Reorganized files.
This commit is contained in:
Sébastien Crozet
parent
c54eb562ec
commit
c58e1ed40d
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@ -7,7 +7,7 @@ use traits::inv::Inv;
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use traits::division_ring::DivisionRing;
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use traits::transpose::Transpose;
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use traits::rlmul::{RMul, LMul};
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use ndim::dvec::{DVec, zero_vec_with_dim};
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use dvec::{DVec, zero_vec_with_dim};
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#[deriving(Eq, ToStr, Clone)]
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pub struct DMat<N>
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@ -133,13 +133,13 @@ LMul<DVec<N>> for DMat<N>
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}
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}
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impl<N: Clone + Copy + Eq + DivisionRing>
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impl<N: Copy + Eq + DivisionRing>
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Inv for DMat<N>
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{
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#[inline]
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fn inverse(&self) -> DMat<N>
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{
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let mut res : DMat<N> = self.clone();
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let mut res : DMat<N> = copy *self;
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res.invert();
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415
src/mat.rs
415
src/mat.rs
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@ -13,330 +13,7 @@ use traits::transpose::Transpose;
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use traits::rlmul::{RMul, LMul};
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use traits::transformation::Transform;
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macro_rules! mat_impl(
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($t: ident, $dim: expr) => (
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impl<N> $t<N>
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{
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#[inline]
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pub fn new(mij: [N, ..$dim * $dim]) -> $t<N>
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{ $t { mij: mij } }
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}
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)
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)
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macro_rules! one_impl(
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($t: ident, [ $($value: ident)|+ ] ) => (
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impl<N: Copy + One + Zero> One for $t<N>
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{
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#[inline]
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fn one() -> $t<N>
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{
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let (_0, _1) = (Zero::zero::<N>(), One::one::<N>());
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return $t::new( [ $( copy $value, )+ ] )
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}
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}
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)
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)
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macro_rules! zero_impl(
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($t: ident, [ $($value: ident)|+ ] ) => (
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impl<N: Copy + Zero> Zero for $t<N>
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{
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#[inline]
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fn zero() -> $t<N>
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{
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let _0 = Zero::zero();
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return $t::new( [ $( copy $value, )+ ] )
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}
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#[inline]
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fn is_zero(&self) -> bool
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{ self.mij.iter().all(|e| e.is_zero()) }
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}
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)
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)
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macro_rules! dim_impl(
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($t: ident, $dim: expr) => (
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impl<N> Dim for $t<N>
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{
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#[inline]
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fn dim() -> uint
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{ $dim }
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}
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)
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)
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macro_rules! mat_indexing_impl(
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($t: ident, $dim: expr) => (
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impl<N: Copy> $t<N>
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{
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#[inline]
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pub fn offset(&self, i: uint, j: uint) -> uint
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{ i * $dim + j }
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#[inline]
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pub fn set(&mut self, i: uint, j: uint, t: &N)
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{
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self.mij[self.offset(i, j)] = copy *t
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}
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#[inline]
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pub fn at(&self, i: uint, j: uint) -> N
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{
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copy self.mij[self.offset(i, j)]
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}
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}
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)
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)
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macro_rules! mul_impl(
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($t: ident, $dim: expr) => (
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impl<N: Copy + Ring>
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Mul<$t<N>, $t<N>> for $t<N>
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{
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fn mul(&self, other: &$t<N>) -> $t<N>
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{
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let mut res: $t<N> = Zero::zero();
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for iterate(0u, $dim) |i|
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{
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for iterate(0u, $dim) |j|
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{
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let mut acc = Zero::zero::<N>();
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for iterate(0u, $dim) |k|
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{ acc = acc + self.at(i, k) * other.at(k, j); }
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res.set(i, j, &acc);
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}
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}
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res
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}
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}
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)
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)
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macro_rules! rmul_impl(
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($t: ident, $v: ident, $dim: expr) => (
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impl<N: Copy + Ring>
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RMul<$v<N>> for $t<N>
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{
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fn rmul(&self, other: &$v<N>) -> $v<N>
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{
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let mut res : $v<N> = Zero::zero();
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for iterate(0u, $dim) |i|
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{
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for iterate(0u, $dim) |j|
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{ res.at[i] = res.at[i] + other.at[j] * self.at(i, j); }
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}
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res
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}
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}
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)
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)
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macro_rules! lmul_impl(
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($t: ident, $v: ident, $dim: expr) => (
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impl<N: Copy + Ring>
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LMul<$v<N>> for $t<N>
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{
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fn lmul(&self, other: &$v<N>) -> $v<N>
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{
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let mut res : $v<N> = Zero::zero();
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for iterate(0u, $dim) |i|
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{
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for iterate(0u, $dim) |j|
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{ res.at[i] = res.at[i] + other.at[j] * self.at(j, i); }
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}
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res
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}
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}
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)
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)
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macro_rules! transform_impl(
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($t: ident, $v: ident) => (
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impl<N: Copy + DivisionRing + Eq>
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Transform<$v<N>> for $t<N>
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{
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#[inline]
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fn transform_vec(&self, v: &$v<N>) -> $v<N>
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{ self.rmul(v) }
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#[inline]
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fn inv_transform(&self, v: &$v<N>) -> $v<N>
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{ self.inverse().transform_vec(v) }
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}
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)
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)
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macro_rules! inv_impl(
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($t: ident, $dim: expr) => (
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impl<N: Copy + Eq + DivisionRing>
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Inv for $t<N>
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{
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#[inline]
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fn inverse(&self) -> $t<N>
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{
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let mut res : $t<N> = copy *self;
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res.invert();
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res
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}
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fn invert(&mut self)
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{
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let mut res: $t<N> = One::one();
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let _0N: N = Zero::zero();
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// inversion using Gauss-Jordan elimination
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for iterate(0u, $dim) |k|
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{
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// search a non-zero value on the k-th column
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// FIXME: would it be worth it to spend some more time searching for the
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// max instead?
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let mut n0 = k; // index of a non-zero entry
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while (n0 != $dim)
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{
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if self.at(n0, k) != _0N
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{ break; }
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n0 = n0 + 1;
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}
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// swap pivot line
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if n0 != k
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{
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for iterate(0u, $dim) |j|
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{
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let off_n0_j = self.offset(n0, j);
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let off_k_j = self.offset(k, j);
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swap(self.mij, off_n0_j, off_k_j);
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swap(res.mij, off_n0_j, off_k_j);
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}
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}
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let pivot = self.at(k, k);
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for iterate(k, $dim) |j|
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{
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let selfval = &(self.at(k, j) / pivot);
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self.set(k, j, selfval);
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}
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for iterate(0u, $dim) |j|
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{
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let resval = &(res.at(k, j) / pivot);
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res.set(k, j, resval);
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}
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for iterate(0u, $dim) |l|
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{
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if l != k
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{
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let normalizer = self.at(l, k);
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for iterate(k, $dim) |j|
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{
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let selfval = &(self.at(l, j) - self.at(k, j) * normalizer);
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self.set(l, j, selfval);
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}
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for iterate(0u, $dim) |j|
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{
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let resval = &(res.at(l, j) - res.at(k, j) * normalizer);
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res.set(l, j, resval);
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}
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}
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}
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}
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*self = res;
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}
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}
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)
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)
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macro_rules! transpose_impl(
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($t: ident, $dim: expr) => (
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impl<N: Copy> Transpose for $t<N>
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{
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#[inline]
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fn transposed(&self) -> $t<N>
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{
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let mut res = copy *self;
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res.transpose();
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res
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}
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fn transpose(&mut self)
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{
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for iterate(1u, $dim) |i|
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{
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for iterate(0u, $dim - 1) |j|
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{
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let off_i_j = self.offset(i, j);
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let off_j_i = self.offset(j, i);
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swap(self.mij, off_i_j, off_j_i);
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}
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}
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}
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}
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)
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)
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macro_rules! approx_eq_impl(
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($t: ident) => (
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impl<N: ApproxEq<N>> ApproxEq<N> for $t<N>
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{
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#[inline]
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fn approx_epsilon() -> N
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{ ApproxEq::approx_epsilon::<N, N>() }
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#[inline]
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fn approx_eq(&self, other: &$t<N>) -> bool
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{
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let mut zip = self.mij.iter().zip(other.mij.iter());
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do zip.all |(a, b)| { a.approx_eq(b) }
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}
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#[inline]
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fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool
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{
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let mut zip = self.mij.iter().zip(other.mij.iter());
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do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
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}
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}
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)
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)
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macro_rules! rand_impl(
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($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
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impl<N: Rand> Rand for $t<N>
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{
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#[inline]
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fn rand<R: Rng>($param: &mut R) -> $t<N>
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{ $t::new([ $( $elem.gen(), )+ ]) }
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}
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)
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)
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mod mat_impl;
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#[deriving(ToStr)]
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pub struct Mat1<N>
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@ -508,93 +185,3 @@ rand_impl!(Mat6, rng, [
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rng | rng | rng | rng | rng | rng |
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rng | rng | rng | rng | rng | rng
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])
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// some specializations:
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impl<N: Copy + DivisionRing>
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Inv for Mat1<N>
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{
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#[inline]
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fn inverse(&self) -> Mat1<N>
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{
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let mut res : Mat1<N> = copy *self;
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res.invert();
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res
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}
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#[inline]
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fn invert(&mut self)
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{
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assert!(!self.mij[0].is_zero());
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self.mij[0] = One::one::<N>() / self.mij[0]
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}
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}
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impl<N: Copy + DivisionRing>
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Inv for Mat2<N>
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{
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#[inline]
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fn inverse(&self) -> Mat2<N>
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{
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let mut res : Mat2<N> = copy *self;
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res.invert();
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res
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}
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#[inline]
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fn invert(&mut self)
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{
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let det = self.mij[0 * 2 + 0] * self.mij[1 * 2 + 1] - self.mij[1 * 2 + 0] * self.mij[0 * 2 + 1];
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assert!(!det.is_zero());
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*self = Mat2::new([self.mij[1 * 2 + 1] / det , -self.mij[0 * 2 + 1] / det,
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-self.mij[1 * 2 + 0] / det, self.mij[0 * 2 + 0] / det])
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}
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}
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impl<N: Copy + DivisionRing>
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Inv for Mat3<N>
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{
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#[inline]
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fn inverse(&self) -> Mat3<N>
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{
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let mut res = copy *self;
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res.invert();
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res
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}
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#[inline]
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fn invert(&mut self)
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{
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let minor_m12_m23 = self.mij[1 * 3 + 1] * self.mij[2 * 3 + 2] - self.mij[2 * 3 + 1] * self.mij[1 * 3 + 2];
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let minor_m11_m23 = self.mij[1 * 3 + 0] * self.mij[2 * 3 + 2] - self.mij[2 * 3 + 0] * self.mij[1 * 3 + 2];
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let minor_m11_m22 = self.mij[1 * 3 + 0] * self.mij[2 * 3 + 1] - self.mij[2 * 3 + 0] * self.mij[1 * 3 + 1];
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let det = self.mij[0 * 3 + 0] * minor_m12_m23
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- self.mij[0 * 3 + 1] * minor_m11_m23
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+ self.mij[0 * 3 + 2] * minor_m11_m22;
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assert!(!det.is_zero());
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*self = Mat3::new( [
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(minor_m12_m23 / det),
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((self.mij[0 * 3 + 2] * self.mij[2 * 3 + 1] - self.mij[2 * 3 + 2] * self.mij[0 * 3 + 1]) / det),
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((self.mij[0 * 3 + 1] * self.mij[1 * 3 + 2] - self.mij[1 * 3 + 1] * self.mij[0 * 3 + 2]) / det),
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(-minor_m11_m23 / det),
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((self.mij[0 * 3 + 0] * self.mij[2 * 3 + 2] - self.mij[2 * 3 + 0] * self.mij[0 * 3 + 2]) / det),
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((self.mij[0 * 3 + 2] * self.mij[1 * 3 + 0] - self.mij[1 * 3 + 2] * self.mij[0 * 3 + 0]) / det),
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(minor_m11_m22 / det),
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((self.mij[0 * 3 + 1] * self.mij[2 * 3 + 0] - self.mij[2 * 3 + 1] * self.mij[0 * 3 + 0]) / det),
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((self.mij[0 * 3 + 0] * self.mij[1 * 3 + 1] - self.mij[1 * 3 + 0] * self.mij[0 * 3 + 1]) / det)
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] )
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}
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}
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@ -0,0 +1,325 @@
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#[macro_escape];
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macro_rules! mat_impl(
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($t: ident, $dim: expr) => (
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impl<N> $t<N>
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{
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#[inline]
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pub fn new(mij: [N, ..$dim * $dim]) -> $t<N>
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{ $t { mij: mij } }
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}
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)
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)
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macro_rules! one_impl(
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($t: ident, [ $($value: ident)|+ ] ) => (
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impl<N: Copy + One + Zero> One for $t<N>
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{
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#[inline]
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fn one() -> $t<N>
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{
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let (_0, _1) = (Zero::zero::<N>(), One::one::<N>());
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return $t::new( [ $( copy $value, )+ ] )
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}
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}
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)
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)
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macro_rules! zero_impl(
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($t: ident, [ $($value: ident)|+ ] ) => (
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impl<N: Copy + Zero> Zero for $t<N>
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{
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#[inline]
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fn zero() -> $t<N>
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{
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let _0 = Zero::zero();
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return $t::new( [ $( copy $value, )+ ] )
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}
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#[inline]
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fn is_zero(&self) -> bool
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{ self.mij.iter().all(|e| e.is_zero()) }
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}
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)
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)
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macro_rules! dim_impl(
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($t: ident, $dim: expr) => (
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impl<N> Dim for $t<N>
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{
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#[inline]
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fn dim() -> uint
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{ $dim }
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}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! mat_indexing_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy> $t<N>
|
||||
{
|
||||
#[inline]
|
||||
pub fn offset(&self, i: uint, j: uint) -> uint
|
||||
{ i * $dim + j }
|
||||
|
||||
#[inline]
|
||||
pub fn set(&mut self, i: uint, j: uint, t: &N)
|
||||
{
|
||||
self.mij[self.offset(i, j)] = copy *t
|
||||
}
|
||||
|
||||
#[inline]
|
||||
pub fn at(&self, i: uint, j: uint) -> N
|
||||
{
|
||||
copy self.mij[self.offset(i, j)]
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! mul_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy + Ring>
|
||||
Mul<$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, $dim: expr) => (
|
||||
impl<N: Copy + Ring>
|
||||
RMul<$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, $dim) |j|
|
||||
{ res.at[i] = res.at[i] + other.at[j] * self.at(i, j); }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! lmul_impl(
|
||||
($t: ident, $v: ident, $dim: expr) => (
|
||||
impl<N: Copy + Ring>
|
||||
LMul<$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, $dim) |j|
|
||||
{ res.at[i] = res.at[i] + other.at[j] * self.at(j, i); }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! transform_impl(
|
||||
($t: ident, $v: ident) => (
|
||||
impl<N: Copy + DivisionRing + Eq>
|
||||
Transform<$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>) -> $v<N>
|
||||
{ self.inverse().transform_vec(v) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! inv_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy + Eq + DivisionRing>
|
||||
Inv for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn inverse(&self) -> $t<N>
|
||||
{
|
||||
let mut res : $t<N> = copy *self;
|
||||
|
||||
res.invert();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
fn invert(&mut self)
|
||||
{
|
||||
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;
|
||||
}
|
||||
|
||||
// swap pivot line
|
||||
if n0 != k
|
||||
{
|
||||
for iterate(0u, $dim) |j|
|
||||
{
|
||||
let off_n0_j = self.offset(n0, j);
|
||||
let off_k_j = self.offset(k, j);
|
||||
|
||||
swap(self.mij, off_n0_j, off_k_j);
|
||||
swap(res.mij, off_n0_j, off_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, $dim) |j|
|
||||
{
|
||||
let resval = &(res.at(l, j) - res.at(k, j) * normalizer);
|
||||
res.set(l, j, resval);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
*self = res;
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! transpose_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy> Transpose for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn transposed(&self) -> $t<N>
|
||||
{
|
||||
let mut res = copy *self;
|
||||
|
||||
res.transpose();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
fn transpose(&mut self)
|
||||
{
|
||||
for iterate(1u, $dim) |i|
|
||||
{
|
||||
for iterate(0u, $dim - 1) |j|
|
||||
{
|
||||
let off_i_j = self.offset(i, j);
|
||||
let off_j_i = self.offset(j, i);
|
||||
|
||||
swap(self.mij, off_i_j, off_j_i);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! approx_eq_impl(
|
||||
($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.mij.iter().zip(other.mij.iter());
|
||||
|
||||
do zip.all |(a, b)| { a.approx_eq(b) }
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool
|
||||
{
|
||||
let mut zip = self.mij.iter().zip(other.mij.iter());
|
||||
|
||||
do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! rand_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Rand> Rand for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn rand<R: Rng>($param: &mut R) -> $t<N>
|
||||
{ $t::new([ $( $elem.gen(), )+ ]) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
|
@ -0,0 +1,94 @@
|
|||
use std::num::{Zero, One};
|
||||
use mat::{Mat1, Mat2, Mat3};
|
||||
use traits::division_ring::DivisionRing;
|
||||
use traits::inv::Inv;
|
||||
|
||||
// some specializations:
|
||||
impl<N: Copy + DivisionRing>
|
||||
Inv for Mat1<N>
|
||||
{
|
||||
#[inline]
|
||||
fn inverse(&self) -> Mat1<N>
|
||||
{
|
||||
let mut res : Mat1<N> = copy *self;
|
||||
|
||||
res.invert();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn invert(&mut self)
|
||||
{
|
||||
assert!(!self.mij[0].is_zero());
|
||||
|
||||
self.mij[0] = One::one::<N>() / self.mij[0]
|
||||
}
|
||||
}
|
||||
|
||||
impl<N: Copy + DivisionRing>
|
||||
Inv for Mat2<N>
|
||||
{
|
||||
#[inline]
|
||||
fn inverse(&self) -> Mat2<N>
|
||||
{
|
||||
let mut res : Mat2<N> = copy *self;
|
||||
|
||||
res.invert();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn invert(&mut self)
|
||||
{
|
||||
let det = self.mij[0 * 2 + 0] * self.mij[1 * 2 + 1] - self.mij[1 * 2 + 0] * self.mij[0 * 2 + 1];
|
||||
|
||||
assert!(!det.is_zero());
|
||||
|
||||
*self = Mat2::new([self.mij[1 * 2 + 1] / det , -self.mij[0 * 2 + 1] / det,
|
||||
-self.mij[1 * 2 + 0] / det, self.mij[0 * 2 + 0] / det])
|
||||
}
|
||||
}
|
||||
|
||||
impl<N: Copy + DivisionRing>
|
||||
Inv for Mat3<N>
|
||||
{
|
||||
#[inline]
|
||||
fn inverse(&self) -> Mat3<N>
|
||||
{
|
||||
let mut res = copy *self;
|
||||
|
||||
res.invert();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn invert(&mut self)
|
||||
{
|
||||
let minor_m12_m23 = self.mij[1 * 3 + 1] * self.mij[2 * 3 + 2] - self.mij[2 * 3 + 1] * self.mij[1 * 3 + 2];
|
||||
let minor_m11_m23 = self.mij[1 * 3 + 0] * self.mij[2 * 3 + 2] - self.mij[2 * 3 + 0] * self.mij[1 * 3 + 2];
|
||||
let minor_m11_m22 = self.mij[1 * 3 + 0] * self.mij[2 * 3 + 1] - self.mij[2 * 3 + 0] * self.mij[1 * 3 + 1];
|
||||
|
||||
let det = self.mij[0 * 3 + 0] * minor_m12_m23
|
||||
- self.mij[0 * 3 + 1] * minor_m11_m23
|
||||
+ self.mij[0 * 3 + 2] * minor_m11_m22;
|
||||
|
||||
assert!(!det.is_zero());
|
||||
|
||||
*self = Mat3::new( [
|
||||
(minor_m12_m23 / det),
|
||||
((self.mij[0 * 3 + 2] * self.mij[2 * 3 + 1] - self.mij[2 * 3 + 2] * self.mij[0 * 3 + 1]) / det),
|
||||
((self.mij[0 * 3 + 1] * self.mij[1 * 3 + 2] - self.mij[1 * 3 + 1] * self.mij[0 * 3 + 2]) / det),
|
||||
|
||||
(-minor_m11_m23 / det),
|
||||
((self.mij[0 * 3 + 0] * self.mij[2 * 3 + 2] - self.mij[2 * 3 + 0] * self.mij[0 * 3 + 2]) / det),
|
||||
((self.mij[0 * 3 + 2] * self.mij[1 * 3 + 0] - self.mij[1 * 3 + 2] * self.mij[0 * 3 + 0]) / det),
|
||||
|
||||
(minor_m11_m22 / det),
|
||||
((self.mij[0 * 3 + 1] * self.mij[2 * 3 + 0] - self.mij[2 * 3 + 1] * self.mij[0 * 3 + 0]) / det),
|
||||
((self.mij[0 * 3 + 0] * self.mij[1 * 3 + 1] - self.mij[1 * 3 + 0] * self.mij[0 * 3 + 1]) / det)
|
||||
] )
|
||||
}
|
||||
}
|
||||
|
|
@ -17,15 +17,12 @@ extern mod std;
|
|||
|
||||
pub mod vec;
|
||||
pub mod mat;
|
||||
|
||||
/// n-dimensional linear algebra (slower).
|
||||
pub mod ndim
|
||||
{
|
||||
pub mod dmat;
|
||||
pub mod dvec;
|
||||
pub mod nvec;
|
||||
pub mod nmat;
|
||||
}
|
||||
|
||||
// specialization for some 1d, 2d and 3d operations
|
||||
pub mod mat_spec;
|
||||
pub mod vec_spec;
|
||||
|
||||
/// Wrappers around raw matrices to restrict their behaviour.
|
||||
pub mod adaptors
|
||||
|
|
|
|||
184
src/ndim/nmat.rs
184
src/ndim/nmat.rs
|
|
@ -1,184 +0,0 @@
|
|||
use std::uint::iterate;
|
||||
use std::num::{One, Zero};
|
||||
use std::rand::{Rand, Rng, RngUtil};
|
||||
use std::cmp::ApproxEq;
|
||||
use traits::dim::Dim;
|
||||
use traits::inv::Inv;
|
||||
use traits::division_ring::DivisionRing;
|
||||
use traits::transpose::Transpose;
|
||||
use traits::rlmul::{RMul, LMul};
|
||||
use ndim::dmat::{DMat, one_mat_with_dim, zero_mat_with_dim, is_zero_mat};
|
||||
use ndim::nvec::NVec;
|
||||
|
||||
// D is a phantom type parameter, used only as a dimensional token.
|
||||
// Its allows use to encode the vector dimension at the type-level.
|
||||
// It can be anything implementing the Dim trait. However, to avoid confusion,
|
||||
// using d0, d1, d2, d3 and d4 tokens are prefered.
|
||||
#[deriving(Eq, ToStr)]
|
||||
pub struct NMat<D, N>
|
||||
{ mij: DMat<N> }
|
||||
|
||||
impl<D: Dim, N: Copy> NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn offset(i: uint, j: uint) -> uint
|
||||
{ i * Dim::dim::<D>() + j }
|
||||
|
||||
#[inline]
|
||||
fn set(&mut self, i: uint, j: uint, t: &N)
|
||||
{ self.mij.set(i, j, t) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N> Dim for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn dim() -> uint
|
||||
{ Dim::dim::<D>() }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy> Index<(uint, uint), N> for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn index(&self, &idx: &(uint, uint)) -> N
|
||||
{ self.mij[idx] }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy + One + Zero> One for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn one() -> NMat<D, N>
|
||||
{ NMat { mij: one_mat_with_dim(Dim::dim::<D>()) } }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy + Zero> Zero for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn zero() -> NMat<D, N>
|
||||
{ NMat { mij: zero_mat_with_dim(Dim::dim::<D>()) } }
|
||||
|
||||
#[inline]
|
||||
fn is_zero(&self) -> bool
|
||||
{ is_zero_mat(&self.mij) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy + Mul<N, N> + Add<N, N> + Zero>
|
||||
Mul<NMat<D, N>, NMat<D, N>> for NMat<D, N>
|
||||
{
|
||||
fn mul(&self, other: &NMat<D, N>) -> NMat<D, N>
|
||||
{
|
||||
let dim = Dim::dim::<D>();
|
||||
let mut res = Zero::zero::<NMat<D, N>>();
|
||||
|
||||
for iterate(0u, dim) |i|
|
||||
{
|
||||
for iterate(0u, dim) |j|
|
||||
{
|
||||
let mut acc: N = Zero::zero();
|
||||
|
||||
for iterate(0u, dim) |k|
|
||||
{ acc = acc + self[(i, k)] * other[(k, j)]; }
|
||||
|
||||
res.set(i, j, &acc);
|
||||
}
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy + Add<N, N> + Mul<N, N> + Zero>
|
||||
RMul<NVec<D, N>> for NMat<D, N>
|
||||
{
|
||||
fn rmul(&self, other: &NVec<D, N>) -> NVec<D, N>
|
||||
{
|
||||
let dim = Dim::dim::<D>();
|
||||
let mut res : NVec<D, N> = Zero::zero();
|
||||
|
||||
for iterate(0u, dim) |i|
|
||||
{
|
||||
for iterate(0u, dim) |j|
|
||||
{ res.at.at[i] = res.at.at[i] + other.at.at[j] * self[(i, j)]; }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy + Add<N, N> + Mul<N, N> + Zero>
|
||||
LMul<NVec<D, N>> for NMat<D, N>
|
||||
{
|
||||
fn lmul(&self, other: &NVec<D, N>) -> NVec<D, N>
|
||||
{
|
||||
let dim = Dim::dim::<D>();
|
||||
let mut res : NVec<D, N> = Zero::zero();
|
||||
|
||||
for iterate(0u, dim) |i|
|
||||
{
|
||||
for iterate(0u, dim) |j|
|
||||
{ res.at.at[i] = res.at.at[i] + other.at.at[j] * self[(j, i)]; }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Clone + Copy + Eq + DivisionRing>
|
||||
Inv for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn inverse(&self) -> NMat<D, N>
|
||||
{ NMat { mij: self.mij.inverse() } }
|
||||
|
||||
#[inline]
|
||||
fn invert(&mut self)
|
||||
{ self.mij.invert() }
|
||||
}
|
||||
|
||||
impl<D: Dim, N:Copy> Transpose for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn transposed(&self) -> NMat<D, N>
|
||||
{
|
||||
let mut res = copy *self;
|
||||
|
||||
res.transpose();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn transpose(&mut self)
|
||||
{ self.mij.transpose() }
|
||||
}
|
||||
|
||||
impl<D, N: ApproxEq<N>> ApproxEq<N> for NMat<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn approx_epsilon() -> N
|
||||
{ ApproxEq::approx_epsilon::<N, N>() }
|
||||
|
||||
#[inline]
|
||||
fn approx_eq(&self, other: &NMat<D, N>) -> bool
|
||||
{ self.mij.approx_eq(&other.mij) }
|
||||
|
||||
#[inline]
|
||||
fn approx_eq_eps(&self, other: &NMat<D, N>, epsilon: &N) -> bool
|
||||
{ self.mij.approx_eq_eps(&other.mij, epsilon) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Rand + Zero + Copy> Rand for NMat<D, N>
|
||||
{
|
||||
fn rand<R: Rng>(rng: &mut R) -> NMat<D, N>
|
||||
{
|
||||
let dim = Dim::dim::<D>();
|
||||
let mut res : NMat<D, N> = Zero::zero();
|
||||
|
||||
for iterate(0u, dim) |i|
|
||||
{
|
||||
for iterate(0u, dim) |j|
|
||||
{ res.set(i, j, &rng.gen()); }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
276
src/ndim/nvec.rs
276
src/ndim/nvec.rs
|
|
@ -1,276 +0,0 @@
|
|||
use std::uint::iterate;
|
||||
use std::num::{Zero, Algebraic, Bounded};
|
||||
use std::rand::{Rand, Rng, RngUtil};
|
||||
use std::vec::{VecIterator, VecMutIterator};
|
||||
use std::cmp::ApproxEq;
|
||||
use std::iterator::{IteratorUtil, FromIterator};
|
||||
use ndim::dvec::{DVec, zero_vec_with_dim, is_zero_vec};
|
||||
use traits::iterable::{Iterable, IterableMut};
|
||||
use traits::basis::Basis;
|
||||
use traits::ring::Ring;
|
||||
use traits::division_ring::DivisionRing;
|
||||
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};
|
||||
|
||||
// D is a phantom parameter, used only as a dimensional token.
|
||||
// Its allows use to encode the vector dimension at the type-level.
|
||||
// It can be anything implementing the Dim trait. However, to avoid confusion,
|
||||
// using d0, d1, d2, d3, ..., d7 (or your own dn) are prefered.
|
||||
#[deriving(Eq, Ord, ToStr)]
|
||||
pub struct NVec<D, N>
|
||||
{ at: DVec<N> }
|
||||
|
||||
|
||||
impl<D: Dim, N> Dim for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn dim() -> uint
|
||||
{ Dim::dim::<D>() }
|
||||
}
|
||||
|
||||
impl<D, N: Clone> Clone for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn clone(&self) -> NVec<D, N>
|
||||
{ NVec{ at: self.at.clone() } }
|
||||
}
|
||||
|
||||
impl<D, N> Iterable<N> for NVec<D, N>
|
||||
{
|
||||
fn iter<'l>(&'l self) -> VecIterator<'l, N>
|
||||
{ self.at.iter() }
|
||||
}
|
||||
|
||||
impl<D, N> IterableMut<N> for NVec<D, N>
|
||||
{
|
||||
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
|
||||
{ self.at.mut_iter() }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Zero + Copy, Iter: Iterator<N>> FromIterator<N, Iter> for NVec<D, N>
|
||||
{
|
||||
fn from_iterator(param: &mut Iter) -> NVec<D, N>
|
||||
{
|
||||
let mut res: NVec<D, N> = Zero::zero();
|
||||
let mut i = 0;
|
||||
|
||||
for param.advance |e|
|
||||
{
|
||||
res.at.at[i] = e;
|
||||
i = i + 1;
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
impl<D, N: Copy + Add<N,N>> Add<NVec<D, N>, NVec<D, N>> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn add(&self, other: &NVec<D, N>) -> NVec<D, N>
|
||||
{ NVec { at: self.at + other.at } }
|
||||
}
|
||||
|
||||
impl<D, N: Copy + Sub<N,N>> Sub<NVec<D, N>, NVec<D, N>> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn sub(&self, other: &NVec<D, N>) -> NVec<D, N>
|
||||
{ NVec { at: self.at - other.at } }
|
||||
}
|
||||
|
||||
impl<D, N: Neg<N>> Neg<NVec<D, N>> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn neg(&self) -> NVec<D, N>
|
||||
{ NVec { at: -self.at } }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Ring>
|
||||
Dot<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn dot(&self, other: &NVec<D, N>) -> N
|
||||
{ self.at.dot(&other.at) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Ring> SubDot<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn sub_dot(&self, a: &NVec<D, N>, b: &NVec<D, N>) -> N
|
||||
{ self.at.sub_dot(&a.at, &b.at) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Mul<N, N>>
|
||||
ScalarMul<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_mul(&self, s: &N) -> NVec<D, N>
|
||||
{ NVec { at: self.at.scalar_mul(s) } }
|
||||
|
||||
#[inline]
|
||||
fn scalar_mul_inplace(&mut self, s: &N)
|
||||
{ self.at.scalar_mul_inplace(s) }
|
||||
}
|
||||
|
||||
|
||||
impl<D: Dim, N: Div<N, N>>
|
||||
ScalarDiv<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_div(&self, s: &N) -> NVec<D, N>
|
||||
{ NVec { at: self.at.scalar_div(s) } }
|
||||
|
||||
#[inline]
|
||||
fn scalar_div_inplace(&mut self, s: &N)
|
||||
{ self.at.scalar_div_inplace(s) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Add<N, N>>
|
||||
ScalarAdd<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_add(&self, s: &N) -> NVec<D, N>
|
||||
{ NVec { at: self.at.scalar_add(s) } }
|
||||
|
||||
#[inline]
|
||||
fn scalar_add_inplace(&mut self, s: &N)
|
||||
{ self.at.scalar_add_inplace(s) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Sub<N, N>>
|
||||
ScalarSub<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_sub(&self, s: &N) -> NVec<D, N>
|
||||
{ NVec { at: self.at.scalar_sub(s) } }
|
||||
|
||||
#[inline]
|
||||
fn scalar_sub_inplace(&mut self, s: &N)
|
||||
{ self.at.scalar_sub_inplace(s) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Clone + Copy + Add<N, N> + Neg<N>> Translation<NVec<D, N>> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn translation(&self) -> NVec<D, N>
|
||||
{ self.clone() }
|
||||
|
||||
#[inline]
|
||||
fn inv_translation(&self) -> NVec<D, N>
|
||||
{ -self.clone() }
|
||||
|
||||
|
||||
#[inline]
|
||||
fn translate_by(&mut self, t: &NVec<D, N>)
|
||||
{ *self = *self + *t; }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Add<N, N> + Copy> Translatable<NVec<D, N>, NVec<D, N>> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn translated(&self, t: &NVec<D, N>) -> NVec<D, N>
|
||||
{ self + *t }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Copy + DivisionRing + Algebraic + Clone>
|
||||
Norm<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn sqnorm(&self) -> N
|
||||
{ self.at.sqnorm() }
|
||||
|
||||
#[inline]
|
||||
fn norm(&self) -> N
|
||||
{ self.at.norm() }
|
||||
|
||||
#[inline]
|
||||
fn normalized(&self) -> NVec<D, N>
|
||||
{
|
||||
let mut res : NVec<D, N> = self.clone();
|
||||
|
||||
res.normalize();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn normalize(&mut self) -> N
|
||||
{ self.at.normalize() }
|
||||
}
|
||||
|
||||
impl<D: Dim,
|
||||
N: Copy + DivisionRing + Algebraic + Clone + ApproxEq<N>>
|
||||
Basis for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[NVec<D, N>]
|
||||
{ DVec::canonical_basis_with_dim(Dim::dim::<D>()).map(|&e| NVec { at: e }) }
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[NVec<D, N>]
|
||||
{ self.at.orthogonal_subspace_basis().map(|&e| NVec { at: e }) }
|
||||
}
|
||||
|
||||
// FIXME: I dont really know how te generalize the cross product int
|
||||
// n-dimensions…
|
||||
// impl<N: Copy + Mul<N, N> + Sub<N, N>> Cross<N> for NVec<D, N>
|
||||
// {
|
||||
// fn cross(&self, other: &NVec<D, N>) -> N
|
||||
// { self.x * other.y - self.y * other.x }
|
||||
// }
|
||||
|
||||
impl<D: Dim, N: Copy + Zero> Zero for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn zero() -> NVec<D, N>
|
||||
{ NVec { at: zero_vec_with_dim(Dim::dim::<D>()) } }
|
||||
|
||||
#[inline]
|
||||
fn is_zero(&self) -> bool
|
||||
{ is_zero_vec(&self.at) }
|
||||
}
|
||||
|
||||
impl<D, N: ApproxEq<N>> ApproxEq<N> for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn approx_epsilon() -> N
|
||||
{ ApproxEq::approx_epsilon::<N, N>() }
|
||||
|
||||
#[inline]
|
||||
fn approx_eq(&self, other: &NVec<D, N>) -> bool
|
||||
{ self.at.approx_eq(&other.at) }
|
||||
|
||||
#[inline]
|
||||
fn approx_eq_eps(&self, other: &NVec<D, N>, epsilon: &N) -> bool
|
||||
{ self.at.approx_eq_eps(&other.at, epsilon) }
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Rand + Zero + Copy> Rand for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn rand<R: Rng>(rng: &mut R) -> NVec<D, N>
|
||||
{
|
||||
let dim = Dim::dim::<D>();
|
||||
let mut res : NVec<D, N> = Zero::zero();
|
||||
|
||||
for iterate(0u, dim) |i|
|
||||
{ res.at.at[i] = rng.gen() }
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
|
||||
impl<D: Dim, N: Bounded + Zero + Add<N, N> + Copy> Bounded for NVec<D, N>
|
||||
{
|
||||
#[inline]
|
||||
fn max_value() -> NVec<D, N>
|
||||
{ Zero::zero::<NVec<D, N>>().scalar_add(&Bounded::max_value()) }
|
||||
|
||||
#[inline]
|
||||
fn min_value() -> NVec<D, N>
|
||||
{ Zero::zero::<NVec<D, N>>().scalar_add(&Bounded::min_value()) }
|
||||
}
|
||||
|
|
@ -7,11 +7,7 @@ use std::rand::{random};
|
|||
#[test]
|
||||
use std::cmp::ApproxEq;
|
||||
#[test]
|
||||
use vec::{Vec1, Vec2, Vec3};
|
||||
#[test]
|
||||
use ndim::nvec::NVec;
|
||||
#[test]
|
||||
use traits::dim::d7;
|
||||
use vec::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6};
|
||||
#[test]
|
||||
use traits::basis::Basis;
|
||||
#[test]
|
||||
|
|
@ -133,7 +129,7 @@ fn test_cross_vec3()
|
|||
|
||||
#[test]
|
||||
fn test_commut_dot_nvec()
|
||||
{ test_commut_dot_impl!(NVec<d7, f64>); }
|
||||
{ test_commut_dot_impl!(Vec6<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_commut_dot_vec3()
|
||||
|
|
@ -160,8 +156,16 @@ fn test_basis_vec3()
|
|||
{ test_basis_impl!(Vec3<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_basis_nvec()
|
||||
{ test_basis_impl!(NVec<d7, f64>); }
|
||||
fn test_basis_vec4()
|
||||
{ test_basis_impl!(Vec4<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_basis_vec5()
|
||||
{ test_basis_impl!(Vec5<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_basis_vec6()
|
||||
{ test_basis_impl!(Vec6<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_subspace_basis_vec1()
|
||||
|
|
@ -176,8 +180,16 @@ fn test_subspace_basis_vec3()
|
|||
{ test_subspace_basis_impl!(Vec3<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_subspace_basis_nvec()
|
||||
{ test_subspace_basis_impl!(NVec<d7, f64>); }
|
||||
fn test_subspace_basis_vec4()
|
||||
{ test_subspace_basis_impl!(Vec4<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_subspace_basis_vec5()
|
||||
{ test_subspace_basis_impl!(Vec5<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_subspace_basis_vec6()
|
||||
{ test_subspace_basis_impl!(Vec6<f64>); }
|
||||
|
||||
#[test]
|
||||
fn test_scalar_op_vec1()
|
||||
|
|
@ -192,8 +204,16 @@ fn test_scalar_op_vec3()
|
|||
{ test_scalar_op_impl!(Vec3<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_scalar_op_nvec()
|
||||
{ test_scalar_op_impl!(NVec<d7, f64>, f64); }
|
||||
fn test_scalar_op_vec4()
|
||||
{ test_scalar_op_impl!(Vec4<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_scalar_op_vec5()
|
||||
{ test_scalar_op_impl!(Vec5<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_scalar_op_vec6()
|
||||
{ test_scalar_op_impl!(Vec6<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_iterator_vec1()
|
||||
|
|
@ -208,5 +228,13 @@ fn test_iterator_vec3()
|
|||
{ test_iterator_impl!(Vec3<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_iterator_nvec()
|
||||
{ test_iterator_impl!(NVec<d7, f64>, f64); }
|
||||
fn test_iterator_vec4()
|
||||
{ test_iterator_impl!(Vec4<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_iterator_vec5()
|
||||
{ test_iterator_impl!(Vec5<f64>, f64); }
|
||||
|
||||
#[test]
|
||||
fn test_iterator_vec6()
|
||||
{ test_iterator_impl!(Vec6<f64>, f64); }
|
||||
|
|
|
|||
514
src/vec.rs
514
src/vec.rs
|
|
@ -1,457 +1,22 @@
|
|||
use std::num::{abs, Zero, One, Algebraic, Bounded};
|
||||
use std::num::{Zero, One, Algebraic, Bounded};
|
||||
use std::rand::{Rand, Rng, RngUtil};
|
||||
use std::vec::{VecIterator, VecMutIterator};
|
||||
use std::iterator::{Iterator, FromIterator};
|
||||
use std::iterator::{Iterator, IteratorUtil, FromIterator};
|
||||
use std::cmp::ApproxEq;
|
||||
use std::uint::iterate;
|
||||
use traits::iterable::{Iterable, IterableMut, FromAnyIterator};
|
||||
use traits::basis::Basis;
|
||||
use traits::cross::Cross;
|
||||
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 std::uint::iterate;
|
||||
|
||||
use std::iterator::IteratorUtil;
|
||||
use traits::ring::Ring;
|
||||
use traits::division_ring::DivisionRing;
|
||||
|
||||
// FIXME: is there a way to split this file:
|
||||
// − one file for macros
|
||||
// − another file for macro calls and specializations
|
||||
// ?
|
||||
mod vec_impl;
|
||||
|
||||
macro_rules! new_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N> $t<N>
|
||||
{
|
||||
#[inline]
|
||||
pub fn new(at: [N, ..$dim]) -> $t<N>
|
||||
{ $t { at: at } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! new_repeat_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Copy> $t<N>
|
||||
{
|
||||
#[inline]
|
||||
pub fn new_repeat($param: N) -> $t<N>
|
||||
{ $t{ at: [ $( copy $elem, )+ ] } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! iterable_impl(
|
||||
($t: ident) => (
|
||||
impl<N> Iterable<N> for $t<N>
|
||||
{
|
||||
fn iter<'l>(&'l self) -> VecIterator<'l, N>
|
||||
{ self.at.iter() }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! iterable_mut_impl(
|
||||
($t: ident) => (
|
||||
impl<N> IterableMut<N> for $t<N>
|
||||
{
|
||||
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
|
||||
{ self.at.mut_iter() }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! eq_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Eq> Eq for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn eq(&self, other: &$t<N>) -> bool
|
||||
{ self.at.iter().zip(other.at.iter()).all(|(a, b)| a == b) }
|
||||
|
||||
#[inline]
|
||||
fn ne(&self, other: &$t<N>) -> bool
|
||||
{ self.at.iter().zip(other.at.iter()).all(|(a, b)| a != b) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! dim_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N> Dim for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn dim() -> uint
|
||||
{ $dim }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
// FIXME: add the possibility to specialize that
|
||||
macro_rules! basis_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy + DivisionRing + Algebraic + ApproxEq<N>> Basis for $t<N>
|
||||
{
|
||||
pub fn canonical_basis() -> ~[$t<N>]
|
||||
{
|
||||
let mut res : ~[$t<N>] = ~[];
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{
|
||||
let mut basis_element : $t<N> = Zero::zero();
|
||||
|
||||
basis_element.at[i] = One::one();
|
||||
|
||||
res.push(basis_element);
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
pub fn orthogonal_subspace_basis(&self) -> ~[$t<N>]
|
||||
{
|
||||
// compute the basis of the orthogonal subspace using Gram-Schmidt
|
||||
// orthogonalization algorithm
|
||||
let mut res : ~[$t<N>] = ~[];
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{
|
||||
let mut basis_element : $t<N> = Zero::zero();
|
||||
|
||||
basis_element.at[i] = One::one();
|
||||
|
||||
if res.len() == $dim - 1
|
||||
{ break; }
|
||||
|
||||
let mut elt = copy basis_element;
|
||||
|
||||
elt = elt - self.scalar_mul(&basis_element.dot(self));
|
||||
|
||||
for res.iter().advance |v|
|
||||
{ elt = elt - v.scalar_mul(&elt.dot(v)) };
|
||||
|
||||
if !elt.sqnorm().approx_eq(&Zero::zero())
|
||||
{ res.push(elt.normalized()); }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! add_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Add<N,N>> Add<$t<N>, $t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn add(&self, other: &$t<N>) -> $t<N>
|
||||
{
|
||||
self.at.iter()
|
||||
.zip(other.at.iter())
|
||||
.transform(|(a, b)| { *a + *b })
|
||||
.collect()
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! sub_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Sub<N,N>> Sub<$t<N>, $t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn sub(&self, other: &$t<N>) -> $t<N>
|
||||
{
|
||||
self.at.iter()
|
||||
.zip(other.at.iter())
|
||||
.transform(| (a, b) | { *a - *b })
|
||||
.collect()
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! neg_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Neg<N>> Neg<$t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn neg(&self) -> $t<N>
|
||||
{ self.at.iter().transform(|a| -a).collect() }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! dot_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Ring> Dot<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn dot(&self, other: &$t<N>) -> N
|
||||
{
|
||||
let mut res = Zero::zero::<N>();
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{ res = res + self.at[i] * other.at[i]; }
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! sub_dot_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Ring> SubDot<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn sub_dot(&self, a: &$t<N>, b: &$t<N>) -> N
|
||||
{
|
||||
let mut res = Zero::zero::<N>();
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{ res = res + (self.at[i] - a.at[i]) * b.at[i]; }
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! scalar_mul_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Mul<N, N>> ScalarMul<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_mul(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a * *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_mul_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] * *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
|
||||
macro_rules! scalar_div_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Div<N, N>> ScalarDiv<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_div(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a / *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_div_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] / *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! scalar_add_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Add<N, N>> ScalarAdd<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_add(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a + *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_add_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] + *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! scalar_sub_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Sub<N, N>> ScalarSub<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_sub(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a - *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_sub_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] - *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! translation_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Add<N, N> + Neg<N>> Translation<$t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn translation(&self) -> $t<N>
|
||||
{ copy *self }
|
||||
|
||||
#[inline]
|
||||
fn inv_translation(&self) -> $t<N>
|
||||
{ -self }
|
||||
|
||||
#[inline]
|
||||
fn translate_by(&mut self, t: &$t<N>)
|
||||
{ *self = *self + *t; }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! translatable_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Add<N, N> + Copy> Translatable<$t<N>, $t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn translated(&self, t: &$t<N>) -> $t<N>
|
||||
{ self + *t }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! norm_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy + 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> = copy *self;
|
||||
|
||||
res.normalize();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn normalize(&mut self) -> N
|
||||
{
|
||||
let l = self.norm();
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] / l; }
|
||||
|
||||
l
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! approx_eq_impl(
|
||||
($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.at.iter().zip(other.at.iter());
|
||||
|
||||
do zip.all |(a, b)| { a.approx_eq(b) }
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool
|
||||
{
|
||||
let mut zip = self.at.iter().zip(other.at.iter());
|
||||
|
||||
do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! zero_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Zero> Zero for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn zero() -> $t<N>
|
||||
{ $t::new_repeat(Zero::zero()) }
|
||||
|
||||
#[inline]
|
||||
fn is_zero(&self) -> bool
|
||||
{ self.at.iter().all(|e| e.is_zero()) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! rand_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Rand> Rand for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn rand<R: Rng>($param: &mut R) -> $t<N>
|
||||
{ $t::new([ $( $elem.gen(), )+ ]) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! from_any_iterator_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Copy> FromAnyIterator<N> for $t<N>
|
||||
{
|
||||
fn from_iterator<'l>($param: &mut VecIterator<'l, N>) -> $t<N>
|
||||
{ $t { at: [ $( copy *$elem.next().unwrap(), )+ ] } }
|
||||
|
||||
fn from_mut_iterator<'l>($param: &mut VecMutIterator<'l, N>) -> $t<N>
|
||||
{ $t { at: [ $( copy *$elem.next().unwrap(), )+ ] } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! from_iterator_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N, Iter: Iterator<N>> FromIterator<N, Iter> for $t<N>
|
||||
{
|
||||
fn from_iterator($param: &mut Iter) -> $t<N>
|
||||
{ $t { at: [ $( $elem.next().unwrap(), )+ ] } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! bounded_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Bounded + Copy> 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()) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
#[deriving(Ord, ToStr)]
|
||||
pub struct Vec1<N>
|
||||
|
|
@ -632,74 +197,3 @@ from_any_iterator_impl!(Vec6, iterator, [iterator | iterator | iterator | iterat
|
|||
bounded_impl!(Vec6)
|
||||
iterable_impl!(Vec6)
|
||||
iterable_mut_impl!(Vec6)
|
||||
|
||||
impl<N: Mul<N, N> + Sub<N, N>> Cross<Vec1<N>> for Vec2<N>
|
||||
{
|
||||
#[inline]
|
||||
fn cross(&self, other : &Vec2<N>) -> Vec1<N>
|
||||
{ Vec1::new([self.at[0] * other.at[1] - self.at[1] * other.at[0]]) }
|
||||
}
|
||||
|
||||
impl<N: Mul<N, N> + Sub<N, N>> Cross<Vec3<N>> for Vec3<N>
|
||||
{
|
||||
#[inline]
|
||||
fn cross(&self, other : &Vec3<N>) -> Vec3<N>
|
||||
{
|
||||
Vec3::new(
|
||||
[self.at[1] * other.at[2] - self.at[2] * other.at[1],
|
||||
self.at[2] * other.at[0] - self.at[0] * other.at[2],
|
||||
self.at[0] * other.at[1] - self.at[1] * other.at[0]]
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
impl<N: One> Basis for Vec1<N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[Vec1<N>]
|
||||
{ ~[ Vec1::new([One::one()]) ] } // FIXME: this should be static
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[Vec1<N>]
|
||||
{ ~[] }
|
||||
}
|
||||
|
||||
impl<N: Copy + One + Zero + Neg<N>> Basis for Vec2<N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[Vec2<N>]
|
||||
{
|
||||
// FIXME: this should be static
|
||||
~[ Vec2::new([One::one(), Zero::zero()]),
|
||||
Vec2::new([Zero::zero(), One::one()]) ]
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[Vec2<N>]
|
||||
{ ~[ Vec2::new([-self.at[1], copy self.at[0]]) ] }
|
||||
}
|
||||
|
||||
impl<N: Copy + DivisionRing + Ord + Algebraic>
|
||||
Basis for Vec3<N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[Vec3<N>]
|
||||
{
|
||||
// FIXME: this should be static
|
||||
~[ Vec3::new([One::one(), Zero::zero(), Zero::zero()]),
|
||||
Vec3::new([Zero::zero(), One::one(), Zero::zero()]),
|
||||
Vec3::new([Zero::zero(), Zero::zero(), One::one()]) ]
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[Vec3<N>]
|
||||
{
|
||||
let a =
|
||||
if abs(copy self.at[0]) > abs(copy self.at[1])
|
||||
{ Vec3::new([copy self.at[2], Zero::zero(), -copy self.at[0]]).normalized() }
|
||||
else
|
||||
{ Vec3::new([Zero::zero(), -self.at[2], copy self.at[1]]).normalized() };
|
||||
|
||||
~[ a.cross(self), a ]
|
||||
}
|
||||
}
|
||||
|
|
|
|||
|
|
@ -0,0 +1,431 @@
|
|||
#[macro_escape];
|
||||
|
||||
macro_rules! new_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N> $t<N>
|
||||
{
|
||||
#[inline]
|
||||
pub fn new(at: [N, ..$dim]) -> $t<N>
|
||||
{ $t { at: at } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! new_repeat_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Copy> $t<N>
|
||||
{
|
||||
#[inline]
|
||||
pub fn new_repeat($param: N) -> $t<N>
|
||||
{ $t{ at: [ $( copy $elem, )+ ] } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! iterable_impl(
|
||||
($t: ident) => (
|
||||
impl<N> Iterable<N> for $t<N>
|
||||
{
|
||||
fn iter<'l>(&'l self) -> VecIterator<'l, N>
|
||||
{ self.at.iter() }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! iterable_mut_impl(
|
||||
($t: ident) => (
|
||||
impl<N> IterableMut<N> for $t<N>
|
||||
{
|
||||
fn mut_iter<'l>(&'l mut self) -> VecMutIterator<'l, N>
|
||||
{ self.at.mut_iter() }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! eq_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Eq> Eq for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn eq(&self, other: &$t<N>) -> bool
|
||||
{ self.at.iter().zip(other.at.iter()).all(|(a, b)| a == b) }
|
||||
|
||||
#[inline]
|
||||
fn ne(&self, other: &$t<N>) -> bool
|
||||
{ self.at.iter().zip(other.at.iter()).all(|(a, b)| a != b) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! dim_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N> Dim for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn dim() -> uint
|
||||
{ $dim }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
// FIXME: add the possibility to specialize that
|
||||
macro_rules! basis_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy + DivisionRing + Algebraic + ApproxEq<N>> Basis for $t<N>
|
||||
{
|
||||
pub fn canonical_basis() -> ~[$t<N>]
|
||||
{
|
||||
let mut res : ~[$t<N>] = ~[];
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{
|
||||
let mut basis_element : $t<N> = Zero::zero();
|
||||
|
||||
basis_element.at[i] = One::one();
|
||||
|
||||
res.push(basis_element);
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
pub fn orthogonal_subspace_basis(&self) -> ~[$t<N>]
|
||||
{
|
||||
// compute the basis of the orthogonal subspace using Gram-Schmidt
|
||||
// orthogonalization algorithm
|
||||
let mut res : ~[$t<N>] = ~[];
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{
|
||||
let mut basis_element : $t<N> = Zero::zero();
|
||||
|
||||
basis_element.at[i] = One::one();
|
||||
|
||||
if res.len() == $dim - 1
|
||||
{ break; }
|
||||
|
||||
let mut elt = copy basis_element;
|
||||
|
||||
elt = elt - self.scalar_mul(&basis_element.dot(self));
|
||||
|
||||
for res.iter().advance |v|
|
||||
{ elt = elt - v.scalar_mul(&elt.dot(v)) };
|
||||
|
||||
if !elt.sqnorm().approx_eq(&Zero::zero())
|
||||
{ res.push(elt.normalized()); }
|
||||
}
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! add_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Add<N,N>> Add<$t<N>, $t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn add(&self, other: &$t<N>) -> $t<N>
|
||||
{
|
||||
self.at.iter()
|
||||
.zip(other.at.iter())
|
||||
.transform(|(a, b)| { *a + *b })
|
||||
.collect()
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! sub_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Sub<N,N>> Sub<$t<N>, $t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn sub(&self, other: &$t<N>) -> $t<N>
|
||||
{
|
||||
self.at.iter()
|
||||
.zip(other.at.iter())
|
||||
.transform(| (a, b) | { *a - *b })
|
||||
.collect()
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! neg_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Neg<N>> Neg<$t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn neg(&self) -> $t<N>
|
||||
{ self.at.iter().transform(|a| -a).collect() }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! dot_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Ring> Dot<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn dot(&self, other: &$t<N>) -> N
|
||||
{
|
||||
let mut res = Zero::zero::<N>();
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{ res = res + self.at[i] * other.at[i]; }
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! sub_dot_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Ring> SubDot<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn sub_dot(&self, a: &$t<N>, b: &$t<N>) -> N
|
||||
{
|
||||
let mut res = Zero::zero::<N>();
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{ res = res + (self.at[i] - a.at[i]) * b.at[i]; }
|
||||
|
||||
res
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! scalar_mul_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Mul<N, N>> ScalarMul<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_mul(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a * *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_mul_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] * *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
|
||||
macro_rules! scalar_div_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Div<N, N>> ScalarDiv<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_div(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a / *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_div_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] / *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! scalar_add_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Add<N, N>> ScalarAdd<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_add(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a + *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_add_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] + *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! scalar_sub_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Sub<N, N>> ScalarSub<N> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn scalar_sub(&self, s: &N) -> $t<N>
|
||||
{ self.at.iter().transform(|a| a - *s).collect() }
|
||||
|
||||
#[inline]
|
||||
fn scalar_sub_inplace(&mut self, s: &N)
|
||||
{
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] - *s; }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! translation_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Add<N, N> + Neg<N>> Translation<$t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn translation(&self) -> $t<N>
|
||||
{ copy *self }
|
||||
|
||||
#[inline]
|
||||
fn inv_translation(&self) -> $t<N>
|
||||
{ -self }
|
||||
|
||||
#[inline]
|
||||
fn translate_by(&mut self, t: &$t<N>)
|
||||
{ *self = *self + *t; }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! translatable_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Add<N, N> + Copy> Translatable<$t<N>, $t<N>> for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn translated(&self, t: &$t<N>) -> $t<N>
|
||||
{ self + *t }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! norm_impl(
|
||||
($t: ident, $dim: expr) => (
|
||||
impl<N: Copy + 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> = copy *self;
|
||||
|
||||
res.normalize();
|
||||
|
||||
res
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn normalize(&mut self) -> N
|
||||
{
|
||||
let l = self.norm();
|
||||
|
||||
for iterate(0u, $dim) |i|
|
||||
{ self.at[i] = self.at[i] / l; }
|
||||
|
||||
l
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! approx_eq_impl(
|
||||
($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.at.iter().zip(other.at.iter());
|
||||
|
||||
do zip.all |(a, b)| { a.approx_eq(b) }
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn approx_eq_eps(&self, other: &$t<N>, epsilon: &N) -> bool
|
||||
{
|
||||
let mut zip = self.at.iter().zip(other.at.iter());
|
||||
|
||||
do zip.all |(a, b)| { a.approx_eq_eps(b, epsilon) }
|
||||
}
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! zero_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Copy + Zero> Zero for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn zero() -> $t<N>
|
||||
{ $t::new_repeat(Zero::zero()) }
|
||||
|
||||
#[inline]
|
||||
fn is_zero(&self) -> bool
|
||||
{ self.at.iter().all(|e| e.is_zero()) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! rand_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Rand> Rand for $t<N>
|
||||
{
|
||||
#[inline]
|
||||
fn rand<R: Rng>($param: &mut R) -> $t<N>
|
||||
{ $t::new([ $( $elem.gen(), )+ ]) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! from_any_iterator_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N: Copy> FromAnyIterator<N> for $t<N>
|
||||
{
|
||||
fn from_iterator<'l>($param: &mut VecIterator<'l, N>) -> $t<N>
|
||||
{ $t { at: [ $( copy *$elem.next().unwrap(), )+ ] } }
|
||||
|
||||
fn from_mut_iterator<'l>($param: &mut VecMutIterator<'l, N>) -> $t<N>
|
||||
{ $t { at: [ $( copy *$elem.next().unwrap(), )+ ] } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! from_iterator_impl(
|
||||
($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
|
||||
impl<N, Iter: Iterator<N>> FromIterator<N, Iter> for $t<N>
|
||||
{
|
||||
fn from_iterator($param: &mut Iter) -> $t<N>
|
||||
{ $t { at: [ $( $elem.next().unwrap(), )+ ] } }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
||||
macro_rules! bounded_impl(
|
||||
($t: ident) => (
|
||||
impl<N: Bounded + Copy> 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()) }
|
||||
}
|
||||
)
|
||||
)
|
||||
|
|
@ -0,0 +1,77 @@
|
|||
use std::num::{Zero, One, abs};
|
||||
use traits::basis::Basis;
|
||||
use traits::cross::Cross;
|
||||
use traits::division_ring::DivisionRing;
|
||||
use traits::norm::Norm;
|
||||
use vec::{Vec1, Vec2, Vec3};
|
||||
|
||||
impl<N: Mul<N, N> + Sub<N, N>> Cross<Vec1<N>> for Vec2<N>
|
||||
{
|
||||
#[inline]
|
||||
fn cross(&self, other : &Vec2<N>) -> Vec1<N>
|
||||
{ Vec1::new([self.at[0] * other.at[1] - self.at[1] * other.at[0]]) }
|
||||
}
|
||||
|
||||
impl<N: Mul<N, N> + Sub<N, N>> Cross<Vec3<N>> for Vec3<N>
|
||||
{
|
||||
#[inline]
|
||||
fn cross(&self, other : &Vec3<N>) -> Vec3<N>
|
||||
{
|
||||
Vec3::new(
|
||||
[self.at[1] * other.at[2] - self.at[2] * other.at[1],
|
||||
self.at[2] * other.at[0] - self.at[0] * other.at[2],
|
||||
self.at[0] * other.at[1] - self.at[1] * other.at[0]]
|
||||
)
|
||||
}
|
||||
}
|
||||
|
||||
impl<N: One> Basis for Vec1<N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[Vec1<N>]
|
||||
{ ~[ Vec1::new([One::one()]) ] } // FIXME: this should be static
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[Vec1<N>]
|
||||
{ ~[] }
|
||||
}
|
||||
|
||||
impl<N: Copy + One + Zero + Neg<N>> Basis for Vec2<N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[Vec2<N>]
|
||||
{
|
||||
// FIXME: this should be static
|
||||
~[ Vec2::new([One::one(), Zero::zero()]),
|
||||
Vec2::new([Zero::zero(), One::one()]) ]
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[Vec2<N>]
|
||||
{ ~[ Vec2::new([-self.at[1], copy self.at[0]]) ] }
|
||||
}
|
||||
|
||||
impl<N: Copy + DivisionRing + Ord + Algebraic>
|
||||
Basis for Vec3<N>
|
||||
{
|
||||
#[inline]
|
||||
fn canonical_basis() -> ~[Vec3<N>]
|
||||
{
|
||||
// FIXME: this should be static
|
||||
~[ Vec3::new([One::one(), Zero::zero(), Zero::zero()]),
|
||||
Vec3::new([Zero::zero(), One::one(), Zero::zero()]),
|
||||
Vec3::new([Zero::zero(), Zero::zero(), One::one()]) ]
|
||||
}
|
||||
|
||||
#[inline]
|
||||
fn orthogonal_subspace_basis(&self) -> ~[Vec3<N>]
|
||||
{
|
||||
let a =
|
||||
if abs(copy self.at[0]) > abs(copy self.at[1])
|
||||
{ Vec3::new([copy self.at[2], Zero::zero(), -copy self.at[0]]).normalized() }
|
||||
else
|
||||
{ Vec3::new([Zero::zero(), -self.at[2], copy self.at[1]]).normalized() };
|
||||
|
||||
~[ a.cross(self), a ]
|
||||
}
|
||||
}
|
||||
Loading…
Reference in New Issue