Add Column + Homogeneous + Indexable traits.

Column: to access a matrix column.
Homogeneous: to convert a matrix/vector from/to homogenous coordinates.
Indexable: to access a matrix/vector element using indices.

src/adaptors/rotmat.rs

@@ -9,6 +9,8 @@ use traits::inv::Inv;
 use traits::transpose::Transpose;
 use traits::rotation::{Rotation, Rotate, Rotatable};
 use traits::transformation::{Transform}; // FIXME: implement Transformation and Transformable
+use traits::homogeneous::ToHomogeneous;
+use traits::indexable::Indexable;
 use vec::Vec1;
 use mat::{Mat2, Mat3};
 use vec::Vec3;
@@ -61,7 +63,7 @@ Rotation<Vec1<N>> for Rotmat<Mat2<N>>
 {
   #[inline]
   fn rotation(&self) -> Vec1<N>
-  { Vec1::new([ -(self.submat.at(0, 1) / self.submat.at(0, 0)).atan() ]) }
+  { Vec1::new([ -(self.submat.at((0, 1)) / self.submat.at((0, 0))).atan() ]) }
 
   #[inline]
   fn inv_rotation(&self) -> Vec1<N>
@@ -200,6 +202,13 @@ Transpose for Rotmat<M>
   { self.submat.transpose() }
 }
 
+// we loose the info that we are a rotation matrix
+impl<M: ToHomogeneous<M2>, M2> ToHomogeneous<M2> for Rotmat<M>
+{
+  fn to_homogeneous(&self) -> M2
+  { self.submat.to_homogeneous() }
+}
+
 impl<N: ApproxEq<N>, M: ApproxEq<N>> ApproxEq<N> for Rotmat<M>
 {
   #[inline]

src/adaptors/transform.rs

@@ -8,6 +8,8 @@ use traits::translation::{Translation, Translate, Translatable};
 use traits::transformation;
 use traits::transformation::{Transformation, Transformable};
 use traits::rlmul::{RMul, LMul};
+use traits::homogeneous::{ToHomogeneous, FromHomogeneous};
+use traits::column::Column;
 
 #[deriving(Eq, ToStr)]
 pub struct Transform<M, V>
@@ -215,6 +217,32 @@ Inv for Transform<M, V>
   }
 }
 
+impl<M: ToHomogeneous<M2>, M2: Dim + Column<V>, V: Copy>
+ToHomogeneous<M2> for Transform<M, V>
+{
+  fn to_homogeneous(&self) -> M2
+  {
+    let mut res = self.submat.to_homogeneous();
+
+    // copy the translation
+    let dim = Dim::dim::<M2>();
+
+    res.set_column(dim - 1, copy self.subtrans);
+
+    res
+  }
+}
+
+impl<M: Column<V> + Dim, M2: FromHomogeneous<M>, V: Copy>
+FromHomogeneous<M> for Transform<M2, V>
+{
+  fn from_homogeneous(m: &M) -> Transform<M2, V>
+  {
+    Transform::new(FromHomogeneous::from_homogeneous(m),
+                   m.column(Dim::dim::<M>() - 1))
+  }
+}
+
 impl<N: ApproxEq<N>, M:ApproxEq<N>, V:ApproxEq<N>>
 ApproxEq<N> for Transform<M, V>
 {

src/mat.rs

@@ -12,6 +12,10 @@ use traits::division_ring::DivisionRing;
 use traits::transpose::Transpose;
 use traits::rlmul::{RMul, LMul};
 use traits::transformation::Transform;
+use traits::homogeneous::{ToHomogeneous, FromHomogeneous};
+use traits::indexable::Indexable;
+use traits::column::Column;
+use traits::iterable::{Iterable, IterableMut};
 
 mod mat_impl;
 
@@ -23,7 +27,7 @@ mat_impl!(Mat1, 1)
 one_impl!(Mat1, [ _1 ])
 zero_impl!(Mat1, [ _0 ])
 dim_impl!(Mat1, 1)
-mat_indexing_impl!(Mat1, 1)
+mat_indexable_impl!(Mat1, 1)
 mul_impl!(Mat1, 1)
 rmul_impl!(Mat1, Vec1, 1)
 lmul_impl!(Mat1, Vec1, 1)
@@ -32,6 +36,9 @@ transform_impl!(Mat1, Vec1)
 transpose_impl!(Mat1, 1)
 approx_eq_impl!(Mat1)
 rand_impl!(Mat1, rng, [ rng ])
+to_homogeneous_impl!(Mat1, Mat2, 1)
+from_homogeneous_impl!(Mat2, Mat1, 1)
+column_impl!(Mat2, 2)
 
 #[deriving(ToStr)]
 pub struct Mat2<N>
@@ -43,7 +50,7 @@ one_impl!(Mat2, [ _1 | _0 |
 zero_impl!(Mat2, [ _0 | _0 |
                    _0 | _0 ])
 dim_impl!(Mat2, 2)
-mat_indexing_impl!(Mat2, 2)
+mat_indexable_impl!(Mat2, 2)
 mul_impl!(Mat2, 2)
 rmul_impl!(Mat2, Vec2, 2)
 lmul_impl!(Mat2, Vec2, 2)
@@ -53,6 +60,8 @@ transpose_impl!(Mat2, 2)
 approx_eq_impl!(Mat2)
 rand_impl!(Mat2, rng, [ rng | rng |
                         rng | rng ])
+to_homogeneous_impl!(Mat2, Mat3, 2)
+from_homogeneous_impl!(Mat3, Mat2, 2)
 
 #[deriving(ToStr)]
 pub struct Mat3<N>
@@ -66,7 +75,7 @@ zero_impl!(Mat3, [ _0 | _0 | _0 |
                   _0 | _0 | _0 |
                   _0 | _0 | _0 ])
 dim_impl!(Mat3, 3)
-mat_indexing_impl!(Mat3, 3)
+mat_indexable_impl!(Mat3, 3)
 mul_impl!(Mat3, 3)
 rmul_impl!(Mat3, Vec3, 3)
 lmul_impl!(Mat3, Vec3, 3)
@@ -77,6 +86,8 @@ approx_eq_impl!(Mat3)
 rand_impl!(Mat3, rng, [ rng | rng | rng |
                         rng | rng | rng |
                         rng | rng | rng])
+to_homogeneous_impl!(Mat3, Mat4, 3)
+from_homogeneous_impl!(Mat4, Mat3, 3)
 
 #[deriving(ToStr)]
 pub struct Mat4<N>
@@ -96,7 +107,7 @@ zero_impl!(Mat4, [
           _0 | _0 | _0 | _0
           ])
 dim_impl!(Mat4, 4)
-mat_indexing_impl!(Mat4, 4)
+mat_indexable_impl!(Mat4, 4)
 mul_impl!(Mat4, 4)
 rmul_impl!(Mat4, Vec4, 4)
 lmul_impl!(Mat4, Vec4, 4)
@@ -110,6 +121,8 @@ rand_impl!(Mat4, rng, [
            rng | rng | rng | rng |
            rng | rng | rng | rng
            ])
+to_homogeneous_impl!(Mat4, Mat5, 4)
+from_homogeneous_impl!(Mat5, Mat4, 4)
 
 #[deriving(ToStr)]
 pub struct Mat5<N>
@@ -131,7 +144,7 @@ zero_impl!(Mat5, [
           _0 | _0 | _0 | _0 | _0
           ])
 dim_impl!(Mat5, 5)
-mat_indexing_impl!(Mat5, 5)
+mat_indexable_impl!(Mat5, 5)
 mul_impl!(Mat5, 5)
 rmul_impl!(Mat5, Vec5, 5)
 lmul_impl!(Mat5, Vec5, 5)
@@ -146,6 +159,8 @@ rand_impl!(Mat5, rng, [
            rng | rng | rng | rng | rng |
            rng | rng | rng | rng | rng
            ])
+to_homogeneous_impl!(Mat5, Mat6, 5)
+from_homogeneous_impl!(Mat6, Mat5, 5)
 
 #[deriving(ToStr)]
 pub struct Mat6<N>
@@ -169,7 +184,7 @@ zero_impl!(Mat6, [
           _0 | _0 | _0 | _0 | _0 | _0
           ])
 dim_impl!(Mat6, 6)
-mat_indexing_impl!(Mat6, 6)
+mat_indexable_impl!(Mat6, 6)
 mul_impl!(Mat6, 6)
 rmul_impl!(Mat6, Vec6, 6)
 lmul_impl!(Mat6, Vec6, 6)

src/mat_impl.rs

@@ -7,6 +7,10 @@ macro_rules! mat_impl(
       #[inline]
       pub fn new(mij: [N, ..$dim * $dim]) -> $t<N>
       { $t { mij: mij } }
+
+      #[inline]
+      pub fn offset(&self, i: uint, j: uint) -> uint
+      { i * $dim + j }
     }
   )
 )
@@ -54,24 +58,49 @@ macro_rules! dim_impl(
   )
 )
 
-macro_rules! mat_indexing_impl(
+macro_rules! mat_indexable_impl(
   ($t: ident, $dim: expr) => (
-    impl<N: Copy> $t<N>
+    impl<N: Copy> Indexable<(uint, uint), N> for $t<N>
     {
       #[inline]
-      pub fn offset(&self, i: uint, j: uint) -> uint
+      pub fn at(&self, (i, j): (uint, uint)) -> N
-      { i * $dim + j }
+      { copy self.mij[self.offset(i, j)] }
 
       #[inline]
-      pub fn set(&mut self, i: uint, j: uint, t: &N)
+      pub fn set(&mut self, (i, j): (uint, uint), t: N)
+      { self.mij[self.offset(i, j)] = t }
+    }
+  )
+)
+
+macro_rules! column_impl(
+  ($t: ident, $dim: expr) => (
+    impl<N: Copy, V: Zero + Iterable<N> + IterableMut<N>> Column<V> for $t<N>
     {
-        self.mij[self.offset(i, j)] = copy *t
+      fn set_column(&mut self, col: uint, v: V)
+      {
+        for v.iter().enumerate().advance |(i, e)|
+        {
+          if i == Dim::dim::<$t<N>>()
+          { break }
+
+          self.at((i, col)) = copy *e;
+        }
       }
 
-      #[inline]
+      fn column(&self, col: uint) -> V
-      pub fn at(&self, i: uint, j: uint) -> N
       {
-        copy self.mij[self.offset(i, j)]
+        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
       }
     }
   )
@@ -93,9 +122,9 @@ macro_rules! mul_impl(
             let mut acc = Zero::zero::<N>();
     
             for iterate(0u, $dim) |k|
-            { acc = acc + self.at(i, k) * other.at(k, j); }
+            { acc = acc + self.at((i, k)) * other.at((k, j)); }
     
-            res.set(i, j, &acc);
+            res.set((i, j), acc);
           }
         }
     
@@ -117,7 +146,7 @@ macro_rules! rmul_impl(
         for iterate(0u, $dim) |i|
         {
           for iterate(0u, $dim) |j|
-          { res.at[i] = res.at[i] + other.at[j] * self.at(i, j); }
+          { res.at[i] = res.at[i] + other.at[j] * self.at((i, j)); }
         }
     
         res
@@ -139,7 +168,7 @@ macro_rules! lmul_impl(
         for iterate(0u, $dim) |i|
         {
           for iterate(0u, $dim) |j|
-          { res.at[i] = res.at[i] + other.at[j] * self.at(j, i); }
+          { res.at[i] = res.at[i] + other.at[j] * self.at((j, i)); }
         }
     
         res
@@ -195,7 +224,7 @@ macro_rules! inv_impl(
     
           while (n0 != $dim)
           {
-            if self.at(n0, k) != _0N
+            if self.at((n0, k)) != _0N
             { break; }
     
             n0 = n0 + 1;
@@ -214,36 +243,36 @@ macro_rules! inv_impl(
             }
           }
     
-          let pivot = self.at(k, k);
+          let pivot = self.at((k, k));
     
           for iterate(k, $dim) |j|
           {
-            let selfval = &(self.at(k, j) / pivot);
+            let selfval = self.at((k, j)) / pivot;
-            self.set(k, j, selfval);
+            self.set((k, j), selfval);
           }
     
           for iterate(0u, $dim) |j|
           {
-            let resval  = &(res.at(k, j)   / pivot);
+            let resval = res.at((k, j)) / pivot;
-            res.set(k, j, resval);
+            res.set((k, j), resval);
           }
     
           for iterate(0u, $dim) |l|
           {
             if l != k
             {
-              let normalizer = self.at(l, k);
+              let normalizer = self.at((l, k));
     
               for iterate(k, $dim) |j|
               {
-                let selfval = &(self.at(l, j) - self.at(k, j) * normalizer);
+                let selfval = self.at((l, j)) - self.at((k, j)) * normalizer;
-                self.set(l, j, selfval);
+                self.set((l, j), selfval);
               }
     
               for iterate(0u, $dim) |j|
               {
-                let resval  = &(res.at(l, j) - res.at(k, j) * normalizer);
+                let resval  = res.at((l, j)) - res.at((k, j)) * normalizer;
-                res.set(l, j, resval);
+                res.set((l, j), resval);
               }
             }
           }
@@ -323,3 +352,46 @@ macro_rules! rand_impl(
     }
   )
 )
+
+macro_rules! to_homogeneous_impl(
+  ($t: ident, $t2: ident, $dim: expr) => (
+    impl<N: One + Zero + Copy> ToHomogeneous<$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, $dim2: expr) => (
+    impl<N: One + Zero + Copy> FromHomogeneous<$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
+      }
+    }
+  )
+)

src/nalgebra.rc

@@ -34,6 +34,8 @@ pub mod adaptors
 /// Useful linear-algebra related traits.
 pub mod traits
 {
+  pub mod indexable;
+  pub mod column;
   pub mod iterable;
   pub mod dot;
   pub mod cross;
@@ -51,6 +53,7 @@ pub mod traits
   pub mod sub_dot;
   pub mod rlmul;
   pub mod scalar_op;
+  pub mod homogeneous;
 }
 
 #[cfg(test)]

src/traits/column.rs

@@ -0,0 +1,5 @@
+pub trait Column<C>
+{
+  fn set_column(&mut self, uint, C);
+  fn column(&self, uint) -> C;
+}

src/traits/homogeneous.rs

@@ -0,0 +1,9 @@
+pub trait ToHomogeneous<U>
+{
+  fn to_homogeneous(&self) -> U;
+}
+
+pub trait FromHomogeneous<U>
+{
+  fn from_homogeneous(&U) -> Self;
+}

src/traits/indexable.rs

@@ -0,0 +1,9 @@
+// FIXME: this trait should not be on nalgebra.
+// however, it is needed because std::ops::Index is (strangely) to poor: it
+// does not have a function to set values.
+// Also, using Index with tuples crashes.
+pub trait Indexable<Index, Res>
+{
+  fn at(&self, Index) -> Res;
+  fn set(&mut self, Index, Res);
+}

src/vec.rs

@@ -14,6 +14,8 @@ 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::{ToHomogeneous, FromHomogeneous};
+use traits::indexable::Indexable;
 
 mod vec_impl;
 
@@ -24,6 +26,7 @@ pub struct Vec1<N>
 
 new_impl!(Vec1, 1)
 new_repeat_impl!(Vec1, elem, [elem])
+indexable_impl!(Vec1)
 dim_impl!(Vec1, 1)
 eq_impl!(Vec1)
 // (specialized) basis_impl!(Vec1, 1)
@@ -41,12 +44,15 @@ translatable_impl!(Vec1)
 norm_impl!(Vec1, 1)
 approx_eq_impl!(Vec1)
 zero_impl!(Vec1)
+one_impl!(Vec1)
 rand_impl!(Vec1, rng, [rng])
 from_iterator_impl!(Vec1, iterator, [iterator])
 from_any_iterator_impl!(Vec1, iterator, [iterator])
 bounded_impl!(Vec1)
 iterable_impl!(Vec1)
 iterable_mut_impl!(Vec1)
+to_homogeneous_impl!(Vec1, Vec2)
+from_homogeneous_impl!(Vec2, Vec1, 2)
 
 #[deriving(Ord, ToStr)]
 pub struct Vec2<N>
@@ -54,6 +60,7 @@ pub struct Vec2<N>
 
 new_impl!(Vec2, 2)
 new_repeat_impl!(Vec2, elem, [elem | elem])
+indexable_impl!(Vec2)
 dim_impl!(Vec2, 2)
 eq_impl!(Vec2)
 // (specialized) basis_impl!(Vec2, 2)
@@ -71,12 +78,15 @@ translatable_impl!(Vec2)
 norm_impl!(Vec2, 2)
 approx_eq_impl!(Vec2)
 zero_impl!(Vec2)
+one_impl!(Vec2)
 rand_impl!(Vec2, rng, [rng | rng])
 from_iterator_impl!(Vec2, iterator, [iterator | iterator])
 from_any_iterator_impl!(Vec2, iterator, [iterator | iterator])
 bounded_impl!(Vec2)
 iterable_impl!(Vec2)
 iterable_mut_impl!(Vec2)
+to_homogeneous_impl!(Vec2, Vec3)
+from_homogeneous_impl!(Vec3, Vec2, 3)
 
 #[deriving(Ord, ToStr)]
 pub struct Vec3<N>
@@ -84,6 +94,7 @@ pub struct Vec3<N>
 
 new_impl!(Vec3, 3)
 new_repeat_impl!(Vec3, elem, [elem | elem | elem])
+indexable_impl!(Vec3)
 dim_impl!(Vec3, 3)
 eq_impl!(Vec3)
 // (specialized) basis_impl!(Vec3, 3)
@@ -101,12 +112,15 @@ translatable_impl!(Vec3)
 norm_impl!(Vec3, 3)
 approx_eq_impl!(Vec3)
 zero_impl!(Vec3)
+one_impl!(Vec3)
 rand_impl!(Vec3, rng, [rng | rng | rng])
 from_iterator_impl!(Vec3, iterator, [iterator | iterator | iterator])
 from_any_iterator_impl!(Vec3, iterator, [iterator | iterator | iterator])
 bounded_impl!(Vec3)
 iterable_impl!(Vec3)
 iterable_mut_impl!(Vec3)
+to_homogeneous_impl!(Vec3, Vec4)
+from_homogeneous_impl!(Vec4, Vec3, 4)
 
 #[deriving(Ord, ToStr)]
 pub struct Vec4<N>
@@ -114,6 +128,7 @@ pub struct Vec4<N>
 
 new_impl!(Vec4, 4)
 new_repeat_impl!(Vec4, elem, [elem | elem | elem | elem])
+indexable_impl!(Vec4)
 dim_impl!(Vec4, 4)
 eq_impl!(Vec4)
 basis_impl!(Vec4, 4)
@@ -131,12 +146,15 @@ translatable_impl!(Vec4)
 norm_impl!(Vec4, 4)
 approx_eq_impl!(Vec4)
 zero_impl!(Vec4)
+one_impl!(Vec4)
 rand_impl!(Vec4, rng, [rng | rng | rng | rng])
 from_iterator_impl!(Vec4, iterator, [iterator | iterator | iterator | iterator])
 from_any_iterator_impl!(Vec4, iterator, [iterator | iterator | iterator | iterator])
 bounded_impl!(Vec4)
 iterable_impl!(Vec4)
 iterable_mut_impl!(Vec4)
+to_homogeneous_impl!(Vec4, Vec5)
+from_homogeneous_impl!(Vec5, Vec4, 5)
 
 #[deriving(Ord, ToStr)]
 pub struct Vec5<N>
@@ -144,6 +162,7 @@ pub struct Vec5<N>
 
 new_impl!(Vec5, 5)
 new_repeat_impl!(Vec5, elem, [elem | elem | elem | elem | elem])
+indexable_impl!(Vec5)
 dim_impl!(Vec5, 5)
 eq_impl!(Vec5)
 basis_impl!(Vec5, 5)
@@ -161,12 +180,15 @@ translatable_impl!(Vec5)
 norm_impl!(Vec5, 5)
 approx_eq_impl!(Vec5)
 zero_impl!(Vec5)
+one_impl!(Vec5)
 rand_impl!(Vec5, rng, [rng | rng | rng | rng | rng])
 from_iterator_impl!(Vec5, iterator, [iterator | iterator | iterator | iterator | iterator])
 from_any_iterator_impl!(Vec5, iterator, [iterator | iterator | iterator | iterator | iterator])
 bounded_impl!(Vec5)
 iterable_impl!(Vec5)
 iterable_mut_impl!(Vec5)
+to_homogeneous_impl!(Vec5, Vec6)
+from_homogeneous_impl!(Vec6, Vec5, 6)
 
 #[deriving(Ord, ToStr)]
 pub struct Vec6<N>
@@ -174,6 +196,7 @@ pub struct Vec6<N>
 
 new_impl!(Vec6, 6)
 new_repeat_impl!(Vec6, elem, [elem | elem | elem | elem | elem | elem])
+indexable_impl!(Vec6)
 dim_impl!(Vec6, 6)
 eq_impl!(Vec6)
 basis_impl!(Vec6, 6)
@@ -191,6 +214,7 @@ translatable_impl!(Vec6)
 norm_impl!(Vec6, 6)
 approx_eq_impl!(Vec6)
 zero_impl!(Vec6)
+one_impl!(Vec6)
 rand_impl!(Vec6, rng, [rng | rng | rng | rng | rng | rng])
 from_iterator_impl!(Vec6, iterator, [iterator | iterator | iterator | iterator | iterator | iterator])
 from_any_iterator_impl!(Vec6, iterator, [iterator | iterator | iterator | iterator | iterator | iterator])

src/vec_impl.rs

@@ -11,6 +11,21 @@ macro_rules! new_impl(
   )
 )
 
+macro_rules! indexable_impl(
+  ($t: ident) => (
+    impl<N: Copy> Indexable<uint, N> for $t<N>
+    {
+      #[inline]
+      pub fn at(&self, i: uint) -> N
+      { copy self.at[i] }
+
+      #[inline]
+      pub fn set(&mut self, i: uint, val: N)
+      { self.at[i] = val }
+    }
+  )
+)
+
 macro_rules! new_repeat_impl(
   ($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
     impl<N: Copy> $t<N>
@@ -381,6 +396,17 @@ macro_rules! zero_impl(
   )
 )
 
+macro_rules! one_impl(
+  ($t: ident) => (
+    impl<N: Copy + One> One for $t<N>
+    {
+      #[inline]
+      fn one() -> $t<N>
+      { $t::new_repeat(One::one()) }
+    }
+  )
+)
+
 macro_rules! rand_impl(
   ($t: ident, $param: ident, [ $($elem: ident)|+ ]) => (
     impl<N: Rand> Rand for $t<N>
@@ -429,3 +455,41 @@ macro_rules! bounded_impl(
     }
   )
 )
+
+macro_rules! to_homogeneous_impl(
+  ($t: ident, $t2: ident) =>
+  {
+    impl<N: Copy + One> ToHomogeneous<$t2<N>> for $t<N>
+    {
+      fn to_homogeneous(&self) -> $t2<N>
+      {
+        let mut res: $t2<N> = One::one();
+
+        for self.iter().zip(res.mut_iter()).advance |(in, out)|
+        { *out = copy *in }
+
+        res
+      }
+    }
+  }
+)
+
+macro_rules! from_homogeneous_impl(
+  ($t: ident, $t2: ident, $dim2: expr) =>
+  {
+    impl<N: Copy + Div<N, N> + One + Zero> FromHomogeneous<$t2<N>> for $t<N>
+    {
+      fn from_homogeneous(v: &$t2<N>) -> $t<N>
+      {
+        let mut res: $t<N> = Zero::zero();
+
+        for v.iter().zip(res.mut_iter()).advance |(in, out)|
+        { *out = copy *in }
+
+        res.scalar_div(&v.at[$dim2 - 1]);
+
+        res
+      }
+    }
+  }
+)