Add SubDot trait and basic implementations.

src/dim1/vec1.rs

@@ -6,6 +6,7 @@ use traits::dim::Dim;
 use traits::dot::Dot;
 use traits::norm::Norm;
 use traits::translation::Translation;
+use traits::sub_dot::SubDot;
 use traits::workarounds::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
 
 #[deriving(Eq)]
@@ -86,12 +87,18 @@ impl<T: Copy + Add<T, T>> Translation<Vec1<T>> for Vec1<T>
   { *self += *t }
 }
 
-impl<T:Copy + Mul<T, T> + Add<T, T> + Algebraic> Dot<T> for Vec1<T>
+impl<T:Copy + Mul<T, T>> Dot<T> for Vec1<T>
 {
   fn dot(&self, other : &Vec1<T>) -> T
   { self.x * other.x } 
 }
 
+impl<T:Copy + Mul<T, T> + Sub<T, T>> SubDot<T> for Vec1<T>
+{
+  fn sub_dot(&self, a: &Vec1<T>, b: &Vec1<T>) -> T
+  { (self.x - a.x) * b.x } 
+}
+
 impl<T:Copy + Mul<T, T> + Add<T, T> + Div<T, T> + Algebraic>
 Norm<T> for Vec1<T>
 {

src/dim2/vec2.rs

@@ -6,6 +6,7 @@ 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;
 use traits::workarounds::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
@@ -103,12 +104,18 @@ impl<T: Copy + Add<T, T>> Translation<Vec2<T>> for Vec2<T>
   { *self += *t; }
 }
 
-impl<T:Copy + Mul<T, T> + Add<T, T> + Algebraic> Dot<T> for Vec2<T>
+impl<T:Copy + Mul<T, T> + Add<T, T>> Dot<T> for Vec2<T>
 {
   fn dot(&self, other : &Vec2<T>) -> T
   { self.x * other.x + self.y * other.y } 
 }
 
+impl<T:Copy + Mul<T, T> + Add<T, T> + Sub<T, T>> SubDot<T> for Vec2<T>
+{
+  fn sub_dot(&self, a: &Vec2<T>, b: &Vec2<T>) -> T
+  { (self.x - a.x) * b.x + (self.y - a.y) * b.y } 
+}
+
 impl<T:Copy + Mul<T, T> + Add<T, T> + Div<T, T> + Algebraic>
 Norm<T> for Vec2<T>
 {

src/dim3/vec3.rs

@@ -5,6 +5,7 @@ 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;
 use traits::workarounds::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
@@ -115,12 +116,18 @@ impl<T:Copy + Neg<T>> Neg<Vec3<T>> for Vec3<T>
   { vec3(-self.x, -self.y, -self.z) }
 }
 
-impl<T:Copy + Mul<T, T> + Add<T, T> + Algebraic> Dot<T> for Vec3<T>
+impl<T:Copy + Mul<T, T> + Add<T, T>> Dot<T> for Vec3<T>
 {
   fn dot(&self, other : &Vec3<T>) -> T
   { self.x * other.x + self.y * other.y + self.z * other.z } 
 }
 
+impl<T:Copy + Mul<T, T> + Add<T, T> + Sub<T, T>> SubDot<T> for Vec3<T>
+{
+  fn sub_dot(&self, a: &Vec3<T>, b: &Vec3<T>) -> T
+  { (self.x - a.x) * b.x + (self.y - a.y) * b.y + (self.z - a.z) * b.z } 
+}
+
 impl<T:Copy + Mul<T, T> + Add<T, T> + Div<T, T> + Algebraic>
 Norm<T> for Vec3<T>
 {

src/nalgebra.rc

@@ -66,6 +66,7 @@ pub mod traits
   pub mod vector_space;
   pub mod ring;
   pub mod division_ring;
+  pub mod sub_dot;
 
   /// This package contains everything done because the current compiler either
   /// crashes or miss features.

src/ndim/nvec.rs

@@ -3,8 +3,11 @@ use core::rand::{Rand, Rng, RngUtil};
 use core::vec::{map_zip, from_elem, map, all, all2};
 use core::cmp::ApproxEq;
 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;
 use traits::workarounds::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
@@ -52,7 +55,7 @@ impl<D, T: Copy + Neg<T>> Neg<NVec<D, T>> for NVec<D, T>
   { NVec { at: map(self.at, |a| -a) } }
 }
 
-impl<D: Dim, T: Copy + Mul<T, T> + Add<T, T> + Algebraic + Zero>
+impl<D: Dim, T: Copy + Ring>
 Dot<T> for NVec<D, T>
 {
   fn dot(&self, other: &NVec<D, T>) -> T
@@ -66,6 +69,19 @@ Dot<T> for NVec<D, T>
   } 
 }
 
+impl<D: Dim, T: Copy + Ring> SubDot<T> for NVec<D, T>
+{
+  fn sub_dot(&self, a: &NVec<D, T>, b: &NVec<D, T>) -> T
+  {
+    let mut res = Zero::zero::<T>();
+
+    for uint::range(0u, Dim::dim::<D>()) |i|
+    { res += (self.at[i] - a.at[i]) * b.at[i]; }
+
+    res
+  } 
+}
+
 impl<D: Dim, T: Copy + Mul<T, T>>
 ScalarMul<T> for NVec<D, T>
 {
@@ -131,8 +147,7 @@ impl<D: Dim, T: Clone + Copy + Add<T, T>> Translation<NVec<D, T>> for NVec<D, T>
   { *self = *self + *t; }
 }
 
-impl<D: Dim, T: Copy + Mul<T, T> + Add<T, T> + Div<T, T> + Algebraic + Zero +
+impl<D: Dim, T: Copy + DivisionRing + Algebraic + Clone>
-                Clone>
 Norm<T> for NVec<D, T>
 {
   fn sqnorm(&self) -> T
@@ -162,8 +177,7 @@ Norm<T> for NVec<D, T>
 }
 
 impl<D: Dim,
-     T: Copy + One + Zero + Neg<T> + Ord + Mul<T, T> + Sub<T, T> + Add<T, T> +
+     T: Copy + DivisionRing + Algebraic + Clone + ApproxEq<T>>
-        Div<T, T> + Algebraic + Clone + ApproxEq<T>>
 Basis for NVec<D, T>
 {
   fn canonical_basis() -> ~[NVec<D, T>]

src/traits/division_ring.rs

@@ -6,3 +6,5 @@ use traits::ring::Ring;
  */
 pub trait DivisionRing : Ring + Div<Self, Self>
 { }
+
+impl<T: Ring + Div<T, T>> DivisionRing for T;

src/traits/ring.rs

@@ -9,3 +9,6 @@ use core::num::{One, Zero};
 pub trait Ring :
 Sub<Self, Self> + Add<Self, Self> + Neg<Self> + Mul<Self, Self> + One + Zero
 { }
+
+impl<T: Sub<T, T> + Add<T, T> + Neg<T> + Mul<T, T> + One + Zero>
+Ring for T;

src/traits/sub_dot.rs

@@ -0,0 +1,12 @@
+pub trait SubDot<T>
+{
+  /**
+   * Short-cut to compute the projecton of a point on a vector, but without
+   * computing intermediate vectors.
+   * This must be equivalent to:
+   *
+   *   (a - b).dot(c)
+   *
+   */
+  fn sub_dot(&self, b: &Self, c: &Self) -> T;
+}