Isometry3d

Isometry3d

• rotation : glam::Quat
• translation : glam::Vec3A

Description

An isometry in three 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(3). This includes translation and rotation, but excludes reflection.

For the two-dimensional version, see [Isometry2d].

Example

Isometries can be created from a given translation and rotation:

# use bevy_math::{Isometry3d, Quat, Vec3};
# use std::f32::consts::FRAC_PI_2;
#
let iso = Isometry3d::new(Vec3::new(2.0, 1.0, 3.0), Quat::from_rotation_z(FRAC_PI_2));

Or from separate parts:

# use bevy_math::{Isometry3d, Quat, Vec3};
# use std::f32::consts::FRAC_PI_2;
#
let iso1 = Isometry3d::from_translation(Vec3::new(2.0, 1.0, 3.0));
let iso2 = Isometry3d::from_rotation(Quat::from_rotation_z(FRAC_PI_2));

The isometries can be used to transform points:

# use approx::assert_relative_eq;
# use bevy_math::{Isometry3d, Quat, Vec3};
# use std::f32::consts::FRAC_PI_2;
#
let iso = Isometry3d::new(Vec3::new(2.0, 1.0, 3.0), Quat::from_rotation_z(FRAC_PI_2));
let point = Vec3::new(4.0, 4.0, 4.0);

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

assert_relative_eq!(result, Vec3::new(-2.0, 5.0, 7.0));

Isometries can also be composed together:

# use bevy_math::{Isometry3d, Quat, Vec3};
# use std::f32::consts::FRAC_PI_2;
#
# let iso = Isometry3d::new(Vec3::new(2.0, 1.0, 3.0), Quat::from_rotation_z(FRAC_PI_2));
# let iso1 = Isometry3d::from_translation(Vec3::new(2.0, 1.0, 3.0));
# let iso2 = Isometry3d::from_rotation(Quat::from_rotation_z(FRAC_PI_2));
#
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::{Isometry3d, Quat, Vec3};
# use std::f32::consts::FRAC_PI_2;
#
let sphere_iso = Isometry3d::from_translation(Vec3::new(2.0, 1.0, 3.0));
let cuboid_iso = Isometry3d::from_rotation(Quat::from_rotation_z(FRAC_PI_2));

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

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

Functions