From 6b4b25acd4f557167fddaf8ce15c519b7a0ad83d Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?S=C3=A9bastien=20Crozet?= <developer@crozet.re>
Date: Sun, 26 Oct 2014 23:16:44 +0100
Subject: [PATCH] Basis: add a method to compute the i-th element of the
 canonical basis.

---
 src/lib.rs                |  6 ++++++
 src/structs/spec/vec.rs   | 41 ++++++++++++++++++++++++++++++++++++++-
 src/structs/spec/vec0.rs  |  5 +++++
 src/structs/vec_macros.rs | 24 ++++++++++++++++-------
 src/traits/structure.rs   |  3 +++
 5 files changed, 71 insertions(+), 8 deletions(-)

diff --git a/src/lib.rs b/src/lib.rs
index 4a633862..eb76abfb 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -915,6 +915,12 @@ pub fn orthonormal_subspace_basis<V: Basis>(v: &V, f: |V| -> bool) {
     Basis::orthonormal_subspace_basis(v, f)
 }
 
+/// Gets the (0-based) i-th element of the canonical basis of V.
+#[inline]
+pub fn canonical_basis_element<V: Basis>(i: uint) -> Option<V> {
+    Basis::canonical_basis_element(i)
+}
+
 /*
  * Row<R>
  */
diff --git a/src/structs/spec/vec.rs b/src/structs/spec/vec.rs
index fa2c9220..01da3a2c 100644
--- a/src/structs/spec/vec.rs
+++ b/src/structs/spec/vec.rs
@@ -75,7 +75,17 @@ impl<N: One> Basis for Vec1<N> {
     }
 
     #[inline(always)]
-    fn orthonormal_subspace_basis(_: &Vec1<N>, _: |Vec1<N>| -> bool ) { }
+    fn orthonormal_subspace_basis(_: &Vec1<N>, _: |Vec1<N>| -> bool) { }
+
+    #[inline]
+    fn canonical_basis_element(i: uint) -> Option<Vec1<N>> {
+        if i == 0 {
+            Some(Vec1::new(One::one()))
+        }
+        else {
+            None
+        }
+    }
 }
 
 impl<N: Clone + One + Zero + Neg<N>> Basis for Vec2<N> {
@@ -89,6 +99,19 @@ impl<N: Clone + One + Zero + Neg<N>> Basis for Vec2<N> {
     fn orthonormal_subspace_basis(n: &Vec2<N>, f: |Vec2<N>| -> bool) {
         f(Vec2::new(-n.y, n.x.clone()));
     }
+
+    #[inline]
+    fn canonical_basis_element(i: uint) -> Option<Vec2<N>> {
+        if i == 0 {
+            Some(Vec2::new(One::one(), Zero::zero()))
+        }
+        else if i == 1 {
+            Some(Vec2::new(Zero::zero(), One::one()))
+        }
+        else {
+            None
+        }
+    }
 }
 
 impl<N: Float> Basis for Vec3<N> {
@@ -112,6 +135,22 @@ impl<N: Float> Basis for Vec3<N> {
         if !f(Cross::cross(&a, n)) { return };
         f(a);
     }
+
+    #[inline]
+    fn canonical_basis_element(i: uint) -> Option<Vec3<N>> {
+        if i == 0 {
+            Some(Vec3::new(One::one(), Zero::zero(), Zero::zero()))
+        }
+        else if i == 1 {
+            Some(Vec3::new(Zero::zero(), One::one(), Zero::zero()))
+        }
+        else if i == 2 {
+            Some(Vec3::new(Zero::zero(), Zero::zero(), One::one()))
+        }
+        else {
+            None
+        }
+    }
 }
 
 // FIXME: this bad: this fixes definitly the number of samples…
diff --git a/src/structs/spec/vec0.rs b/src/structs/spec/vec0.rs
index c4796f68..07008827 100644
--- a/src/structs/spec/vec0.rs
+++ b/src/structs/spec/vec0.rs
@@ -79,6 +79,11 @@ impl<N> Basis for vec::Vec0<N> {
 
     #[inline(always)]
     fn orthonormal_subspace_basis(_: &vec::Vec0<N>, _: |vec::Vec0<N>| -> bool) { }
+
+    #[inline(always)]
+    fn canonical_basis_element(_: uint) -> Option<vec::Vec0<N>> {
+        None
+    }
 }
 
 impl<N, T> Add<T, vec::Vec0<N>> for vec::Vec0<N> {
diff --git a/src/structs/vec_macros.rs b/src/structs/vec_macros.rs
index e35fd59d..75c2c8ff 100644
--- a/src/structs/vec_macros.rs
+++ b/src/structs/vec_macros.rs
@@ -297,13 +297,7 @@ macro_rules! basis_impl(
             #[inline]
             fn canonical_basis(f: |$t<N>| -> bool) {
                 for i in range(0u, $dim) {
-                    let mut basis_element : $t<N> = Zero::zero();
-
-                    unsafe {
-                        basis_element.set_fast(i, One::one());
-                    }
-
-                    if !f(basis_element) { return }
+                    if !f(Basis::canonical_basis_element(i).unwrap()) { return }
                 }
             }
 
@@ -341,6 +335,22 @@ macro_rules! basis_impl(
                     }
                 }
             }
+
+            #[inline]
+            fn canonical_basis_element(i: uint) -> Option<$t<N>> {
+                if i < $dim {
+                    let mut basis_element : $t<N> = Zero::zero();
+
+                    unsafe {
+                        basis_element.set_fast(i, One::one());
+                    }
+
+                    Some(basis_element)
+                }
+                else {
+                    None
+                }
+            }
         }
     )
 )
diff --git a/src/traits/structure.rs b/src/traits/structure.rs
index ca97ab30..f7b90bff 100644
--- a/src/traits/structure.rs
+++ b/src/traits/structure.rs
@@ -46,6 +46,9 @@ pub trait Basis {
 
     /// Iterates through a basis of the subspace orthogonal to `self`.
     fn orthonormal_subspace_basis(&Self, |Self| -> bool);
+
+    /// Gets the ith element of the canonical basis.
+    fn canonical_basis_element(i: uint) -> Option<Self>;
 }
 
 /// Trait to access rows of a matrix or a vector.