Struct rin::math::geometry::Isometry[−][src]

#[repr(C)]
pub struct Isometry<N, D, R> where
    N: Scalar,
    D: DimName,
    DefaultAllocator: Allocator<N, D, U1>,  {
    pub rotation: R,
    pub translation: Translation<N, D>,
}

A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).

This is also known as an element of a Special Euclidean (SE) group. The Isometry type can either represent a 2D or 3D isometry. A 2D isometry is composed of:

A translation part of type Translation2
A rotation part which can either be a UnitComplex or a Rotation2. A 3D isometry is composed of:
A translation part of type Translation3
A rotation part which can either be a UnitQuaternion or a Rotation3.

Note that instead of using the Isometry type in your code directly, you should use one of its aliases: Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3. Though keep in mind that all the documentation of all the methods of these aliases will also appears on this page.

Construction

From a 2D vector and/or an angle new, translation, rotation…
From a 3D vector and/or an axis-angle new, translation, rotation…
From a 3D eye position and target point look_at, look_at_lh, face_towards…
From the translation and rotation parts from_parts…

Transformation and composition

Note that transforming vectors and points can be done by multiplication, e.g., isometry * point. Composing an isometry with another transformation can also be done by multiplication or division.

Transformation of a vector or a point transform_vector, inverse_transform_point…
Inversion and in-place composition inverse, append_rotation_wrt_point_mut…
Interpolation lerp_slerp…

Conversion to a matrix

Conversion to a matrix to_matrix…

Fields

rotation: R

The pure rotational part of this isometry.

translation: Translation<N, D>

The pure translational part of this isometry.

Implementations

`impl<N, D, R> Isometry<N, D, R> where N: Scalar, D: DimName, R: AbstractRotation<N, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

From the translation and rotation parts

`pub fn from_parts( translation: Translation<N, D>, rotation: R ) -> Isometry<N, D, R>`[src]

Creates a new isometry from its rotational and translational parts.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::PI);
let iso = Isometry3::from_parts(tra, rot);

assert_relative_eq!(iso * Point3::new(1.0, 2.0, 3.0), Point3::new(-1.0, 2.0, 0.0), epsilon = 1.0e-6);

`impl<N, D, R> Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

Inversion and in-place composition

`#[must_use = "Did you mean to use inverse_mut()?"] pub fn inverse(&self) -> Isometry<N, D, R>`[src]

Inverts self.

Example

let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let inv = iso.inverse();
let pt = Point2::new(1.0, 2.0);

assert_eq!(inv * (iso * pt), pt);

`pub fn inverse_mut(&mut self)`[src]

Inverts self in-place.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let pt = Point2::new(1.0, 2.0);
let transformed_pt = iso * pt;
iso.inverse_mut();

assert_eq!(iso * transformed_pt, pt);

`pub fn inv_mul(&self, rhs: &Isometry<N, D, R>) -> Isometry<N, D, R>`[src]

Computes self.inverse() * rhs in a more efficient way.

Example

let mut iso1 = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let mut iso2 = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_4);

assert_eq!(iso1.inverse() * iso2, iso1.inv_mul(&iso2));

`pub fn append_translation_mut(&mut self, t: &Translation<N, D>)`[src]

Appends to self the given translation in-place.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let tra = Translation2::new(3.0, 4.0);
// Same as `iso = tra * iso`.
iso.append_translation_mut(&tra);

assert_eq!(iso.translation, Translation2::new(4.0, 6.0));

`pub fn append_rotation_mut(&mut self, r: &R)`[src]

Appends to self the given rotation in-place.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::PI / 6.0);
let rot = UnitComplex::new(f32::consts::PI / 2.0);
// Same as `iso = rot * iso`.
iso.append_rotation_mut(&rot);

assert_relative_eq!(iso, Isometry2::new(Vector2::new(-2.0, 1.0), f32::consts::PI * 2.0 / 3.0), epsilon = 1.0e-6);

`pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>)`[src]

Appends in-place to self a rotation centered at the point p, i.e., the rotation that lets p invariant.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let pt = Point2::new(1.0, 0.0);
iso.append_rotation_wrt_point_mut(&rot, &pt);

assert_relative_eq!(iso * pt, Point2::new(-2.0, 0.0), epsilon = 1.0e-6);

`pub fn append_rotation_wrt_center_mut(&mut self, r: &R)`[src]

Appends in-place to self a rotation centered at the point with coordinates self.translation.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
iso.append_rotation_wrt_center_mut(&rot);

// The translation part should not have changed.
assert_eq!(iso.translation.vector, Vector2::new(1.0, 2.0));
assert_eq!(iso.rotation, UnitComplex::new(f32::consts::PI));

`impl<N, D, R> Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

Transformation of a vector or a point

`pub fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>`[src]

Transform the given point by this isometry.

This is the same as the multiplication self * pt.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.transform_point(&Point3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, 2.0), epsilon = 1.0e-6);

`pub fn transform_vector( &self, v: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer> ) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>`[src]

Transform the given vector by this isometry, ignoring the translation component of the isometry.

This is the same as the multiplication self * v.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);

`pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>`[src]

Transform the given point by the inverse of this isometry. This may be less expensive than computing the entire isometry inverse and then transforming the point.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Point3::new(0.0, 2.0, 1.0), epsilon = 1.0e-6);

`pub fn inverse_transform_vector( &self, v: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer> ) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>`[src]

Transform the given vector by the inverse of this isometry, ignoring the translation component of the isometry. This may be less expensive than computing the entire isometry inverse and then transforming the point.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);

`pub fn inverse_transform_unit_vector( &self, v: &Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> ) -> Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>`[src]

Transform the given unit vector by the inverse of this isometry, ignoring the translation component of the isometry. This may be less expensive than computing the entire isometry inverse and then transforming the point.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::z() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.inverse_transform_unit_vector(&Vector3::x_axis());
assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);

`impl<N, D, R> Isometry<N, D, R> where N: SimdRealField, D: DimName, DefaultAllocator: Allocator<N, D, U1>,` [src]

Conversion to a matrix

pub fn to_homogeneous( &self ) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where D: DimNameAdd<U1>, R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>, DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, [src]

Converts this isometry into its equivalent homogeneous transformation matrix.

This is the same as self.to_matrix().

Example

let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
let expected = Matrix3::new(0.8660254, -0.5,      10.0,
                            0.5,       0.8660254, 20.0,
                            0.0,       0.0,       1.0);

assert_relative_eq!(iso.to_homogeneous(), expected, epsilon = 1.0e-6);

pub fn to_matrix( &self ) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where D: DimNameAdd<U1>, R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>, DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, [src]

Converts this isometry into its equivalent homogeneous transformation matrix.

This is the same as self.to_homogeneous().

Example

let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
let expected = Matrix3::new(0.8660254, -0.5,      10.0,
                            0.5,       0.8660254, 20.0,
                            0.0,       0.0,       1.0);

assert_relative_eq!(iso.to_matrix(), expected, epsilon = 1.0e-6);

`impl<N, D, R> Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn identity() -> Isometry<N, D, R>`[src]

Creates a new identity isometry.

Example


let iso = Isometry2::identity();
let pt = Point2::new(1.0, 2.0);
assert_eq!(iso * pt, pt);

let iso = Isometry3::identity();
let pt = Point3::new(1.0, 2.0, 3.0);
assert_eq!(iso * pt, pt);

`pub fn rotation_wrt_point(r: R, p: Point<N, D>) -> Isometry<N, D, R>`[src]

The isometry that applies the rotation r with its axis passing through the point p. This effectively lets p invariant.

Example

let rot = UnitComplex::new(f32::consts::PI);
let pt = Point2::new(1.0, 0.0);
let iso = Isometry2::rotation_wrt_point(rot, pt);

assert_eq!(iso * pt, pt); // The rotation center is not affected.
assert_relative_eq!(iso * Point2::new(1.0, 2.0), Point2::new(1.0, -2.0), epsilon = 1.0e-6);

`impl<N> Isometry<N, U2, Rotation<N, U2>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField,` [src]

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

`pub fn new( translation: Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>, angle: N ) -> Isometry<N, U2, Rotation<N, U2>>`[src]

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: N, y: N) -> Isometry<N, U2, Rotation<N, U2>>`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation(angle: N) -> Isometry<N, U2, Rotation<N, U2>>`[src]

Creates a new isometry from the given rotation angle.

`impl<N> Isometry<N, U2, Unit<Complex<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField,` [src]

`pub fn new( translation: Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>, angle: N ) -> Isometry<N, U2, Unit<Complex<N>>>`[src]

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

Its rotational part is represented as an unit complex number.

Example

let iso = IsometryMatrix2::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: N, y: N) -> Isometry<N, U2, Unit<Complex<N>>>`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation(angle: N) -> Isometry<N, U2, Unit<Complex<N>>>`[src]

Creates a new isometry from the given rotation angle.

`impl<N> Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField,` [src]

Construction from a 3D vector and/or an axis-angle

`pub fn new( translation: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>, axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

Creates a new isometry from a translation and a rotation axis-angle.

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

`pub fn translation(x: N, y: N, z: N) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation( axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

Creates a new isometry from the given rotation angle.

`impl<N> Isometry<N, U3, Rotation<N, U3>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField,` [src]

`pub fn new( translation: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>, axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Rotation<N, U3>>`[src]

Creates a new isometry from a translation and a rotation axis-angle.

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

`pub fn translation(x: N, y: N, z: N) -> Isometry<N, U3, Rotation<N, U3>>`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation( axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Rotation<N, U3>>`[src]

Creates a new isometry from the given rotation angle.

`impl<N> Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField,` [src]

Construction from a 3D eye position and target point

`pub fn face_towards( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

Creates an isometry that corresponds to the local frame of an observer standing at the point eye and looking toward target.

It maps the z axis to the view direction target - eyeand the origin to the eye.

Arguments

eye - The observer position.
target - The target position.
up - Vertical direction. The only requirement of this parameter is to not be collinear to eye - at. Non-collinearity is not checked.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

`pub fn new_observer_frame( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

👎 Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

`pub fn look_at_rh( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

Builds a right-handed look-at view matrix.

It maps the view direction target - eye to the negative z axis to and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local -z axis.

Arguments

eye - The eye position.
target - The target position.
up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

`pub fn look_at_lh( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Unit<Quaternion<N>>>`[src]

Builds a left-handed look-at view matrix.

It maps the view direction target - eye to the positive z axis and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local z axis.

Arguments

eye - The eye position.
target - The target position.
up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

`impl<N> Isometry<N, U3, Rotation<N, U3>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField,` [src]

`pub fn face_towards( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Rotation<N, U3>>`[src]

Creates an isometry that corresponds to the local frame of an observer standing at the point eye and looking toward target.

It maps the z axis to the view direction target - eyeand the origin to the eye.

Arguments

eye - The observer position.
target - The target position.
up - Vertical direction. The only requirement of this parameter is to not be collinear to eye - at. Non-collinearity is not checked.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

`pub fn new_observer_frame( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Rotation<N, U3>>`[src]

👎 Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

`pub fn look_at_rh( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Rotation<N, U3>>`[src]

Builds a right-handed look-at view matrix.

It maps the view direction target - eye to the negative z axis to and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local -z axis.

Arguments

eye - The eye position.
target - The target position.
up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

`pub fn look_at_lh( eye: &Point<N, U3>, target: &Point<N, U3>, up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Isometry<N, U3, Rotation<N, U3>>`[src]

Builds a left-handed look-at view matrix.

It maps the view direction target - eye to the positive z axis and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local z axis.

Arguments

eye - The eye position.
target - The target position.
up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

`impl<N> Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField,` [src]

Interpolation

`pub fn lerp_slerp( &self, other: &Isometry<N, U3, Unit<Quaternion<N>>>, t: N ) -> Isometry<N, U3, Unit<Quaternion<N>>> where N: RealField,` [src]

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 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = Isometry3::from_parts(t1, q1);
let iso2 = Isometry3::from_parts(t2, q2);

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

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

`pub fn try_lerp_slerp( &self, other: &Isometry<N, U3, Unit<Quaternion<N>>>, t: N, epsilon: N ) -> Option<Isometry<N, U3, Unit<Quaternion<N>>>> where N: RealField,` [src]

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

Retuns None if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined).

Examples:


let t1 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = Isometry3::from_parts(t1, q1);
let iso2 = Isometry3::from_parts(t2, q2);

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

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

`impl<N> Isometry<N, U3, Rotation<N, U3>> where N: SimdRealField,` [src]

`pub fn lerp_slerp( &self, other: &Isometry<N, U3, Rotation<N, U3>>, t: N ) -> Isometry<N, U3, Rotation<N, U3>> where N: RealField,` [src]

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 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = IsometryMatrix3::from_parts(t1, q1);
let iso2 = IsometryMatrix3::from_parts(t2, q2);

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

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

`pub fn try_lerp_slerp( &self, other: &Isometry<N, U3, Rotation<N, U3>>, t: N, epsilon: N ) -> Option<Isometry<N, U3, Rotation<N, U3>>> where N: RealField,` [src]

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

Retuns None if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined).

Examples:


let t1 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = IsometryMatrix3::from_parts(t1, q1);
let iso2 = IsometryMatrix3::from_parts(t2, q2);

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

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

`impl<N> Isometry<N, U2, Unit<Complex<N>>> where N: SimdRealField,` [src]

`pub fn lerp_slerp( &self, other: &Isometry<N, U2, Unit<Complex<N>>>, t: N ) -> Isometry<N, U2, Unit<Complex<N>>> where N: RealField,` [src]

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 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
let q2 = UnitComplex::new(-std::f32::consts::PI);
let iso1 = Isometry2::from_parts(t1, q1);
let iso2 = Isometry2::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);

`impl<N> Isometry<N, U2, Rotation<N, U2>> where N: SimdRealField,` [src]

`pub fn lerp_slerp( &self, other: &Isometry<N, U2, Rotation<N, U2>>, t: N ) -> Isometry<N, U2, Rotation<N, U2>> where N: RealField,` [src]

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);

Trait Implementations

`impl<N, D, R> AbsDiffEq<Isometry<N, D, R>> for Isometry<N, D, R> where N: RealField, D: DimName, R: AbstractRotation<N, D> + AbsDiffEq<R, Epsilon = <N as AbsDiffEq<N>>::Epsilon>, DefaultAllocator: Allocator<N, D, U1>, <N as AbsDiffEq<N>>::Epsilon: Copy,` [src]

`type Epsilon = <N as AbsDiffEq<N>>::Epsilon`

Used for specifying relative comparisons.

`pub fn default_epsilon( ) -> <Isometry<N, D, R> as AbsDiffEq<Isometry<N, D, R>>>::Epsilon`[src]

`pub fn abs_diff_eq( &self, other: &Isometry<N, D, R>, epsilon: <Isometry<N, D, R> as AbsDiffEq<Isometry<N, D, R>>>::Epsilon ) -> bool`[src]

`pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool`[src]

`impl<N, D, R> Clone for Isometry<N, D, R> where N: Scalar, D: DimName, R: Clone, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn clone(&self) -> Isometry<N, D, R>`[src]

`pub fn clone_from(&mut self, source: &Self)`1.0.0 [src]

`impl<N, D, R> Debug for Isometry<N, D, R> where N: Debug + Scalar, D: Debug + DimName, R: Debug, DefaultAllocator: Allocator<N, D, U1>,` [src]

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

`impl<'de, N, D, R> Deserialize<'de> for Isometry<N, D, R> where N: Scalar, D: DimName, R: Deserialize<'de>, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<N, D, U1>, <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Deserialize<'de>,` [src]

`pub fn deserialize<D>( deserializer: D ) -> Result<Isometry<N, D, R>, <D as Deserializer<'de>>::Error> where __D: Deserializer<'de>,` [src]

`impl<N, D, R> Display for Isometry<N, D, R> where N: RealField + Display, D: DimName, R: Display, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<usize, D, U1>,` [src]

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

`impl<'b, N, D, R> Div<&'b Isometry<N, D, R>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Isometry<N, D, R> ) -> <Isometry<N, D, R> as Div<&'b Isometry<N, D, R>>>::Output`[src]

`impl<'b, N, D, R> Div<&'b Isometry<N, D, R>> for Similarity<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Isometry<N, D, R> ) -> <Similarity<N, D, R> as Div<&'b Isometry<N, D, R>>>::Output`[src]

`impl<'a, 'b, N, D, R> Div<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Isometry<N, D, R> ) -> <&'a Similarity<N, D, R> as Div<&'b Isometry<N, D, R>>>::Output`[src]

`impl<'a, 'b, N, D, R> Div<&'b Isometry<N, D, R>> for &'a Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Isometry<N, D, R> ) -> <&'a Isometry<N, D, R> as Div<&'b Isometry<N, D, R>>>::Output`[src]

`impl<'a, 'b, N, D> Div<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, right: &'b Isometry<N, D, Rotation<N, D>> ) -> <&'a Rotation<N, D> as Div<&'b Isometry<N, D, Rotation<N, D>>>>::Output`[src]

`impl<'b, N, D> Div<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, right: &'b Isometry<N, D, Rotation<N, D>> ) -> <Rotation<N, D> as Div<&'b Isometry<N, D, Rotation<N, D>>>>::Output`[src]

`impl<'b, N> Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, right: &'b Isometry<N, U3, Unit<Quaternion<N>>> ) -> <Unit<Quaternion<N>> as Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>>>::Output`[src]

`impl<'a, 'b, N> Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, right: &'b Isometry<N, U3, Unit<Quaternion<N>>> ) -> <&'a Unit<Quaternion<N>> as Div<&'b Isometry<N, U3, Unit<Quaternion<N>>>>>::Output`[src]

`impl<'a, 'b, N, D> Div<&'b Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Rotation<N, D> ) -> <&'a Isometry<N, D, Rotation<N, D>> as Div<&'b Rotation<N, D>>>::Output`[src]

`impl<'b, N, D> Div<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Rotation<N, D> ) -> <Isometry<N, D, Rotation<N, D>> as Div<&'b Rotation<N, D>>>::Output`[src]

`impl<'b, N, D, R> Div<&'b Similarity<N, D, R>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Similarity<N, D, R> ) -> <Isometry<N, D, R> as Div<&'b Similarity<N, D, R>>>::Output`[src]

`impl<'a, 'b, N, D, R> Div<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Similarity<N, D, R> ) -> <&'a Isometry<N, D, R> as Div<&'b Similarity<N, D, R>>>::Output`[src]

`impl<'b, N> Div<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U2, U1>, DefaultAllocator: Allocator<N, U2, U1>,` [src]

`type Output = Isometry<N, U2, Unit<Complex<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Unit<Complex<N>> ) -> <Isometry<N, U2, Unit<Complex<N>>> as Div<&'b Unit<Complex<N>>>>::Output`[src]

`impl<'a, 'b, N> Div<&'b Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U2, U1>, DefaultAllocator: Allocator<N, U2, U1>,` [src]

`type Output = Isometry<N, U2, Unit<Complex<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Unit<Complex<N>> ) -> <&'a Isometry<N, U2, Unit<Complex<N>>> as Div<&'b Unit<Complex<N>>>>::Output`[src]

`impl<'b, N> Div<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Unit<Quaternion<N>> ) -> <Isometry<N, U3, Unit<Quaternion<N>>> as Div<&'b Unit<Quaternion<N>>>>::Output`[src]

`impl<'a, 'b, N> Div<&'b Unit<Quaternion<N>>> for &'a Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: &'b Unit<Quaternion<N>> ) -> <&'a Isometry<N, U3, Unit<Quaternion<N>>> as Div<&'b Unit<Quaternion<N>>>>::Output`[src]

`impl<N, D, R> Div<Isometry<N, D, R>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Isometry<N, D, R> ) -> <Isometry<N, D, R> as Div<Isometry<N, D, R>>>::Output`[src]

`impl<N, D, R> Div<Isometry<N, D, R>> for Similarity<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Isometry<N, D, R> ) -> <Similarity<N, D, R> as Div<Isometry<N, D, R>>>::Output`[src]

`impl<'a, N, D, R> Div<Isometry<N, D, R>> for &'a Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Isometry<N, D, R> ) -> <&'a Isometry<N, D, R> as Div<Isometry<N, D, R>>>::Output`[src]

`impl<'a, N, D, R> Div<Isometry<N, D, R>> for &'a Similarity<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Isometry<N, D, R> ) -> <&'a Similarity<N, D, R> as Div<Isometry<N, D, R>>>::Output`[src]

`impl<N, D> Div<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, right: Isometry<N, D, Rotation<N, D>> ) -> <Rotation<N, D> as Div<Isometry<N, D, Rotation<N, D>>>>::Output`[src]

`impl<'a, N, D> Div<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, right: Isometry<N, D, Rotation<N, D>> ) -> <&'a Rotation<N, D> as Div<Isometry<N, D, Rotation<N, D>>>>::Output`[src]

`impl<N> Div<Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, right: Isometry<N, U3, Unit<Quaternion<N>>> ) -> <Unit<Quaternion<N>> as Div<Isometry<N, U3, Unit<Quaternion<N>>>>>::Output`[src]

`impl<'a, N> Div<Isometry<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, right: Isometry<N, U3, Unit<Quaternion<N>>> ) -> <&'a Unit<Quaternion<N>> as Div<Isometry<N, U3, Unit<Quaternion<N>>>>>::Output`[src]

`impl<N, D> Div<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Rotation<N, D> ) -> <Isometry<N, D, Rotation<N, D>> as Div<Rotation<N, D>>>::Output`[src]

`impl<'a, N, D> Div<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where N: SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Isometry<N, D, Rotation<N, D>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Rotation<N, D> ) -> <&'a Isometry<N, D, Rotation<N, D>> as Div<Rotation<N, D>>>::Output`[src]

`impl<N, D, R> Div<Similarity<N, D, R>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Similarity<N, D, R> ) -> <Isometry<N, D, R> as Div<Similarity<N, D, R>>>::Output`[src]

`impl<'a, N, D, R> Div<Similarity<N, D, R>> for &'a Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`type Output = Similarity<N, D, R>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Similarity<N, D, R> ) -> <&'a Isometry<N, D, R> as Div<Similarity<N, D, R>>>::Output`[src]

`impl<'a, N> Div<Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U2, U1>, DefaultAllocator: Allocator<N, U2, U1>,` [src]

`type Output = Isometry<N, U2, Unit<Complex<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Unit<Complex<N>> ) -> <&'a Isometry<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output`[src]

`impl<N> Div<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U2, U1>, DefaultAllocator: Allocator<N, U2, U1>,` [src]

`type Output = Isometry<N, U2, Unit<Complex<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Unit<Complex<N>> ) -> <Isometry<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output`[src]

`impl<N> Div<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Unit<Quaternion<N>> ) -> <Isometry<N, U3, Unit<Quaternion<N>>> as Div<Unit<Quaternion<N>>>>::Output`[src]

`impl<'a, N> Div<Unit<Quaternion<N>>> for &'a Isometry<N, U3, Unit<Quaternion<N>>> where N: SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U4, U1>, DefaultAllocator: Allocator<N, U3, U1>,` [src]

`type Output = Isometry<N, U3, Unit<Quaternion<N>>>`

The resulting type after applying the / operator.

`pub fn div( self, rhs: Unit<Quaternion<N>> ) -> <&'a Isometry<N, U3, Unit<Quaternion<N>>> as Div<Unit<Quaternion<N>>>>::Output`[src]

`impl<'b, N, D, R> DivAssign<&'b Isometry<N, D, R>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn div_assign(&mut self, rhs: &'b Isometry<N, D, R>)`[src]

`impl<'b, N, D, R> DivAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn div_assign(&mut self, rhs: &'b Isometry<N, D, R>)`[src]

`impl<'b, N, D> DivAssign<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<N, D, D>,` [src]

`pub fn div_assign(&mut self, rhs: &'b Rotation<N, D>)`[src]

`impl<'b, N> DivAssign<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U2, U2>, DefaultAllocator: Allocator<N, U2, U2>,` [src]

`pub fn div_assign(&mut self, rhs: &'b Unit<Complex<N>>)`[src]

`impl<'b, N> DivAssign<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U3, U3>, DefaultAllocator: Allocator<N, U3, U3>,` [src]

`pub fn div_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)`[src]

`impl<N, D, R> DivAssign<Isometry<N, D, R>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn div_assign(&mut self, rhs: Isometry<N, D, R>)`[src]

`impl<N, D, R> DivAssign<Isometry<N, D, R>> for Similarity<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn div_assign(&mut self, rhs: Isometry<N, D, R>)`[src]

`impl<N, D> DivAssign<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField, D: DimName, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<N, D, D>,` [src]

`pub fn div_assign(&mut self, rhs: Rotation<N, D>)`[src]

`impl<N> DivAssign<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U2, U2>, DefaultAllocator: Allocator<N, U2, U2>,` [src]

`pub fn div_assign(&mut self, rhs: Unit<Complex<N>>)`[src]

`impl<N> DivAssign<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField, <N as SimdValue>::Element: SimdRealField, DefaultAllocator: Allocator<N, U3, U3>, DefaultAllocator: Allocator<N, U3, U3>,` [src]

`pub fn div_assign(&mut self, rhs: Unit<Quaternion<N>>)`[src]

`impl<'a> From<&'a Isometry<f32, U2, Unit<Complex<f32>>>> for Model`[src]

`pub fn from(i: &Isometry<f32, U2, Unit<Complex<f32>>>) -> Model`[src]

`impl<'a> From<&'a Isometry<f32, U3, Unit<Quaternion<f32>>>> for Model`[src]

`pub fn from(i: &Isometry<f32, U3, Unit<Quaternion<f32>>>) -> Model`[src]

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 16]> for Isometry<N, D, R> where N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>, D: DimName, R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 16]>, <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>, <N as SimdValue>::Element: Scalar, <N as SimdValue>::Element: Copy, <R as SimdValue>::Element: Scalar, <R as SimdValue>::Element: Copy, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, [src]

`pub fn from( arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 16] ) -> Isometry<N, D, R>`[src]

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 2]> for Isometry<N, D, R> where N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>, D: DimName, R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 2]>, <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>, <N as SimdValue>::Element: Scalar, <N as SimdValue>::Element: Copy, <R as SimdValue>::Element: Scalar, <R as SimdValue>::Element: Copy, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, [src]

`pub fn from( arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 2] ) -> Isometry<N, D, R>`[src]

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 4]> for Isometry<N, D, R> where N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>, D: DimName, R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 4]>, <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>, <N as SimdValue>::Element: Scalar, <N as SimdValue>::Element: Copy, <R as SimdValue>::Element: Scalar, <R as SimdValue>::Element: Copy, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, [src]

`pub fn from( arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 4] ) -> Isometry<N, D, R>`[src]

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 8]> for Isometry<N, D, R> where N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>, D: DimName, R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 8]>, <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>, <N as SimdValue>::Element: Scalar, <N as SimdValue>::Element: Copy, <R as SimdValue>::Element: Scalar, <R as SimdValue>::Element: Copy, DefaultAllocator: Allocator<N, D, U1>, DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, [src]

`pub fn from( arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 8] ) -> Isometry<N, D, R>`[src]

impl<N, D, R> From<Isometry<N, D, R>> for Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where N: SimdRealField, D: DimName + DimNameAdd<U1>, R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>, DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, DefaultAllocator: Allocator<N, D, U1>, [src]

`pub fn from( iso: Isometry<N, D, R> ) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>`[src]

`impl From<Isometry<f32, U3, Unit<Quaternion<f32>>>> for Node`[src]

`pub fn from(i: Isometry<f32, U3, Unit<Quaternion<f32>>>) -> Node`[src]

`impl<N, D, R> From<Translation<N, D>> for Isometry<N, D, R> where N: SimdRealField, D: DimName, R: AbstractRotation<N, D>, DefaultAllocator: Allocator<N, D, U1>,` [src]

`pub fn from(tra: Translation<N, D>) -> Isometry<N, D, R>`[src]

`impl<N, D, R> Hash for Isometry<N, D, R> where N: Scalar + Hash, D: DimName + Hash, R: Hash, DefaultAllocator: Allocator<N, D, U1>, <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Hash,` [src]

`pub fn hash<H>(&self, state: &mut H) where H: Hasher,` [src]

`pub fn hash_slice<H>(data: &[Self], state: &mut H) where H: Hasher,` 1.3.0 [src]

`impl<N> IsometryOps<N> for Isometry<N, U3, Unit<Quaternion<N>>> where N: RealField,` [src]

`pub fn absolute_transform_vector( &self, v: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> ) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>`[src]