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geometric operations

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Adam Nemecek 2019-03-21 11:34:06 -07:00 committed by Sébastien Crozet
parent 1e614db227
commit e416360fc9
1 changed files with 75 additions and 0 deletions
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src/geometry/quaternion.rs
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@ -307,6 +307,81 @@ impl<N: Real> Quaternion<N> {
self.coords.dot(&rhs.coords)
}
/// Calculates the inner product (also known as the dot product).
/// See "Foundations of Game Engine Development, Volume 1: Mathematics" by Lengyel
/// Formula 4.89.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::Quaternion;
/// let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
/// let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
/// let expected = Quaternion::new(-20.0, 0.0, 0.0, 0.0);
/// let result = a.inner(&b);
/// assert_relative_eq!(expected, result, epsilon = 1.0e-5);
#[inline]
pub fn inner(&self, other: &Self) -> Self {
(self * other + other * self).half()
}
/// Calculates the outer product (also known as the wedge product).
/// See "Foundations of Game Engine Development, Volume 1: Mathematics" by Lengyel
/// Formula 4.89.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::Quaternion;
/// let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
/// let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
/// let expected = Quaternion::new(0.0, -5.0, 18.0, -11.0);
/// let result = a.outer(&b);
/// assert_relative_eq!(expected, result, epsilon = 1.0e-5);
/// ```
#[inline]
pub fn outer(&self, other: &Self) -> Self {
(self * other - other * self).half()
}
/// Calculates the projection of `self` onto `other` (also known as the parallel).
/// See "Foundations of Game Engine Development, Volume 1: Mathematics" by Lengyel
/// Formula 4.94.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::Quaternion;
/// let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
/// let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
/// let expected = Quaternion::new(0.0, 3.333333333333333, 1.3333333333333333, 0.6666666666666666);
/// let result = a.project(&b).unwrap();
/// assert_relative_eq!(expected, result, epsilon = 1.0e-5);
/// ```
#[inline]
pub fn project(&self, other: &Self) -> Option<Self> {
self.inner(other).right_div(other)
}
/// Calculates the rejection of `self` from `other` (also known as the perpendicular).
/// See "Foundations of Game Engine Development, Volume 1: Mathematics" by Lengyel
/// Formula 4.94.
///
/// # Example
/// ```
/// # #[macro_use] extern crate approx;
/// # use nalgebra::Quaternion;
/// let a = Quaternion::new(0.0, 2.0, 3.0, 4.0);
/// let b = Quaternion::new(0.0, 5.0, 2.0, 1.0);
/// let expected = Quaternion::new(0.0, -1.3333333333333333, 1.6666666666666665, 3.3333333333333335);
/// let result = a.reject(&b).unwrap();
/// assert_relative_eq!(expected, result, epsilon = 1.0e-5);
/// ```
#[inline]
pub fn reject(&self, other: &Self) -> Option<Self> {
self.outer(other).right_div(other)
}
/// The polar decomposition of this quaternion.
///
/// Returns, from left to right: the quaternion norm, the half rotation angle, the rotation