#[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, Point, Point3, Rotation2, Rotation3, Scalar, Similarity,
Translation, UnitComplex, UnitQuaternion,
};
impl<T: SimdRealField, R, const D: usize> Default for Similarity<T, R, D>
where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
fn default() -> Self {
Self::identity()
}
}
impl<T: SimdRealField, R, const D: usize> Similarity<T, R, D>
where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
/// Creates a new identity similarity.
///
/// # Example
/// ```
/// # use nalgebra::{Similarity2, Point2, Similarity3, Point3};
///
/// let sim = Similarity2::identity();
/// let pt = Point2::new(1.0, 2.0);
/// assert_eq!(sim * pt, pt);
///
/// let sim = Similarity3::identity();
/// let pt = Point3::new(1.0, 2.0, 3.0);
/// assert_eq!(sim * pt, pt);
/// ```
#[inline]
pub fn identity() -> Self {
Self::from_isometry(Isometry::identity(), T::one())
}
}
impl<T: SimdRealField, R, const D: usize> One for Similarity<T, R, D>
where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
/// Creates a new identity similarity.
#[inline]
fn one() -> Self {
Self::identity()
}
}
#[cfg(feature = "rand-no-std")]
impl<T: crate::RealField, R, const D: usize> Distribution<Similarity<T, R, D>> for Standard
where
R: AbstractRotation<T, D>,
Standard: Distribution<T> + Distribution<R>,
{
/// Generate an arbitrary random variate for testing purposes.
#[inline]
fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<T, R, D> {
let mut s = rng.gen();
while relative_eq!(s, T::zero()) {
s = rng.gen()
}
Similarity::from_isometry(rng.gen(), s)
}
}
impl<T: SimdRealField, R, const D: usize> Similarity<T, R, D>
where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,
{
/// The similarity that applies the scaling factor `scaling`, followed by the rotation `r` with
/// its axis passing through the point `p`.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity2, Point2, UnitComplex};
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
/// let pt = Point2::new(3.0, 2.0);
/// let sim = Similarity2::rotation_wrt_point(rot, pt, 4.0);
///
/// assert_relative_eq!(sim * Point2::new(1.0, 2.0), Point2::new(-3.0, 3.0), epsilon = 1.0e-6);
/// ```
#[inline]
pub fn rotation_wrt_point(r: R, p: Point<T, D>, scaling: T) -> Self {
let shift = r.transform_vector(&-&p.coords);
Self::from_parts(Translation::from(shift + p.coords), r, scaling)
}
}
#[cfg(feature = "arbitrary")]
impl<T, R, const D: usize> Arbitrary for Similarity<T, R, D>
where
T: crate::RealField + Arbitrary + Send,
T::Element: crate::RealField,
R: AbstractRotation<T, D> + Arbitrary + Send,
Owned<T, crate::Const<D>>: Send,
{
#[inline]
fn arbitrary(rng: &mut Gen) -> Self {
let mut s: T = Arbitrary::arbitrary(rng);
while s.is_zero() {
s = Arbitrary::arbitrary(rng)
}
Self::from_isometry(Arbitrary::arbitrary(rng), s)
}
}
/*
*
* Constructors for various static dimensions.
*
*/
// 2D similarity.
impl<T: SimdRealField> Similarity<T, Rotation2<T>, 2>
where
T::Element: SimdRealField,
{
/// Creates a new similarity from a translation, a rotation, and an uniform scaling factor.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{SimilarityMatrix2, Vector2, Point2};
/// let sim = SimilarityMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
///
/// assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);
/// ```
#[inline]
pub fn new(translation: Vector2<T>, angle: T, scaling: T) -> Self {
Self::from_parts(
Translation::from(translation),
Rotation2::new(angle),
scaling,
)
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::SimilarityMatrix2;
/// let sim = SimilarityMatrix2::<f64>::identity();
/// let sim2 = sim.cast::<f32>();
/// assert_eq!(sim2, SimilarityMatrix2::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> Similarity<To, Rotation2<To>, 2>
where
Similarity<To, Rotation2<To>, 2>: SupersetOf<Self>,
{
crate::convert(self)
}
}
impl<T: SimdRealField> Similarity<T, UnitComplex<T>, 2>
where
T::Element: SimdRealField,
{
/// Creates a new similarity from a translation and a rotation angle.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity2, Vector2, Point2};
/// let sim = Similarity2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);
///
/// assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);
/// ```
#[inline]
pub fn new(translation: Vector2<T>, angle: T, scaling: T) -> Self {
Self::from_parts(
Translation::from(translation),
UnitComplex::new(angle),
scaling,
)
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Similarity2;
/// let sim = Similarity2::<f64>::identity();
/// let sim2 = sim.cast::<f32>();
/// assert_eq!(sim2, Similarity2::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> Similarity<To, UnitComplex<To>, 2>
where
Similarity<To, UnitComplex<To>, 2>: SupersetOf<Self>,
{
crate::convert(self)
}
}
// 3D rotation.
macro_rules! similarity_construction_impl(
($Rot: ident) => {
impl<T: SimdRealField> Similarity<T, $Rot<T>, 3>
where T::Element: SimdRealField {
/// Creates a new similarity from a translation, rotation axis-angle, and scaling
/// factor.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Similarity3, SimilarityMatrix3, 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);
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let sim = Similarity3::new(translation, axisangle, 3.0);
/// assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
/// assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
///
/// // Similarity with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
/// let sim = SimilarityMatrix3::new(translation, axisangle, 3.0);
/// assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
/// assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);
/// ```
#[inline]
pub fn new(translation: Vector3<T>, axisangle: Vector3<T>, scaling: T) -> Self
{
Self::from_isometry(Isometry::<_, $Rot<T>, 3>::new(translation, axisangle), scaling)
}
/// Cast the components of `self` to another type.
///
/// # Example
/// ```
/// # use nalgebra::Similarity3;
/// let sim = Similarity3::<f64>::identity();
/// let sim2 = sim.cast::<f32>();
/// assert_eq!(sim2, Similarity3::<f32>::identity());
/// ```
pub fn cast<To: Scalar>(self) -> Similarity<To, $Rot<To>, 3>
where
Similarity<To, $Rot<To>, 3>: SupersetOf<Self>,
{
crate::convert(self)
}
/// Creates an similarity that corresponds to a scaling factor and a local frame of
/// an observer standing at the point `eye` and looking toward `target`.
///
/// It maps the view direction `target - eye` to the positive `z` axis 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::{Similarity3, SimilarityMatrix3, 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();
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let sim = Similarity3::face_towards(&eye, &target, &up, 3.0);
/// assert_eq!(sim * Point3::origin(), eye);
/// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
///
/// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
/// let sim = SimilarityMatrix3::face_towards(&eye, &target, &up, 3.0);
/// assert_eq!(sim * Point3::origin(), eye);
/// assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);
/// ```
#[inline]
pub fn face_towards(eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T)
-> Self {
Self::from_isometry(Isometry::<_, $Rot<T>, 3>::face_towards(eye, target, up), scaling)
}
/// Deprecated: Use [`SimilarityMatrix3::face_towards`](Self::face_towards) instead.
#[deprecated(note="renamed to `face_towards`")]
pub fn new_observer_frames(eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T)
-> Self {
Self::face_towards(eye, target, up, scaling)
}
/// Builds a right-handed look-at view matrix including scaling factor.
///
/// This conforms to the common notion of right handed look-at matrix from the computer
/// graphics community.
///
/// # 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::{Similarity3, SimilarityMatrix3, 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();
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let iso = Similarity3::look_at_rh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);
///
/// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
/// let iso = SimilarityMatrix3::look_at_rh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);
/// ```
#[inline]
pub fn look_at_rh(eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T)
-> Self {
Self::from_isometry(Isometry::<_, $Rot<T>, 3>::look_at_rh(eye, target, up), scaling)
}
/// Builds a left-handed look-at view matrix including a scaling factor.
///
/// This conforms to the common notion of left handed look-at matrix from the computer
/// graphics community.
///
/// # 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::{Similarity3, SimilarityMatrix3, 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();
///
/// // Similarity with its rotation part represented as a UnitQuaternion
/// let sim = Similarity3::look_at_lh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);
///
/// // Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
/// let sim = SimilarityMatrix3::look_at_lh(&eye, &target, &up, 3.0);
/// assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);
/// ```
#[inline]
pub fn look_at_lh(eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T)
-> Self {
Self::from_isometry(Isometry::<_, $Rot<T>, 3>::look_at_lh(eye, target, up), scaling)
}
}
}
);
similarity_construction_impl!(Rotation3);
similarity_construction_impl!(UnitQuaternion);