Isometry2d

Isometry2d

• rotation : bevy_math::rotation2d::Rot2
• translation : glam::Vec2

Description

An isometry in two dimensions, representing a rotation followed by a translation. This can often be useful for expressing relative positions and transformations from one position to another.

In particular, this type represents a distance-preserving transformation known as a rigid motion or a direct motion, and belongs to the special Euclidean group SE(2). This includes translation and rotation, but excludes reflection.

For the three-dimensional version, see [Isometry3d].

Example

Isometries can be created from a given translation and rotation:

# use bevy_math::{Isometry2d, Rot2, Vec2};
#
let iso = Isometry2d::new(Vec2::new(2.0, 1.0), Rot2::degrees(90.0));

Or from separate parts:

# use bevy_math::{Isometry2d, Rot2, Vec2};
#
let iso1 = Isometry2d::from_translation(Vec2::new(2.0, 1.0));
let iso2 = Isometry2d::from_rotation(Rot2::degrees(90.0));

The isometries can be used to transform points:

# use approx::assert_abs_diff_eq;
# use bevy_math::{Isometry2d, Rot2, Vec2};
#
let iso = Isometry2d::new(Vec2::new(2.0, 1.0), Rot2::degrees(90.0));
let point = Vec2::new(4.0, 4.0);

// These are equivalent
let result = iso.transform_point(point);
let result = iso * point;

assert_eq!(result, Vec2::new(-2.0, 5.0));

Isometries can also be composed together:

# use bevy_math::{Isometry2d, Rot2, Vec2};
#
# let iso = Isometry2d::new(Vec2::new(2.0, 1.0), Rot2::degrees(90.0));
# let iso1 = Isometry2d::from_translation(Vec2::new(2.0, 1.0));
# let iso2 = Isometry2d::from_rotation(Rot2::degrees(90.0));
#
assert_eq!(iso1 * iso2, iso);

One common operation is to compute an isometry representing the relative positions of two objects for things like intersection tests. This can be done with an inverse transformation:

# use bevy_math::{Isometry2d, Rot2, Vec2};
#
let circle_iso = Isometry2d::from_translation(Vec2::new(2.0, 1.0));
let rectangle_iso = Isometry2d::from_rotation(Rot2::degrees(90.0));

// Compute the relative position and orientation between the two shapes
let relative_iso = circle_iso.inverse() * rectangle_iso;

// Or alternatively, to skip an extra rotation operation:
let relative_iso = circle_iso.inverse_mul(rectangle_iso);

Functions