ultraviolet 0.2.0-alpha5

//! Bivectors, i.e. oriented areas.
//!
//! A bivector is an *oriented area*, and is equivalent
//! to the result of the exterior (wedge) product of two vectors, i.e.
//! `u ∧ v`. This means it is the *oriented area* of the parallelogram
//! created by attaching two vectors and then extending them into a parallelogram.
//!
//! This may be hard to visualize at first, but bivectors are as fundamental as vectors. If vectors
//! are a representation of *lines*, then bivectors are a representation of *planes*.
//!
//! A normalized bivector can be thought of as representing a plane of rotation and the *direction of rotation*
//! inside that plane such that a *positive* rotation follows the orientation of the bivector. When
//! you obtain a bivector by taking the exterior product of two vectors, the positive direction of rotation
//! is defined as the one that *brings the first vector closer to the second*. For example, a bivector
//! created by taking the exterior product `x ∧ y` of the x and y basis vectors will create a unit
//! bivector that represents the xy plane, with orientation such that a positive rotation of `x` inside
//! the plane would bring `x` closer to `y`. This is why positive rotation is generally defined as
//! "counter clockwise" in 2d, since such a rotation brings `x` to `y`.
//!
//! Much like vectors can be represented as a linear combination of *basis vectors*, i.e.
//! a vector "component representation," bivectors can be represented as a linear combination
//! of *basis bivectors*. If the basis vectors are the unit vectors in the direction of each
//! canonical axis of a space, then the basis bivectors are the *unit area planes* in each of the
//! canonical planes.
//!
//! In 2d, there is only one basis plane, the xy plane, which represents all of 2d space. As such, in 2d
//! there is only *one* basis bivector, while there are *two* basis vectors. This means that a 2d bivector
//! has only one component.
//!
//! In 3d, there are three basis planes, the xy plane, the xz plane, and the yz plane, which are respectively
//! the planes parallel to those combinations of the x, y, and z basis vectors. Therefore, a 3d bivector has
//! three components, each of which represents the *projected area* of that bivector onto one of the three
//! basis bivectors. This is analogous to how vector components represent the *projected length* of that vector
//! onto each unit vector.
use wide::f32x4;

use crate::util::*;
use crate::vec::*;

use std::ops::*;

macro_rules! bivec2s {
    ($(($bn:ident) => $t:ident),+) => {
        $(
        /// A bivector in 2d space.
        ///
        /// Since in 2d there is only one plane in the whole of 2d space, a 2d bivector
        /// has only one component.
        ///
        /// Please see the module level documentation for more information on bivectors generally!
        #[derive(Clone, Copy, Debug)]
        pub struct $bn {
            pub xy: $t
        }

        impl $bn {
            #[inline]
            pub fn new(xy: $t) -> Self {
                Self {
                    xy
                }
            }

            #[inline]
            pub fn unit_xy() -> Self {
                Self::new($t::from(1.0))
            }
        }

        impl EqualsEps for $bn {
            fn eq_eps(self, other: Self) -> bool {
                self.xy.eq_eps(other.xy)
            }
        }

        impl Add for $bn {
            type Output = Self;
            #[inline]
            fn add(mut self, rhs: $bn) -> Self {
                self += rhs;
                self
            }
        }

        impl AddAssign for $bn {
            #[inline]
            fn add_assign(&mut self, rhs: $bn) {
                self.xy += rhs.xy;
            }
        }

        impl Sub for $bn {
            type Output = Self;
            #[inline]
            fn sub(mut self, rhs: $bn) -> Self {
                self -= rhs;
                self
            }
        }

        impl SubAssign for $bn {
            #[inline]
            fn sub_assign(&mut self, rhs: $bn) {
                self.xy -= rhs.xy;
            }
        }

        impl Mul for $bn {
            type Output = Self;
            #[inline]
            fn mul(mut self, rhs: $bn) -> Self {
                self *= rhs;
                self
            }
        }

        impl Mul<$bn> for $t {
            type Output = $bn;
            #[inline]
            fn mul(self, mut rhs: $bn) -> $bn {
                rhs *= self;
                rhs
            }
        }

        impl Mul<$t> for $bn {
            type Output = Self;
            #[inline]
            fn mul(mut self, rhs: $t) -> Self {
                self *= rhs;
                self
            }
        }

        impl MulAssign for $bn {
            #[inline]
            fn mul_assign(&mut self, rhs: Self) {
                self.xy *= rhs.xy;
            }
        }

        impl MulAssign<$t> for $bn {
            #[inline]
            fn mul_assign(&mut self, rhs: $t) {
                self.xy *= rhs;
            }
        }

        impl Div for $bn {
            type Output = Self;
            #[inline]
            fn div(mut self, rhs: $bn) -> Self {
                self /= rhs;
                self
            }
        }

        impl Div<$t> for $bn {
            type Output = $bn;
            #[inline]
            fn div(mut self, rhs: $t) -> $bn {
                self.xy /= rhs;
                self
            }
        }

        impl DivAssign for $bn {
            #[inline]
            fn div_assign(&mut self, rhs: $bn) {
                self.xy /= rhs.xy;
            }
        }

        impl DivAssign<$t> for $bn {
            #[inline]
            fn div_assign(&mut self, rhs: $t) {
                self.xy /= rhs;
            }
        }

        impl Neg for $bn {
            type Output = Self;
            #[inline]
            fn neg(mut self) -> Self {
                self.xy = -self.xy;
                self
            }
        }
        )+
    }
}

bivec2s!((Bivec2) => f32, (WBivec2) => f32x4);

macro_rules! bivec3s {
    ($($bn:ident => ($vt:ident, $t:ident)),+) => {
        $(
        /// A bivector in 3d space.
        ///
        /// In 3d, a bivector has 3 components, each one representing the signed *projected area* of the bivector
        /// onto one of the 3 *basis bivectors*, which can be thought of as corresponding to each of hte
        /// three basis planes. This is analogous to the components of a 3d vector, which correspond to the
        /// *projected length* of the vector onto the three basis *vectors. Since in 3d, there are three
        /// components for both vectors and bivectors, 3d bivectors have been historically confused with
        /// 3d vectors quite a lot.
        ///
        /// Please see the module level documentation for more information on bivectors generally!
        #[derive(Clone, Copy, Debug)]
        pub struct $bn {
            pub xy: $t,
            pub xz: $t,
            pub yz: $t,
        }

        impl EqualsEps for $bn {
            fn eq_eps(self, other: Self) -> bool {
                self.xy.eq_eps(other.xy) && self.xz.eq_eps(other.xz) && self.yz.eq_eps(other.yz)
            }
        }

        impl $bn {
            #[inline]
            pub fn new(xy: $t, xz: $t, yz: $t) -> Self {
                Self {
                    xy, xz, yz
                }
            }

            /// Create the bivector which represents the same plane of rotation as a given
            /// normalized 'axis vector'
            #[inline]
            pub fn from_normalized_axis(v: $vt) -> Self {
                Self::new(v.z, v.y, v.x)
            }

            #[inline]
            pub fn unit_xy() -> Self {
                Self::new($t::from(1.0), $t::from(0.0), $t::from(0.0))
            }

            #[inline]
            pub fn unit_xz() -> Self {
                Self::new($t::from(0.0), $t::from(1.0), $t::from(0.0))
            }

            #[inline]
            pub fn unit_yz() -> Self {
                Self::new($t::from(0.0), $t::from(0.0), $t::from(1.0))
            }
        }

        impl Add for $bn {
            type Output = Self;
            #[inline]
            fn add(mut self, rhs: $bn) -> Self {
                self += rhs;
                self
            }
        }

        impl AddAssign for $bn {
            #[inline]
            fn add_assign(&mut self, rhs: $bn) {
                self.xy += rhs.xy;
                self.xz += rhs.xz;
                self.yz += rhs.yz;
            }
        }

        impl Sub for $bn {
            type Output = Self;
            #[inline]
            fn sub(mut self, rhs: $bn) -> Self {
                self -= rhs;
                self
            }
        }

        impl SubAssign for $bn {
            #[inline]
            fn sub_assign(&mut self, rhs: $bn) {
                self.xy -= rhs.xy;
                self.xz -= rhs.xz;
                self.yz -= rhs.yz;
            }
        }

        impl Mul for $bn {
            type Output = Self;
            #[inline]
            fn mul(mut self, rhs: $bn) -> Self {
                self *= rhs;
                self
            }
        }

        impl Mul<$bn> for $t {
            type Output = $bn;
            #[inline]
            fn mul(self, mut rhs: $bn) -> $bn {
                rhs *= self;
                rhs
            }
        }

        impl Mul<$t> for $bn {
            type Output = Self;
            #[inline]
            fn mul(mut self, rhs: $t) -> Self {
                self *= rhs;
                self
            }
        }

        impl MulAssign for $bn {
            #[inline]
            fn mul_assign(&mut self, rhs: Self) {
                self.xy *= rhs.xy;
                self.xz *= rhs.xz;
                self.yz *= rhs.yz;
            }
        }

        impl MulAssign<$t> for $bn {
            #[inline]
            fn mul_assign(&mut self, rhs: $t) {
                self.xy *= rhs;
                self.xz *= rhs;
                self.yz *= rhs;
            }
        }

        impl Div for $bn {
            type Output = Self;
            #[inline]
            fn div(mut self, rhs: $bn) -> Self {
                self /= rhs;
                self
            }
        }

        impl Div<$t> for $bn {
            type Output = $bn;
            #[inline]
            fn div(mut self, rhs: $t) -> $bn {
                self.xy /= rhs;
                self
            }
        }

        impl DivAssign for $bn {
            #[inline]
            fn div_assign(&mut self, rhs: $bn) {
                self.xy /= rhs.xy;
                self.xz /= rhs.xz;
                self.yz /= rhs.yz;
            }
        }

        impl DivAssign<$t> for $bn {
            #[inline]
            fn div_assign(&mut self, rhs: $t) {
                self.xy /= rhs;
                self.xz /= rhs;
                self.yz /= rhs;
            }
        }

        impl Neg for $bn {
            type Output = Self;
            #[inline]
            fn neg(mut self) -> Self {
                self.xy = -self.xy;
                self.xz = -self.xz;
                self.yz = -self.yz;
                self
            }
        }
        )+
    }
}

bivec3s!(Bivec3 => (Vec3, f32), WBivec3 => (Wec3, f32x4));