#[repr(C)]pub struct Rotation3D<T, Src, Dst> {
pub i: T,
pub j: T,
pub k: T,
pub r: T,
/* private fields */
}
canvas
only.Expand description
A transform that can represent rotations in 3d, represented as a quaternion.
Most methods expect the quaternion to be normalized.
When in doubt, use unit_quaternion
instead of quaternion
to create
a rotation as the former will ensure that its result is normalized.
Some people use the x, y, z, w
(or w, x, y, z
) notations. The equivalence is
as follows: x -> i
, y -> j
, z -> k
, w -> r
.
The memory layout of this type corresponds to the x, y, z, w
notation
Fields§
§i: T
Component multiplied by the imaginary number i
.
j: T
Component multiplied by the imaginary number j
.
k: T
Component multiplied by the imaginary number k
.
r: T
The real part.
Implementations§
§impl<T, Src, Dst> Rotation3D<T, Src, Dst>
impl<T, Src, Dst> Rotation3D<T, Src, Dst>
pub fn quaternion(a: T, b: T, c: T, r: T) -> Rotation3D<T, Src, Dst>
pub fn quaternion(a: T, b: T, c: T, r: T) -> Rotation3D<T, Src, Dst>
Creates a rotation around from a quaternion representation.
The parameters are a, b, c and r compose the quaternion a*i + b*j + c*k + r
where a
, b
and c
describe the vector part and the last parameter r
is
the real part.
The resulting quaternion is not necessarily normalized. See unit_quaternion
.
pub fn identity() -> Rotation3D<T, Src, Dst>
pub fn identity() -> Rotation3D<T, Src, Dst>
Creates the identity rotation.
§impl<T, Src, Dst> Rotation3D<T, Src, Dst>where
T: Copy,
impl<T, Src, Dst> Rotation3D<T, Src, Dst>where
T: Copy,
pub fn vector_part(&self) -> Vector3D<T, UnknownUnit>
pub fn vector_part(&self) -> Vector3D<T, UnknownUnit>
Returns the vector part (i, j, k) of this quaternion.
pub fn cast_unit<Src2, Dst2>(&self) -> Rotation3D<T, Src2, Dst2>
pub fn cast_unit<Src2, Dst2>(&self) -> Rotation3D<T, Src2, Dst2>
Cast the unit, preserving the numeric value.
§Example
enum Local {}
enum World {}
enum Local2 {}
enum World2 {}
let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);
assert_eq!(to_world.i, to_world.cast_unit::<Local2, World2>().i);
assert_eq!(to_world.j, to_world.cast_unit::<Local2, World2>().j);
assert_eq!(to_world.k, to_world.cast_unit::<Local2, World2>().k);
assert_eq!(to_world.r, to_world.cast_unit::<Local2, World2>().r);
pub fn to_untyped(&self) -> Rotation3D<T, UnknownUnit, UnknownUnit>
pub fn to_untyped(&self) -> Rotation3D<T, UnknownUnit, UnknownUnit>
Drop the units, preserving only the numeric value.
§Example
enum Local {}
enum World {}
let to_world: Rotation3D<_, Local, World> = Rotation3D::quaternion(1, 2, 3, 4);
assert_eq!(to_world.i, to_world.to_untyped().i);
assert_eq!(to_world.j, to_world.to_untyped().j);
assert_eq!(to_world.k, to_world.to_untyped().k);
assert_eq!(to_world.r, to_world.to_untyped().r);
pub fn from_untyped(
r: &Rotation3D<T, UnknownUnit, UnknownUnit>,
) -> Rotation3D<T, Src, Dst>
pub fn from_untyped( r: &Rotation3D<T, UnknownUnit, UnknownUnit>, ) -> Rotation3D<T, Src, Dst>
Tag a unitless value with units.
§Example
use euclid::UnknownUnit;
enum Local {}
enum World {}
let rot: Rotation3D<_, UnknownUnit, UnknownUnit> = Rotation3D::quaternion(1, 2, 3, 4);
assert_eq!(rot.i, Rotation3D::<_, Local, World>::from_untyped(&rot).i);
assert_eq!(rot.j, Rotation3D::<_, Local, World>::from_untyped(&rot).j);
assert_eq!(rot.k, Rotation3D::<_, Local, World>::from_untyped(&rot).k);
assert_eq!(rot.r, Rotation3D::<_, Local, World>::from_untyped(&rot).r);
§impl<T, Src, Dst> Rotation3D<T, Src, Dst>where
T: Real,
impl<T, Src, Dst> Rotation3D<T, Src, Dst>where
T: Real,
pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> Rotation3D<T, Src, Dst>
pub fn unit_quaternion(i: T, j: T, k: T, r: T) -> Rotation3D<T, Src, Dst>
Creates a rotation around from a quaternion representation and normalizes it.
The parameters are a, b, c and r compose the quaternion a*i + b*j + c*k + r
before normalization, where a
, b
and c
describe the vector part and the
last parameter r
is the real part.
pub fn around_axis(
axis: Vector3D<T, Src>,
angle: Angle<T>,
) -> Rotation3D<T, Src, Dst>
pub fn around_axis( axis: Vector3D<T, Src>, angle: Angle<T>, ) -> Rotation3D<T, Src, Dst>
Creates a rotation around a given axis.
pub fn around_x(angle: Angle<T>) -> Rotation3D<T, Src, Dst>
pub fn around_x(angle: Angle<T>) -> Rotation3D<T, Src, Dst>
Creates a rotation around the x axis.
pub fn around_y(angle: Angle<T>) -> Rotation3D<T, Src, Dst>
pub fn around_y(angle: Angle<T>) -> Rotation3D<T, Src, Dst>
Creates a rotation around the y axis.
pub fn around_z(angle: Angle<T>) -> Rotation3D<T, Src, Dst>
pub fn around_z(angle: Angle<T>) -> Rotation3D<T, Src, Dst>
Creates a rotation around the z axis.
pub fn euler(
roll: Angle<T>,
pitch: Angle<T>,
yaw: Angle<T>,
) -> Rotation3D<T, Src, Dst>
pub fn euler( roll: Angle<T>, pitch: Angle<T>, yaw: Angle<T>, ) -> Rotation3D<T, Src, Dst>
Creates a rotation from Euler angles.
The rotations are applied in roll then pitch then yaw order.
- Roll (also called bank) is a rotation around the x axis.
- Pitch (also called bearing) is a rotation around the y axis.
- Yaw (also called heading) is a rotation around the z axis.
pub fn inverse(&self) -> Rotation3D<T, Dst, Src>
pub fn inverse(&self) -> Rotation3D<T, Dst, Src>
Returns the inverse of this rotation.
pub fn norm(&self) -> T
pub fn norm(&self) -> T
Computes the norm of this quaternion.
pub fn square_norm(&self) -> T
pub fn square_norm(&self) -> T
Computes the squared norm of this quaternion.
pub fn normalize(&self) -> Rotation3D<T, Src, Dst>
pub fn normalize(&self) -> Rotation3D<T, Src, Dst>
Returns a unit quaternion from this one.
pub fn is_normalized(&self) -> boolwhere
T: ApproxEq<T>,
pub fn is_normalized(&self) -> boolwhere
T: ApproxEq<T>,
Returns true
if norm of this quaternion is (approximately) one.
pub fn slerp(
&self,
other: &Rotation3D<T, Src, Dst>,
t: T,
) -> Rotation3D<T, Src, Dst>where
T: ApproxEq<T>,
pub fn slerp(
&self,
other: &Rotation3D<T, Src, Dst>,
t: T,
) -> Rotation3D<T, Src, Dst>where
T: ApproxEq<T>,
Spherical linear interpolation between this rotation and another rotation.
t
is expected to be between zero and one.
pub fn lerp(
&self,
other: &Rotation3D<T, Src, Dst>,
t: T,
) -> Rotation3D<T, Src, Dst>
pub fn lerp( &self, other: &Rotation3D<T, Src, Dst>, t: T, ) -> Rotation3D<T, Src, Dst>
Basic Linear interpolation between this rotation and another rotation.
pub fn transform_point3d(&self, point: Point3D<T, Src>) -> Point3D<T, Dst>where
T: ApproxEq<T>,
pub fn transform_point3d(&self, point: Point3D<T, Src>) -> Point3D<T, Dst>where
T: ApproxEq<T>,
Returns the given 3d point transformed by this rotation.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_point2d(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>where
T: ApproxEq<T>,
pub fn transform_point2d(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>where
T: ApproxEq<T>,
Returns the given 2d point transformed by this rotation then projected on the xy plane.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_vector3d(&self, vector: Vector3D<T, Src>) -> Vector3D<T, Dst>where
T: ApproxEq<T>,
pub fn transform_vector3d(&self, vector: Vector3D<T, Src>) -> Vector3D<T, Dst>where
T: ApproxEq<T>,
Returns the given 3d vector transformed by this rotation.
The input vector must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_vector2d(&self, vector: Vector2D<T, Src>) -> Vector2D<T, Dst>where
T: ApproxEq<T>,
pub fn transform_vector2d(&self, vector: Vector2D<T, Src>) -> Vector2D<T, Dst>where
T: ApproxEq<T>,
Returns the given 2d vector transformed by this rotation then projected on the xy plane.
The input vector must be use the unit Src, and the returned point has the unit Dst.
pub fn to_transform(&self) -> Transform3D<T, Src, Dst>where
T: ApproxEq<T>,
pub fn to_transform(&self) -> Transform3D<T, Src, Dst>where
T: ApproxEq<T>,
Returns the matrix representation of this rotation.
pub fn then<NewDst>(
&self,
other: &Rotation3D<T, Dst, NewDst>,
) -> Rotation3D<T, Src, NewDst>where
T: ApproxEq<T>,
pub fn then<NewDst>(
&self,
other: &Rotation3D<T, Dst, NewDst>,
) -> Rotation3D<T, Src, NewDst>where
T: ApproxEq<T>,
Returns a rotation representing this rotation followed by the other rotation.
Trait Implementations§
§impl<T, Src, Dst> ApproxEq<T> for Rotation3D<T, Src, Dst>
impl<T, Src, Dst> ApproxEq<T> for Rotation3D<T, Src, Dst>
§fn approx_epsilon() -> T
fn approx_epsilon() -> T
§fn approx_eq_eps(&self, other: &Rotation3D<T, Src, Dst>, eps: &T) -> bool
fn approx_eq_eps(&self, other: &Rotation3D<T, Src, Dst>, eps: &T) -> bool
true
if this object is approximately equal to the other one, using
a provided epsilon value.§fn approx_eq(&self, other: &Self) -> bool
fn approx_eq(&self, other: &Self) -> bool
true
if this object is approximately equal to the other one, using
the approx_epsilon
epsilon value.§impl<T, Src, Dst> Clone for Rotation3D<T, Src, Dst>where
T: Clone,
impl<T, Src, Dst> Clone for Rotation3D<T, Src, Dst>where
T: Clone,
§fn clone(&self) -> Rotation3D<T, Src, Dst>
fn clone(&self) -> Rotation3D<T, Src, Dst>
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read more§impl<T, Src, Dst> Debug for Rotation3D<T, Src, Dst>where
T: Debug,
impl<T, Src, Dst> Debug for Rotation3D<T, Src, Dst>where
T: Debug,
§impl<T, Src, Dst> From<Rotation3D<T, Src, Dst>> for RigidTransform3D<T, Src, Dst>
impl<T, Src, Dst> From<Rotation3D<T, Src, Dst>> for RigidTransform3D<T, Src, Dst>
§fn from(rot: Rotation3D<T, Src, Dst>) -> RigidTransform3D<T, Src, Dst>
fn from(rot: Rotation3D<T, Src, Dst>) -> RigidTransform3D<T, Src, Dst>
§impl<T, Src, Dst> Hash for Rotation3D<T, Src, Dst>where
T: Hash,
impl<T, Src, Dst> Hash for Rotation3D<T, Src, Dst>where
T: Hash,
§impl<T, Src, Dst> PartialEq for Rotation3D<T, Src, Dst>where
T: PartialEq,
impl<T, Src, Dst> PartialEq for Rotation3D<T, Src, Dst>where
T: PartialEq,
impl<T, Src, Dst> Copy for Rotation3D<T, Src, Dst>where
T: Copy,
impl<T, Src, Dst> Eq for Rotation3D<T, Src, Dst>where
T: Eq,
Auto Trait Implementations§
impl<T, Src, Dst> Freeze for Rotation3D<T, Src, Dst>where
T: Freeze,
impl<T, Src, Dst> RefUnwindSafe for Rotation3D<T, Src, Dst>
impl<T, Src, Dst> Send for Rotation3D<T, Src, Dst>
impl<T, Src, Dst> Sync for Rotation3D<T, Src, Dst>
impl<T, Src, Dst> Unpin for Rotation3D<T, Src, Dst>
impl<T, Src, Dst> UnwindSafe for Rotation3D<T, Src, Dst>
Blanket Implementations§
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T: Real + Zero + Arithmetics + Clone,
Swp: WhitePoint<T>,
Dwp: WhitePoint<T>,
D: AdaptFrom<S, Swp, Dwp, T>,
impl<S, D, Swp, Dwp, T> AdaptInto<D, Swp, Dwp, T> for Swhere
T: Real + Zero + Arithmetics + Clone,
Swp: WhitePoint<T>,
Dwp: WhitePoint<T>,
D: AdaptFrom<S, Swp, Dwp, T>,
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M: TransformMatrix<T>,
fn adapt_into_using<M>(self, method: M) -> Dwhere
M: TransformMatrix<T>,
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fn adapt_into(self) -> D
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