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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 simba::scalar::RealField;
use simba::simd::SimdRealField;
use crate::base::allocator::Allocator;
use crate::base::dimension::{DimName, U2, U3};
use crate::base::{DefaultAllocator, Vector2, Vector3};
use crate::geometry::{
AbstractRotation, Isometry, Point, Point3, Rotation2, Rotation3, Similarity, Translation,
UnitComplex, UnitQuaternion,
};
impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
where
N::Element: SimdRealField,
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, 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(), N::one())
}
}
impl<N: SimdRealField, D: DimName, R> One for Similarity<N, D, R>
where
N::Element: SimdRealField,
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
{
/// Creates a new identity similarity.
#[inline]
fn one() -> Self {
Self::identity()
}
}
impl<N: RealField, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard
where
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, D>,
Standard: Distribution<N> + Distribution<R>,
{
#[inline]
fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<N, D, R> {
let mut s = rng.gen();
while relative_eq!(s, N::zero()) {
s = rng.gen()
}
Similarity::from_isometry(rng.gen(), s)
}
}
impl<N: SimdRealField, D: DimName, R> Similarity<N, D, R>
where
N::Element: SimdRealField,
R: AbstractRotation<N, D>,
DefaultAllocator: Allocator<N, 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<N, D>, scaling: N) -> Self {
let shift = r.transform_vector(&-&p.coords);
Self::from_parts(Translation::from(shift + p.coords), r, scaling)
}
}
#[cfg(feature = "arbitrary")]
impl<N, D: DimName, R> Arbitrary for Similarity<N, D, R>
where
N: RealField + Arbitrary + Send,
N::Element: RealField,
R: AbstractRotation<N, D> + Arbitrary + Send,
DefaultAllocator: Allocator<N, D>,
Owned<N, D>: Send,
{
#[inline]
fn arbitrary<G: Gen>(rng: &mut G) -> Self {
let mut s: N = 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<N: SimdRealField> Similarity<N, U2, Rotation2<N>>
where
N::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<N>, angle: N, scaling: N) -> Self {
Self::from_parts(
Translation::from(translation),
Rotation2::new(angle),
scaling,
)
}
}
impl<N: SimdRealField> Similarity<N, U2, UnitComplex<N>>
where
N::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<N>, angle: N, scaling: N) -> Self {
Self::from_parts(
Translation::from(translation),
UnitComplex::new(angle),
scaling,
)
}
}
// 3D rotation.
macro_rules! similarity_construction_impl(
($Rot: ty) => {
impl<N: SimdRealField> Similarity<N, U3, $Rot>
where N::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<N>, axisangle: Vector3<N>, scaling: N) -> Self
{
Self::from_isometry(Isometry::<_, U3, $Rot>::new(translation, axisangle), scaling)
}
/// 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<N>,
target: &Point3<N>,
up: &Vector3<N>,
scaling: N)
-> Self {
Self::from_isometry(Isometry::<_, U3, $Rot>::face_towards(eye, target, up), scaling)
}
/// Deprecated: Use [SimilarityMatrix3::face_towards] instead.
#[deprecated(note="renamed to `face_towards`")]
pub fn new_observer_frames(eye: &Point3<N>,
target: &Point3<N>,
up: &Vector3<N>,
scaling: N)
-> 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<N>,
target: &Point3<N>,
up: &Vector3<N>,
scaling: N)
-> Self {
Self::from_isometry(Isometry::<_, U3, $Rot>::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<N>,
target: &Point3<N>,
up: &Vector3<N>,
scaling: N)
-> Self {
Self::from_isometry(Isometry::<_, _, $Rot>::look_at_lh(eye, target, up), scaling)
}
}
}
);
similarity_construction_impl!(Rotation3<N>);
similarity_construction_impl!(UnitQuaternion<N>);