565 lines
19 KiB
Rust
565 lines
19 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 vec::{
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Vec4,
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Vector4,
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MutableVector,
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NumericVector,
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MutableNumericVector,
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vec4,
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dvec4,
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};
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use mat::{
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Mat3,
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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 4 x 4 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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* * `w` - the fourth column vector of the matrix
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*/
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#[deriving_eq]
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pub struct Mat4<T> { x: Vec4<T>, y: Vec4<T>, z: Vec4<T>, w: Vec4<T> }
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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix<T, Vec4<T>> for Mat4<T> {
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#[inline(always)]
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fn col(&self, i: uint) -> Vec4<T> { self[i] }
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#[inline(always)]
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fn row(&self, i: uint) -> Vec4<T> {
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Vector4::new(self[0][i],
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self[1][i],
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self[2][i],
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self[3][i])
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}
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/**
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* Construct a 4 x 4 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 c3
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* +-----+-----+-----+-----+
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* r0 | val | 0 | 0 | 0 |
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* +-----+-----+-----+-----+
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* r1 | 0 | val | 0 | 0 |
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* +-----+-----+-----+-----+
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* r2 | 0 | 0 | val | 0 |
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* +-----+-----+-----+-----+
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* r3 | 0 | 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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fn from_value(value: T) -> Mat4<T> {
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Matrix4::new(value, zero(), zero(), zero(),
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zero(), value, zero(), zero(),
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zero(), zero(), value, zero(),
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zero(), 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 c3
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* +----+----+----+----+
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* r0 | 1 | 0 | 0 | 0 |
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* +----+----+----+----+
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* r1 | 0 | 1 | 0 | 0 |
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* +----+----+----+----+
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* r2 | 0 | 0 | 1 | 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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fn identity() -> Mat4<T> {
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Matrix4::new( one::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), one::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), one::<T>(), zero::<T>(),
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zero::<T>(), 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 c3
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* +----+----+----+----+
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* r0 | 0 | 0 | 0 | 0 |
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* +----+----+----+----+
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* r1 | 0 | 0 | 0 | 0 |
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* +----+----+----+----+
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* r2 | 0 | 0 | 0 | 0 |
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* +----+----+----+----+
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* r3 | 0 | 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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fn zero() -> Mat4<T> {
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Matrix4::new(zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>(),
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zero::<T>(), zero::<T>(), zero::<T>(), zero::<T>())
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}
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#[inline(always)]
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fn mul_t(&self, value: T) -> Mat4<T> {
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Matrix4::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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self[3].mul_t(value))
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}
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#[inline(always)]
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fn mul_v(&self, vec: &Vec4<T>) -> Vec4<T> {
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Vector4::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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self.row(3).dot(vec))
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}
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#[inline(always)]
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fn add_m(&self, other: &Mat4<T>) -> Mat4<T> {
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Matrix4::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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self[3].add_v(&other[3]))
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}
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#[inline(always)]
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fn sub_m(&self, other: &Mat4<T>) -> Mat4<T> {
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Matrix4::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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self[3].sub_v(&other[3]))
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}
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#[inline(always)]
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fn mul_m(&self, other: &Mat4<T>) -> Mat4<T> {
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Matrix4::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(3).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(3).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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self.row(3).dot(&other.col(2)),
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self.row(0).dot(&other.col(3)),
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self.row(1).dot(&other.col(3)),
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self.row(2).dot(&other.col(3)),
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self.row(3).dot(&other.col(3)))
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}
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fn dot(&self, other: &Mat4<T>) -> T {
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other.transpose().mul_m(self).trace()
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}
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fn determinant(&self) -> T {
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let m0: Mat3<T> = Matrix3::new(self[1][1], self[2][1], self[3][1],
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self[1][2], self[2][2], self[3][2],
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self[1][3], self[2][3], self[3][3]);
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let m1: Mat3<T> = Matrix3::new(self[0][1], self[2][1], self[3][1],
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self[0][2], self[2][2], self[3][2],
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self[0][3], self[2][3], self[3][3]);
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let m2: Mat3<T> = Matrix3::new(self[0][1], self[1][1], self[3][1],
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self[0][2], self[1][2], self[3][2],
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self[0][3], self[1][3], self[3][3]);
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let m3: Mat3<T> = Matrix3::new(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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self[0][3], self[1][3], self[2][3]);
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self[0][0] * m0.determinant() -
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self[1][0] * m1.determinant() +
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self[2][0] * m2.determinant() -
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self[3][0] * m3.determinant()
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}
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fn trace(&self) -> T {
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self[0][0] + self[1][1] + self[2][2] + self[3][3]
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}
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fn inverse(&self) -> Option<Mat4<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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// Gauss Jordan Elimination with partial pivoting
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// So take this matrix, A, augmented with the identity
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// and essentially reduce [A|I]
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let mut A = *self;
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let mut I: Mat4<T> = Matrix::identity();
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for uint::range(0, 4) |j| {
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// Find largest element in col j
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let mut i1 = j;
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for uint::range(j + 1, 4) |i| {
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if abs(A[j][i]) > abs(A[j][i1]) {
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i1 = i;
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}
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}
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unsafe {
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// Swap columns i1 and j in A and I to
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// put pivot on diagonal
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A.swap_cols(i1, j);
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I.swap_cols(i1, j);
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// Scale col j to have a unit diagonal
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I.col_mut(j).div_self_t(&A[j][j]);
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A.col_mut(j).div_self_t(&A[j][j]);
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// Eliminate off-diagonal elems in col j of A,
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// doing identical ops to I
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for uint::range(0, 4) |i| {
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if i != j {
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I.col_mut(i).sub_self_v(&I[j].mul_t(A[i][j]));
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A.col_mut(i).sub_self_v(&A[j].mul_t(A[i][j]));
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}
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}
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}
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}
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Some(I)
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}
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}
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#[inline(always)]
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fn transpose(&self) -> Mat4<T> {
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Matrix4::new(self[0][0], self[1][0], self[2][0], self[3][0],
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self[0][1], self[1][1], self[2][1], self[3][1],
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self[0][2], self[1][2], self[2][2], self[3][2],
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self[0][3], self[1][3], self[2][3], self[3][3])
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}
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#[inline(always)]
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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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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[0][3].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[1][3].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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self[2][3].fuzzy_eq(&zero()) &&
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self[3][0].fuzzy_eq(&zero()) &&
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self[3][1].fuzzy_eq(&zero()) &&
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self[3][2].fuzzy_eq(&zero())
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}
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#[inline(always)]
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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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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[0][3].fuzzy_eq(&self[3][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[1][3].fuzzy_eq(&self[3][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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self[2][3].fuzzy_eq(&self[3][2]) &&
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self[3][0].fuzzy_eq(&self[0][3]) &&
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self[3][1].fuzzy_eq(&self[1][3]) &&
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self[3][2].fuzzy_eq(&self[2][3])
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}
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#[inline(always)]
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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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fn to_ptr(&self) -> *T {
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unsafe {
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transmute::<*Mat4<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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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Matrix4<T, Vec4<T>> for Mat4<T> {
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/**
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* Construct a 4 x 4 matrix
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*
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* # Arguments
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*
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* * `c0r0`, `c0r1`, `c0r2`, `c0r3` - the first column of the matrix
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* * `c1r0`, `c1r1`, `c1r2`, `c1r3` - the second column of the matrix
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* * `c2r0`, `c2r1`, `c2r2`, `c2r3` - the third column of the matrix
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* * `c3r0`, `c3r1`, `c3r2`, `c3r3` - the fourth column of the matrix
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*
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* ~~~
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* c0 c1 c2 c3
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* +------+------+------+------+
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* r0 | c0r0 | c1r0 | c2r0 | c3r0 |
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* +------+------+------+------+
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* r1 | c0r1 | c1r1 | c2r1 | c3r1 |
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* +------+------+------+------+
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* r2 | c0r2 | c1r2 | c2r2 | c3r2 |
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* +------+------+------+------+
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* r3 | c0r3 | c1r3 | c2r3 | c3r3 |
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* +------+------+------+------+
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* ~~~
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*/
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#[inline(always)]
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fn new(c0r0: T, c0r1: T, c0r2: T, c0r3: T,
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c1r0: T, c1r1: T, c1r2: T, c1r3: T,
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c2r0: T, c2r1: T, c2r2: T, c2r3: T,
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c3r0: T, c3r1: T, c3r2: T, c3r3: T) -> Mat4<T> {
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Matrix4::from_cols(Vector4::new::<T,Vec4<T>>(c0r0, c0r1, c0r2, c0r3),
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Vector4::new::<T,Vec4<T>>(c1r0, c1r1, c1r2, c1r3),
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Vector4::new::<T,Vec4<T>>(c2r0, c2r1, c2r2, c2r3),
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Vector4::new::<T,Vec4<T>>(c3r0, c3r1, c3r2, c3r3))
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}
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/**
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* Construct a 4 x 4 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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* * `c3` - the fourth column vector of the matrix
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*
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* ~~~
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* c0 c1 c2 c3
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* +------+------+------+------+
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* r0 | c0.x | c1.x | c2.x | c3.x |
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* +------+------+------+------+
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* r1 | c0.y | c1.y | c2.y | c3.y |
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* +------+------+------+------+
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* r2 | c0.z | c1.z | c2.z | c3.z |
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* +------+------+------+------+
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* r3 | c0.w | c1.w | c2.w | c3.w |
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* +------+------+------+------+
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* ~~~
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*/
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#[inline(always)]
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fn from_cols(c0: Vec4<T>,
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c1: Vec4<T>,
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c2: Vec4<T>,
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c3: Vec4<T>) -> Mat4<T> {
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Mat4 { x: c0, y: c1, z: c2, w: c3 }
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}
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}
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impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> MutableMatrix<T, Vec4<T>> for Mat4<T> {
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#[inline(always)]
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fn col_mut(&mut self, i: uint) -> &'self mut Vec4<T> {
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match i {
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0 => &mut self.x,
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1 => &mut self.y,
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2 => &mut self.z,
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3 => &mut self.w,
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_ => fail!(fmt!("index out of bounds: expected an index from 0 to 3, but found %u", i))
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}
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}
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#[inline(always)]
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fn swap_cols(&mut self, a: uint, b: uint) {
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swap(self.col_mut(a),
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self.col_mut(b));
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}
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#[inline(always)]
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fn swap_rows(&mut self, a: uint, b: uint) {
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self.x.swap(a, b);
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self.y.swap(a, b);
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self.z.swap(a, b);
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self.w.swap(a, b);
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}
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#[inline(always)]
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fn set(&mut self, other: &Mat4<T>) {
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(*self) = (*other);
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}
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#[inline(always)]
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fn to_identity(&mut self) {
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(*self) = Matrix::identity();
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}
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#[inline(always)]
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fn to_zero(&mut self) {
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(*self) = Matrix::zero();
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}
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#[inline(always)]
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fn mul_self_t(&mut self, value: T) {
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self.col_mut(0).mul_self_t(&value);
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self.col_mut(1).mul_self_t(&value);
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self.col_mut(2).mul_self_t(&value);
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self.col_mut(3).mul_self_t(&value);
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}
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#[inline(always)]
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fn add_self_m(&mut self, other: &Mat4<T>) {
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self.col_mut(0).add_self_v(&other[0]);
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self.col_mut(1).add_self_v(&other[1]);
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self.col_mut(2).add_self_v(&other[2]);
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self.col_mut(3).add_self_v(&other[3]);
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}
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|
||
#[inline(always)]
|
||
fn sub_self_m(&mut self, other: &Mat4<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]);
|
||
self.col_mut(3).sub_self_v(&other[3]);
|
||
}
|
||
|
||
#[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(0).index_mut(3), self.col_mut(3).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(1).index_mut(3), self.col_mut(3).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));
|
||
swap(self.col_mut(2).index_mut(3), self.col_mut(3).index_mut(2));
|
||
|
||
swap(self.col_mut(3).index_mut(0), self.col_mut(0).index_mut(3));
|
||
swap(self.col_mut(3).index_mut(1), self.col_mut(1).index_mut(3));
|
||
swap(self.col_mut(3).index_mut(2), self.col_mut(2).index_mut(3));
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + FuzzyEq<T> + Add<T,T> + Sub<T,T> + Mul<T,T> + Div<T,T> + Neg<T>> Neg<Mat4<T>> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn neg(&self) -> Mat4<T> {
|
||
Matrix4::from_cols(-self[0], -self[1], -self[2], -self[3])
|
||
}
|
||
}
|
||
|
||
impl<T:Copy> Index<uint, Vec4<T>> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn index(&self, i: uint) -> Vec4<T> {
|
||
unsafe { do buf_as_slice(
|
||
transmute::<*Mat4<T>, *Vec4<T>>(
|
||
to_unsafe_ptr(self)), 4) |slice| { slice[i] }
|
||
}
|
||
}
|
||
}
|
||
|
||
impl<T:Copy + Float + FuzzyEq<T>> FuzzyEq<T> for Mat4<T> {
|
||
#[inline(always)]
|
||
fn fuzzy_eq(&self, other: &Mat4<T>) -> bool {
|
||
self.fuzzy_eq_eps(other, &Number::from(FUZZY_EPSILON))
|
||
}
|
||
|
||
#[inline(always)]
|
||
fn fuzzy_eq_eps(&self, other: &Mat4<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) &&
|
||
self[3].fuzzy_eq_eps(&other[3], 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 mat4 = Mat4<f32>; // a 4×4 single-precision floating-point matrix
|
||
pub type dmat4 = Mat4<f64>; // a 4×4 double-precision floating-point matrix
|
||
|
||
// Static method wrappers for GLSL-style types
|
||
|
||
impl mat4 {
|
||
#[inline(always)] fn new(c0r0: f32, c0r1: f32, c0r2: f32, c0r3: f32, c1r0: f32, c1r1: f32, c1r2: f32, c1r3: f32, c2r0: f32, c2r1: f32, c2r2: f32, c2r3: f32, c3r0: f32, c3r1: f32, c3r2: f32, c3r3: f32)
|
||
-> mat4 { Matrix4::new(c0r0, c0r1, c0r2, c0r3, c1r0, c1r1, c1r2, c1r3, c2r0, c2r1, c2r2, c2r3, c3r0, c3r1, c3r2, c3r3) }
|
||
#[inline(always)] fn from_cols(c0: vec4, c1: vec4, c2: vec4, c3: vec4)
|
||
-> mat4 { Matrix4::from_cols(c0, c1, c2, c3) }
|
||
#[inline(always)] fn from_value(v: f32) -> mat4 { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] fn identity() -> mat4 { Matrix::identity() }
|
||
#[inline(always)] fn zero() -> mat4 { Matrix::zero() }
|
||
|
||
#[inline(always)] fn dim() -> uint { 4 }
|
||
#[inline(always)] fn rows() -> uint { 4 }
|
||
#[inline(always)] fn cols() -> uint { 4 }
|
||
#[inline(always)] fn size_of() -> uint { size_of::<mat4>() }
|
||
}
|
||
|
||
impl dmat4 {
|
||
#[inline(always)] fn new(c0r0: f64, c0r1: f64, c0r2: f64, c0r3: f64, c1r0: f64, c1r1: f64, c1r2: f64, c1r3: f64, c2r0: f64, c2r1: f64, c2r2: f64, c2r3: f64, c3r0: f64, c3r1: f64, c3r2: f64, c3r3: f64)
|
||
-> dmat4 { Matrix4::new(c0r0, c0r1, c0r2, c0r3, c1r0, c1r1, c1r2, c1r3, c2r0, c2r1, c2r2, c2r3, c3r0, c3r1, c3r2, c3r3) }
|
||
#[inline(always)] fn from_cols(c0: dvec4, c1: dvec4, c2: dvec4, c3: dvec4)
|
||
-> dmat4 { Matrix4::from_cols(c0, c1, c2, c3) }
|
||
#[inline(always)] fn from_value(v: f64) -> dmat4 { Matrix::from_value(v) }
|
||
|
||
#[inline(always)] fn identity() -> dmat4 { Matrix::identity() }
|
||
#[inline(always)] fn zero() -> dmat4 { Matrix::zero() }
|
||
|
||
#[inline(always)] fn dim() -> uint { 4 }
|
||
#[inline(always)] fn rows() -> uint { 4 }
|
||
#[inline(always)] fn cols() -> uint { 4 }
|
||
#[inline(always)] fn size_of() -> uint { size_of::<dmat4>() }
|
||
}
|