2012-11-15 02:23:39 +00:00
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use core::cast::transmute;
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2012-11-22 01:09:04 +00:00
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use core::cmp::{Eq, Ord};
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2012-11-22 00:38:39 +00:00
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use core::ptr::to_unsafe_ptr;
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2012-11-25 12:05:47 +00:00
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use core::sys::size_of;
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2012-11-15 02:23:39 +00:00
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use core::vec::raw::buf_as_slice;
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use std::cmp::FuzzyEq;
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2012-12-01 04:55:45 +00:00
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use dim::{Dimensional, ToPtr};
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2012-11-26 06:48:46 +00:00
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use funs::common::*;
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use funs::exponential::*;
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use funs::triganomic::*;
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2012-11-15 02:23:39 +00:00
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use mat::{Mat3, Mat4};
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2012-12-03 05:39:32 +00:00
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use num::kinds::{Float, Number};
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2012-11-15 02:23:39 +00:00
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use vec::Vec3;
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2012-11-20 11:37:10 +00:00
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///
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/// The base quaternion trait
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///
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2012-12-03 06:19:53 +00:00
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static pure fn identity() -> self; /// The multiplicative identity
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static pure fn zero() -> self; /// The additive identity
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2012-12-03 22:23:13 +00:00
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pub trait Quaternion<T>: Dimensional<T>, ToPtr<T>, Eq, Neg<self> {
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2012-11-20 06:57:32 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn mul_t(&self, value: T) -> self;
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pure fn div_t(&self, value: T) -> self;
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2012-11-15 02:23:39 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T>;
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2012-11-15 02:23:39 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn add_q(&self, other: &self) -> self;
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pure fn sub_q(&self, other: &self) -> self;
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pure fn mul_q(&self, other: &self) -> self;
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2012-11-15 02:23:39 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn dot(&self, other: &self) -> T;
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2012-11-15 02:23:39 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn conjugate(&self) -> self;
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pure fn inverse(&self) -> self;
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pure fn length2(&self) -> T;
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pure fn length(&self) -> T;
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pure fn normalize(&self) -> self;
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2012-11-15 02:23:39 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn nlerp(&self, other: &self, amount: T) -> self;
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pure fn slerp(&self, other: &self, amount: T) -> self;
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2012-11-15 02:23:39 +00:00
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2012-11-30 03:13:20 +00:00
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pure fn to_mat3(&self) -> Mat3<T>;
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pure fn to_mat4(&self) -> Mat4<T>;
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2012-11-15 02:23:39 +00:00
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}
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pub trait ToQuat<T> {
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pure fn to_Quat() -> Quat<T>;
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}
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2012-11-21 04:01:21 +00:00
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pub struct Quat<T> { s: T, v: Vec3<T> }
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2012-11-15 02:23:39 +00:00
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2012-11-21 04:01:21 +00:00
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pub impl<T> Quat<T> {
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2012-11-15 02:23:39 +00:00
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#[inline(always)]
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2012-11-21 04:01:21 +00:00
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static pure fn new(s: T, vx: T, vy: T, vz: T) -> Quat<T> {
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Quat::from_sv(move s, move Vec3::new(move vx, move vy, move vz))
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-21 04:01:21 +00:00
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static pure fn from_sv(s: T, v: Vec3<T>) -> Quat<T> {
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Quat { s: move s, v: move v }
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2012-11-15 02:23:39 +00:00
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}
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}
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2012-12-01 04:55:45 +00:00
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pub impl<T> Quat<T>: Dimensional<T> {
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2012-12-01 04:19:21 +00:00
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#[inline(always)]
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static pure fn dim() -> uint { 4 }
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#[inline(always)]
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static pure fn size_of() -> uint { size_of::<Quat<T>>() }
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}
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pub impl<T:Copy> Quat<T>: Index<uint, T> {
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#[inline(always)]
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pure fn index(i: uint) -> T {
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unsafe { do buf_as_slice(
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transmute::<*Quat<T>, *T>(
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to_unsafe_ptr(&self)), 4) |slice| { slice[i] }
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}
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}
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}
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2012-12-01 04:55:45 +00:00
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pub impl<T:Copy> Quat<T>: ToPtr<T> {
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#[inline(always)]
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pure fn to_ptr(&self) -> *T {
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to_unsafe_ptr(&self[0])
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}
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}
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2012-12-03 01:10:14 +00:00
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pub impl<T:Copy Float Exp Extent InvTrig> Quat<T>: Quaternion<T> {
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2012-11-20 06:57:32 +00:00
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#[inline(always)]
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static pure fn identity() -> Quat<T> {
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2012-12-03 06:19:53 +00:00
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Quat::new(Number::from(1),
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Number::from(0),
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Number::from(0),
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Number::from(0))
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2012-11-20 06:57:32 +00:00
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}
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#[inline(always)]
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static pure fn zero() -> Quat<T> {
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2012-12-03 06:19:53 +00:00
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Quat::new(Number::from(0),
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Number::from(0),
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Number::from(0),
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Number::from(0))
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2012-11-20 06:57:32 +00:00
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}
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2012-11-15 02:23:39 +00:00
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn mul_t(&self, value: T) -> Quat<T> {
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2012-11-15 02:23:39 +00:00
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Quat::new(self[0] * value,
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self[1] * value,
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self[2] * value,
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self[3] * value)
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn div_t(&self, value: T) -> Quat<T> {
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2012-11-15 02:23:39 +00:00
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Quat::new(self[0] / value,
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self[1] / value,
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self[2] / value,
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self[3] / value)
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T> {
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2012-11-21 04:01:21 +00:00
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let tmp = self.v.cross(vec).add_v(&vec.mul_t(self.s));
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2012-12-03 06:19:53 +00:00
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self.v.cross(&tmp).mul_t(Number::from(2)).add_v(vec)
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn add_q(&self, other: &Quat<T>) -> Quat<T> {
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2012-11-15 02:23:39 +00:00
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Quat::new(self[0] + other[0],
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self[1] + other[1],
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self[2] + other[2],
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self[3] + other[3])
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn sub_q(&self, other: &Quat<T>) -> Quat<T> {
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2012-11-15 02:23:39 +00:00
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Quat::new(self[0] - other[0],
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self[1] - other[1],
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self[2] - other[2],
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self[3] - other[3])
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn mul_q(&self, other: &Quat<T>) -> Quat<T> {
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2012-11-21 04:01:21 +00:00
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Quat::new(self.s * other.s - self.v.x * other.v.x - self.v.y * other.v.y - self.v.z * other.v.z,
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self.s * other.v.x + self.v.x * other.s + self.v.y * other.v.z - self.v.z * other.v.y,
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self.s * other.v.y + self.v.y * other.s + self.v.z * other.v.x - self.v.x * other.v.z,
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self.s * other.v.z + self.v.z * other.s + self.v.x * other.v.y - self.v.y * other.v.x)
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn dot(&self, other: &Quat<T>) -> T {
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2012-11-21 04:01:21 +00:00
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self.s * other.s + self.v.dot(&other.v)
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn conjugate(&self) -> Quat<T> {
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2012-11-21 04:01:21 +00:00
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Quat::from_sv(self.s, -self.v)
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn inverse(&self) -> Quat<T> {
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2012-11-21 04:01:21 +00:00
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self.conjugate().div_t(self.length2())
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn length2(&self) -> T {
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2012-11-21 04:01:21 +00:00
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self.s * self.s + self.v.length2()
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn length(&self) -> T {
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2012-11-15 02:23:39 +00:00
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self.length2().sqrt()
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn normalize(&self) -> Quat<T> {
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2012-12-03 06:19:53 +00:00
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let mut n: T = Number::from(1);
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2012-11-15 02:23:39 +00:00
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n /= self.length();
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return self.mul_t(n);
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn nlerp(&self, other: &Quat<T>, amount: T) -> Quat<T> {
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2012-12-03 06:19:53 +00:00
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let _1: T = Number::from(1);
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2012-11-15 02:23:39 +00:00
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self.mul_t(_1 - amount).add_q(&other.mul_t(amount)).normalize()
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}
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/**
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* Spherical Linear Intoperlation
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*
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* Both quaternions should be normalized first, or else strange things will
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* will happen...
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*
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* Note: The `acos` used in `slerp` is an expensive operation, so unless your
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* quarternions a far away from each other it's generally more advisable to
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* use nlerp when you know your rotations are going to be small.
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*
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* See *[Understanding Slerp, Then Not Using It]
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* (http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/)*
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* for more information. The [Arcsynthesis OpenGL tutorial]
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* (http://www.arcsynthesis.org/gltut/Positioning/Tut08%20Interpolation.html)
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* also provides a good explanation.
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*/
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn slerp(&self, other: &Quat<T>, amount: T) -> Quat<T> {
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2012-12-03 22:24:03 +00:00
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let dot = self.dot(other);
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2012-11-15 02:23:39 +00:00
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// if quaternions are close together use `nlerp`
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2012-12-03 06:19:53 +00:00
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let dot_threshold = Number::from(0.9995);
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2012-11-15 02:23:39 +00:00
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if dot > dot_threshold { return self.nlerp(other, amount) }
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2012-12-03 06:19:53 +00:00
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let robust_dot = dot.clamp(&-Number::from(1), &Number::from(1)); // stay within the domain of acos()
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2012-11-15 02:23:39 +00:00
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let theta_0 = acos(&robust_dot); // the angle between the quaternions
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let theta = theta_0 * amount; // the fraction of theta specified by `amount`
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let q = other.sub_q(&self.mul_t(robust_dot))
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.normalize();
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self.mul_t(cos(&theta)).add_q(&q.mul_t(sin(&theta)))
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn to_mat3(&self) -> Mat3<T> {
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2012-11-21 04:01:21 +00:00
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let x2 = self.v.x + self.v.x;
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let y2 = self.v.y + self.v.y;
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let z2 = self.v.z + self.v.z;
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2012-11-15 02:23:39 +00:00
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2012-11-21 04:01:21 +00:00
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let xx2 = x2 * self.v.x;
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let xy2 = x2 * self.v.y;
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let xz2 = x2 * self.v.z;
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2012-11-15 02:23:39 +00:00
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2012-11-21 04:01:21 +00:00
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let yy2 = y2 * self.v.y;
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let yz2 = y2 * self.v.z;
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let zz2 = z2 * self.v.z;
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2012-11-15 02:23:39 +00:00
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2012-11-21 04:01:21 +00:00
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let sy2 = y2 * self.s;
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let sz2 = z2 * self.s;
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let sx2 = x2 * self.s;
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2012-11-15 02:23:39 +00:00
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2012-12-03 22:24:03 +00:00
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let _1: T = Number::from(1);
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2012-11-15 02:23:39 +00:00
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2012-11-21 04:01:21 +00:00
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Mat3::new(_1 - yy2 - zz2, xy2 - sz2, xz2 + sy2,
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xy2 + sz2, _1 - xx2 - zz2, yz2 - sx2,
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xz2 - sy2, yz2 + sx2, _1 - xx2 - yy2)
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-30 03:13:20 +00:00
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pure fn to_mat4(&self) -> Mat4<T> {
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2012-11-22 00:36:33 +00:00
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self.to_mat3().to_mat4()
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2012-11-15 02:23:39 +00:00
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}
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}
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2012-12-01 04:19:21 +00:00
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pub impl<T:Copy Num> Quat<T>: Neg<Quat<T>> {
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2012-11-15 02:23:39 +00:00
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#[inline(always)]
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2012-12-01 04:19:21 +00:00
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pure fn neg(&self) -> Quat<T> {
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Quat::new(-self[0], -self[1], -self[2], -self[3])
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2012-11-15 02:23:39 +00:00
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}
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}
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2012-11-29 11:30:40 +00:00
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pub impl<T:Copy Eq> Quat<T>: Eq {
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2012-11-15 02:23:39 +00:00
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#[inline(always)]
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2012-11-29 03:14:42 +00:00
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pure fn eq(&self, other: &Quat<T>) -> bool {
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2012-11-29 11:30:40 +00:00
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self[0] == other[0] &&
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self[1] == other[1] &&
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self[2] == other[2] &&
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self[3] == other[3]
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2012-11-15 02:23:39 +00:00
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}
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#[inline(always)]
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2012-11-29 03:14:42 +00:00
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pure fn ne(&self, other: &Quat<T>) -> bool {
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!(self == other)
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2012-11-15 02:23:39 +00:00
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}
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}
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pub impl<T:Copy FuzzyEq> Quat<T>: FuzzyEq {
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#[inline(always)]
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pure fn fuzzy_eq(other: &Quat<T>) -> bool {
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self[0].fuzzy_eq(&other[0]) &&
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self[1].fuzzy_eq(&other[1]) &&
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self[2].fuzzy_eq(&other[2]) &&
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self[3].fuzzy_eq(&other[3])
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}
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2012-11-20 05:35:06 +00:00
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}
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2012-12-03 01:10:14 +00:00
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// // Operator Overloads
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// pub impl<T, Result, RHS: QuatAddRHS<T, Result>> Quat<T>: Add<RHS,Result> {
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// #[inline(always)]
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// pure fn add(rhs: &RHS) -> Result {
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// rhs.quat_add_rhs(&self)
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// }
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// }
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// pub impl<T, Result, RHS: QuatSubRHS<T, Result>> Quat<T>: Sub<RHS,Result> {
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// #[inline(always)]
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// pure fn sub(&self, rhs: &RHS) -> Result {
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// rhs.quat_sub_rhs(self)
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// }
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// }
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// pub impl<T, Result, RHS: QuatMulRHS<T, Result>> Quat<T>: Mul<RHS,Result> {
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// #[inline(always)]
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// pure fn mul(&self, rhs: &RHS) -> Result {
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// rhs.quat_mul_rhs(self)
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// }
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// }
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// pub impl<T, Result, RHS: QuatDivRHS<T, Result>> Quat<T>: Div<RHS,Result> {
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// #[inline(always)]
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// pure fn div(&self, rhs: &RHS) -> Result {
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// rhs.quat_div_rhs(self)
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// }
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// }
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// // RHS Traits for Operator overloads
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|
// pub trait QuatAddRHS<T, Result> { pure fn quat_add_rhs(&self, lhs: &Quat<T>) -> Result; }
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// pub trait QuatSubRHS<T, Result> { pure fn quat_sub_rhs(&self, lhs: &Quat<T>) -> Result; }
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// pub trait QuatMulRHS<T, Result> { pure fn quat_mul_rhs(&self, lhs: &Quat<T>) -> Result; }
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// pub trait QuatDivRHS<T, Result> { pure fn quat_div_rhs(&self, lhs: &Quat<T>) -> Result; }
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|
// // Quat/Scalar Multiplication
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|
// pub impl f32: QuatMulRHS<f32, Quat<f32>> { #[inline(always)] pure fn quat_mul_rhs(&self, lhs: &Quat<f32>) -> Quat<f32> { lhs.mul_t(self) } }
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|
// pub impl f64: QuatMulRHS<f64, Quat<f64>> { #[inline(always)] pure fn quat_mul_rhs(&self, lhs: &Quat<f64>) -> Quat<f64> { lhs.mul_t(self) } }
|
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|
// pub impl float: QuatMulRHS<float, Quat<float>> { #[inline(always)] pure fn quat_mul_rhs(&self, lhs: &Quat<float>) -> Quat<float> { lhs.mul_t(self) } }
|
|
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|
|
|
|
|
// // Quat/Scalar Division
|
|
|
|
// pub impl f32: QuatDivRHS<f32, Quat<f32>> { #[inline(always)] pure fn quat_div_rhs(&self, lhs: &Quat<f32>) -> Quat<f32> { lhs.div_t(self) } }
|
|
|
|
// pub impl f64: QuatDivRHS<f64, Quat<f64>> { #[inline(always)] pure fn quat_div_rhs(&self, lhs: &Quat<f64>) -> Quat<f64> { lhs.div_t(self) } }
|
|
|
|
// pub impl float: QuatDivRHS<float, Quat<float>> { #[inline(always)] pure fn quat_div_rhs(&self, lhs: &Quat<float>) -> Quat<float> { lhs.div_t(self) } }
|
|
|
|
|
|
|
|
// // Quat/Vector Multiplication
|
|
|
|
// pub impl<T:Copy Num NumCast Exp Extent Ord InvTrig> Vec3<T>: QuatMulRHS<T, Vec3<T>> {
|
|
|
|
// #[inline(always)]
|
|
|
|
// pure fn quat_mul_rhs(&self, lhs: &Quat<T>) -> Vec3<T> {
|
|
|
|
// lhs.mul_v(self)
|
|
|
|
// }
|
|
|
|
// }
|
|
|
|
|
|
|
|
// // // Quat/Quat Addition
|
|
|
|
// // pub impl<T:Copy Num NumCast Exp Extent Ord InvTrig> Quat<T>: QuatAddRHS<Quat<T>, Quat<T>> {
|
|
|
|
// // #[inline(always)]
|
|
|
|
// // pure fn quat_add_rhs(&self, lhs: &Quat<T>) -> Quat<T> {
|
|
|
|
// // lhs.add_q(self)
|
|
|
|
// // }
|
|
|
|
// // }
|
|
|
|
|
|
|
|
// // Quat/Quat Subtraction
|
|
|
|
// pub impl<T:Copy Num NumCast Exp Extent Ord InvTrig> Quat<T>: QuatSubRHS<T, Quat<T>> {
|
|
|
|
// #[inline(always)]
|
|
|
|
// pure fn quat_sub_rhs(&self, lhs: &Quat<T>) -> Quat<T> {
|
|
|
|
// lhs.sub_q(self)
|
|
|
|
// }
|
|
|
|
// }
|
|
|
|
|
|
|
|
// // Quat/Quat Multiplication
|
|
|
|
// pub impl<T:Copy Num NumCast Exp Extent Ord InvTrig> Quat<T>: QuatMulRHS<T, Quat<T>> {
|
|
|
|
// #[inline(always)]
|
|
|
|
// pure fn quat_mul_rhs(&self, lhs: &Quat<T>) -> Quat<T> {
|
|
|
|
// lhs.mul_q(self)
|
|
|
|
// }
|
|
|
|
// }
|