632 lines
No EOL
20 KiB
Rust
632 lines
No EOL
20 KiB
Rust
use core::cast::transmute;
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use core::cmp::Eq;
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use core::ptr::to_unsafe_ptr;
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use core::util::swap;
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use core::sys::size_of;
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use core::vec::raw::buf_as_slice;
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use std::cmp::{FuzzyEq, FUZZY_EPSILON};
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use numeric::*;
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use numeric::number::Number;
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use numeric::number::Number::{zero,one};
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use quat::Quat;
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use vec::{
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Vec3,
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Vector3,
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vec3,
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dvec3,
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};
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use mat::{
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Mat4,
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Matrix,
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Matrix3,
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Matrix4,
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MutableMatrix,
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};
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/**
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* A 3 x 3 column major matrix
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*
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* # Type parameters
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*
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* * `T` - The type of the elements of the matrix. Should be a floating point type.
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*
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* # Fields
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*
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* * `x` - the first column vector of the matrix
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* * `y` - the second column vector of the matrix
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* * `z` - the third column vector of the matrix
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*/
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#[deriving_eq]
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pub struct Mat3<T> { x: Vec3<T>, y: Vec3<T>, z: Vec3<T> }
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pub impl<T:Copy Float FuzzyEq<T>> Mat3<T>: Matrix<T, Vec3<T>> {
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#[inline(always)]
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pure fn col(&self, i: uint) -> Vec3<T> { self[i] }
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#[inline(always)]
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pure fn row(&self, i: uint) -> Vec3<T> {
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Vector3::new(self[0][i],
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self[1][i],
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self[2][i])
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}
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/**
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* Construct a 3 x 3 diagonal matrix with the major diagonal set to `value`
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*
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* # Arguments
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*
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* * `value` - the value to set the major diagonal to
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*
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* ~~~
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* c0 c1 c2
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* +-----+-----+-----+
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* r0 | val | 0 | 0 |
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* +-----+-----+-----+
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* r1 | 0 | val | 0 |
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* +-----+-----+-----+
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* r2 | 0 | 0 | val |
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* +-----+-----+-----+
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* ~~~
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*/
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#[inline(always)]
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static pure fn from_value(value: T) -> Mat3<T> {
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Matrix3::new(value, zero(), zero(),
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zero(), value, zero(),
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zero(), zero(), value)
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}
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/**
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* Returns the multiplicative identity matrix
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* ~~~
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* c0 c1 c2
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* +----+----+----+
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* r0 | 1 | 0 | 0 |
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* +----+----+----+
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* r1 | 0 | 1 | 0 |
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* +----+----+----+
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* r2 | 0 | 0 | 1 |
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* +----+----+----+
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* ~~~
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*/
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#[inline(always)]
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static pure fn identity() -> Mat3<T> {
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Matrix3::new( one::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), one::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), one::<T>())
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}
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/**
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* Returns the additive identity matrix
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* ~~~
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* c0 c1 c2
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* +----+----+----+
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* r0 | 0 | 0 | 0 |
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* +----+----+----+
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* r1 | 0 | 0 | 0 |
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* +----+----+----+
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* r2 | 0 | 0 | 0 |
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* +----+----+----+
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* ~~~
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*/
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#[inline(always)]
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static pure fn zero() -> Mat3<T> {
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Matrix3::new(zero::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), zero::<T>())
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}
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#[inline(always)]
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pure fn mul_t(&self, value: T) -> Mat3<T> {
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Matrix3::from_cols(self[0].mul_t(value),
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self[1].mul_t(value),
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self[2].mul_t(value))
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}
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#[inline(always)]
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pure fn mul_v(&self, vec: &Vec3<T>) -> Vec3<T> {
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Vector3::new(self.row(0).dot(vec),
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self.row(1).dot(vec),
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self.row(2).dot(vec))
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}
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#[inline(always)]
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pure fn add_m(&self, other: &Mat3<T>) -> Mat3<T> {
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Matrix3::from_cols(self[0].add_v(&other[0]),
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self[1].add_v(&other[1]),
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self[2].add_v(&other[2]))
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}
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#[inline(always)]
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pure fn sub_m(&self, other: &Mat3<T>) -> Mat3<T> {
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Matrix3::from_cols(self[0].sub_v(&other[0]),
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self[1].sub_v(&other[1]),
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self[2].sub_v(&other[2]))
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}
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#[inline(always)]
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pure fn mul_m(&self, other: &Mat3<T>) -> Mat3<T> {
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Matrix3::new(self.row(0).dot(&other.col(0)),
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self.row(1).dot(&other.col(0)),
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self.row(2).dot(&other.col(0)),
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self.row(0).dot(&other.col(1)),
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self.row(1).dot(&other.col(1)),
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self.row(2).dot(&other.col(1)),
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self.row(0).dot(&other.col(2)),
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self.row(1).dot(&other.col(2)),
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self.row(2).dot(&other.col(2)))
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}
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pure fn dot(&self, other: &Mat3<T>) -> T {
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other.transpose().mul_m(self).trace()
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}
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pure fn determinant(&self) -> T {
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self.col(0).dot(&self.col(1).cross(&self.col(2)))
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}
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pure fn trace(&self) -> T {
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self[0][0] + self[1][1] + self[2][2]
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}
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// #[inline(always)]
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pure fn inverse(&self) -> Option<Mat3<T>> {
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let d = self.determinant();
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if d.fuzzy_eq(&zero()) {
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None
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} else {
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let m: Mat3<T> = Matrix3::from_cols(self[1].cross(&self[2]).div_t(d),
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self[2].cross(&self[0]).div_t(d),
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self[0].cross(&self[1]).div_t(d));
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Some(m.transpose())
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}
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}
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#[inline(always)]
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pure fn transpose(&self) -> Mat3<T> {
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Matrix3::new(self[0][0], self[1][0], self[2][0],
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self[0][1], self[1][1], self[2][1],
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self[0][2], self[1][2], self[2][2])
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}
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#[inline(always)]
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pure fn is_identity(&self) -> bool {
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self.fuzzy_eq(&Matrix::identity())
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}
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#[inline(always)]
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pure fn is_diagonal(&self) -> bool {
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self[0][1].fuzzy_eq(&zero()) &&
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self[0][2].fuzzy_eq(&zero()) &&
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self[1][0].fuzzy_eq(&zero()) &&
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self[1][2].fuzzy_eq(&zero()) &&
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self[2][0].fuzzy_eq(&zero()) &&
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self[2][1].fuzzy_eq(&zero())
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}
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#[inline(always)]
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pure fn is_rotated(&self) -> bool {
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!self.fuzzy_eq(&Matrix::identity())
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}
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#[inline(always)]
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pure fn is_symmetric(&self) -> bool {
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self[0][1].fuzzy_eq(&self[1][0]) &&
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self[0][2].fuzzy_eq(&self[2][0]) &&
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self[1][0].fuzzy_eq(&self[0][1]) &&
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self[1][2].fuzzy_eq(&self[2][1]) &&
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self[2][0].fuzzy_eq(&self[0][2]) &&
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self[2][1].fuzzy_eq(&self[1][2])
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}
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#[inline(always)]
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pure fn is_invertible(&self) -> bool {
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!self.determinant().fuzzy_eq(&zero())
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}
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#[inline(always)]
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pure fn to_ptr(&self) -> *T {
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unsafe {
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transmute::<*Mat3<T>, *T>(
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to_unsafe_ptr(self)
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)
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}
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}
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}
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pub impl<T:Copy Float FuzzyEq<T>> Mat3<T>: Matrix3<T, Vec3<T>> {
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/**
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* Construct a 3 x 3 matrix
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*
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* # Arguments
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*
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* * `c0r0`, `c0r1`, `c0r2` - the first column of the matrix
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* * `c1r0`, `c1r1`, `c1r2` - the second column of the matrix
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* * `c2r0`, `c2r1`, `c2r2` - the third column of the matrix
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*
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* ~~~
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* c0 c1 c2
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* +------+------+------+
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* r0 | c0r0 | c1r0 | c2r0 |
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* +------+------+------+
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* r1 | c0r1 | c1r1 | c2r1 |
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* +------+------+------+
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* r2 | c0r2 | c1r2 | c2r2 |
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* +------+------+------+
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* ~~~
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*/
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#[inline(always)]
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static pure fn new(c0r0:T, c0r1:T, c0r2:T,
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c1r0:T, c1r1:T, c1r2:T,
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c2r0:T, c2r1:T, c2r2:T) -> Mat3<T> {
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Matrix3::from_cols(Vector3::new::<T,Vec3<T>>(c0r0, c0r1, c0r2),
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Vector3::new::<T,Vec3<T>>(c1r0, c1r1, c1r2),
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Vector3::new::<T,Vec3<T>>(c2r0, c2r1, c2r2))
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}
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/**
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* Construct a 3 x 3 matrix from column vectors
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*
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* # Arguments
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*
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* * `c0` - the first column vector of the matrix
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* * `c1` - the second column vector of the matrix
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* * `c2` - the third column vector of the matrix
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*
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* ~~~
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* c0 c1 c2
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* +------+------+------+
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* r0 | c0.x | c1.x | c2.x |
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* +------+------+------+
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* r1 | c0.y | c1.y | c2.y |
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* +------+------+------+
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* r2 | c0.z | c1.z | c2.z |
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* +------+------+------+
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* ~~~
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*/
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#[inline(always)]
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static pure fn from_cols(c0: Vec3<T>,
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c1: Vec3<T>,
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c2: Vec3<T>) -> Mat3<T> {
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Mat3 { x: c0, y: c1, z: c2 }
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}
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/**
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* Construct a matrix from an angular rotation around the `x` axis
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*/
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#[inline(always)]
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static pure fn from_angle_x(radians: T) -> Mat3<T> {
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// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
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let cos_theta = cos(radians);
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let sin_theta = sin(radians);
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Matrix3::new( one(), zero(), zero(),
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zero(), cos_theta, sin_theta,
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zero(), -sin_theta, cos_theta)
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}
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/**
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* Construct a matrix from an angular rotation around the `y` axis
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*/
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#[inline(always)]
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static pure fn from_angle_y(radians: T) -> Mat3<T> {
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// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
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let cos_theta = cos(radians);
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let sin_theta = sin(radians);
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Matrix3::new(cos_theta, zero(), -sin_theta,
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zero(), one(), zero(),
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sin_theta, zero(), cos_theta)
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}
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/**
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* Construct a matrix from an angular rotation around the `z` axis
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*/
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#[inline(always)]
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static pure fn from_angle_z(radians: T) -> Mat3<T> {
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// http://en.wikipedia.org/wiki/Rotation_matrix#Basic_rotations
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let cos_theta = cos(radians);
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let sin_theta = sin(radians);
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Matrix3::new( cos_theta, sin_theta, zero(),
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-sin_theta, cos_theta, zero(),
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zero(), zero(), one())
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}
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/**
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* Construct a matrix from Euler angles
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*
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* # Arguments
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*
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* * `theta_x` - the angular rotation around the `x` axis (pitch)
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* * `theta_y` - the angular rotation around the `y` axis (yaw)
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* * `theta_z` - the angular rotation around the `z` axis (roll)
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*/
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#[inline(always)]
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static pure fn from_angle_xyz(radians_x: T, radians_y: T, radians_z: T) -> Mat3<T> {
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// http://en.wikipedia.org/wiki/Rotation_matrix#General_rotations
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let cx = cos(radians_x);
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let sx = sin(radians_x);
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let cy = cos(radians_y);
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let sy = sin(radians_y);
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let cz = cos(radians_z);
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let sz = sin(radians_z);
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Matrix3::new( cy*cz, cy*sz, -sy,
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-cx*sz + sx*sy*cz, cx*cz + sx*sy*sz, sx*cy,
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sx*sz + cx*sy*cz, -sx*cz + cx*sy*sz, cx*cy)
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}
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/**
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* Construct a matrix from an axis and an angular rotation
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*/
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#[inline(always)]
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static pure fn from_angle_axis(radians: T, axis: &Vec3<T>) -> Mat3<T> {
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let c = cos(radians);
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let s = sin(radians);
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let _1_c = one::<T>() - c;
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let x = axis.x;
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let y = axis.y;
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let z = axis.z;
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Matrix3::new(_1_c*x*x + c, _1_c*x*y + s*z, _1_c*x*z - s*y,
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_1_c*x*y - s*z, _1_c*y*y + c, _1_c*y*z + s*x,
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_1_c*x*z + s*y, _1_c*y*z - s*x, _1_c*z*z + c)
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}
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#[inline(always)]
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static pure fn from_axes(x: Vec3<T>, y: Vec3<T>, z: Vec3<T>) -> Mat3<T> {
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Matrix3::from_cols(x, y, z)
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}
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#[inline(always)]
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static pure fn look_at(dir: &Vec3<T>, up: &Vec3<T>) -> Mat3<T> {
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let dir_ = dir.normalize();
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let side = dir_.cross(&up.normalize());
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let up_ = side.cross(&dir_).normalize();
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Matrix3::from_axes(up_, side, dir_)
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}
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/**
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* Returns the the matrix with an extra row and column added
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* ~~~
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* c0 c1 c2 c0 c1 c2 c3
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* +----+----+----+ +----+----+----+----+
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* r0 | a | b | c | r0 | a | b | c | 0 |
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* +----+----+----+ +----+----+----+----+
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* r1 | d | e | f | => r1 | d | e | f | 0 |
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* +----+----+----+ +----+----+----+----+
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* r2 | g | h | i | r2 | g | h | i | 0 |
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* +----+----+----+ +----+----+----+----+
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* r3 | 0 | 0 | 0 | 1 |
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* +----+----+----+----+
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* ~~~
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*/
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#[inline(always)]
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pure fn to_mat4(&self) -> Mat4<T> {
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Matrix4::new(self[0][0], self[0][1], self[0][2], zero(),
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self[1][0], self[1][1], self[1][2], zero(),
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self[2][0], self[2][1], self[2][2], zero(),
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zero(), zero(), zero(), one())
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}
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/**
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* Convert the matrix to a quaternion
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*/
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#[inline(always)]
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pure fn to_quat(&self) -> Quat<T> {
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// Implemented using a mix of ideas from jMonkeyEngine and Ken Shoemake's
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// paper on Quaternions: http://www.cs.ucr.edu/~vbz/resources/Quatut.pdf
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let mut s;
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let w, x, y, z;
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let trace = self.trace();
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let _1: T = Number::from(1.0);
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let half: T = Number::from(0.5);
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if trace >= zero() {
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s = (_1 + trace).sqrt();
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w = half * s;
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s = half / s;
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x = (self[1][2] - self[2][1]) * s;
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y = (self[2][0] - self[0][2]) * s;
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z = (self[0][1] - self[1][0]) * s;
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} else if (self[0][0] > self[1][1]) && (self[0][0] > self[2][2]) {
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s = (half + (self[0][0] - self[1][1] - self[2][2])).sqrt();
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w = half * s;
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s = half / s;
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x = (self[0][1] - self[1][0]) * s;
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y = (self[2][0] - self[0][2]) * s;
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z = (self[1][2] - self[2][1]) * s;
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} else if self[1][1] > self[2][2] {
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s = (half + (self[1][1] - self[0][0] - self[2][2])).sqrt();
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w = half * s;
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s = half / s;
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x = (self[0][1] - self[1][0]) * s;
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y = (self[1][2] - self[2][1]) * s;
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z = (self[2][0] - self[0][2]) * s;
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} else {
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s = (half + (self[2][2] - self[0][0] - self[1][1])).sqrt();
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w = half * s;
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s = half / s;
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x = (self[2][0] - self[0][2]) * s;
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y = (self[1][2] - self[2][1]) * s;
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z = (self[0][1] - self[1][0]) * s;
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}
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Quat::new(w, x, y, z)
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}
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}
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pub impl<T:Copy Float FuzzyEq<T>> Mat3<T>: MutableMatrix<T, Vec3<T>> {
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#[inline(always)]
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fn col_mut(&mut self, i: uint) -> &self/mut Vec3<T> {
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||
match i {
|
||
0 => &mut self.x,
|
||
1 => &mut self.y,
|
||
2 => &mut self.z,
|
||
_ => fail!(fmt!("index out of bounds: expected an index from 0 to 2, but found %u", i))
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn swap_cols(&mut self, a: uint, b: uint) {
|
||
swap(self.col_mut(a),
|
||
self.col_mut(b));
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn swap_rows(&mut self, a: uint, b: uint) {
|
||
self.x.swap(a, b);
|
||
self.y.swap(a, b);
|
||
self.z.swap(a, b);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn set(&mut self, other: &Mat3<T>) {
|
||
(*self) = (*other);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_identity(&mut self) {
|
||
(*self) = Matrix::identity();
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn to_zero(&mut self) {
|
||
(*self) = Matrix::zero();
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn mul_self_t(&mut self, value: T) {
|
||
self.col_mut(0).mul_self_t(&value);
|
||
self.col_mut(1).mul_self_t(&value);
|
||
self.col_mut(2).mul_self_t(&value);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn add_self_m(&mut self, other: &Mat3<T>) {
|
||
self.col_mut(0).add_self_v(&other[0]);
|
||
self.col_mut(1).add_self_v(&other[1]);
|
||
self.col_mut(2).add_self_v(&other[2]);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn sub_self_m(&mut self, other: &Mat3<T>) {
|
||
self.col_mut(0).sub_self_v(&other[0]);
|
||
self.col_mut(1).sub_self_v(&other[1]);
|
||
self.col_mut(2).sub_self_v(&other[2]);
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn invert_self(&mut self) {
|
||
match self.inverse() {
|
||
Some(m) => (*self) = m,
|
||
None => fail!(~"Couldn't invert the matrix!")
|
||
}
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn transpose_self(&mut self) {
|
||
swap(self.col_mut(0).index_mut(1), self.col_mut(1).index_mut(0));
|
||
swap(self.col_mut(0).index_mut(2), self.col_mut(2).index_mut(0));
|
||
|
||
swap(self.col_mut(1).index_mut(0), self.col_mut(0).index_mut(1));
|
||
swap(self.col_mut(1).index_mut(2), self.col_mut(2).index_mut(1));
|
||
|
||
swap(self.col_mut(2).index_mut(0), self.col_mut(0).index_mut(2));
|
||
swap(self.col_mut(2).index_mut(1), self.col_mut(1).index_mut(2));
|
||
}
|
||
}
|
||
|
||
pub impl<T:Copy> Mat3<T>: Index<uint, Vec3<T>> {
|
||
#[inline(always)]
|
||
pure fn index(&self, i: uint) -> Vec3<T> {
|
||
unsafe { do buf_as_slice(
|
||
transmute::<*Mat3<T>, *Vec3<T>>(
|
||
to_unsafe_ptr(self)), 3) |slice| { slice[i] }
|
||
}
|
||
}
|
||
}
|
||
|
||
pub impl<T:Copy Float FuzzyEq<T>> Mat3<T>: Neg<Mat3<T>> {
|
||
#[inline(always)]
|
||
pure fn neg(&self) -> Mat3<T> {
|
||
Matrix3::from_cols(-self[0], -self[1], -self[2])
|
||
}
|
||
}
|
||
|
||
pub impl<T:Copy Float FuzzyEq<T>> Mat3<T>: FuzzyEq<T> {
|
||
#[inline(always)]
|
||
pure fn fuzzy_eq(&self, other: &Mat3<T>) -> bool {
|
||
self.fuzzy_eq_eps(other, &Number::from(FUZZY_EPSILON))
|
||
}
|
||
|
||
#[inline(always)]
|
||
pure fn fuzzy_eq_eps(&self, other: &Mat3<T>, epsilon: &T) -> bool {
|
||
self[0].fuzzy_eq_eps(&other[0], epsilon) &&
|
||
self[1].fuzzy_eq_eps(&other[1], epsilon) &&
|
||
self[2].fuzzy_eq_eps(&other[2], epsilon)
|
||
}
|
||
}
|
||
|
||
// GLSL-style type aliases, corresponding to Section 4.1.6 of the [GLSL 4.30.6 specification]
|
||
// (http://www.opengl.org/registry/doc/GLSLangSpec.4.30.6.pdf).
|
||
|
||
pub type mat3 = Mat3<f32>; // a 3×3 single-precision floating-point matrix
|
||
pub type dmat3 = Mat3<f64>; // a 3×3 double-precision floating-point matrix
|
||
|
||
// Static method wrappers for GLSL-style types
|
||
|
||
pub impl mat3 {
|
||
#[inline(always)] static pure fn new(c0r0: f32, c0r1: f32, c0r2: f32, c1r0: f32, c1r1: f32, c1r2: f32, c2r0: f32, c2r1: f32, c2r2: f32)
|
||
-> mat3 { Matrix3::new(c0r0, c0r1, c0r2, c1r0, c1r1, c1r2, c2r0, c2r1, c2r2) }
|
||
#[inline(always)] static pure fn from_cols(c0: vec3, c1: vec3, c2: vec3)
|
||
-> mat3 { Matrix3::from_cols(move c0, move c1, move c2) }
|
||
#[inline(always)] static pure fn from_value(v: f32) -> mat3 { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] static pure fn identity() -> mat3 { Matrix::identity() }
|
||
#[inline(always)] static pure fn zero() -> mat3 { Matrix::zero() }
|
||
|
||
#[inline(always)] static pure fn from_angle_x(radians: f32) -> mat3 { Matrix3::from_angle_x(radians) }
|
||
#[inline(always)] static pure fn from_angle_y(radians: f32) -> mat3 { Matrix3::from_angle_y(radians) }
|
||
#[inline(always)] static pure fn from_angle_z(radians: f32) -> mat3 { Matrix3::from_angle_z(radians) }
|
||
#[inline(always)] static pure fn from_angle_xyz(radians_x: f32, radians_y: f32, radians_z: f32) -> mat3 { Matrix3::from_angle_xyz(radians_x, radians_y, radians_z) }
|
||
#[inline(always)] static pure fn from_angle_axis(radians: f32, axis: &vec3) -> mat3 { Matrix3::from_angle_axis(radians, axis) }
|
||
#[inline(always)] static pure fn from_axes(x: vec3, y: vec3, z: vec3) -> mat3 { Matrix3::from_axes(x, y, z) }
|
||
#[inline(always)] static pure fn look_at(dir: &vec3, up: &vec3) -> mat3 { Matrix3::look_at(dir, up) }
|
||
|
||
#[inline(always)] static pure fn dim() -> uint { 3 }
|
||
#[inline(always)] static pure fn rows() -> uint { 3 }
|
||
#[inline(always)] static pure fn cols() -> uint { 3 }
|
||
#[inline(always)] static pure fn size_of() -> uint { size_of::<mat3>() }
|
||
}
|
||
|
||
|
||
pub impl dmat3 {
|
||
#[inline(always)] static pure fn new(c0r0: f64, c0r1: f64, c0r2: f64, c1r0: f64, c1r1: f64, c1r2: f64, c2r0: f64, c2r1: f64, c2r2: f64)
|
||
-> dmat3 { Matrix3::new(c0r0, c0r1, c0r2, c1r0, c1r1, c1r2, c2r0, c2r1, c2r2) }
|
||
#[inline(always)] static pure fn from_cols(c0: dvec3, c1: dvec3, c2: dvec3)
|
||
-> dmat3 { Matrix3::from_cols(move c0, move c1, move c2) }
|
||
#[inline(always)] static pure fn from_value(v: f64) -> dmat3 { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] static pure fn identity() -> dmat3 { Matrix::identity() }
|
||
#[inline(always)] static pure fn zero() -> dmat3 { Matrix::zero() }
|
||
|
||
#[inline(always)] static pure fn dim() -> uint { 3 }
|
||
#[inline(always)] static pure fn rows() -> uint { 3 }
|
||
#[inline(always)] static pure fn cols() -> uint { 3 }
|
||
#[inline(always)] static pure fn size_of() -> uint { size_of::<dmat3>() }
|
||
} |