356 lines
11 KiB
Rust
356 lines
11 KiB
Rust
// Copyright 2013 The Lmath Developers. For a full listing of the authors,
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// refer to the AUTHORS file at the top-level directory of this distribution.
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//
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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use core::Dimensional;
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use core::{Mat3, ToMat3};
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use core::Vec3;
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#[path = "../num_macros.rs"]
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mod num_macros;
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mod dim_macros;
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// GLSL-style type aliases
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pub type quat = Quat<f32>;
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pub type dquat = Quat<f64>;
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// Rust-style type aliases
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pub type Quatf = Quat<float>;
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pub type Quatf32 = Quat<f32>;
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pub type Quatf64 = Quat<f64>;
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/// A quaternion in scalar/vector form
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#[deriving(Clone, Eq)]
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pub struct Quat<T> { s: T, v: Vec3<T> }
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impl_dimensional!(Quat, T, 4)
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impl_swap!(Quat)
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pub trait ToQuat<T> {
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pub fn to_quat(&self) -> Quat<T>;
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}
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impl<T> Quat<T> {
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/// Construct the quaternion from one scalar component and three
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/// imaginary components
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///
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/// # Arguments
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///
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/// - `w`: the scalar component
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/// - `xi`: the fist imaginary component
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/// - `yj`: the second imaginary component
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/// - `zk`: the third imaginary component
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#[inline]
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pub fn new(w: T, xi: T, yj: T, zk: T) -> Quat<T> {
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Quat::from_sv(w, Vec3::new(xi, yj, zk))
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}
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/// Construct the quaternion from a scalar and a vector
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///
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/// # Arguments
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///
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/// - `s`: the scalar component
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/// - `v`: a vector containing the three imaginary components
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#[inline]
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pub fn from_sv(s: T, v: Vec3<T>) -> Quat<T> {
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Quat { s: s, v: v }
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}
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}
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impl<T:Clone + Real> Quat<T> {
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/// The multiplicative identity, ie: `q = 1 + 0i + 0j + 0i`
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#[inline]
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pub fn identity() -> Quat<T> {
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Quat::from_sv(one!(T), Vec3::zero())
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}
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/// The additive identity, ie: `q = 0 + 0i + 0j + 0i`
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#[inline]
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pub fn zero() -> Quat<T> {
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Quat::new(zero!(T), zero!(T), zero!(T), zero!(T))
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}
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#[inline]
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pub fn from_angle_x(radians: T) -> Quat<T> {
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Quat::new((radians / two!(T)).cos(), radians.sin(), zero!(T), zero!(T))
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}
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#[inline]
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pub fn from_angle_y(radians: T) -> Quat<T> {
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Quat::new((radians / two!(T)).cos(), zero!(T), radians.sin(), zero!(T))
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}
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#[inline]
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pub fn from_angle_z(radians: T) -> Quat<T> {
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Quat::new((radians / two!(T)).cos(), zero!(T), zero!(T), radians.sin())
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}
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pub fn from_angle_xyz(radians_x: T, radians_y: T, radians_z: T) -> Quat<T> {
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// http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles#Conversion
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let xdiv2 = radians_x / two!(T);
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let ydiv2 = radians_y / two!(T);
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let zdiv2 = radians_z / two!(T);
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Quat::new(zdiv2.cos() * xdiv2.cos() * ydiv2.cos() + zdiv2.sin() * xdiv2.sin() * ydiv2.sin(),
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zdiv2.sin() * xdiv2.cos() * ydiv2.cos() - zdiv2.cos() * xdiv2.sin() * ydiv2.sin(),
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zdiv2.cos() * xdiv2.sin() * ydiv2.cos() + zdiv2.sin() * xdiv2.cos() * ydiv2.sin(),
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zdiv2.cos() * xdiv2.cos() * ydiv2.sin() - zdiv2.sin() * xdiv2.sin() * ydiv2.cos())
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}
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#[inline]
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pub fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Quat<T> {
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let half = radians / two!(T);
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Quat::from_sv(half.cos(), axis.mul_t(half.sin()))
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}
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pub fn get_angle_axis(&self) -> (T, Vec3<T>) {
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fail!(~"Not yet implemented.")
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}
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/// The result of multiplying the quaternion a scalar
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#[inline]
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pub fn mul_t(&self, value: T) -> Quat<T> {
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Quat::from_sv(self.s * value, self.v.mul_t(value))
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}
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/// The result of dividing the quaternion a scalar
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#[inline]
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pub fn div_t(&self, value: T) -> Quat<T> {
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Quat::from_sv(self.s / value, self.v.div_t(value))
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}
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/// The result of multiplying the quaternion by a vector
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#[inline]
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pub fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T> {
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let tmp = self.v.cross(vec).add_v(&vec.mul_t(self.s.clone()));
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self.v.cross(&tmp).mul_t(two!(T)).add_v(vec)
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}
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/// The sum of this quaternion and `other`
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#[inline]
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pub fn add_q(&self, other: &Quat<T>) -> Quat<T> {
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Quat::new(*self.index(0) + *other.index(0),
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*self.index(1) + *other.index(1),
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*self.index(2) + *other.index(2),
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*self.index(3) + *other.index(3))
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}
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/// The sum of this quaternion and `other`
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#[inline]
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pub fn sub_q(&self, other: &Quat<T>) -> Quat<T> {
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Quat::new(*self.index(0) - *other.index(0),
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*self.index(1) - *other.index(1),
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*self.index(2) - *other.index(2),
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*self.index(3) - *other.index(3))
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}
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/// The the result of multipliplying the quaternion by `other`
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pub fn mul_q(&self, other: &Quat<T>) -> Quat<T> {
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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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}
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/// The dot product of the quaternion and `other`
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#[inline]
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pub fn dot(&self, other: &Quat<T>) -> T {
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self.s * other.s + self.v.dot(&other.v)
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}
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/// The conjugate of the quaternion
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#[inline]
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pub fn conjugate(&self) -> Quat<T> {
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Quat::from_sv(self.s.clone(), -self.v.clone())
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}
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/// The multiplicative inverse of the quaternion
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#[inline]
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pub fn inverse(&self) -> Quat<T> {
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self.conjugate().div_t(self.magnitude2())
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}
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/// The squared magnitude of the quaternion. This is useful for
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/// magnitude comparisons where the exact magnitude does not need to be
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/// calculated.
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#[inline]
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pub fn magnitude2(&self) -> T {
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self.s * self.s + self.v.length2()
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}
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/// The magnitude of the quaternion
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///
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/// # Performance notes
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///
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/// For instances where the exact magnitude of the quaternion does not need
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/// to be known, for example for quaternion-quaternion magnitude comparisons,
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/// it is advisable to use the `magnitude2` method instead.
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#[inline]
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pub fn magnitude(&self) -> T {
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self.magnitude2().sqrt()
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}
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/// The normalized quaternion
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#[inline]
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pub fn normalize(&self) -> Quat<T> {
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self.mul_t(one!(T) / self.magnitude())
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}
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/// Normalised linear interpolation
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///
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/// # Return value
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///
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/// The intoperlated quaternion
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pub fn nlerp(&self, other: &Quat<T>, amount: T) -> Quat<T> {
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self.mul_t(one!(T) - amount).add_q(&other.mul_t(amount)).normalize()
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}
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}
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impl<T:Clone + Num> ToMat3<T> for Quat<T> {
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/// Convert the quaternion to a 3 x 3 rotation matrix
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pub fn to_mat3(&self) -> Mat3<T> {
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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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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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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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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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let _1: T = one!(T);
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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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}
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}
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impl<T:Clone + Float> Neg<Quat<T>> for Quat<T> {
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#[inline]
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pub fn neg(&self) -> Quat<T> {
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Quat::from_sv(-self.s, -self.v)
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}
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}
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impl<T:Clone + Float> Quat<T> {
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#[inline]
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pub fn look_at(dir: &Vec3<T>, up: &Vec3<T>) -> Quat<T> {
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Mat3::look_at(dir, up).to_quat()
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}
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#[inline]
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pub fn from_axes(x: Vec3<T>, y: Vec3<T>, z: Vec3<T>) -> Quat<T> {
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Mat3::from_axes(x, y, z).to_quat()
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}
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/// Spherical Linear Intoperlation
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///
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/// Perform a spherical linear interpolation between the quaternion and
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/// `other`. Both quaternions should be normalized first.
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///
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/// # Return value
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///
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/// The intoperlated quaternion
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///
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/// # Performance notes
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///
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/// The `acos` operation used in `slerp` is an expensive operation, so unless
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/// your quarternions a far away from each other it's generally more advisable
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/// to use `nlerp` when you know your rotations are going to be small.
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///
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/// - [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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/// - [Arcsynthesis OpenGL tutorial]
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/// (http://www.arcsynthesis.org/gltut/Positioning/Tut08%20Interpolation.html)
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pub fn slerp(&self, other: &Quat<T>, amount: T) -> Quat<T> {
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use std::num::cast;
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let dot = self.dot(other);
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let dot_threshold = cast(0.9995);
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// if quaternions are close together use `nlerp`
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if dot > dot_threshold {
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self.nlerp(other, amount)
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} else {
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// stay within the domain of acos()
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let robust_dot = dot.clamp(&-one!(T), &one!(T));
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let theta_0 = robust_dot.acos(); // 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(theta.cos())
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.add_q(&q.mul_t(theta.sin()))
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}
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}
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}
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impl<T:Clone + Eq + ApproxEq<T>> ApproxEq<T> for Quat<T> {
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#[inline]
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pub fn approx_epsilon() -> T {
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ApproxEq::approx_epsilon::<T,T>()
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}
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#[inline]
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pub fn approx_eq(&self, other: &Quat<T>) -> bool {
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self.approx_eq_eps(other, &ApproxEq::approx_epsilon::<T,T>())
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}
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#[inline]
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pub fn approx_eq_eps(&self, other: &Quat<T>, epsilon: &T) -> bool {
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self.s.approx_eq_eps(&other.s, epsilon) &&
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self.v.approx_eq_eps(&other.v, epsilon)
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}
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}
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#[cfg(test)]
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mod tests {
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use core::mat::*;
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use core::quat::*;
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use core::vec::*;
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#[test]
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fn test_from_angle_axis() {
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let v = Vec3::new(1f, 0f, 0f);
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let q = Quat::from_angle_axis((-45f).to_radians(), &Vec3::new(0f, 0f, -1f));
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// http://www.wolframalpha.com/input/?i={1,0}+rotate+-45+degrees
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assert_approx_eq!(q.mul_v(&v), Vec3::new(1f/2f.sqrt(), 1f/2f.sqrt(), 0f));
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assert_eq!(q.mul_v(&v).length(), v.length());
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assert_approx_eq!(q.to_mat3(), Mat3::new( 1f/2f.sqrt(), 1f/2f.sqrt(), 0f,
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-1f/2f.sqrt(), 1f/2f.sqrt(), 0f,
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0f, 0f, 1f));
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}
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#[test]
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fn test_approx_eq() {
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assert!(!Quat::new::<float>(0.000001, 0.000001, 0.000001, 0.000001)
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.approx_eq(&Quat::new::<float>(0.0, 0.0, 0.0, 0.0)));
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assert!(Quat::new::<float>(0.0000001, 0.0000001, 0.0000001, 0.0000001)
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.approx_eq(&Quat::new::<float>(0.0, 0.0, 0.0, 0.0)));
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}
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}
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