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#[cfg(feature = "arbitrary")]
use crate::base::storage::Owned;
#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
use num::One;
use rand::distributions::{Distribution, Standard};
use rand::Rng;
use alga::general::RealField;
use alga::linear::Rotation as AlgaRotation;
use crate::base::allocator::Allocator;
use crate::base::dimension::{DimName, U2, U3};
use crate::base::{DefaultAllocator, Vector2, Vector3};
use crate::geometry::{
Isometry, Point, Point3, Rotation, Rotation2, Rotation3, Translation, UnitComplex,
UnitQuaternion, Translation2, Translation3
};
impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>
where DefaultAllocator: Allocator<N, D>
{
/// Creates a new identity isometry.
///
/// # Example
///
/// ```
/// # use nalgebra::{Isometry2, Point2, Isometry3, Point3};
///
/// 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);
/// ```
#[inline]
pub fn identity() -> Self {
Self::from_parts(Translation::identity(), R::identity())
}
/// The isometry that applies the rotation `r` with its axis passing through the point `p`.
/// This effectively lets `p` invariant.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry2, Point2, UnitComplex};
/// 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);
/// ```
#[inline]
pub fn rotation_wrt_point(r: R, p: Point<N, D>) -> Self {
let shift = r.transform_vector(&-&p.coords);
Self::from_parts(Translation::from(shift + p.coords), r)
}
}
impl<N: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> One for Isometry<N, D, R>
where DefaultAllocator: Allocator<N, D>
{
/// Creates a new identity isometry.
#[inline]
fn one() -> Self {
Self::identity()
}
}
impl<N: RealField, D: DimName, R> Distribution<Isometry<N, D, R>> for Standard
where
R: AlgaRotation<Point<N, D>>,
Standard: Distribution<N> + Distribution<R>,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Isometry<N, D, R> {
Isometry::from_parts(rng.gen(), rng.gen())
}
}
#[cfg(feature = "arbitrary")]
impl<N, D: DimName, R> Arbitrary for Isometry<N, D, R>
where
N: RealField + Arbitrary + Send,
R: AlgaRotation<Point<N, D>> + Arbitrary + Send,
Owned<N, D>: Send,
DefaultAllocator: Allocator<N, D>,
{
#[inline]
fn arbitrary<G: Gen>(rng: &mut G) -> Self {
Self::from_parts(Arbitrary::arbitrary(rng), Arbitrary::arbitrary(rng))
}
}
/*
*
* Constructors for various static dimensions.
*
*/
// 2D rotation.
impl<N: RealField> Isometry<N, U2, Rotation2<N>> {
/// Creates a new 2D isometry from a translation and a rotation angle.
///
/// Its rotational part is represented as a 2x2 rotation matrix.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{Isometry2, Vector2, Point2};
/// 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));
/// ```
#[inline]
pub fn new(translation: Vector2<N>, angle: N) -> Self {
Self::from_parts(
Translation::from(translation),
Rotation::<N, U2>::new(angle),
)
}
/// Creates a new isometry from the given translation coordinates.
#[inline]
pub fn translation(x: N, y: N) -> Self {
Self::new(Vector2::new(x, y), N::zero())
}
/// Creates a new isometry from the given rotation angle.
#[inline]
pub fn rotation(angle: N) -> Self {
Self::new(Vector2::zeros(), angle)
}
}
impl<N: RealField> Isometry<N, U2, UnitComplex<N>> {
/// Creates a new 2D isometry from a translation and a rotation angle.
///
/// Its rotational part is represented as an unit complex number.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{IsometryMatrix2, Point2, Vector2};
/// 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));
/// ```
#[inline]
pub fn new(translation: Vector2<N>, angle: N) -> Self {
Self::from_parts(
Translation::from(translation),
UnitComplex::from_angle(angle),
)
}
/// Creates a new isometry from the given translation coordinates.
#[inline]
pub fn translation(x: N, y: N) -> Self {
Self::from_parts(Translation2::new(x, y), UnitComplex::identity())
}
/// Creates a new isometry from the given rotation angle.
#[inline]
pub fn rotation(angle: N) -> Self {
Self::new(Vector2::zeros(), angle)
}
}
// 3D rotation.
macro_rules! isometry_construction_impl(
($RotId: ident < $($RotParams: ident),*>, $RRDim: ty, $RCDim: ty) => {
impl<N: RealField> Isometry<N, U3, $RotId<$($RotParams),*>> {
/// Creates a new isometry from a translation and a rotation axis-angle.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
/// 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);
/// ```
#[inline]
pub fn new(translation: Vector3<N>, axisangle: Vector3<N>) -> Self {
Self::from_parts(
Translation::from(translation),
$RotId::<$($RotParams),*>::from_scaled_axis(axisangle))
}
/// Creates a new isometry from the given translation coordinates.
#[inline]
pub fn translation(x: N, y: N, z: N) -> Self {
Self::from_parts(Translation3::new(x, y, z), $RotId::identity())
}
/// Creates a new isometry from the given rotation angle.
#[inline]
pub fn rotation(axisangle: Vector3<N>) -> Self {
Self::new(Vector3::zeros(), axisangle)
}
/// 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 - eye`and 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
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
/// 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());
/// ```
#[inline]
pub fn face_towards(eye: &Point3<N>,
target: &Point3<N>,
up: &Vector3<N>)
-> Self {
Self::from_parts(
Translation::from(eye.coords.clone()),
$RotId::face_towards(&(target - eye), up))
}
/// Deprecated: Use [Isometry::face_towards] instead.
#[deprecated(note="renamed to `face_towards`")]
pub fn new_observer_frame(eye: &Point3<N>,
target: &Point3<N>,
up: &Vector3<N>)
-> Self {
Self::face_towards(eye, target, up)
}
/// 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
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
/// 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());
/// ```
#[inline]
pub fn look_at_rh(eye: &Point3<N>,
target: &Point3<N>,
up: &Vector3<N>)
-> Self {
let rotation = $RotId::look_at_rh(&(target - eye), up);
let trans = &rotation * (-eye);
Self::from_parts(Translation::from(trans.coords), rotation)
}
/// 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
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};
/// 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());
/// ```
#[inline]
pub fn look_at_lh(eye: &Point3<N>,
target: &Point3<N>,
up: &Vector3<N>)
-> Self {
let rotation = $RotId::look_at_lh(&(target - eye), up);
let trans = &rotation * (-eye);
Self::from_parts(Translation::from(trans.coords), rotation)
}
}
}
);
isometry_construction_impl!(Rotation3<N>, U3, U3);
isometry_construction_impl!(UnitQuaternion<N>, U4, U1);