From 6723693b49147398f5e23b1456005ac04ab90b9b Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?S=C3=A9bastien=20Crozet?= <developer@crozet.re>
Date: Thu, 27 Jun 2013 16:16:07 +0000
Subject: [PATCH] Refined traits for rotation/translation/transformation.

---
 src/adaptors/rotmat.rs       | 31 +++++++++++------
 src/adaptors/transform.rs    | 66 ++++++++++++++++++++++++++----------
 src/dim1/vec1.rs             | 15 ++++----
 src/dim2/vec2.rs             | 15 ++++----
 src/dim3/vec3.rs             | 15 ++++----
 src/nalgebra.rc              |  1 +
 src/ndim/dvec.rs             | 15 ++++----
 src/ndim/nvec.rs             | 15 ++++----
 src/tests/mat.rs             |  4 +--
 src/traits/rotation.rs       | 21 ++++++------
 src/traits/transformation.rs | 13 +++++++
 src/traits/translation.rs    | 14 +++++---
 12 files changed, 149 insertions(+), 76 deletions(-)
 create mode 100644 src/traits/transformation.rs

diff --git a/src/adaptors/rotmat.rs b/src/adaptors/rotmat.rs
index e6708def..162eb1a9 100644
--- a/src/adaptors/rotmat.rs
+++ b/src/adaptors/rotmat.rs
@@ -5,7 +5,7 @@ use traits::rlmul::{RMul, LMul};
 use traits::dim::Dim;
 use traits::inv::Inv;
 use traits::transpose::Transpose;
-use traits::rotation::Rotation;
+use traits::rotation::{Rotation, Rotatable};
 use traits::delta_transform::{DeltaTransform, DeltaTransformVector};
 use dim1::vec1::Vec1;
 use dim2::mat2::Mat2;
@@ -57,38 +57,47 @@ pub fn rotmat3<N: Copy + Trigonometric + Neg<N> + One + Sub<N, N> + Add<N, N> +
 }
 
 impl<N: Div<N, N> + Trigonometric + Neg<N> + Mul<N, N> + Add<N, N> + Copy>
-Rotation<Vec1<N>, Rotmat<Mat2<N>>> for Rotmat<Mat2<N>>
+Rotation<Vec1<N>> for Rotmat<Mat2<N>>
 {
   #[inline(always)]
   fn rotation(&self) -> Vec1<N>
   { Vec1::new(-(self.submat.m12 / self.submat.m11).atan()) }
 
-  #[inline(always)]
-  fn rotated(&self, rot: &Vec1<N>) -> Rotmat<Mat2<N>>
-  { rotmat2(copy rot.x) * *self }
-
   #[inline(always)]
   fn rotate(&mut self, rot: &Vec1<N>)
   { *self = self.rotated(rot) }
 }
 
+impl<N: Div<N, N> + Trigonometric + Neg<N> + Mul<N, N> + Add<N, N> + Copy>
+Rotatable<Vec1<N>, Rotmat<Mat2<N>>> for Rotmat<Mat2<N>>
+{
+  #[inline(always)]
+  fn rotated(&self, rot: &Vec1<N>) -> Rotmat<Mat2<N>>
+  { rotmat2(copy rot.x) * *self }
+}
+
 impl<N: Div<N, N> + Trigonometric + Neg<N> + Mul<N, N> + Add<N, N> + Copy +
         One + Sub<N, N>>
-Rotation<(Vec3<N>, N), Rotmat<Mat3<N>>> for Rotmat<Mat3<N>>
+Rotation<(Vec3<N>, N)> for Rotmat<Mat3<N>>
 {
   #[inline(always)]
   fn rotation(&self) -> (Vec3<N>, N)
   { fail!("Not yet implemented.") }
 
-  #[inline(always)]
-  fn rotated(&self, &(axis, angle): &(Vec3<N>, N)) -> Rotmat<Mat3<N>>
-  { rotmat3(&axis, angle) * *self }
-
   #[inline(always)]
   fn rotate(&mut self, rot: &(Vec3<N>, N))
   { *self = self.rotated(rot) }
 }
 
+impl<N: Div<N, N> + Trigonometric + Neg<N> + Mul<N, N> + Add<N, N> + Copy +
+        One + Sub<N, N>>
+Rotatable<(Vec3<N>, N), Rotmat<Mat3<N>>> for Rotmat<Mat3<N>>
+{
+  #[inline(always)]
+  fn rotated(&self, &(axis, angle): &(Vec3<N>, N)) -> Rotmat<Mat3<N>>
+  { rotmat3(&axis, angle) * *self }
+}
+
 impl<N: Copy + Rand + Trigonometric + Neg<N>> Rand for Rotmat<Mat2<N>>
 {
   #[inline(always)]
diff --git a/src/adaptors/transform.rs b/src/adaptors/transform.rs
index 0ae2e6bf..78019a2c 100644
--- a/src/adaptors/transform.rs
+++ b/src/adaptors/transform.rs
@@ -3,8 +3,9 @@ use std::rand::{Rand, Rng, RngUtil};
 use std::cmp::ApproxEq;
 use traits::dim::Dim;
 use traits::inv::Inv;
-use traits::rotation::Rotation;
-use traits::translation::Translation;
+use traits::rotation::{Rotation, Rotatable};
+use traits::translation::{Translation, Translatable};
+use traits::transformation::{Transformation, Transformable};
 use traits::transpose::Transpose;
 use traits::delta_transform::{DeltaTransform, DeltaTransformVector};
 use traits::rlmul::{RMul, LMul};
@@ -73,31 +74,51 @@ impl<M: LMul<V>, V: Add<V, V>> LMul<V> for Transform<M, V>
   { self.submat.lmul(other) + self.subtrans }
 }
 
-impl<M: Copy, V: Translation<V, Res>, Res> Translation<V, Transform<M, Res>> for Transform<M, V>
+impl<M, V: Translation<V>> Translation<V> for Transform<M, V>
 {
   #[inline(always)]
   fn translation(&self) -> V
   { self.subtrans.translation() }
 
-  #[inline(always)]
-  fn translated(&self, t: &V) -> Transform<M, Res>
-  { Transform::new(copy self.submat, self.subtrans.translated(t)) }
-
   #[inline(always)]
   fn translate(&mut self, t: &V)
   { self.subtrans.translate(t) }
 }
 
-impl<M: Rotation<AV, Res> + One,
-     Res: RMul<V>,
+impl<M: Copy, V: Translatable<V, Res>, Res: Translation<V>>
+Translatable<V, Transform<M, Res>> for Transform<M, V>
+{
+  #[inline(always)]
+  fn translated(&self, t: &V) -> Transform<M, Res>
+  { Transform::new(copy self.submat, self.subtrans.translated(t)) }
+}
+
+impl<M: Rotation<AV> + RMul<V> + One,
      V,
      AV>
-Rotation<AV, Transform<Res, V>> for Transform<M, V>
+Rotation<AV> for Transform<M, V>
 {
   #[inline(always)]
   fn rotation(&self) -> AV
   { self.submat.rotation() }
 
+  #[inline(always)]
+  fn rotate(&mut self, rot: &AV)
+  {
+    // FIXME: this does not seem opitmal
+    let mut delta = One::one::<M>();
+    delta.rotate(rot);
+    self.submat.rotate(rot);
+    self.subtrans = delta.rmul(&self.subtrans);
+  }
+}
+
+impl<M: Rotatable<AV, Res> + One,
+     Res: Rotation<AV> + RMul<V>,
+     V,
+     AV>
+Rotatable<AV, Transform<Res, V>> for Transform<M, V>
+{
   #[inline(always)]
   fn rotated(&self, rot: &AV) -> Transform<Res, V>
   {
@@ -106,15 +127,24 @@ Rotation<AV, Transform<Res, V>> for Transform<M, V>
 
     Transform::new(self.submat.rotated(rot), delta.rmul(&self.subtrans))
   }
+}
 
-  #[inline(always)]
-  fn rotate(&mut self, rot: &AV)
-  {
-    // FIXME: this does not seem opitmal
-    let delta = One::one::<M>().rotated(rot);
-    self.submat.rotate(rot);
-    self.subtrans = delta.rmul(&self.subtrans);
-  }
+impl<M: RMul<V> + Mul<M, M> + Copy, V: Add<V, V> + Copy> Transformation<Transform<M, V>> for Transform<M, V>
+{
+  fn transformation(&self) -> Transform<M, V>
+  { copy *self }
+
+  fn transform_by(&mut self, other: &Transform<M, V>)
+  { *self = other * *self; }
+}
+
+// FIXME: constraints are too restrictive.
+// Should be: Transformable<M2, // Transform<Res, V> ...
+impl<M: RMul<V> + Mul<M, M>, V: Add<V, V>>
+Transformable<Transform<M, V>, Transform<M, V>> for Transform<M, V>
+{
+  fn transformed(&self, t: &Transform<M, V>) -> Transform<M, V>
+  { t * *self }
 }
 
 impl<M: Copy, V> DeltaTransform<M> for Transform<M, V>
diff --git a/src/dim1/vec1.rs b/src/dim1/vec1.rs
index 919768ab..9259820c 100644
--- a/src/dim1/vec1.rs
+++ b/src/dim1/vec1.rs
@@ -5,7 +5,7 @@ use traits::basis::Basis;
 use traits::dim::Dim;
 use traits::dot::Dot;
 use traits::norm::Norm;
-use traits::translation::Translation;
+use traits::translation::{Translation, Translatable};
 use traits::sub_dot::SubDot;
 use traits::flatten::Flatten;
 use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
@@ -91,21 +91,24 @@ ScalarSub<N> for Vec1<N>
   { self.x = self.x - *s; }
 }
 
-impl<N: Copy + Add<N, N>> Translation<Vec1<N>, Vec1<N>> for Vec1<N>
+impl<N: Copy + Add<N, N>> Translation<Vec1<N>> for Vec1<N>
 {
   #[inline(always)]
   fn translation(&self) -> Vec1<N>
   { copy *self }
 
-  #[inline(always)]
-  fn translated(&self, t: &Vec1<N>) -> Vec1<N>
-  { self + *t }
-
   #[inline(always)]
   fn translate(&mut self, t: &Vec1<N>)
   { *self = *self + *t }
 }
 
+impl<N: Add<N, N>> Translatable<Vec1<N>, Vec1<N>> for Vec1<N>
+{
+  #[inline(always)]
+  fn translated(&self, t: &Vec1<N>) -> Vec1<N>
+  { self + *t }
+}
+
 impl<N: Mul<N, N>> Dot<N> for Vec1<N>
 {
   #[inline(always)]
diff --git a/src/dim2/vec2.rs b/src/dim2/vec2.rs
index bfa7cbcb..fbddbe23 100644
--- a/src/dim2/vec2.rs
+++ b/src/dim2/vec2.rs
@@ -9,7 +9,7 @@ use traits::dot::Dot;
 use traits::sub_dot::SubDot;
 use traits::norm::Norm;
 use traits::flatten::Flatten;
-use traits::translation::Translation;
+use traits::translation::{Translation, Translatable};
 use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
 
 #[deriving(Eq, Ord, ToStr)]
@@ -108,21 +108,24 @@ ScalarSub<N> for Vec2<N>
   }
 }
 
-impl<N: Copy + Add<N, N>> Translation<Vec2<N>, Vec2<N>> for Vec2<N>
+impl<N: Copy + Add<N, N>> Translation<Vec2<N>> for Vec2<N>
 {
   #[inline(always)]
   fn translation(&self) -> Vec2<N>
   { copy *self }
 
-  #[inline(always)]
-  fn translated(&self, t: &Vec2<N>) -> Vec2<N>
-  { self + *t }
-
   #[inline(always)]
   fn translate(&mut self, t: &Vec2<N>)
   { *self = *self + *t; }
 }
 
+impl<N: Add<N, N>> Translatable<Vec2<N>, Vec2<N>> for Vec2<N>
+{
+  #[inline(always)]
+  fn translated(&self, t: &Vec2<N>) -> Vec2<N>
+  { self + *t }
+}
+
 impl<N: Mul<N, N> + Add<N, N>> Dot<N> for Vec2<N>
 {
   #[inline(always)]
diff --git a/src/dim3/vec3.rs b/src/dim3/vec3.rs
index 1955d0e4..42054899 100644
--- a/src/dim3/vec3.rs
+++ b/src/dim3/vec3.rs
@@ -8,7 +8,7 @@ use traits::dot::Dot;
 use traits::sub_dot::SubDot;
 use traits::norm::Norm;
 use traits::flatten::Flatten;
-use traits::translation::Translation;
+use traits::translation::{Translation, Translatable};
 use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
 
 #[deriving(Eq, Ord, ToStr)]
@@ -112,21 +112,24 @@ ScalarSub<N> for Vec3<N>
   }
 }
 
-impl<N: Copy + Add<N, N>> Translation<Vec3<N>, Vec3<N>> for Vec3<N>
+impl<N: Copy + Add<N, N>> Translation<Vec3<N>> for Vec3<N>
 {
   #[inline(always)]
   fn translation(&self) -> Vec3<N>
   { copy *self }
 
-  #[inline(always)]
-  fn translated(&self, t: &Vec3<N>) -> Vec3<N>
-  { self + *t }
-
   #[inline(always)]
   fn translate(&mut self, t: &Vec3<N>)
   { *self = *self + *t; }
 }
 
+impl<N: Add<N, N>> Translatable<Vec3<N>, Vec3<N>> for Vec3<N>
+{
+  #[inline(always)]
+  fn translated(&self, t: &Vec3<N>) -> Vec3<N>
+  { self + *t }
+}
+
 
 
 impl<N: Neg<N>> Neg<Vec3<N>> for Vec3<N>
diff --git a/src/nalgebra.rc b/src/nalgebra.rc
index 86832a48..aeb28824 100644
--- a/src/nalgebra.rc
+++ b/src/nalgebra.rc
@@ -64,6 +64,7 @@ pub mod traits
   pub mod norm;
   pub mod rotation;
   pub mod translation;
+  pub mod transformation;
   pub mod delta_transform;
   pub mod vector_space;
   pub mod ring;
diff --git a/src/ndim/dvec.rs b/src/ndim/dvec.rs
index fdd51baf..09bb8e89 100644
--- a/src/ndim/dvec.rs
+++ b/src/ndim/dvec.rs
@@ -8,7 +8,7 @@ use traits::division_ring::DivisionRing;
 use traits::dot::Dot;
 use traits::sub_dot::SubDot;
 use traits::norm::Norm;
-use traits::translation::Translation;
+use traits::translation::{Translation, Translatable};
 use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
 
 #[deriving(Eq, Ord, ToStr, Clone)]
@@ -196,21 +196,24 @@ ScalarSub<N> for DVec<N>
   }
 }
 
-impl<N: Clone + Copy + Add<N, N>> Translation<DVec<N>, DVec<N>> for DVec<N>
+impl<N: Clone + Copy + Add<N, N>> Translation<DVec<N>> for DVec<N>
 {
   #[inline(always)]
   fn translation(&self) -> DVec<N>
   { self.clone() }
 
-  #[inline(always)]
-  fn translated(&self, t: &DVec<N>) -> DVec<N>
-  { self + *t }
-
   #[inline(always)]
   fn translate(&mut self, t: &DVec<N>)
   { *self = *self + *t; }
 }
 
+impl<N: Add<N, N> + Copy> Translatable<DVec<N>, DVec<N>> for DVec<N>
+{
+  #[inline(always)]
+  fn translated(&self, t: &DVec<N>) -> DVec<N>
+  { self + *t }
+}
+
 impl<N: Copy + DivisionRing + Algebraic + Clone>
 Norm<N> for DVec<N>
 {
diff --git a/src/ndim/nvec.rs b/src/ndim/nvec.rs
index fccd6dd9..93a1b309 100644
--- a/src/ndim/nvec.rs
+++ b/src/ndim/nvec.rs
@@ -11,7 +11,7 @@ use traits::dim::Dim;
 use traits::dot::Dot;
 use traits::sub_dot::SubDot;
 use traits::norm::Norm;
-use traits::translation::Translation;
+use traits::translation::{Translation, Translatable};
 use traits::flatten::Flatten;
 use traits::scalar_op::{ScalarMul, ScalarDiv, ScalarAdd, ScalarSub};
 
@@ -123,21 +123,24 @@ ScalarSub<N> for NVec<D, N>
   { self.at.scalar_sub_inplace(s) }
 }
 
-impl<D: Dim, N: Clone + Copy + Add<N, N>> Translation<NVec<D, N>, NVec<D, N>> for NVec<D, N>
+impl<D: Dim, N: Clone + Copy + Add<N, N>> Translation<NVec<D, N>> for NVec<D, N>
 {
   #[inline(always)]
   fn translation(&self) -> NVec<D, N>
   { self.clone() }
 
-  #[inline(always)]
-  fn translated(&self, t: &NVec<D, N>) -> NVec<D, N>
-  { self + *t }
-
   #[inline(always)]
   fn translate(&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(always)]
+  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>
 {
diff --git a/src/tests/mat.rs b/src/tests/mat.rs
index c4ff87fd..ace9df27 100644
--- a/src/tests/mat.rs
+++ b/src/tests/mat.rs
@@ -3,13 +3,13 @@ use std::vec;
 #[test]
 use std::num::{Real, Zero, One, abs};
 #[test]
-use std::rand::{random};
+use std::rand::random;
 #[test]
 use std::cmp::ApproxEq;
 #[test]
 use traits::inv::Inv;
 #[test]
-use traits::rotation::Rotation;
+use traits::rotation::{Rotation, Rotatable};
 #[test]
 use traits::dim::d7;
 #[test]
diff --git a/src/traits/rotation.rs b/src/traits/rotation.rs
index ce89bc25..101da942 100644
--- a/src/traits/rotation.rs
+++ b/src/traits/rotation.rs
@@ -1,19 +1,22 @@
-use traits::translation::Translation;
+use traits::translation::{Translation, Translatable};
 
 /// Trait of object which represent a rotation, and to wich new rotations can
 /// be appended. A rotation is assumed to be an isomitry without translation
 /// and without reflexion.
-pub trait Rotation<V, Res>
+pub trait Rotation<V>
 {
   /// Gets the rotation associated with this object.
   fn rotation(&self) -> V;
 
+  /// In-place version of `rotated`.
+  fn rotate(&mut self, &V);
+}
+
+pub trait Rotatable<V, Res: Rotation<V>>
+{
   /// Appends a rotation from an alternative representation. Such
   /// representation has the same format as the one returned by `rotation`.
   fn rotated(&self, &V) -> Res;
-
-  /// In-place version of `rotated`.
-  fn rotate(&mut self, &V);
 }
 
 /**
@@ -24,13 +27,11 @@ pub trait Rotation<V, Res>
  *   - `point`:   the center of rotation.
  */
 #[inline(always)]
-pub fn rotate_wrt_point<M: Translation<LV, ResT>,
-                        ResT: Rotation<AV, Res> + Translation<LV, ResT2>,
-                        ResT2,
-                        Res,
+pub fn rotate_wrt_point<M: Translatable<LV, M2>,
+                        M2: Rotation<AV> + Translation<LV>,
                         LV: Neg<LV>,
                         AV>
-       (m: &M, ammount: &AV, center: &LV) -> ResT
+       (m: &M, ammount: &AV, center: &LV) -> M2
 {
   let mut res = m.translated(&-center);
 
diff --git a/src/traits/transformation.rs b/src/traits/transformation.rs
new file mode 100644
index 00000000..62cff98f
--- /dev/null
+++ b/src/traits/transformation.rs
@@ -0,0 +1,13 @@
+pub trait Transformation<M>
+{
+  fn transformation(&self) -> M;
+
+  // XXX: we must use "transform_by" instead of "transform" because of a
+  // conflict with some iterator function…
+  fn transform_by(&mut self, &M);
+}
+
+pub trait Transformable<M, Res: Transformation<M>>
+{
+  fn transformed(&self, &M) -> Res;
+}
diff --git a/src/traits/translation.rs b/src/traits/translation.rs
index ead1bdfb..705f5d3b 100644
--- a/src/traits/translation.rs
+++ b/src/traits/translation.rs
@@ -1,14 +1,18 @@
 /// Trait of object which represent a translation, and to wich new translation
 /// can be appended.
-pub trait Translation<V, Res>
+pub trait Translation<V>
 {
+  // FIXME: add a "from translation: translantion(V) -> Self ?
   /// Gets the translation associated with this object.
   fn translation(&self) -> V;
 
-  /// Appends a translation from an alternative representation. Such
-  /// representation has the same format as the one returned by `translation`.
-  fn translated(&self, &V) -> Res;
-
   /// In-place version of `translate`.
   fn translate(&mut self, &V);
 }
+
+pub trait Translatable<V, Res: Translation<V>>
+{
+  /// Appends a translation from an alternative representation. Such
+  /// representation has the same format as the one returned by `translation`.
+  fn translated(&self, &V) -> Res;
+}