Type Alias nalgebra::geometry::IsometryMatrix2

pub type IsometryMatrix2<T> = Isometry<T, Rotation2<T>, 2>;

A 2-dimensional direct isometry using a rotation matrix for its rotational part.

Because this is an alias, not all its methods are listed here. See the Isometry type too.

Also known as a rigid-body motion, or as an element of SE(2).

Aliased Type

struct IsometryMatrix2<T> {
    pub rotation: Rotation<T, 2>,
    pub translation: Translation<T, 2>,
}

Fields

rotation: Rotation<T, 2>

The pure rotational part of this isometry.

translation: Translation<T, 2>

The pure translational part of this isometry.

Implementations

impl<T: SimdRealField> IsometryMatrix2<T>

where T::Element: SimdRealField,

Construction from a 2D vector and/or a rotation angle

pub fn new(translation: Vector2<T>, angle: T) -> Self

Creates a new 2D isometry from a translation and a rotation angle.

Its rotational part is represented as a 2x2 rotation matrix.

Example

let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);

assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));

pub fn translation(x: T, y: T) -> Self

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: T) -> Self

Creates a new isometry from the given rotation angle.

pub fn cast<To: Scalar>(self) -> IsometryMatrix2<To>

where IsometryMatrix2<To>: SupersetOf<Self>,

Cast the components of self to another type.

Example

let iso = IsometryMatrix2::<f64>::identity();
let iso2 = iso.cast::<f32>();
assert_eq!(iso2, IsometryMatrix2::<f32>::identity());

impl<T: SimdRealField> IsometryMatrix2<T>

pub fn lerp_slerp(&self, other: &Self, t: T) -> Self

where T: RealField,

Interpolates between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Panics if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined). Use .try_lerp_slerp instead to avoid the panic.

Examples:

let t1 = Translation2::new(1.0, 2.0);
let t2 = Translation2::new(4.0, 8.0);
let q1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
let q2 = Rotation2::new(-std::f32::consts::PI);
let iso1 = IsometryMatrix2::from_parts(t1, q1);
let iso2 = IsometryMatrix2::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);