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Flattened the `traits` submodules.

This commit is contained in:
Sébastien Crozet 2013-07-22 10:26:20 +02:00
parent e548e1fa5e
commit ff24f70332
7 changed files with 1278 additions and 1244 deletions
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209
src/mat.rs
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@ -1,209 +0,0 @@
use std::cast;
use std::uint::iterate;
use std::num::{One, Zero};
use std::cmp::ApproxEq;
use std::iterator::IteratorUtil;
use std::vec::{VecIterator, VecMutIterator};
use vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
use traits::dim::Dim;
use traits::ring::Ring;
use traits::inv::Inv;
use traits::division_ring::DivisionRing;
use traits::transpose::Transpose;
use traits::rlmul::{RMul, LMul};
use traits::transformation::Transform;
use traits::homogeneous::{FromHomogeneous, ToHomogeneous};
use traits::indexable::Indexable;
use traits::column::Column;
use traits::iterable::{Iterable, IterableMut};
mod mat_impl;
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat1<N>
{ m11: N }
mat_impl!(Mat1, 1, m11)
one_impl!(Mat1, _1)
iterable_impl!(Mat1, 1)
iterable_mut_impl!(Mat1, 1)
dim_impl!(Mat1, 1)
indexable_impl!(Mat1, 1)
mul_impl!(Mat1, 1)
rmul_impl!(Mat1, Vec1, 1)
lmul_impl!(Mat1, Vec1, 1)
transform_impl!(Mat1, Vec1)
// (specialized) inv_impl!(Mat1, 1)
transpose_impl!(Mat1, 1)
approx_eq_impl!(Mat1)
column_impl!(Mat1, 1)
to_homogeneous_impl!(Mat1, Mat2, 1, 2)
from_homogeneous_impl!(Mat1, Mat2, 1, 2)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat2<N>
{
m11: N, m12: N,
m21: N, m22: N
}
mat_impl!(Mat2, 2, m11, m12,
m21, m22)
one_impl!(Mat2, _1, _0,
_0, _1)
iterable_impl!(Mat2, 2)
iterable_mut_impl!(Mat2, 2)
dim_impl!(Mat2, 2)
indexable_impl!(Mat2, 2)
mul_impl!(Mat2, 2)
rmul_impl!(Mat2, Vec2, 2)
lmul_impl!(Mat2, Vec2, 2)
transform_impl!(Mat2, Vec2)
// (specialized) inv_impl!(Mat2, 2)
transpose_impl!(Mat2, 2)
approx_eq_impl!(Mat2)
column_impl!(Mat2, 2)
to_homogeneous_impl!(Mat2, Mat3, 2, 3)
from_homogeneous_impl!(Mat2, Mat3, 2, 3)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat3<N>
{
m11: N, m12: N, m13: N,
m21: N, m22: N, m23: N,
m31: N, m32: N, m33: N
}
mat_impl!(Mat3, 3, m11, m12, m13,
m21, m22, m23,
m31, m32, m33)
one_impl!(Mat3, _1, _0, _0,
_0, _1, _0,
_0, _0, _1)
iterable_impl!(Mat3, 3)
iterable_mut_impl!(Mat3, 3)
dim_impl!(Mat3, 3)
indexable_impl!(Mat3, 3)
mul_impl!(Mat3, 3)
rmul_impl!(Mat3, Vec3, 3)
lmul_impl!(Mat3, Vec3, 3)
transform_impl!(Mat3, Vec3)
// (specialized) inv_impl!(Mat3, 3)
transpose_impl!(Mat3, 3)
approx_eq_impl!(Mat3)
column_impl!(Mat3, 3)
to_homogeneous_impl!(Mat3, Mat4, 3, 4)
from_homogeneous_impl!(Mat3, Mat4, 3, 4)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat4<N>
{
m11: N, m12: N, m13: N, m14: N,
m21: N, m22: N, m23: N, m24: N,
m31: N, m32: N, m33: N, m34: N,
m41: N, m42: N, m43: N, m44: N
}
mat_impl!(Mat4, 4,
m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44
)
one_impl!(Mat4, _1, _0, _0, _0,
_0, _1, _0, _0,
_0, _0, _1, _0,
_0, _0, _0, _1)
iterable_impl!(Mat4, 4)
iterable_mut_impl!(Mat4, 4)
dim_impl!(Mat4, 4)
indexable_impl!(Mat4, 4)
mul_impl!(Mat4, 4)
rmul_impl!(Mat4, Vec4, 4)
lmul_impl!(Mat4, Vec4, 4)
transform_impl!(Mat4, Vec4)
inv_impl!(Mat4, 4)
transpose_impl!(Mat4, 4)
approx_eq_impl!(Mat4)
column_impl!(Mat4, 4)
to_homogeneous_impl!(Mat4, Mat5, 4, 5)
from_homogeneous_impl!(Mat4, Mat5, 4, 5)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat5<N>
{
m11: N, m12: N, m13: N, m14: N, m15: N,
m21: N, m22: N, m23: N, m24: N, m25: N,
m31: N, m32: N, m33: N, m34: N, m35: N,
m41: N, m42: N, m43: N, m44: N, m45: N,
m51: N, m52: N, m53: N, m54: N, m55: N
}
mat_impl!(Mat5, 5,
m11, m12, m13, m14, m15,
m21, m22, m23, m24, m25,
m31, m32, m33, m34, m35,
m41, m42, m43, m44, m45,
m51, m52, m53, m54, m55
)
one_impl!(Mat5,
_1, _0, _0, _0, _0,
_0, _1, _0, _0, _0,
_0, _0, _1, _0, _0,
_0, _0, _0, _1, _0,
_0, _0, _0, _0, _1
)
iterable_impl!(Mat5, 5)
iterable_mut_impl!(Mat5, 5)
dim_impl!(Mat5, 5)
indexable_impl!(Mat5, 5)
mul_impl!(Mat5, 5)
rmul_impl!(Mat5, Vec5, 5)
lmul_impl!(Mat5, Vec5, 5)
transform_impl!(Mat5, Vec5)
inv_impl!(Mat5, 5)
transpose_impl!(Mat5, 5)
approx_eq_impl!(Mat5)
column_impl!(Mat5, 5)
to_homogeneous_impl!(Mat5, Mat6, 5, 6)
from_homogeneous_impl!(Mat5, Mat6, 5, 6)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat6<N>
{
m11: N, m12: N, m13: N, m14: N, m15: N, m16: N,
m21: N, m22: N, m23: N, m24: N, m25: N, m26: N,
m31: N, m32: N, m33: N, m34: N, m35: N, m36: N,
m41: N, m42: N, m43: N, m44: N, m45: N, m46: N,
m51: N, m52: N, m53: N, m54: N, m55: N, m56: N,
m61: N, m62: N, m63: N, m64: N, m65: N, m66: N
}
mat_impl!(Mat6, 6,
m11, m12, m13, m14, m15, m16,
m21, m22, m23, m24, m25, m26,
m31, m32, m33, m34, m35, m36,
m41, m42, m43, m44, m45, m46,
m51, m52, m53, m54, m55, m56,
m61, m62, m63, m64, m65, m66
)
one_impl!(Mat6,
_1, _0, _0, _0, _0, _0,
_0, _1, _0, _0, _0, _0,
_0, _0, _1, _0, _0, _0,
_0, _0, _0, _1, _0, _0,
_0, _0, _0, _0, _1, _0,
_0, _0, _0, _0, _0, _1
)
iterable_impl!(Mat6, 6)
iterable_mut_impl!(Mat6, 6)
dim_impl!(Mat6, 6)
indexable_impl!(Mat6, 6)
mul_impl!(Mat6, 6)
rmul_impl!(Mat6, Vec6, 6)
lmul_impl!(Mat6, Vec6, 6)
transform_impl!(Mat6, Vec6)
inv_impl!(Mat6, 6)
transpose_impl!(Mat6, 6)
approx_eq_impl!(Mat6)
column_impl!(Mat6, 6)

601
src/mat_impl.rs
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@ -1,408 +1,209 @@
#[macro_escape];
use std::cast;
use std::uint::iterate;
use std::num::{One, Zero};
use std::cmp::ApproxEq;
use std::iterator::IteratorUtil;
use std::vec::{VecIterator, VecMutIterator};
use vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
use traits::dim::Dim;
use traits::ring::Ring;
use traits::inv::Inv;
use traits::division_ring::DivisionRing;
use traits::transpose::Transpose;
use traits::rlmul::{RMul, LMul};
use traits::transformation::Transform;
use traits::homogeneous::{FromHomogeneous, ToHomogeneous};
use traits::indexable::Indexable;
use traits::column::Column;
use traits::iterable::{Iterable, IterableMut};
macro_rules! mat_impl(
($t: ident, $dim: expr, $comp0: ident $(,$compN: ident)*) => (
impl<N> $t<N>
{
#[inline]
pub fn new($comp0: N $(, $compN: N )*) -> $t<N>
{
$t {
$comp0: $comp0
$(, $compN: $compN )*
}
}
}
)
mod mat_macros;
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat1<N>
{ m11: N }
mat_impl!(Mat1, 1, m11)
one_impl!(Mat1, _1)
iterable_impl!(Mat1, 1)
iterable_mut_impl!(Mat1, 1)
dim_impl!(Mat1, 1)
indexable_impl!(Mat1, 1)
mul_impl!(Mat1, 1)
rmul_impl!(Mat1, Vec1, 1)
lmul_impl!(Mat1, Vec1, 1)
transform_impl!(Mat1, Vec1)
// (specialized) inv_impl!(Mat1, 1)
transpose_impl!(Mat1, 1)
approx_eq_impl!(Mat1)
column_impl!(Mat1, 1)
to_homogeneous_impl!(Mat1, Mat2, 1, 2)
from_homogeneous_impl!(Mat1, Mat2, 1, 2)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat2<N>
{
m11: N, m12: N,
m21: N, m22: N
}
mat_impl!(Mat2, 2, m11, m12,
m21, m22)
one_impl!(Mat2, _1, _0,
_0, _1)
iterable_impl!(Mat2, 2)
iterable_mut_impl!(Mat2, 2)
dim_impl!(Mat2, 2)
indexable_impl!(Mat2, 2)
mul_impl!(Mat2, 2)
rmul_impl!(Mat2, Vec2, 2)
lmul_impl!(Mat2, Vec2, 2)
transform_impl!(Mat2, Vec2)
// (specialized) inv_impl!(Mat2, 2)
transpose_impl!(Mat2, 2)
approx_eq_impl!(Mat2)
column_impl!(Mat2, 2)
to_homogeneous_impl!(Mat2, Mat3, 2, 3)
from_homogeneous_impl!(Mat2, Mat3, 2, 3)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat3<N>
{
m11: N, m12: N, m13: N,
m21: N, m22: N, m23: N,
m31: N, m32: N, m33: N
}
mat_impl!(Mat3, 3, m11, m12, m13,
m21, m22, m23,
m31, m32, m33)
one_impl!(Mat3, _1, _0, _0,
_0, _1, _0,
_0, _0, _1)
iterable_impl!(Mat3, 3)
iterable_mut_impl!(Mat3, 3)
dim_impl!(Mat3, 3)
indexable_impl!(Mat3, 3)
mul_impl!(Mat3, 3)
rmul_impl!(Mat3, Vec3, 3)
lmul_impl!(Mat3, Vec3, 3)
transform_impl!(Mat3, Vec3)
// (specialized) inv_impl!(Mat3, 3)
transpose_impl!(Mat3, 3)
approx_eq_impl!(Mat3)
column_impl!(Mat3, 3)
to_homogeneous_impl!(Mat3, Mat4, 3, 4)
from_homogeneous_impl!(Mat3, Mat4, 3, 4)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat4<N>
{
m11: N, m12: N, m13: N, m14: N,
m21: N, m22: N, m23: N, m24: N,
m31: N, m32: N, m33: N, m34: N,
m41: N, m42: N, m43: N, m44: N
}
mat_impl!(Mat4, 4,
m11, m12, m13, m14,
m21, m22, m23, m24,
m31, m32, m33, m34,
m41, m42, m43, m44
)
one_impl!(Mat4, _1, _0, _0, _0,
_0, _1, _0, _0,
_0, _0, _1, _0,
_0, _0, _0, _1)
iterable_impl!(Mat4, 4)
iterable_mut_impl!(Mat4, 4)
dim_impl!(Mat4, 4)
indexable_impl!(Mat4, 4)
mul_impl!(Mat4, 4)
rmul_impl!(Mat4, Vec4, 4)
lmul_impl!(Mat4, Vec4, 4)
transform_impl!(Mat4, Vec4)
inv_impl!(Mat4, 4)
transpose_impl!(Mat4, 4)
approx_eq_impl!(Mat4)
column_impl!(Mat4, 4)
to_homogeneous_impl!(Mat4, Mat5, 4, 5)
from_homogeneous_impl!(Mat4, Mat5, 4, 5)
macro_rules! iterable_impl(
($t: ident, $dim: expr) => (
impl<N> Iterable<N> for $t<N>
{
fn iter<'l>(&'l self) -> VecIterator<'l, N>
{ unsafe { cast::transmute::<&'l $t<N>, &'l [N, ..$dim * $dim]>(self).iter() } }
}
)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat5<N>
{
m11: N, m12: N, m13: N, m14: N, m15: N,
m21: N, m22: N, m23: N, m24: N, m25: N,
m31: N, m32: N, m33: N, m34: N, m35: N,
m41: N, m42: N, m43: N, m44: N, m45: N,
m51: N, m52: N, m53: N, m54: N, m55: N
}
mat_impl!(Mat5, 5,
m11, m12, m13, m14, m15,
m21, m22, m23, m24, m25,
m31, m32, m33, m34, m35,
m41, m42, m43, m44, m45,
m51, m52, m53, m54, m55
)
macro_rules! iterable_mut_impl(
($t: ident, $dim: expr) => (
impl<N> IterableMut<N> for $t<N>
{
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
{ unsafe { cast::transmute::<&'l mut $t<N>, &'l mut [N, ..$dim * $dim]>(self).mut_iter() } }
}
)
one_impl!(Mat5,
_1, _0, _0, _0, _0,
_0, _1, _0, _0, _0,
_0, _0, _1, _0, _0,
_0, _0, _0, _1, _0,
_0, _0, _0, _0, _1
)
iterable_impl!(Mat5, 5)
iterable_mut_impl!(Mat5, 5)
dim_impl!(Mat5, 5)
indexable_impl!(Mat5, 5)
mul_impl!(Mat5, 5)
rmul_impl!(Mat5, Vec5, 5)
lmul_impl!(Mat5, Vec5, 5)
transform_impl!(Mat5, Vec5)
inv_impl!(Mat5, 5)
transpose_impl!(Mat5, 5)
approx_eq_impl!(Mat5)
column_impl!(Mat5, 5)
to_homogeneous_impl!(Mat5, Mat6, 5, 6)
from_homogeneous_impl!(Mat5, Mat6, 5, 6)
macro_rules! one_impl(
($t: ident, $value0: ident $(, $valueN: ident)* ) => (
impl<N: Clone + One + Zero> One for $t<N>
{
#[inline]
fn one() -> $t<N>
{
let (_0, _1) = (Zero::zero::<N>(), One::one::<N>());
return $t::new($value0.clone() $(, $valueN.clone() )*)
}
}
)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Mat6<N>
{
m11: N, m12: N, m13: N, m14: N, m15: N, m16: N,
m21: N, m22: N, m23: N, m24: N, m25: N, m26: N,
m31: N, m32: N, m33: N, m34: N, m35: N, m36: N,
m41: N, m42: N, m43: N, m44: N, m45: N, m46: N,
m51: N, m52: N, m53: N, m54: N, m55: N, m56: N,
m61: N, m62: N, m63: N, m64: N, m65: N, m66: N
}
mat_impl!(Mat6, 6,
m11, m12, m13, m14, m15, m16,
m21, m22, m23, m24, m25, m26,
m31, m32, m33, m34, m35, m36,
m41, m42, m43, m44, m45, m46,
m51, m52, m53, m54, m55, m56,
m61, m62, m63, m64, m65, m66
)
macro_rules! dim_impl(
($t: ident, $dim: expr) => (
impl<N> Dim for $t<N>
{
#[inline]
fn dim() -> uint
{ $dim }
}
)
)
macro_rules! indexable_impl(
($t: ident, $dim: expr) => (
impl<N: Clone> Indexable<(uint, uint), N> for $t<N>
{
#[inline]
pub fn at(&self, (i, j): (uint, uint)) -> N
{ unsafe { cast::transmute::<&$t<N>, &[N, ..$dim * $dim]>(self)[i * $dim + j].clone() } }
#[inline]
pub fn set(&mut self, (i, j): (uint, uint), val: N)
{ unsafe { cast::transmute::<&mut $t<N>, &mut [N, ..$dim * $dim]>(self)[i * $dim + j] = val } }
#[inline]
pub fn swap(&mut self, (i1, j1): (uint, uint), (i2, j2): (uint, uint))
{
unsafe {
cast::transmute::<&mut $t<N>, &mut [N, ..$dim * $dim]>(self)
.swap(i1 * $dim + j1, i2 * $dim + j2)
}
}
}
)
)
macro_rules! column_impl(
($t: ident, $dim: expr) => (
impl<N: Clone, V: Zero + Iterable<N> + IterableMut<N>> Column<V> for $t<N>
{
fn set_column(&mut self, col: uint, v: V)
{
for v.iter().enumerate().advance |(i, e)|
{
if i == Dim::dim::<$t<N>>()
{ break }
self.set((i, col), e.clone());
}
}
fn column(&self, col: uint) -> V
{
let mut res = Zero::zero::<V>();
for res.mut_iter().enumerate().advance |(i, e)|
{
if i >= Dim::dim::<$t<N>>()
{ break }
*e = self.at((i, col));
}
res
}
}
)
)
macro_rules! mul_impl(
($t: ident, $dim: expr) => (
impl<N: Clone + Ring>
Mul<$t<N>, $t<N>> for $t<N>
{
fn mul(&self, other: &$t<N>) -> $t<N>
{
let mut res: $t<N> = Zero::zero();
for iterate(0u, $dim) |i|
{
for iterate(0u, $dim) |j|
{
let mut acc = Zero::zero::<N>();
for iterate(0u, $dim) |k|
{ acc = acc + self.at((i, k)) * other.at((k, j)); }
res.set((i, j), acc);
}
}
res
}
}
)
)
macro_rules! rmul_impl(
($t: ident, $v: ident, $dim: expr) => (
impl<N: Clone + Ring>
RMul<$v<N>> for $t<N>
{
fn rmul(&self, other: &$v<N>) -> $v<N>
{
let mut res : $v<N> = Zero::zero();
for iterate(0u, $dim) |i|
{
for iterate(0u, $dim) |j|
{
let val = res.at(i) + other.at(j) * self.at((i, j));
res.set(i, val)
}
}
res
}
}
)
)
macro_rules! lmul_impl(
($t: ident, $v: ident, $dim: expr) => (
impl<N: Clone + Ring>
LMul<$v<N>> for $t<N>
{
fn lmul(&self, other: &$v<N>) -> $v<N>
{
let mut res : $v<N> = Zero::zero();
for iterate(0u, $dim) |i|
{
for iterate(0u, $dim) |j|
{
let val = res.at(i) + other.at(j) * self.at((j, i));
res.set(i, val)
}
}
res
}
}
)
)
macro_rules! transform_impl(
($t: ident, $v: ident) => (
impl<N: Clone + DivisionRing + Eq>
Transform<$v<N>> for $t<N>
{
#[inline]
fn transform_vec(&self, v: &$v<N>) -> $v<N>
{ self.rmul(v) }
#[inline]
fn inv_transform(&self, v: &$v<N>) -> $v<N>
{
match self.inverse()
{
Some(t) => t.transform_vec(v),
None => fail!("Cannot use inv_transform on a non-inversible matrix.")
}
}
}
)
)
macro_rules! inv_impl(
($t: ident, $dim: expr) => (
impl<N: Clone + Eq + DivisionRing>
Inv for $t<N>
{
#[inline]
fn inverse(&self) -> Option<$t<N>>
{
let mut res : $t<N> = self.clone();
if res.inplace_inverse()
{ Some(res) }
else
{ None }
}
fn inplace_inverse(&mut self) -> bool
{
let mut res: $t<N> = One::one();
let _0N: N = Zero::zero();
// inversion using Gauss-Jordan elimination
for iterate(0u, $dim) |k|
{
// search a non-zero value on the k-th column
// FIXME: would it be worth it to spend some more time searching for the
// max instead?
let mut n0 = k; // index of a non-zero entry
while (n0 != $dim)
{
if self.at((n0, k)) != _0N
{ break; }
n0 = n0 + 1;
}
if n0 == $dim
{ return false }
// swap pivot line
if n0 != k
{
for iterate(0u, $dim) |j|
{
self.swap((n0, j), (k, j));
res.swap((n0, j), (k, j));
}
}
let pivot = self.at((k, k));
for iterate(k, $dim) |j|
{
let selfval = self.at((k, j)) / pivot;
self.set((k, j), selfval);
}
for iterate(0u, $dim) |j|
{
let resval = res.at((k, j)) / pivot;
res.set((k, j), resval);
}
for iterate(0u, $dim) |l|
{
if l != k
{
let normalizer = self.at((l, k));
for iterate(k, $dim) |j|
{
let selfval = self.at((l, j)) - self.at((k, j)) * normalizer;
self.set((l, j), selfval);
}
for iterate(0u, $dim) |j|
{
let resval = res.at((l, j)) - res.at((k, j)) * normalizer;
res.set((l, j), resval);
}
}
}
}
*self = res;
true
}
}
)
)
macro_rules! transpose_impl(
($t: ident, $dim: expr) => (
impl<N: Clone> Transpose for $t<N>
{
#[inline]
fn transposed(&self) -> $t<N>
{
let mut res = self.clone();
res.transpose();
res
}
fn transpose(&mut self)
{
for iterate(1u, $dim) |i|
{
for iterate(0u, $dim - 1) |j|
{ self.swap((i, j), (j, i)) }
}
}
}
)
)
macro_rules! approx_eq_impl(
($t: ident) => (
impl<N: ApproxEq<N>> ApproxEq<N> for $t<N>
{
#[inline]
fn approx_epsilon() -> N
{ ApproxEq::approx_epsilon::<N, N>() }
#[inline]
fn approx_eq(&self, other: &$t<N>) -> bool
{
let mut zip = self.iter().zip(other.iter());
do zip.all |(a, b)| { a.approx_eq(b) }
}
#[inline]
fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool
{
let mut zip = self.iter().zip(other.iter());
do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
}
}
)
)
macro_rules! to_homogeneous_impl(
($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
impl<N: One + Zero + Clone> ToHomogeneous<$t2<N>> for $t<N>
{
fn to_homogeneous(&self) -> $t2<N>
{
let mut res: $t2<N> = One::one();
for iterate(0, $dim) |i|
{
for iterate(0, $dim) |j|
{ res.set((i, j), self.at((i, j))) }
}
res
}
}
)
)
macro_rules! from_homogeneous_impl(
($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
impl<N: One + Zero + Clone> FromHomogeneous<$t2<N>> for $t<N>
{
fn from_homogeneous(m: &$t2<N>) -> $t<N>
{
let mut res: $t<N> = One::one();
for iterate(0, $dim2) |i|
{
for iterate(0, $dim2) |j|
{ res.set((i, j), m.at((i, j))) }
}
// FIXME: do we have to deal the lost components
// (like if the 1 is not a 1… do we have to divide?)
res
}
}
)
one_impl!(Mat6,
_1, _0, _0, _0, _0, _0,
_0, _1, _0, _0, _0, _0,
_0, _0, _1, _0, _0, _0,
_0, _0, _0, _1, _0, _0,
_0, _0, _0, _0, _1, _0,
_0, _0, _0, _0, _0, _1
)
iterable_impl!(Mat6, 6)
iterable_mut_impl!(Mat6, 6)
dim_impl!(Mat6, 6)
indexable_impl!(Mat6, 6)
mul_impl!(Mat6, 6)
rmul_impl!(Mat6, Vec6, 6)
lmul_impl!(Mat6, Vec6, 6)
transform_impl!(Mat6, Vec6)
inv_impl!(Mat6, 6)
transpose_impl!(Mat6, 6)
approx_eq_impl!(Mat6)
column_impl!(Mat6, 6)

408
src/mat_macros.rs Normal file
View File

@ -0,0 +1,408 @@
#[macro_escape];
macro_rules! mat_impl(
($t: ident, $dim: expr, $comp0: ident $(,$compN: ident)*) => (
impl<N> $t<N>
{
#[inline]
pub fn new($comp0: N $(, $compN: N )*) -> $t<N>
{
$t {
$comp0: $comp0
$(, $compN: $compN )*
}
}
}
)
)
macro_rules! iterable_impl(
($t: ident, $dim: expr) => (
impl<N> Iterable<N> for $t<N>
{
fn iter<'l>(&'l self) -> VecIterator<'l, N>
{ unsafe { cast::transmute::<&'l $t<N>, &'l [N, ..$dim * $dim]>(self).iter() } }
}
)
)
macro_rules! iterable_mut_impl(
($t: ident, $dim: expr) => (
impl<N> IterableMut<N> for $t<N>
{
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
{ unsafe { cast::transmute::<&'l mut $t<N>, &'l mut [N, ..$dim * $dim]>(self).mut_iter() } }
}
)
)
macro_rules! one_impl(
($t: ident, $value0: ident $(, $valueN: ident)* ) => (
impl<N: Clone + One + Zero> One for $t<N>
{
#[inline]
fn one() -> $t<N>
{
let (_0, _1) = (Zero::zero::<N>(), One::one::<N>());
return $t::new($value0.clone() $(, $valueN.clone() )*)
}
}
)
)
macro_rules! dim_impl(
($t: ident, $dim: expr) => (
impl<N> Dim for $t<N>
{
#[inline]
fn dim() -> uint
{ $dim }
}
)
)
macro_rules! indexable_impl(
($t: ident, $dim: expr) => (
impl<N: Clone> Indexable<(uint, uint), N> for $t<N>
{
#[inline]
pub fn at(&self, (i, j): (uint, uint)) -> N
{ unsafe { cast::transmute::<&$t<N>, &[N, ..$dim * $dim]>(self)[i * $dim + j].clone() } }
#[inline]
pub fn set(&mut self, (i, j): (uint, uint), val: N)
{ unsafe { cast::transmute::<&mut $t<N>, &mut [N, ..$dim * $dim]>(self)[i * $dim + j] = val } }
#[inline]
pub fn swap(&mut self, (i1, j1): (uint, uint), (i2, j2): (uint, uint))
{
unsafe {
cast::transmute::<&mut $t<N>, &mut [N, ..$dim * $dim]>(self)
.swap(i1 * $dim + j1, i2 * $dim + j2)
}
}
}
)
)
macro_rules! column_impl(
($t: ident, $dim: expr) => (
impl<N: Clone, V: Zero + Iterable<N> + IterableMut<N>> Column<V> for $t<N>
{
fn set_column(&mut self, col: uint, v: V)
{
for v.iter().enumerate().advance |(i, e)|
{
if i == Dim::dim::<$t<N>>()
{ break }
self.set((i, col), e.clone());
}
}
fn column(&self, col: uint) -> V
{
let mut res = Zero::zero::<V>();
for res.mut_iter().enumerate().advance |(i, e)|
{
if i >= Dim::dim::<$t<N>>()
{ break }
*e = self.at((i, col));
}
res
}
}
)
)
macro_rules! mul_impl(
($t: ident, $dim: expr) => (
impl<N: Clone + Ring>
Mul<$t<N>, $t<N>> for $t<N>
{
fn mul(&self, other: &$t<N>) -> $t<N>
{
let mut res: $t<N> = Zero::zero();
for iterate(0u, $dim) |i|
{
for iterate(0u, $dim) |j|
{
let mut acc = Zero::zero::<N>();
for iterate(0u, $dim) |k|
{ acc = acc + self.at((i, k)) * other.at((k, j)); }
res.set((i, j), acc);
}
}
res
}
}
)
)
macro_rules! rmul_impl(
($t: ident, $v: ident, $dim: expr) => (
impl<N: Clone + Ring>
RMul<$v<N>> for $t<N>
{
fn rmul(&self, other: &$v<N>) -> $v<N>
{
let mut res : $v<N> = Zero::zero();
for iterate(0u, $dim) |i|
{
for iterate(0u, $dim) |j|
{
let val = res.at(i) + other.at(j) * self.at((i, j));
res.set(i, val)
}
}
res
}
}
)
)
macro_rules! lmul_impl(
($t: ident, $v: ident, $dim: expr) => (
impl<N: Clone + Ring>
LMul<$v<N>> for $t<N>
{
fn lmul(&self, other: &$v<N>) -> $v<N>
{
let mut res : $v<N> = Zero::zero();
for iterate(0u, $dim) |i|
{
for iterate(0u, $dim) |j|
{
let val = res.at(i) + other.at(j) * self.at((j, i));
res.set(i, val)
}
}
res
}
}
)
)
macro_rules! transform_impl(
($t: ident, $v: ident) => (
impl<N: Clone + DivisionRing + Eq>
Transform<$v<N>> for $t<N>
{
#[inline]
fn transform_vec(&self, v: &$v<N>) -> $v<N>
{ self.rmul(v) }
#[inline]
fn inv_transform(&self, v: &$v<N>) -> $v<N>
{
match self.inverse()
{
Some(t) => t.transform_vec(v),
None => fail!("Cannot use inv_transform on a non-inversible matrix.")
}
}
}
)
)
macro_rules! inv_impl(
($t: ident, $dim: expr) => (
impl<N: Clone + Eq + DivisionRing>
Inv for $t<N>
{
#[inline]
fn inverse(&self) -> Option<$t<N>>
{
let mut res : $t<N> = self.clone();
if res.inplace_inverse()
{ Some(res) }
else
{ None }
}
fn inplace_inverse(&mut self) -> bool
{
let mut res: $t<N> = One::one();
let _0N: N = Zero::zero();
// inversion using Gauss-Jordan elimination
for iterate(0u, $dim) |k|
{
// search a non-zero value on the k-th column
// FIXME: would it be worth it to spend some more time searching for the
// max instead?
let mut n0 = k; // index of a non-zero entry
while (n0 != $dim)
{
if self.at((n0, k)) != _0N
{ break; }
n0 = n0 + 1;
}
if n0 == $dim
{ return false }
// swap pivot line
if n0 != k
{
for iterate(0u, $dim) |j|
{
self.swap((n0, j), (k, j));
res.swap((n0, j), (k, j));
}
}
let pivot = self.at((k, k));
for iterate(k, $dim) |j|
{
let selfval = self.at((k, j)) / pivot;
self.set((k, j), selfval);
}
for iterate(0u, $dim) |j|
{
let resval = res.at((k, j)) / pivot;
res.set((k, j), resval);
}
for iterate(0u, $dim) |l|
{
if l != k
{
let normalizer = self.at((l, k));
for iterate(k, $dim) |j|
{
let selfval = self.at((l, j)) - self.at((k, j)) * normalizer;
self.set((l, j), selfval);
}
for iterate(0u, $dim) |j|
{
let resval = res.at((l, j)) - res.at((k, j)) * normalizer;
res.set((l, j), resval);
}
}
}
}
*self = res;
true
}
}
)
)
macro_rules! transpose_impl(
($t: ident, $dim: expr) => (
impl<N: Clone> Transpose for $t<N>
{
#[inline]
fn transposed(&self) -> $t<N>
{
let mut res = self.clone();
res.transpose();
res
}
fn transpose(&mut self)
{
for iterate(1u, $dim) |i|
{
for iterate(0u, $dim - 1) |j|
{ self.swap((i, j), (j, i)) }
}
}
}
)
)
macro_rules! approx_eq_impl(
($t: ident) => (
impl<N: ApproxEq<N>> ApproxEq<N> for $t<N>
{
#[inline]
fn approx_epsilon() -> N
{ ApproxEq::approx_epsilon::<N, N>() }
#[inline]
fn approx_eq(&self, other: &$t<N>) -> bool
{
let mut zip = self.iter().zip(other.iter());
do zip.all |(a, b)| { a.approx_eq(b) }
}
#[inline]
fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool
{
let mut zip = self.iter().zip(other.iter());
do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
}
}
)
)
macro_rules! to_homogeneous_impl(
($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
impl<N: One + Zero + Clone> ToHomogeneous<$t2<N>> for $t<N>
{
fn to_homogeneous(&self) -> $t2<N>
{
let mut res: $t2<N> = One::one();
for iterate(0, $dim) |i|
{
for iterate(0, $dim) |j|
{ res.set((i, j), self.at((i, j))) }
}
res
}
}
)
)
macro_rules! from_homogeneous_impl(
($t: ident, $t2: ident, $dim: expr, $dim2: expr) => (
impl<N: One + Zero + Clone> FromHomogeneous<$t2<N>> for $t<N>
{
fn from_homogeneous(m: &$t2<N>) -> $t<N>
{
let mut res: $t<N> = One::one();
for iterate(0, $dim2) |i|
{
for iterate(0, $dim2) |j|
{ res.set((i, j), m.at((i, j))) }
}
// FIXME: do we have to deal the lost components
// (like if the 1 is not a 1… do we have to divide?)
res
}
}
)
)

42
src/nalgebra.rc
View File

@ -13,10 +13,10 @@
extern mod std;
extern mod extra;
pub mod vec;
pub mod mat;
pub mod dmat;
pub mod dvec;
mod dmat;
mod dvec;
mod vec_impl;
mod mat_impl;
// specialization for some 1d, 2d and 3d operations
pub mod mat_spec;
@ -30,9 +30,43 @@ pub mod adaptors
pub mod transform;
}
pub mod vec
{
pub use vec_impl::*;
pub use dvec::*;
pub use traits::sample::*;
pub use traits::dot::*;
pub use traits::cross::*;
pub use traits::basis::*;
pub use traits::norm::*;
pub use traits::vector_space::*;
pub use traits::sub_dot::*;
pub use traits::scalar_op::*;
}
pub mod mat
{
pub use mat_impl::*;
pub use dmat::*;
pub use traits::column::*;
pub use traits::inv::*;
pub use traits::transpose::*;
pub use traits::rotation::*;
pub use traits::translation::*;
pub use traits::transformation::*;
}
/// Useful linear-algebra related traits.
pub mod traits
{
pub use traits::indexable::*;
pub use traits::iterable::*;
pub use traits::dim::*;
pub use traits::ring::*;
pub use traits::division_ring::*;
pub use traits::rlmul::*;
pub use traits::homogeneous::*;
pub mod sample;
pub mod indexable;
pub mod column;

227
src/vec.rs
View File

@ -1,227 +0,0 @@
use std::cast;
use std::num::{Zero, One, Algebraic, Bounded};
use std::rand::Rng;
use std::vec::{VecIterator, VecMutIterator};
use std::iterator::{Iterator, IteratorUtil, FromIterator};
use std::cmp::ApproxEq;
use std::uint::iterate;
use traits::iterable::{Iterable, IterableMut};
use traits::basis::Basis;
use traits::dim::Dim;
use traits::dot::Dot;
use traits::sub_dot::SubDot;
use traits::norm::Norm;
use traits::translation::{Translation, Translatable};
use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
use traits::ring::Ring;
use traits::division_ring::DivisionRing;
use traits::homogeneous::{FromHomogeneous, ToHomogeneous};
use traits::indexable::Indexable;
mod vec_impl;
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, Rand, Zero, ToStr)]
pub struct Vec0<N>;
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec1<N>
{ x: N }
new_impl!(Vec1, x)
indexable_impl!(Vec1, 1)
new_repeat_impl!(Vec1, val, x)
dim_impl!(Vec1, 1)
// (specialized) basis_impl!(Vec1, 1)
add_impl!(Vec1, x)
sub_impl!(Vec1, x)
neg_impl!(Vec1, x)
dot_impl!(Vec1, x)
sub_dot_impl!(Vec1, x)
scalar_mul_impl!(Vec1, x)
scalar_div_impl!(Vec1, x)
scalar_add_impl!(Vec1, x)
scalar_sub_impl!(Vec1, x)
translation_impl!(Vec1)
translatable_impl!(Vec1)
norm_impl!(Vec1)
approx_eq_impl!(Vec1, x)
one_impl!(Vec1)
from_iterator_impl!(Vec1, iterator)
bounded_impl!(Vec1)
iterable_impl!(Vec1, 1)
iterable_mut_impl!(Vec1, 1)
to_homogeneous_impl!(Vec1, Vec2, y, x)
from_homogeneous_impl!(Vec1, Vec2, y, x)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec2<N>
{
x: N,
y: N
}
new_impl!(Vec2, x, y)
indexable_impl!(Vec2, 2)
new_repeat_impl!(Vec2, val, x, y)
dim_impl!(Vec2, 2)
// (specialized) basis_impl!(Vec2, 1)
add_impl!(Vec2, x, y)
sub_impl!(Vec2, x, y)
neg_impl!(Vec2, x, y)
dot_impl!(Vec2, x, y)
sub_dot_impl!(Vec2, x, y)
scalar_mul_impl!(Vec2, x, y)
scalar_div_impl!(Vec2, x, y)
scalar_add_impl!(Vec2, x, y)
scalar_sub_impl!(Vec2, x, y)
translation_impl!(Vec2)
translatable_impl!(Vec2)
norm_impl!(Vec2)
approx_eq_impl!(Vec2, x, y)
one_impl!(Vec2)
from_iterator_impl!(Vec2, iterator, iterator)
bounded_impl!(Vec2)
iterable_impl!(Vec2, 2)
iterable_mut_impl!(Vec2, 2)
to_homogeneous_impl!(Vec2, Vec3, z, x, y)
from_homogeneous_impl!(Vec2, Vec3, z, x, y)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec3<N>
{
x: N,
y: N,
z: N
}
new_impl!(Vec3, x, y, z)
indexable_impl!(Vec3, 3)
new_repeat_impl!(Vec3, val, x, y, z)
dim_impl!(Vec3, 3)
// (specialized) basis_impl!(Vec3, 1)
add_impl!(Vec3, x, y, z)
sub_impl!(Vec3, x, y, z)
neg_impl!(Vec3, x, y, z)
dot_impl!(Vec3, x, y, z)
sub_dot_impl!(Vec3, x, y, z)
scalar_mul_impl!(Vec3, x, y, z)
scalar_div_impl!(Vec3, x, y, z)
scalar_add_impl!(Vec3, x, y, z)
scalar_sub_impl!(Vec3, x, y, z)
translation_impl!(Vec3)
translatable_impl!(Vec3)
norm_impl!(Vec3)
approx_eq_impl!(Vec3, x, y, z)
one_impl!(Vec3)
from_iterator_impl!(Vec3, iterator, iterator, iterator)
bounded_impl!(Vec3)
iterable_impl!(Vec3, 3)
iterable_mut_impl!(Vec3, 3)
to_homogeneous_impl!(Vec3, Vec4, w, x, y, z)
from_homogeneous_impl!(Vec3, Vec4, w, x, y, z)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec4<N>
{
x: N,
y: N,
z: N,
w: N
}
new_impl!(Vec4, x, y, z, w)
indexable_impl!(Vec4, 4)
new_repeat_impl!(Vec4, val, x, y, z, w)
dim_impl!(Vec4, 4)
basis_impl!(Vec4, 4)
add_impl!(Vec4, x, y, z, w)
sub_impl!(Vec4, x, y, z, w)
neg_impl!(Vec4, x, y, z, w)
dot_impl!(Vec4, x, y, z, w)
sub_dot_impl!(Vec4, x, y, z, w)
scalar_mul_impl!(Vec4, x, y, z, w)
scalar_div_impl!(Vec4, x, y, z, w)
scalar_add_impl!(Vec4, x, y, z, w)
scalar_sub_impl!(Vec4, x, y, z, w)
translation_impl!(Vec4)
translatable_impl!(Vec4)
norm_impl!(Vec4)
approx_eq_impl!(Vec4, x, y, z, w)
one_impl!(Vec4)
from_iterator_impl!(Vec4, iterator, iterator, iterator, iterator)
bounded_impl!(Vec4)
iterable_impl!(Vec4, 4)
iterable_mut_impl!(Vec4, 4)
to_homogeneous_impl!(Vec4, Vec5, a, x, y, z, w)
from_homogeneous_impl!(Vec4, Vec5, a, x, y, z, w)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec5<N>
{
x: N,
y: N,
z: N,
w: N,
a: N,
}
new_impl!(Vec5, x, y, z, w, a)
indexable_impl!(Vec5, 5)
new_repeat_impl!(Vec5, val, x, y, z, w, a)
dim_impl!(Vec5, 5)
basis_impl!(Vec5, 5)
add_impl!(Vec5, x, y, z, w, a)
sub_impl!(Vec5, x, y, z, w, a)
neg_impl!(Vec5, x, y, z, w, a)
dot_impl!(Vec5, x, y, z, w, a)
sub_dot_impl!(Vec5, x, y, z, w, a)
scalar_mul_impl!(Vec5, x, y, z, w, a)
scalar_div_impl!(Vec5, x, y, z, w, a)
scalar_add_impl!(Vec5, x, y, z, w, a)
scalar_sub_impl!(Vec5, x, y, z, w, a)
translation_impl!(Vec5)
translatable_impl!(Vec5)
norm_impl!(Vec5)
approx_eq_impl!(Vec5, x, y, z, w, a)
one_impl!(Vec5)
from_iterator_impl!(Vec5, iterator, iterator, iterator, iterator, iterator)
bounded_impl!(Vec5)
iterable_impl!(Vec5, 5)
iterable_mut_impl!(Vec5, 5)
to_homogeneous_impl!(Vec5, Vec6, b, x, y, z, w, a)
from_homogeneous_impl!(Vec5, Vec6, b, x, y, z, w, a)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec6<N>
{
x: N,
y: N,
z: N,
w: N,
a: N,
b: N
}
new_impl!(Vec6, x, y, z, w, a, b)
indexable_impl!(Vec6, 6)
new_repeat_impl!(Vec6, val, x, y, z, w, a, b)
dim_impl!(Vec6, 6)
basis_impl!(Vec6, 6)
add_impl!(Vec6, x, y, z, w, a, b)
sub_impl!(Vec6, x, y, z, w, a, b)
neg_impl!(Vec6, x, y, z, w, a, b)
dot_impl!(Vec6, x, y, z, w, a, b)
sub_dot_impl!(Vec6, x, y, z, w, a, b)
scalar_mul_impl!(Vec6, x, y, z, w, a, b)
scalar_div_impl!(Vec6, x, y, z, w, a, b)
scalar_add_impl!(Vec6, x, y, z, w, a, b)
scalar_sub_impl!(Vec6, x, y, z, w, a, b)
translation_impl!(Vec6)
translatable_impl!(Vec6)
norm_impl!(Vec6)
approx_eq_impl!(Vec6, x, y, z, w, a, b)
one_impl!(Vec6)
from_iterator_impl!(Vec6, iterator, iterator, iterator, iterator, iterator, iterator)
bounded_impl!(Vec6)
iterable_impl!(Vec6, 6)
iterable_mut_impl!(Vec6, 6)

617
src/vec_impl.rs
View File

@ -1,418 +1,227 @@
#[macro_escape];
use std::cast;
use std::num::{Zero, One, Algebraic, Bounded};
use std::rand::Rng;
use std::vec::{VecIterator, VecMutIterator};
use std::iterator::{Iterator, IteratorUtil, FromIterator};
use std::cmp::ApproxEq;
use std::uint::iterate;
use traits::iterable::{Iterable, IterableMut};
use traits::basis::Basis;
use traits::dim::Dim;
use traits::dot::Dot;
use traits::sub_dot::SubDot;
use traits::norm::Norm;
use traits::translation::{Translation, Translatable};
use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
use traits::ring::Ring;
use traits::division_ring::DivisionRing;
use traits::homogeneous::{FromHomogeneous, ToHomogeneous};
use traits::indexable::Indexable;
macro_rules! new_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N> $t<N>
{
#[inline]
pub fn new($comp0: N $( , $compN: N )*) -> $t<N>
{
$t {
$comp0: $comp0
$(, $compN: $compN )*
}
}
}
)
)
mod vec_macros;
macro_rules! indexable_impl(
($t: ident, $dim: expr) => (
impl<N: Clone> Indexable<uint, N> for $t<N>
{
#[inline]
pub fn at(&self, i: uint) -> N
{ unsafe { cast::transmute::<&$t<N>, &[N, ..$dim]>(self)[i].clone() } }
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, Rand, Zero, ToStr)]
pub struct Vec0<N>;
#[inline]
pub fn set(&mut self, i: uint, val: N)
{ unsafe { cast::transmute::<&mut $t<N>, &mut [N, ..$dim]>(self)[i] = val } }
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec1<N>
{ x: N }
#[inline]
pub fn swap(&mut self, i1: uint, i2: uint)
{ unsafe { cast::transmute::<&mut $t<N>, &mut [N, ..$dim]>(self).swap(i1, i2) } }
}
)
)
new_impl!(Vec1, x)
indexable_impl!(Vec1, 1)
new_repeat_impl!(Vec1, val, x)
dim_impl!(Vec1, 1)
// (specialized) basis_impl!(Vec1, 1)
add_impl!(Vec1, x)
sub_impl!(Vec1, x)
neg_impl!(Vec1, x)
dot_impl!(Vec1, x)
sub_dot_impl!(Vec1, x)
scalar_mul_impl!(Vec1, x)
scalar_div_impl!(Vec1, x)
scalar_add_impl!(Vec1, x)
scalar_sub_impl!(Vec1, x)
translation_impl!(Vec1)
translatable_impl!(Vec1)
norm_impl!(Vec1)
approx_eq_impl!(Vec1, x)
one_impl!(Vec1)
from_iterator_impl!(Vec1, iterator)
bounded_impl!(Vec1)
iterable_impl!(Vec1, 1)
iterable_mut_impl!(Vec1, 1)
to_homogeneous_impl!(Vec1, Vec2, y, x)
from_homogeneous_impl!(Vec1, Vec2, y, x)
macro_rules! new_repeat_impl(
($t: ident, $param: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone> $t<N>
{
#[inline]
pub fn new_repeat($param: N) -> $t<N>
{
$t{
$comp0: $param.clone()
$(, $compN: $param.clone() )*
}
}
}
)
)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec2<N>
{
x: N,
y: N
}
macro_rules! iterable_impl(
($t: ident, $dim: expr) => (
impl<N> Iterable<N> for $t<N>
{
fn iter<'l>(&'l self) -> VecIterator<'l, N>
{ unsafe { cast::transmute::<&'l $t<N>, &'l [N, ..$dim]>(self).iter() } }
}
)
)
new_impl!(Vec2, x, y)
indexable_impl!(Vec2, 2)
new_repeat_impl!(Vec2, val, x, y)
dim_impl!(Vec2, 2)
// (specialized) basis_impl!(Vec2, 1)
add_impl!(Vec2, x, y)
sub_impl!(Vec2, x, y)
neg_impl!(Vec2, x, y)
dot_impl!(Vec2, x, y)
sub_dot_impl!(Vec2, x, y)
scalar_mul_impl!(Vec2, x, y)
scalar_div_impl!(Vec2, x, y)
scalar_add_impl!(Vec2, x, y)
scalar_sub_impl!(Vec2, x, y)
translation_impl!(Vec2)
translatable_impl!(Vec2)
norm_impl!(Vec2)
approx_eq_impl!(Vec2, x, y)
one_impl!(Vec2)
from_iterator_impl!(Vec2, iterator, iterator)
bounded_impl!(Vec2)
iterable_impl!(Vec2, 2)
iterable_mut_impl!(Vec2, 2)
to_homogeneous_impl!(Vec2, Vec3, z, x, y)
from_homogeneous_impl!(Vec2, Vec3, z, x, y)
macro_rules! iterable_mut_impl(
($t: ident, $dim: expr) => (
impl<N> IterableMut<N> for $t<N>
{
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
{ unsafe { cast::transmute::<&'l mut $t<N>, &'l mut [N, ..$dim]>(self).mut_iter() } }
}
)
)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec3<N>
{
x: N,
y: N,
z: N
}
macro_rules! dim_impl(
($t: ident, $dim: expr) => (
impl<N> Dim for $t<N>
{
#[inline]
fn dim() -> uint
{ $dim }
}
)
)
new_impl!(Vec3, x, y, z)
indexable_impl!(Vec3, 3)
new_repeat_impl!(Vec3, val, x, y, z)
dim_impl!(Vec3, 3)
// (specialized) basis_impl!(Vec3, 1)
add_impl!(Vec3, x, y, z)
sub_impl!(Vec3, x, y, z)
neg_impl!(Vec3, x, y, z)
dot_impl!(Vec3, x, y, z)
sub_dot_impl!(Vec3, x, y, z)
scalar_mul_impl!(Vec3, x, y, z)
scalar_div_impl!(Vec3, x, y, z)
scalar_add_impl!(Vec3, x, y, z)
scalar_sub_impl!(Vec3, x, y, z)
translation_impl!(Vec3)
translatable_impl!(Vec3)
norm_impl!(Vec3)
approx_eq_impl!(Vec3, x, y, z)
one_impl!(Vec3)
from_iterator_impl!(Vec3, iterator, iterator, iterator)
bounded_impl!(Vec3)
iterable_impl!(Vec3, 3)
iterable_mut_impl!(Vec3, 3)
to_homogeneous_impl!(Vec3, Vec4, w, x, y, z)
from_homogeneous_impl!(Vec3, Vec4, w, x, y, z)
macro_rules! basis_impl(
($t: ident, $dim: expr) => (
impl<N: Clone + DivisionRing + Algebraic + ApproxEq<N>> Basis for $t<N>
{
pub fn canonical_basis(f: &fn($t<N>))
{
for iterate(0u, $dim) |i|
{
let mut basis_element : $t<N> = Zero::zero();
basis_element.set(i, One::one());
f(basis_element);
}
}
pub fn orthonormal_subspace_basis(&self, f: &fn($t<N>))
{
// compute the basis of the orthogonal subspace using Gram-Schmidt
// orthogonalization algorithm
let mut basis: ~[$t<N>] = ~[];
for iterate(0u, $dim) |i|
{
let mut basis_element : $t<N> = Zero::zero();
basis_element.set(i, One::one());
if basis.len() == $dim - 1
{ break; }
let mut elt = basis_element.clone();
elt = elt - self.scalar_mul(&basis_element.dot(self));
for basis.iter().advance |v|
{ elt = elt - v.scalar_mul(&elt.dot(v)) };
if !elt.sqnorm().approx_eq(&Zero::zero())
{
let new_element = elt.normalized();
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec4<N>
{
x: N,
y: N,
z: N,
w: N
}
f(new_element.clone());
new_impl!(Vec4, x, y, z, w)
indexable_impl!(Vec4, 4)
new_repeat_impl!(Vec4, val, x, y, z, w)
dim_impl!(Vec4, 4)
basis_impl!(Vec4, 4)
add_impl!(Vec4, x, y, z, w)
sub_impl!(Vec4, x, y, z, w)
neg_impl!(Vec4, x, y, z, w)
dot_impl!(Vec4, x, y, z, w)
sub_dot_impl!(Vec4, x, y, z, w)
scalar_mul_impl!(Vec4, x, y, z, w)
scalar_div_impl!(Vec4, x, y, z, w)
scalar_add_impl!(Vec4, x, y, z, w)
scalar_sub_impl!(Vec4, x, y, z, w)
translation_impl!(Vec4)
translatable_impl!(Vec4)
norm_impl!(Vec4)
approx_eq_impl!(Vec4, x, y, z, w)
one_impl!(Vec4)
from_iterator_impl!(Vec4, iterator, iterator, iterator, iterator)
bounded_impl!(Vec4)
iterable_impl!(Vec4, 4)
iterable_mut_impl!(Vec4, 4)
to_homogeneous_impl!(Vec4, Vec5, a, x, y, z, w)
from_homogeneous_impl!(Vec4, Vec5, a, x, y, z, w)
basis.push(new_element);
}
}
}
}
)
)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec5<N>
{
x: N,
y: N,
z: N,
w: N,
a: N,
}
macro_rules! add_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + Add<N,N>> Add<$t<N>, $t<N>> for $t<N>
{
#[inline]
fn add(&self, other: &$t<N>) -> $t<N>
{ $t::new(self.$comp0 + other.$comp0 $(, self.$compN + other.$compN)*) }
}
)
)
new_impl!(Vec5, x, y, z, w, a)
indexable_impl!(Vec5, 5)
new_repeat_impl!(Vec5, val, x, y, z, w, a)
dim_impl!(Vec5, 5)
basis_impl!(Vec5, 5)
add_impl!(Vec5, x, y, z, w, a)
sub_impl!(Vec5, x, y, z, w, a)
neg_impl!(Vec5, x, y, z, w, a)
dot_impl!(Vec5, x, y, z, w, a)
sub_dot_impl!(Vec5, x, y, z, w, a)
scalar_mul_impl!(Vec5, x, y, z, w, a)
scalar_div_impl!(Vec5, x, y, z, w, a)
scalar_add_impl!(Vec5, x, y, z, w, a)
scalar_sub_impl!(Vec5, x, y, z, w, a)
translation_impl!(Vec5)
translatable_impl!(Vec5)
norm_impl!(Vec5)
approx_eq_impl!(Vec5, x, y, z, w, a)
one_impl!(Vec5)
from_iterator_impl!(Vec5, iterator, iterator, iterator, iterator, iterator)
bounded_impl!(Vec5)
iterable_impl!(Vec5, 5)
iterable_mut_impl!(Vec5, 5)
to_homogeneous_impl!(Vec5, Vec6, b, x, y, z, w, a)
from_homogeneous_impl!(Vec5, Vec6, b, x, y, z, w, a)
macro_rules! sub_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + Sub<N,N>> Sub<$t<N>, $t<N>> for $t<N>
{
#[inline]
fn sub(&self, other: &$t<N>) -> $t<N>
{ $t::new(self.$comp0 - other.$comp0 $(, self.$compN - other.$compN)*) }
}
)
)
#[deriving(Eq, Ord, Encodable, Decodable, Clone, DeepClone, IterBytes, Rand, Zero, ToStr)]
pub struct Vec6<N>
{
x: N,
y: N,
z: N,
w: N,
a: N,
b: N
}
macro_rules! neg_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Neg<N>> Neg<$t<N>> for $t<N>
{
#[inline]
fn neg(&self) -> $t<N>
{ $t::new(-self.$comp0 $(, -self.$compN )*) }
}
)
)
macro_rules! dot_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Ring> Dot<N> for $t<N>
{
#[inline]
fn dot(&self, other: &$t<N>) -> N
{ self.$comp0 * other.$comp0 $(+ self.$compN * other.$compN )* }
}
)
)
macro_rules! sub_dot_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Ring> SubDot<N> for $t<N>
{
#[inline]
fn sub_dot(&self, a: &$t<N>, b: &$t<N>) -> N
{ (self.$comp0 - a.$comp0) * b.$comp0 $(+ (self.$compN - a.$compN) * b.$compN )* }
}
)
)
macro_rules! scalar_mul_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Mul<N, N>> ScalarMul<N> for $t<N>
{
#[inline]
fn scalar_mul(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 * *s $(, self.$compN * *s)*) }
#[inline]
fn scalar_mul_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 * *s;
$(self.$compN = self.$compN * *s;)*
}
}
)
)
macro_rules! scalar_div_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Div<N, N>> ScalarDiv<N> for $t<N>
{
#[inline]
fn scalar_div(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 / *s $(, self.$compN / *s)*) }
#[inline]
fn scalar_div_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 / *s;
$(self.$compN = self.$compN / *s;)*
}
}
)
)
macro_rules! scalar_add_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Add<N, N>> ScalarAdd<N> for $t<N>
{
#[inline]
fn scalar_add(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 + *s $(, self.$compN + *s)*) }
#[inline]
fn scalar_add_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 + *s;
$(self.$compN = self.$compN + *s;)*
}
}
)
)
macro_rules! scalar_sub_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Sub<N, N>> ScalarSub<N> for $t<N>
{
#[inline]
fn scalar_sub(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 - *s $(, self.$compN - *s)*) }
#[inline]
fn scalar_sub_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 - *s;
$(self.$compN = self.$compN - *s;)*
}
}
)
)
macro_rules! translation_impl(
($t: ident) => (
impl<N: Clone + Add<N, N> + Neg<N>> Translation<$t<N>> for $t<N>
{
#[inline]
fn translation(&self) -> $t<N>
{ self.clone() }
#[inline]
fn inv_translation(&self) -> $t<N>
{ -self }
#[inline]
fn translate_by(&mut self, t: &$t<N>)
{ *self = *self + *t; }
}
)
)
macro_rules! translatable_impl(
($t: ident) => (
impl<N: Add<N, N> + Neg<N> + Clone> Translatable<$t<N>, $t<N>> for $t<N>
{
#[inline]
fn translated(&self, t: &$t<N>) -> $t<N>
{ self + *t }
}
)
)
macro_rules! norm_impl(
($t: ident) => (
impl<N: Clone + DivisionRing + Algebraic> Norm<N> for $t<N>
{
#[inline]
fn sqnorm(&self) -> N
{ self.dot(self) }
#[inline]
fn norm(&self) -> N
{ self.sqnorm().sqrt() }
#[inline]
fn normalized(&self) -> $t<N>
{
let mut res : $t<N> = self.clone();
res.normalize();
res
}
#[inline]
fn normalize(&mut self) -> N
{
let l = self.norm();
self.scalar_div_inplace(&l);
l
}
}
)
)
macro_rules! approx_eq_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: ApproxEq<N>> ApproxEq<N> for $t<N>
{
#[inline]
fn approx_epsilon() -> N
{ ApproxEq::approx_epsilon::<N, N>() }
#[inline]
fn approx_eq(&self, other: &$t<N>) -> bool
{ self.$comp0.approx_eq(&other.$comp0) $(&& self.$compN.approx_eq(&other.$compN))* }
#[inline]
fn approx_eq_eps(&self, other: &$t<N>, eps: &N) -> bool
{ self.$comp0.approx_eq_eps(&other.$comp0, eps) $(&& self.$compN.approx_eq_eps(&other.$compN, eps))* }
}
)
)
macro_rules! one_impl(
($t: ident) => (
impl<N: Clone + One> One for $t<N>
{
#[inline]
fn one() -> $t<N>
{ $t::new_repeat(One::one()) }
}
)
)
macro_rules! from_iterator_impl(
($t: ident, $param0: ident $(, $paramN: ident)*) => (
impl<N, Iter: Iterator<N>> FromIterator<N, Iter> for $t<N>
{
fn from_iterator($param0: &mut Iter) -> $t<N>
{ $t::new($param0.next().unwrap() $(, $paramN.next().unwrap())*) }
}
)
)
macro_rules! bounded_impl(
($t: ident) => (
impl<N: Bounded + Clone> Bounded for $t<N>
{
#[inline]
fn max_value() -> $t<N>
{ $t::new_repeat(Bounded::max_value()) }
#[inline]
fn min_value() -> $t<N>
{ $t::new_repeat(Bounded::min_value()) }
}
)
)
macro_rules! to_homogeneous_impl(
($t: ident, $t2: ident, $extra: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + One + Zero> ToHomogeneous<$t2<N>> for $t<N>
{
fn to_homogeneous(&self) -> $t2<N>
{
let mut res: $t2<N> = One::one();
res.$comp0 = self.$comp0.clone();
$( res.$compN = self.$compN.clone(); )*
res
}
}
)
)
macro_rules! from_homogeneous_impl(
($t: ident, $t2: ident, $extra: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + Div<N, N> + One + Zero> FromHomogeneous<$t2<N>> for $t<N>
{
fn from_homogeneous(v: &$t2<N>) -> $t<N>
{
let mut res: $t<N> = Zero::zero();
res.$comp0 = v.$comp0.clone();
$( res.$compN = v.$compN.clone(); )*
res.scalar_div(&v.$extra);
res
}
}
)
)
new_impl!(Vec6, x, y, z, w, a, b)
indexable_impl!(Vec6, 6)
new_repeat_impl!(Vec6, val, x, y, z, w, a, b)
dim_impl!(Vec6, 6)
basis_impl!(Vec6, 6)
add_impl!(Vec6, x, y, z, w, a, b)
sub_impl!(Vec6, x, y, z, w, a, b)
neg_impl!(Vec6, x, y, z, w, a, b)
dot_impl!(Vec6, x, y, z, w, a, b)
sub_dot_impl!(Vec6, x, y, z, w, a, b)
scalar_mul_impl!(Vec6, x, y, z, w, a, b)
scalar_div_impl!(Vec6, x, y, z, w, a, b)
scalar_add_impl!(Vec6, x, y, z, w, a, b)
scalar_sub_impl!(Vec6, x, y, z, w, a, b)
translation_impl!(Vec6)
translatable_impl!(Vec6)
norm_impl!(Vec6)
approx_eq_impl!(Vec6, x, y, z, w, a, b)
one_impl!(Vec6)
from_iterator_impl!(Vec6, iterator, iterator, iterator, iterator, iterator, iterator)
bounded_impl!(Vec6)
iterable_impl!(Vec6, 6)
iterable_mut_impl!(Vec6, 6)

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#[macro_escape];
macro_rules! new_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N> $t<N>
{
#[inline]
pub fn new($comp0: N $( , $compN: N )*) -> $t<N>
{
$t {
$comp0: $comp0
$(, $compN: $compN )*
}
}
}
)
)
macro_rules! indexable_impl(
($t: ident, $dim: expr) => (
impl<N: Clone> Indexable<uint, N> for $t<N>
{
#[inline]
pub fn at(&self, i: uint) -> N
{ unsafe { cast::transmute::<&$t<N>, &[N, ..$dim]>(self)[i].clone() } }
#[inline]
pub fn set(&mut self, i: uint, val: N)
{ unsafe { cast::transmute::<&mut $t<N>, &mut [N, ..$dim]>(self)[i] = val } }
#[inline]
pub fn swap(&mut self, i1: uint, i2: uint)
{ unsafe { cast::transmute::<&mut $t<N>, &mut [N, ..$dim]>(self).swap(i1, i2) } }
}
)
)
macro_rules! new_repeat_impl(
($t: ident, $param: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone> $t<N>
{
#[inline]
pub fn new_repeat($param: N) -> $t<N>
{
$t{
$comp0: $param.clone()
$(, $compN: $param.clone() )*
}
}
}
)
)
macro_rules! iterable_impl(
($t: ident, $dim: expr) => (
impl<N> Iterable<N> for $t<N>
{
fn iter<'l>(&'l self) -> VecIterator<'l, N>
{ unsafe { cast::transmute::<&'l $t<N>, &'l [N, ..$dim]>(self).iter() } }
}
)
)
macro_rules! iterable_mut_impl(
($t: ident, $dim: expr) => (
impl<N> IterableMut<N> for $t<N>
{
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
{ unsafe { cast::transmute::<&'l mut $t<N>, &'l mut [N, ..$dim]>(self).mut_iter() } }
}
)
)
macro_rules! dim_impl(
($t: ident, $dim: expr) => (
impl<N> Dim for $t<N>
{
#[inline]
fn dim() -> uint
{ $dim }
}
)
)
macro_rules! basis_impl(
($t: ident, $dim: expr) => (
impl<N: Clone + DivisionRing + Algebraic + ApproxEq<N>> Basis for $t<N>
{
pub fn canonical_basis(f: &fn($t<N>))
{
for iterate(0u, $dim) |i|
{
let mut basis_element : $t<N> = Zero::zero();
basis_element.set(i, One::one());
f(basis_element);
}
}
pub fn orthonormal_subspace_basis(&self, f: &fn($t<N>))
{
// compute the basis of the orthogonal subspace using Gram-Schmidt
// orthogonalization algorithm
let mut basis: ~[$t<N>] = ~[];
for iterate(0u, $dim) |i|
{
let mut basis_element : $t<N> = Zero::zero();
basis_element.set(i, One::one());
if basis.len() == $dim - 1
{ break; }
let mut elt = basis_element.clone();
elt = elt - self.scalar_mul(&basis_element.dot(self));
for basis.iter().advance |v|
{ elt = elt - v.scalar_mul(&elt.dot(v)) };
if !elt.sqnorm().approx_eq(&Zero::zero())
{
let new_element = elt.normalized();
f(new_element.clone());
basis.push(new_element);
}
}
}
}
)
)
macro_rules! add_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + Add<N,N>> Add<$t<N>, $t<N>> for $t<N>
{
#[inline]
fn add(&self, other: &$t<N>) -> $t<N>
{ $t::new(self.$comp0 + other.$comp0 $(, self.$compN + other.$compN)*) }
}
)
)
macro_rules! sub_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + Sub<N,N>> Sub<$t<N>, $t<N>> for $t<N>
{
#[inline]
fn sub(&self, other: &$t<N>) -> $t<N>
{ $t::new(self.$comp0 - other.$comp0 $(, self.$compN - other.$compN)*) }
}
)
)
macro_rules! neg_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Neg<N>> Neg<$t<N>> for $t<N>
{
#[inline]
fn neg(&self) -> $t<N>
{ $t::new(-self.$comp0 $(, -self.$compN )*) }
}
)
)
macro_rules! dot_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Ring> Dot<N> for $t<N>
{
#[inline]
fn dot(&self, other: &$t<N>) -> N
{ self.$comp0 * other.$comp0 $(+ self.$compN * other.$compN )* }
}
)
)
macro_rules! sub_dot_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Ring> SubDot<N> for $t<N>
{
#[inline]
fn sub_dot(&self, a: &$t<N>, b: &$t<N>) -> N
{ (self.$comp0 - a.$comp0) * b.$comp0 $(+ (self.$compN - a.$compN) * b.$compN )* }
}
)
)
macro_rules! scalar_mul_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Mul<N, N>> ScalarMul<N> for $t<N>
{
#[inline]
fn scalar_mul(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 * *s $(, self.$compN * *s)*) }
#[inline]
fn scalar_mul_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 * *s;
$(self.$compN = self.$compN * *s;)*
}
}
)
)
macro_rules! scalar_div_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Div<N, N>> ScalarDiv<N> for $t<N>
{
#[inline]
fn scalar_div(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 / *s $(, self.$compN / *s)*) }
#[inline]
fn scalar_div_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 / *s;
$(self.$compN = self.$compN / *s;)*
}
}
)
)
macro_rules! scalar_add_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Add<N, N>> ScalarAdd<N> for $t<N>
{
#[inline]
fn scalar_add(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 + *s $(, self.$compN + *s)*) }
#[inline]
fn scalar_add_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 + *s;
$(self.$compN = self.$compN + *s;)*
}
}
)
)
macro_rules! scalar_sub_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Sub<N, N>> ScalarSub<N> for $t<N>
{
#[inline]
fn scalar_sub(&self, s: &N) -> $t<N>
{ $t::new(self.$comp0 - *s $(, self.$compN - *s)*) }
#[inline]
fn scalar_sub_inplace(&mut self, s: &N)
{
self.$comp0 = self.$comp0 - *s;
$(self.$compN = self.$compN - *s;)*
}
}
)
)
macro_rules! translation_impl(
($t: ident) => (
impl<N: Clone + Add<N, N> + Neg<N>> Translation<$t<N>> for $t<N>
{
#[inline]
fn translation(&self) -> $t<N>
{ self.clone() }
#[inline]
fn inv_translation(&self) -> $t<N>
{ -self }
#[inline]
fn translate_by(&mut self, t: &$t<N>)
{ *self = *self + *t; }
}
)
)
macro_rules! translatable_impl(
($t: ident) => (
impl<N: Add<N, N> + Neg<N> + Clone> Translatable<$t<N>, $t<N>> for $t<N>
{
#[inline]
fn translated(&self, t: &$t<N>) -> $t<N>
{ self + *t }
}
)
)
macro_rules! norm_impl(
($t: ident) => (
impl<N: Clone + DivisionRing + Algebraic> Norm<N> for $t<N>
{
#[inline]
fn sqnorm(&self) -> N
{ self.dot(self) }
#[inline]
fn norm(&self) -> N
{ self.sqnorm().sqrt() }
#[inline]
fn normalized(&self) -> $t<N>
{
let mut res : $t<N> = self.clone();
res.normalize();
res
}
#[inline]
fn normalize(&mut self) -> N
{
let l = self.norm();
self.scalar_div_inplace(&l);
l
}
}
)
)
macro_rules! approx_eq_impl(
($t: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: ApproxEq<N>> ApproxEq<N> for $t<N>
{
#[inline]
fn approx_epsilon() -> N
{ ApproxEq::approx_epsilon::<N, N>() }
#[inline]
fn approx_eq(&self, other: &$t<N>) -> bool
{ self.$comp0.approx_eq(&other.$comp0) $(&& self.$compN.approx_eq(&other.$compN))* }
#[inline]
fn approx_eq_eps(&self, other: &$t<N>, eps: &N) -> bool
{ self.$comp0.approx_eq_eps(&other.$comp0, eps) $(&& self.$compN.approx_eq_eps(&other.$compN, eps))* }
}
)
)
macro_rules! one_impl(
($t: ident) => (
impl<N: Clone + One> One for $t<N>
{
#[inline]
fn one() -> $t<N>
{ $t::new_repeat(One::one()) }
}
)
)
macro_rules! from_iterator_impl(
($t: ident, $param0: ident $(, $paramN: ident)*) => (
impl<N, Iter: Iterator<N>> FromIterator<N, Iter> for $t<N>
{
fn from_iterator($param0: &mut Iter) -> $t<N>
{ $t::new($param0.next().unwrap() $(, $paramN.next().unwrap())*) }
}
)
)
macro_rules! bounded_impl(
($t: ident) => (
impl<N: Bounded + Clone> Bounded for $t<N>
{
#[inline]
fn max_value() -> $t<N>
{ $t::new_repeat(Bounded::max_value()) }
#[inline]
fn min_value() -> $t<N>
{ $t::new_repeat(Bounded::min_value()) }
}
)
)
macro_rules! to_homogeneous_impl(
($t: ident, $t2: ident, $extra: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + One + Zero> ToHomogeneous<$t2<N>> for $t<N>
{
fn to_homogeneous(&self) -> $t2<N>
{
let mut res: $t2<N> = One::one();
res.$comp0 = self.$comp0.clone();
$( res.$compN = self.$compN.clone(); )*
res
}
}
)
)
macro_rules! from_homogeneous_impl(
($t: ident, $t2: ident, $extra: ident, $comp0: ident $(,$compN: ident)*) => (
impl<N: Clone + Div<N, N> + One + Zero> FromHomogeneous<$t2<N>> for $t<N>
{
fn from_homogeneous(v: &$t2<N>) -> $t<N>
{
let mut res: $t<N> = Zero::zero();
res.$comp0 = v.$comp0.clone();
$( res.$compN = v.$compN.clone(); )*
res.scalar_div(&v.$extra);
res
}
}
)
)