nalgebra/geometry/isometry_construction.rs
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#[cfg(feature = "arbitrary")]
use crate::base::storage::Owned;
#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
use num::One;
#[cfg(feature = "rand-no-std")]
use rand::{
distributions::{Distribution, Standard},
Rng,
};
use simba::scalar::SupersetOf;
use simba::simd::SimdRealField;
use crate::base::{Vector2, Vector3};
use crate::{
AbstractRotation, Isometry, Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3, Point,
Point3, Rotation, Rotation3, Scalar, Translation, Translation2, Translation3, UnitComplex,
UnitQuaternion,
};
impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> Default for Isometry<T, R, D>
where
T::Element: SimdRealField,
{
fn default() -> Self {
Self::identity()
}
}
impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> Isometry<T, R, D>
where
T::Element: SimdRealField,
{
/// 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<T, D>) -> Self {
let shift = r.transform_vector(&-&p.coords);
Self::from_parts(Translation::from(shift + p.coords), r)
}
}
impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> One for Isometry<T, R, D>
where
T::Element: SimdRealField,
{
/// Creates a new identity isometry.
#[inline]
fn one() -> Self {
Self::identity()
}
}
#[cfg(feature = "rand-no-std")]
impl<T: crate::RealField, R, const D: usize> Distribution<Isometry<T, R, D>> for Standard
where
R: AbstractRotation<T, D>,
Standard: Distribution<T> + Distribution<R>,
{
#[inline]
fn sample<G: Rng + ?Sized>(&self, rng: &mut G) -> Isometry<T, R, D> {
Isometry::from_parts(rng.gen(), rng.gen())
}
}
#[cfg(feature = "arbitrary")]
impl<T, R, const D: usize> Arbitrary for Isometry<T, R, D>
where
T: SimdRealField + Arbitrary + Send,
T::Element: SimdRealField,
R: AbstractRotation<T, D> + Arbitrary + Send,
Owned<T, crate::Const<D>>: Send,
{
#[inline]
fn arbitrary(rng: &mut Gen) -> Self {
Self::from_parts(Arbitrary::arbitrary(rng), Arbitrary::arbitrary(rng))
}
}
/*
*
* Constructors for various static dimensions.
*
*/
/// # Construction from a 2D vector and/or a rotation angle
impl<T: SimdRealField> IsometryMatrix2<T>
where
T::Element: SimdRealField,
{
/// 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<T>, angle: T) -> Self {
Self::from_parts(Translation::from(translation), Rotation::<T, 2>::new(angle))
}
/// Creates a new isometry from the given translation coordinates.
#[inline]
pub fn translation(x: T, y: T) -> Self {
Self::new(Vector2::new(x, y), T::zero())
}
/// Creates a new isometry from the given rotation angle.
#[inline]
pub fn rotation(angle: T) -> Self {
Self::new(Vector2::zeros(), angle)
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::IsometryMatrix2;
/// let iso = IsometryMatrix2::<f64>::identity();
/// let iso2 = iso.cast::<f32>();
/// assert_eq!(iso2, IsometryMatrix2::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> IsometryMatrix2<To>
where
IsometryMatrix2<To>: SupersetOf<Self>,
{
crate::convert(self)
}
}
impl<T: SimdRealField> Isometry2<T>
where
T::Element: SimdRealField,
{
/// 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<T>, angle: T) -> 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: T, y: T) -> Self {
Self::from_parts(Translation2::new(x, y), UnitComplex::identity())
}
/// Creates a new isometry from the given rotation angle.
#[inline]
pub fn rotation(angle: T) -> Self {
Self::new(Vector2::zeros(), angle)
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Isometry2;
/// let iso = Isometry2::<f64>::identity();
/// let iso2 = iso.cast::<f32>();
/// assert_eq!(iso2, Isometry2::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> Isometry2<To>
where
Isometry2<To>: SupersetOf<Self>,
{
crate::convert(self)
}
}
// 3D rotation.
macro_rules! basic_isometry_construction_impl(
($RotId: ident < $($RotParams: ident),*>) => {
/// 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<T>, axisangle: Vector3<T>) -> 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: T, y: T, z: T) -> Self {
Self::from_parts(Translation3::new(x, y, z), $RotId::identity())
}
/// Creates a new isometry from the given rotation angle.
#[inline]
pub fn rotation(axisangle: Vector3<T>) -> Self {
Self::new(Vector3::zeros(), axisangle)
}
}
);
macro_rules! look_at_isometry_construction_impl(
($RotId: ident < $($RotParams: ident),*>) => {
/// 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<T>,
target: &Point3<T>,
up: &Vector3<T>)
-> 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<T>,
target: &Point3<T>,
up: &Vector3<T>)
-> 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<T>,
target: &Point3<T>,
up: &Vector3<T>)
-> 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 left 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<T>,
target: &Point3<T>,
up: &Vector3<T>)
-> Self {
let rotation = $RotId::look_at_lh(&(target - eye), up);
let trans = &rotation * (-eye);
Self::from_parts(Translation::from(trans.coords), rotation)
}
}
);
/// # Construction from a 3D vector and/or an axis-angle
impl<T: SimdRealField> Isometry3<T>
where
T::Element: SimdRealField,
{
basic_isometry_construction_impl!(UnitQuaternion<T>);
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Isometry3;
/// let iso = Isometry3::<f64>::identity();
/// let iso2 = iso.cast::<f32>();
/// assert_eq!(iso2, Isometry3::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> Isometry3<To>
where
Isometry3<To>: SupersetOf<Self>,
{
crate::convert(self)
}
}
impl<T: SimdRealField> IsometryMatrix3<T>
where
T::Element: SimdRealField,
{
basic_isometry_construction_impl!(Rotation3<T>);
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::IsometryMatrix3;
/// let iso = IsometryMatrix3::<f64>::identity();
/// let iso2 = iso.cast::<f32>();
/// assert_eq!(iso2, IsometryMatrix3::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> IsometryMatrix3<To>
where
IsometryMatrix3<To>: SupersetOf<Self>,
{
crate::convert(self)
}
}
/// # Construction from a 3D eye position and target point
impl<T: SimdRealField> Isometry3<T>
where
T::Element: SimdRealField,
{
look_at_isometry_construction_impl!(UnitQuaternion<T>);
}
impl<T: SimdRealField> IsometryMatrix3<T>
where
T::Element: SimdRealField,
{
look_at_isometry_construction_impl!(Rotation3<T>);
}