unit_complex_construction.rs - source
Description: Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/geometry/unit_complex_construction.rs`.
Keywords: rust, rustlang, rust-lang

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    #[cfg(feature = "arbitrary")]
    use quickcheck::{Arbitrary, Gen};

    #[cfg(feature = "rand-no-std")]
    use rand::{
        distributions::{Distribution, Standard},
        Rng,
    };

    use num::One;
    use num_complex::Complex;

    use crate::base::dimension::{U1, U2};
    use crate::base::storage::Storage;
    use crate::base::{Matrix2, Scalar, Unit, Vector, Vector2};
    use crate::geometry::{Rotation2, UnitComplex};
    use simba::scalar::{RealField, SupersetOf};
    use simba::simd::SimdRealField;

    impl<T: SimdRealField> Default for UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        fn default() -> Self {
            Self::identity()
        }
    }

    /// # Identity
    impl<T: SimdRealField> UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        /// The unit complex number multiplicative identity.
        ///
        /// # Example
        /// ```
        /// # use nalgebra::UnitComplex;
        /// let rot1 = UnitComplex::identity();
        /// let rot2 = UnitComplex::new(1.7);
        ///
        /// assert_eq!(rot1 * rot2, rot2);
        /// assert_eq!(rot2 * rot1, rot2);
        /// ```
        #[inline]
        pub fn identity() -> Self {
            Self::new_unchecked(Complex::new(T::one(), T::zero()))
        }
    }

    /// # Construction from a 2D rotation angle
    impl<T: SimdRealField> UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        /// Builds the unit complex number corresponding to the rotation with the given angle.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{UnitComplex, Point2};
        /// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
        ///
        /// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
        /// ```
        #[inline]
        pub fn new(angle: T) -> Self {
            let (sin, cos) = angle.simd_sin_cos();
            Self::from_cos_sin_unchecked(cos, sin)
        }

        /// Builds the unit complex number corresponding to the rotation with the angle.
        ///
        /// Same as `Self::new(angle)`.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{UnitComplex, Point2};
        /// let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);
        ///
        /// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
        /// ```
        // TODO: deprecate this.
        #[inline]
        pub fn from_angle(angle: T) -> Self {
            Self::new(angle)
        }

        /// Builds the unit complex number from the sinus and cosinus of the rotation angle.
        ///
        /// The input values are not checked to actually be cosines and sine of the same value.
        /// Is is generally preferable to use the `::new(angle)` constructor instead.
        ///
        /// # Example
        ///
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use std::f32;
        /// # use nalgebra::{UnitComplex, Vector2, Point2};
        /// let angle = f32::consts::FRAC_PI_2;
        /// let rot = UnitComplex::from_cos_sin_unchecked(angle.cos(), angle.sin());
        ///
        /// assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));
        /// ```
        #[inline]
        pub fn from_cos_sin_unchecked(cos: T, sin: T) -> Self {
            Self::new_unchecked(Complex::new(cos, sin))
        }

        /// Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.
        ///
        /// This is generally used in the context of generic programming. Using
        /// the `::new(angle)` method instead is more common.
        #[inline]
        pub fn from_scaled_axis<SB: Storage<T, U1>>(axisangle: Vector<T, U1, SB>) -> Self {
            Self::from_angle(axisangle[0].clone())
        }
    }

    /// # Construction from an existing 2D matrix or complex number
    impl<T: SimdRealField> UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        /// Cast the components of `self` to another type.
        ///
        /// # Example
        /// ```
        /// #[macro_use] extern crate approx;
        /// # use nalgebra::UnitComplex;
        /// let c = UnitComplex::new(1.0f64);
        /// let c2 = c.cast::<f32>();
        /// assert_relative_eq!(c2, UnitComplex::new(1.0f32));
        /// ```
        pub fn cast<To: Scalar>(self) -> UnitComplex<To>
        where
            UnitComplex<To>: SupersetOf<Self>,
        {
            crate::convert(self)
        }

        /// The underlying complex number.
        ///
        /// Same as `self.as_ref()`.
        ///
        /// # Example
        /// ```
        /// # extern crate num_complex;
        /// # use num_complex::Complex;
        /// # use nalgebra::UnitComplex;
        /// let angle = 1.78f32;
        /// let rot = UnitComplex::new(angle);
        /// assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));
        /// ```
        #[inline]
        #[must_use]
        pub fn complex(&self) -> &Complex<T> {
            self.as_ref()
        }

        /// Creates a new unit complex number from a complex number.
        ///
        /// The input complex number will be normalized.
        #[inline]
        pub fn from_complex(q: Complex<T>) -> Self {
            Self::from_complex_and_get(q).0
        }

        /// Creates a new unit complex number from a complex number.
        ///
        /// The input complex number will be normalized. Returns the norm of the complex number as well.
        #[inline]
        pub fn from_complex_and_get(q: Complex<T>) -> (Self, T) {
            let norm = (q.im.clone() * q.im.clone() + q.re.clone() * q.re.clone()).simd_sqrt();
            (Self::new_unchecked(q / norm.clone()), norm)
        }

        /// Builds the unit complex number from the corresponding 2D rotation matrix.
        ///
        /// # Example
        /// ```
        /// # use nalgebra::{Rotation2, UnitComplex};
        /// let rot = Rotation2::new(1.7);
        /// let complex = UnitComplex::from_rotation_matrix(&rot);
        /// assert_eq!(complex, UnitComplex::new(1.7));
        /// ```
        // TODO: add UnitComplex::from(...) instead?
        #[inline]
        pub fn from_rotation_matrix(rotmat: &Rotation2<T>) -> Self {
            Self::new_unchecked(Complex::new(rotmat[(0, 0)].clone(), rotmat[(1, 0)].clone()))
        }

        /// Builds a rotation from a basis assumed to be orthonormal.
        ///
        /// In order to get a valid unit-quaternion, the input must be an
        /// orthonormal basis, i.e., all vectors are normalized, and the are
        /// all orthogonal to each other. These invariants are not checked
        /// by this method.
        pub fn from_basis_unchecked(basis: &[Vector2<T>; 2]) -> Self {
            let mat = Matrix2::from_columns(&basis[..]);
            let rot = Rotation2::from_matrix_unchecked(mat);
            Self::from_rotation_matrix(&rot)
        }

        /// Builds an unit complex by extracting the rotation part of the given transformation `m`.
        ///
        /// This is an iterative method. See `.from_matrix_eps` to provide mover
        /// convergence parameters and starting solution.
        /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
        pub fn from_matrix(m: &Matrix2<T>) -> Self
        where
            T: RealField,
        {
            Rotation2::from_matrix(m).into()
        }

        /// Builds an unit complex by extracting the rotation part of the given transformation `m`.
        ///
        /// This implements "A Robust Method to Extract the Rotational Part of Deformations" by Müller et al.
        ///
        /// # Parameters
        ///
        /// * `m`: the matrix from which the rotational part is to be extracted.
        /// * `eps`: the angular errors tolerated between the current rotation and the optimal one.
        /// * `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
        /// * `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close
        ///           to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other
        ///           guesses come to mind.
        pub fn from_matrix_eps(m: &Matrix2<T>, eps: T, max_iter: usize, guess: Self) -> Self
        where
            T: RealField,
        {
            let guess = Rotation2::from(guess);
            Rotation2::from_matrix_eps(m, eps, max_iter, guess).into()
        }

        /// The unit complex number needed to make `self` and `other` coincide.
        ///
        /// The result is such that: `self.rotation_to(other) * self == other`.
        ///
        /// # Example
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use nalgebra::UnitComplex;
        /// let rot1 = UnitComplex::new(0.1);
        /// let rot2 = UnitComplex::new(1.7);
        /// let rot_to = rot1.rotation_to(&rot2);
        ///
        /// assert_relative_eq!(rot_to * rot1, rot2);
        /// assert_relative_eq!(rot_to.inverse() * rot2, rot1);
        /// ```
        #[inline]
        #[must_use]
        pub fn rotation_to(&self, other: &Self) -> Self {
            other / self
        }

        /// Raise this unit complex number to a given floating power.
        ///
        /// This returns the unit complex number that identifies a rotation angle equal to
        /// `self.angle() × n`.
        ///
        /// # Example
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use nalgebra::UnitComplex;
        /// let rot = UnitComplex::new(0.78);
        /// let pow = rot.powf(2.0);
        /// assert_relative_eq!(pow.angle(), 2.0 * 0.78);
        /// ```
        #[inline]
        #[must_use]
        pub fn powf(&self, n: T) -> Self {
            Self::from_angle(self.angle() * n)
        }
    }

    /// # Construction from two vectors
    impl<T: SimdRealField> UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        /// The unit complex needed to make `a` and `b` be collinear and point toward the same
        /// direction.
        ///
        /// # Example
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use nalgebra::{Vector2, UnitComplex};
        /// let a = Vector2::new(1.0, 2.0);
        /// let b = Vector2::new(2.0, 1.0);
        /// let rot = UnitComplex::rotation_between(&a, &b);
        /// assert_relative_eq!(rot * a, b);
        /// assert_relative_eq!(rot.inverse() * b, a);
        /// ```
        #[inline]
        pub fn rotation_between<SB, SC>(a: &Vector<T, U2, SB>, b: &Vector<T, U2, SC>) -> Self
        where
            T: RealField,
            SB: Storage<T, U2>,
            SC: Storage<T, U2>,
        {
            Self::scaled_rotation_between(a, b, T::one())
        }

        /// The smallest rotation needed to make `a` and `b` collinear and point toward the same
        /// direction, raised to the power `s`.
        ///
        /// # Example
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use nalgebra::{Vector2, UnitComplex};
        /// let a = Vector2::new(1.0, 2.0);
        /// let b = Vector2::new(2.0, 1.0);
        /// let rot2 = UnitComplex::scaled_rotation_between(&a, &b, 0.2);
        /// let rot5 = UnitComplex::scaled_rotation_between(&a, &b, 0.5);
        /// assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
        /// assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);
        /// ```
        #[inline]
        pub fn scaled_rotation_between<SB, SC>(
            a: &Vector<T, U2, SB>,
            b: &Vector<T, U2, SC>,
            s: T,
        ) -> Self
        where
            T: RealField,
            SB: Storage<T, U2>,
            SC: Storage<T, U2>,
        {
            // TODO: code duplication with Rotation.
            if let (Some(na), Some(nb)) = (
                Unit::try_new(a.clone_owned(), T::zero()),
                Unit::try_new(b.clone_owned(), T::zero()),
            ) {
                Self::scaled_rotation_between_axis(&na, &nb, s)
            } else {
                Self::identity()
            }
        }

        /// The unit complex needed to make `a` and `b` be collinear and point toward the same
        /// direction.
        ///
        /// # Example
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use nalgebra::{Unit, Vector2, UnitComplex};
        /// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
        /// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
        /// let rot = UnitComplex::rotation_between_axis(&a, &b);
        /// assert_relative_eq!(rot * a, b);
        /// assert_relative_eq!(rot.inverse() * b, a);
        /// ```
        #[inline]
        pub fn rotation_between_axis<SB, SC>(
            a: &Unit<Vector<T, U2, SB>>,
            b: &Unit<Vector<T, U2, SC>>,
        ) -> Self
        where
            SB: Storage<T, U2>,
            SC: Storage<T, U2>,
        {
            Self::scaled_rotation_between_axis(a, b, T::one())
        }

        /// The smallest rotation needed to make `a` and `b` collinear and point toward the same
        /// direction, raised to the power `s`.
        ///
        /// # Example
        /// ```
        /// # #[macro_use] extern crate approx;
        /// # use nalgebra::{Unit, Vector2, UnitComplex};
        /// let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
        /// let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
        /// let rot2 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.2);
        /// let rot5 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.5);
        /// assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
        /// assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);
        /// ```
        #[inline]
        pub fn scaled_rotation_between_axis<SB, SC>(
            na: &Unit<Vector<T, U2, SB>>,
            nb: &Unit<Vector<T, U2, SC>>,
            s: T,
        ) -> Self
        where
            SB: Storage<T, U2>,
            SC: Storage<T, U2>,
        {
            let sang = na.perp(nb);
            let cang = na.dot(nb);

            Self::from_angle(sang.simd_atan2(cang) * s)
        }
    }

    impl<T: SimdRealField> One for UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        #[inline]
        fn one() -> Self {
            Self::identity()
        }
    }

    #[cfg(feature = "rand")]
    impl<T: SimdRealField> Distribution<UnitComplex<T>> for Standard
    where
        T::Element: SimdRealField,
        rand_distr::UnitCircle: Distribution<[T; 2]>,
    {
        /// Generate a uniformly distributed random `UnitComplex`.
        #[inline]
        fn sample<'a, R: Rng + ?Sized>(&self, rng: &mut R) -> UnitComplex<T> {
            let x = rng.sample(rand_distr::UnitCircle);
            UnitComplex::new_unchecked(Complex::new(x[0].clone(), x[1].clone()))
        }
    }

    #[cfg(feature = "arbitrary")]
    impl<T: SimdRealField + Arbitrary> Arbitrary for UnitComplex<T>
    where
        T::Element: SimdRealField,
    {
        #[inline]
        fn arbitrary(g: &mut Gen) -> Self {
            UnitComplex::from_angle(T::arbitrary(g))
        }
    }