From 490997c93f70443ca20d249b2228e86831e5ff26 Mon Sep 17 00:00:00 2001
From: Brendan Zabarauskas <bjzaba@yahoo.com.au>
Date: Tue, 3 Nov 2015 15:50:07 +1100
Subject: [PATCH] Add an alias to Vector::Scalar in Point

---
 src/point.rs     | 49 +++++++++++++++++++++++++++---------------------
 src/rotation.rs  |  4 ++--
 src/transform.rs | 17 +++++++++--------
 3 files changed, 39 insertions(+), 31 deletions(-)

diff --git a/src/point.rs b/src/point.rs
index 2b21109..c2d0568 100644
--- a/src/point.rs
+++ b/src/point.rs
@@ -68,7 +68,7 @@ impl<S: BaseNum> Point3<S> {
 /// Specifies the numeric operations for point types.
 pub trait Point: Clone where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: Array1<Element = <<Self as Point>::Vector as Vector>::Scalar>,
+    Self: Array1<Element = <Self as Point>::Scalar>,
     // FIXME: blocked by rust-lang/rust#20671
     //
     // for<'a, 'b> &'a Self: Add<&'b V, Output = Self>,
@@ -78,8 +78,13 @@ pub trait Point: Clone where
     // for<'a> &'a Self: Div<S, Output = Self>,
     // for<'a> &'a Self: Rem<S, Output = Self>,
 {
+    /// The associated scalar.
+    ///
+    /// Due to the equality constraints demanded by `Self::Vector`, this is effectively just an
+    /// alias to `Self::Vector::Scalar`.
+    type Scalar: BaseNum;
     /// The associated displacement vector.
-    type Vector: Vector;
+    type Vector: Vector<Scalar = Self::Scalar>;
 
     /// Create a point at the origin.
     fn origin() -> Self;
@@ -91,13 +96,13 @@ pub trait Point: Clone where
 
     /// Multiply each component by a scalar, returning the new point.
     #[must_use]
-    fn mul_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Self;
+    fn mul_s(&self, scalar: Self::Scalar) -> Self;
     /// Divide each component by a scalar, returning the new point.
     #[must_use]
-    fn div_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Self;
+    fn div_s(&self, scalar: Self::Scalar) -> Self;
     /// Subtract a scalar from each component, returning the new point.
     #[must_use]
-    fn rem_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Self;
+    fn rem_s(&self, scalar: Self::Scalar) -> Self;
 
     /// Add a vector to this point, returning the new point.
     #[must_use]
@@ -106,17 +111,17 @@ pub trait Point: Clone where
     fn sub_p(&self, p: &Self) -> Self::Vector;
 
     /// Multiply each component by a scalar, in-place.
-    fn mul_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar);
+    fn mul_self_s(&mut self, scalar: Self::Scalar);
     /// Divide each component by a scalar, in-place.
-    fn div_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar);
+    fn div_self_s(&mut self, scalar: Self::Scalar);
     /// Take the remainder of each component by a scalar, in-place.
-    fn rem_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar);
+    fn rem_self_s(&mut self, scalar: Self::Scalar);
 
     /// Add a vector to this point, in-place.
     fn add_self_v(&mut self, v: &Self::Vector);
 
     /// This is a weird one, but its useful for plane calculations.
-    fn dot(&self, v: &Self::Vector) -> <<Self as Point>::Vector as Vector>::Scalar;
+    fn dot(&self, v: &Self::Vector) -> Self::Scalar;
 
     #[must_use]
     fn min(&self, p: &Self) -> Self;
@@ -130,6 +135,7 @@ impl<S: BaseNum> Array1 for Point2<S> {
 }
 
 impl<S: BaseNum> Point for Point2<S> {
+    type Scalar = S;
     type Vector = Vector2<S>;
 
     #[inline]
@@ -147,26 +153,26 @@ impl<S: BaseNum> Point for Point2<S> {
         Vector2::new(self.x, self.y)
     }
 
-    #[inline] fn mul_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Point2<S> { self * scalar }
-    #[inline] fn div_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Point2<S> { self / scalar }
-    #[inline] fn rem_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Point2<S> { self % scalar }
+    #[inline] fn mul_s(&self, scalar: S) -> Point2<S> { self * scalar }
+    #[inline] fn div_s(&self, scalar: S) -> Point2<S> { self / scalar }
+    #[inline] fn rem_s(&self, scalar: S) -> Point2<S> { self % scalar }
     #[inline] fn add_v(&self, v: &Vector2<S>) -> Point2<S> { self + v }
     #[inline] fn sub_p(&self, p: &Point2<S>) -> Vector2<S> { self - p }
 
     #[inline]
-    fn mul_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar) {
+    fn mul_self_s(&mut self, scalar: S) {
         self.x = self.x * scalar;
         self.y = self.y * scalar;
     }
 
     #[inline]
-    fn div_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar) {
+    fn div_self_s(&mut self, scalar: S) {
         self.x = self.x / scalar;
         self.y = self.y / scalar;
     }
 
     #[inline]
-    fn rem_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar) {
+    fn rem_self_s(&mut self, scalar: S) {
         self.x = self.x % scalar;
         self.y = self.y % scalar;
     }
@@ -209,6 +215,7 @@ impl<S: BaseNum> Array1 for Point3<S> {
 }
 
 impl<S: BaseNum> Point for Point3<S> {
+    type Scalar = S;
     type Vector = Vector3<S>;
 
     #[inline]
@@ -226,28 +233,28 @@ impl<S: BaseNum> Point for Point3<S> {
         Vector3::new(self.x, self.y, self.z)
     }
 
-    #[inline] fn mul_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Point3<S> { self * scalar }
-    #[inline] fn div_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Point3<S> { self / scalar }
-    #[inline] fn rem_s(&self, scalar: <<Self as Point>::Vector as Vector>::Scalar) -> Point3<S> { self % scalar }
+    #[inline] fn mul_s(&self, scalar: S) -> Point3<S> { self * scalar }
+    #[inline] fn div_s(&self, scalar: S) -> Point3<S> { self / scalar }
+    #[inline] fn rem_s(&self, scalar: S) -> Point3<S> { self % scalar }
     #[inline] fn add_v(&self, v: &Vector3<S>) -> Point3<S> { self + v }
     #[inline] fn sub_p(&self, p: &Point3<S>) -> Vector3<S> { self - p }
 
     #[inline]
-    fn mul_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar) {
+    fn mul_self_s(&mut self, scalar: S) {
         self.x = self.x * scalar;
         self.y = self.y * scalar;
         self.z = self.z * scalar;
     }
 
     #[inline]
-    fn div_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar) {
+    fn div_self_s(&mut self, scalar: S) {
         self.x = self.x / scalar;
         self.y = self.y / scalar;
         self.z = self.z / scalar;
     }
 
     #[inline]
-    fn rem_self_s(&mut self, scalar: <<Self as Point>::Vector as Vector>::Scalar) {
+    fn rem_self_s(&mut self, scalar: S) {
         self.x = self.x % scalar;
         self.y = self.y % scalar;
         self.z = self.z % scalar;
diff --git a/src/rotation.rs b/src/rotation.rs
index 7e1fed6..068bfcc 100644
--- a/src/rotation.rs
+++ b/src/rotation.rs
@@ -27,8 +27,8 @@ use vector::{Vector, Vector2, Vector3};
 /// creates a circular motion, and preserves at least one point in the space.
 pub trait Rotation<P: Point>: PartialEq + Sized where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    Self: ApproxEq<Epsilon = <<P as Point>::Vector as Vector>::Scalar>,
-    <<P as Point>::Vector as Vector>::Scalar: BaseFloat,
+    Self: ApproxEq<Epsilon = <P as Point>::Scalar>,
+    <P as Point>::Scalar: BaseFloat,
 {
     /// Create the identity transform (causes no transformation).
     fn one() -> Self;
diff --git a/src/transform.rs b/src/transform.rs
index 5a0e2fb..a1583ab 100644
--- a/src/transform.rs
+++ b/src/transform.rs
@@ -80,12 +80,12 @@ pub struct Decomposed<V: Vector, R> {
 
 impl<P: Point, R: Rotation<P>> Transform<P> for Decomposed<P::Vector, R> where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    <<P as Point>::Vector as Vector>::Scalar: BaseFloat,
+    <P as Point>::Scalar: BaseFloat,
 {
     #[inline]
     fn one() -> Decomposed<P::Vector, R> {
         Decomposed {
-            scale: <<P as Point>::Vector as Vector>::Scalar::one(),
+            scale: <P as Point>::Scalar::one(),
             rot: R::one(),
             disp: P::Vector::zero(),
         }
@@ -96,7 +96,7 @@ impl<P: Point, R: Rotation<P>> Transform<P> for Decomposed<P::Vector, R> where
         let rot = R::look_at(&center.sub_p(eye), up);
         let disp = rot.rotate_vector(&P::origin().sub_p(eye));
         Decomposed {
-            scale: <<P as Point>::Vector as Vector>::Scalar::one(),
+            scale: <P as Point>::Scalar::one(),
             rot: rot,
             disp: disp,
         }
@@ -121,10 +121,10 @@ impl<P: Point, R: Rotation<P>> Transform<P> for Decomposed<P::Vector, R> where
     }
 
     fn invert(&self) -> Option<Decomposed<P::Vector, R>> {
-        if self.scale.approx_eq(&<<P as Point>::Vector as Vector>::Scalar::zero()) {
+        if self.scale.approx_eq(&<P as Point>::Scalar::zero()) {
             None
         } else {
-            let s = <<P as Point>::Vector as Vector>::Scalar::one() / self.scale;
+            let s = <P as Point>::Scalar::one() / self.scale;
             let r = self.rot.invert();
             let d = r.rotate_vector(&self.disp).mul_s(-s);
             Some(Decomposed {
@@ -215,7 +215,8 @@ impl<S: BaseFloat> Transform3<S> for AffineMatrix3<S> {}
 /// A trait that allows extracting components (rotation, translation, scale)
 /// from an arbitrary transformations
 pub trait ToComponents<P: Point, R: Rotation<P>> where
-    <<P as Point>::Vector as Vector>::Scalar: BaseFloat,
+    // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
+    <P as Point>::Scalar: BaseFloat,
 {
     /// Extract the (scale, rotation, translation) triple
     fn decompose(&self) -> (P::Vector, R, P::Vector);
@@ -226,7 +227,7 @@ pub trait ToComponents3<S: BaseFloat, R: Rotation3<S>>: ToComponents<Point3<S>,
 
 pub trait CompositeTransform<P: Point, R: Rotation<P>>: Transform<P> + ToComponents<P, R> where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    <<P as Point>::Vector as Vector>::Scalar: BaseFloat,
+    <P as Point>::Scalar: BaseFloat,
 {}
 
 pub trait CompositeTransform2<S: BaseFloat, R: Rotation2<S>>: Transform2<S> + ToComponents2<S, R> {}
@@ -234,7 +235,7 @@ pub trait CompositeTransform3<S: BaseFloat, R: Rotation3<S>>: Transform3<S> + To
 
 impl<P: Point, R: Rotation<P> + Clone> ToComponents<P, R> for Decomposed<P::Vector, R> where
     // FIXME: Ugly type signatures - blocked by rust-lang/rust#24092
-    <<P as Point>::Vector as Vector>::Scalar: BaseFloat,
+    <P as Point>::Scalar: BaseFloat,
 {
     fn decompose(&self) -> (P::Vector, R, P::Vector) {
         (P::Vector::one().mul_s(self.scale), self.rot.clone(), self.disp.clone())