[−][src]Struct nalgebra::geometry::Isometry

#[repr(C)]
pub struct Isometry<N: RealField, D: DimName, R> where
    DefaultAllocator: Allocator<N, D>,  {
    pub rotation: R,
    pub translation: Translation<N, D>,
    // some fields omitted
}

A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.

Fields

rotation: R

The pure rotational part of this isometry.

translation: Translation<N, D>

The pure translational part of this isometry.

Methods

`impl<N: RealField, D: DimName, R: Rotation<Point<N, D>>> Isometry<N, D, R> where DefaultAllocator: Allocator<N, D>,` [src]

`pub fn from_parts(translation: Translation<N, D>, rotation: R) -> Self`[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);

`pub fn inverse(&self) -> Self`[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 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));

`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: &VectorN<N, D>) -> VectorN<N, D>`[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: &VectorN<N, D>) -> VectorN<N, D>`[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);

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

`pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>> where D: DimNameAdd<U1>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>, DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,` [src]

Converts this isometry into its equivalent homogeneous transformation 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);

`impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R> where DefaultAllocator: Allocator<N, D>,` [src]

`pub fn identity() -> Self`[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>) -> Self`[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: RealField> Isometry<N, U2, Rotation2<N>>`[src]

`pub fn new(translation: Vector2<N>, angle: N) -> Self`[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) -> Self`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation(angle: N) -> Self`[src]

Creates a new isometry from the given rotation angle.

`impl<N: RealField> Isometry<N, U2, UnitComplex<N>>`[src]

`pub fn new(translation: Vector2<N>, angle: N) -> Self`[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) -> Self`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation(angle: N) -> Self`[src]

Creates a new isometry from the given rotation angle.

`impl<N: RealField> Isometry<N, U3, Rotation3<N>>`[src]

`pub fn new(translation: Vector3<N>, axisangle: Vector3<N>) -> Self`[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) -> Self`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation(axisangle: Vector3<N>) -> Self`[src]

Creates a new isometry from the given rotation angle.

`pub fn face_towards( eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N> ) -> Self`[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: &Point3<N>, target: &Point3<N>, up: &Vector3<N> ) -> Self`[src]

Deprecated:

renamed to face_towards

Deprecated: Use [Isometry::face_towards] instead.

`pub fn look_at_rh(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self`[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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self`[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: RealField> Isometry<N, U3, UnitQuaternion<N>>`[src]

`pub fn new(translation: Vector3<N>, axisangle: Vector3<N>) -> Self`[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) -> Self`[src]

Creates a new isometry from the given translation coordinates.

`pub fn rotation(axisangle: Vector3<N>) -> Self`[src]

Creates a new isometry from the given rotation angle.

`pub fn face_towards( eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N> ) -> Self`[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: &Point3<N>, target: &Point3<N>, up: &Vector3<N> ) -> Self`[src]

Deprecated:

renamed to face_towards

Deprecated: Use [Isometry::face_towards] instead.

`pub fn look_at_rh(eye: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self`[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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self`[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());

Trait Implementations

`impl<N: RealField, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Isometry<N, D, R> where DefaultAllocator: Allocator<N, D>, Owned<N, D>: Copy,` [src]

`impl<N: RealField, D: DimName, R> Eq for Isometry<N, D, R> where R: Rotation<Point<N, D>> + Eq, DefaultAllocator: Allocator<N, D>,` [src]

`impl<N: RealField, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Isometry<N, D, R> where DefaultAllocator: Allocator<N, D>,` [src]

`fn clone(&self) -> Self`[src]

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

Performs copy-assignment from source. Read more

`impl<N: RealField, D: DimName, R> PartialEq<Isometry<N, D, R>> for Isometry<N, D, R> where R: Rotation<Point<N, D>> + PartialEq, DefaultAllocator: Allocator<N, D>,` [src]

`fn eq(&self, right: &Self) -> bool`[src]

`#[must_use] fn ne(&self, other: &Rhs) -> bool`1.0.0[src]

This method tests for !=.

`impl<N: RealField, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>> where D: DimNameAdd<U1>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>, DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D>,` [src]

`fn from(iso: Isometry<N, D, R>) -> Self`[src]

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

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

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

Feeds a slice of this type into the given [Hasher]. Read more

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

`fn fmt(&self, f: &mut Formatter) -> Result`[src]