D vector as a 4D vector where w is 0.0.

This method assumes that self contains a valid affine transform.

pub fn abs_diff_eq(&self, other: Mat4, max_abs_diff: f32) -> bool

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 4x4 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 transform_point3a(&self, other: Vec3A) -> Vec3A

Transforms the given Vec3A as 3D point.

This is the equivalent of multiplying the Vec3A as a 4D vector where w is 1.0.

pub fn transform_vector3a(&self, other: Vec3A) -> Vec3A

Transforms the give Vec3A as 3D vector.

This is the equivalent of multiplying the Vec3A as a 4D vector where w is 0.0.

pub fn as_f64(&self) -> DMat4

Trait Implementations

impl Add<Mat4> for Mat4

type Output = Mat4

The resulting type after applying the + operator.

pub fn add(self, other: Mat4) -> <Mat4 as Add<Mat4>>::Output

Performs the + operation.

impl AsMut<[f32; 16]> for Mat4

pub fn as_mut(&mut self) -> &mut [f32; 16]

Performs the conversion.

impl AsRef<[f32; 16]> for Mat4

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

Performs the conversion.

impl Clone for Mat4

pub fn clone(&self) -> Mat4

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Mat4

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

Formats the value using the given formatter.

impl Default for Mat4

pub fn default() -> Mat4

Returns the “default value” for a type.

impl Deref for Mat4

type Target = Columns4<Vec4>

The resulting type after dereferencing.

pub fn deref(&self) -> &<Mat4 as Deref>::Target

Dereferences the value.

impl DerefMut for Mat4

pub fn deref_mut(&mut self) -> &mut <Mat4 as Deref>::Target

Mutably dereferences the value.

impl<'de> Deserialize<'de> for Mat4

pub fn deserialize<D>(
    deserializer: D
) -> Result<Mat4, <D as Deserializer<'de>>::Error> where
    D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

impl Display for Mat4

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

Formats the value using the given formatter.

impl Distribution<Mat4> for Standard

pub fn sample<R>(&self, rng: &mut R) -> Mat4 where
    R: Rng + ?Sized, 

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl From<Affine3A> for Mat4

pub fn from(m: Affine3A) -> Mat4

Performs the conversion.

impl From<Mat4> for Mat3

pub fn from(m: Mat4) -> Mat3

Creates a 3x3 matrix from the top left submatrix of the given 4x4 matrix.

impl From<Mat4> for Mat3A

pub fn from(m: Mat4) -> Mat3A

Creates a 3x3 matrix from the top left submatrix of the given 4x4 matrix.

impl Mat4LookTo for Mat4

fn look_to_rh(eye: Vec3, dir: Vec3, up: Vec3) -> Mat4

fn look_to_lh(eye: Vec3, dir: Vec3, up: Vec3) -> Mat4

impl Mul<Affine3A> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

pub fn mul(self, rhs: Affine3A) -> <Mat4 as Mul<Affine3A>>::Output

Performs the * operation.

impl Mul<Mat4> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

pub fn mul(self, other: Mat4) -> <Mat4 as Mul<Mat4>>::Output

Performs the * operation.

impl Mul<Mat4> for Affine3A

type Output = Mat4

The resulting type after applying the * operator.

pub fn mul(self, rhs: Mat4) -> <Affine3A as Mul<Mat4>>::Output

Performs the * operation.

impl Mul<Vec4> for Mat4

type Output = Vec4

The resulting type after applying the * operator.

pub fn mul(self, other: Vec4) -> <Mat4 as Mul<Vec4>>::Output

Performs the * operation.

impl Mul<f32> for Mat4

type Output = Mat4

The resulting type after applying the * operator.

pub fn mul(self, other: f32) -> <Mat4 as Mul<f32>>::Output

Performs the * operation.

impl PartialEq<Mat4> for Mat4

pub fn eq(&self, other: &Mat4) -> bool

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=.

impl<'a> Product<&'a Mat4> for Mat4

pub fn product<I>(iter: I) -> Mat4 where
    I: Iterator<Item = &'a Mat4>, 

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl Serialize for Mat4

pub 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 Sub<Mat4> for Mat4

type Output = Mat4

The resulting type after applying the - operator.

pub fn sub(self, other: Mat4) -> <Mat4 as Sub<Mat4>>::Output

Performs the - operation.

impl<'a> Sum<&'a Mat4> for Mat4

pub fn sum<I>(iter: I) -> Mat4 where
    I: Iterator<Item = &'a Mat4>, 

Method which takes an iterator and generates Self from the elements by “summing up” the items.

impl Copy for Mat4