diff --git a/src/geom/geom.rs b/src/geom/geom.rs
index f9874ff..ed9db33 100644
--- a/src/geom/geom.rs
+++ b/src/geom/geom.rs
@@ -14,7 +14,7 @@
 // limitations under the License.
 
 pub use self::plane::Plane;
-pub use self::point::{Point2, Point3};
+pub use self::point::{Point, Point2, Point3};
 pub use self::ray::Ray3;
 
 pub mod plane;
diff --git a/src/geom/plane.rs b/src/geom/plane.rs
index 781ce8d..2691f44 100644
--- a/src/geom/plane.rs
+++ b/src/geom/plane.rs
@@ -14,7 +14,7 @@
 // limitations under the License.
 
 use core::{Vec3, Vec4, Mat3};
-use geom::{Point3, Ray3};
+use geom::{Point, Point3, Ray3};
 
 #[path = "../num_macros.rs"]
 mod num_macros;
@@ -34,7 +34,7 @@ pub struct Plane<T> {
     dist: T,
 }
 
-impl<T:Clone + Real> Plane<T> {
+impl<T:Clone + Float> Plane<T> {
     /// # Arguments
     ///
     /// - `a`: the `x` component of the normal
@@ -60,7 +60,7 @@ impl<T:Clone + Real> Plane<T> {
 
     /// Compute the distance from the plane to the point
     pub fn distance(&self, pos: &Point3<T>) -> T {
-        self.norm.dot(&**pos) + self.dist
+        self.norm.dot(pos.as_vec()) + self.dist
     }
 
     /// Computes the point at which `ray` intersects the plane
@@ -79,14 +79,14 @@ impl<T:Clone + Real> Plane<T> {
     }
 }
 
-impl<T:Clone + Real + ApproxEq<T>> Plane<T> {
+impl<T:Clone + Float> Plane<T> {
     /// Constructs a plane that passes through the the three points `a`, `b` and `c`
     pub fn from_3p(a: Point3<T>,
                    b: Point3<T>,
                    c: Point3<T>) -> Option<Plane<T>> {
         // create two vectors that run parallel to the plane
-        let v0 = (*b).sub_v(&*a);
-        let v1 = (*c).sub_v(&*a);
+        let v0 = b.as_vec().sub_v(a.as_vec());
+        let v1 = c.as_vec().sub_v(a.as_vec());
         // find the vector that is perpendicular to v1 and v2
         let mut norm = v0.cross(&v1);
 
@@ -95,7 +95,7 @@ impl<T:Clone + Real + ApproxEq<T>> Plane<T> {
         } else {
             // compute the normal and the distance to the plane
             norm.normalize_self();
-            let dist = -a.dot(&norm);
+            let dist = -a.as_vec().dot(&norm);
 
             Some(Plane::from_nd(norm, dist))
         }
@@ -115,7 +115,7 @@ impl<T:Clone + Real + ApproxEq<T>> Plane<T> {
         } else {
             // The end-point of the ray is at the three-plane intersection between
             // `self`, `other`, and a tempory plane positioned at the origin
-            do Plane::from_nd(ray_dir.clone(), zero!(T)).intersection_3pl(self, other).map |ray_pos| {
+            do Plane::from_nd(ray_dir.clone(), zero!(T)).intersection_3pl(self, other).map |&ray_pos| {
                 Ray3 {
                     pos: ray_pos.clone(),
                     dir: ray_dir.clone(),
@@ -136,9 +136,11 @@ impl<T:Clone + Real + ApproxEq<T>> Plane<T> {
                            self.norm.y.clone(), other_a.norm.y.clone(), other_b.norm.y.clone(),
                            self.norm.z.clone(), other_a.norm.z.clone(), other_b.norm.z.clone());
         do mx.inverse().map |m| {
-            Point3(m.mul_v(&Vec3::new(self.dist.clone(),
-                                      other_a.dist.clone(),
-                                      other_b.dist.clone())))
+            Point::from_vec(
+                m.mul_v(&Vec3::new(self.dist.clone(),
+                                   other_a.dist.clone(),
+                                   other_b.dist.clone()))
+            )
         }
     }
 }
@@ -189,7 +191,7 @@ mod tests {
         let p1 = Plane::from_abcd(0.0, -1.0, 0.0, 2.0);
         let p2 = Plane::from_abcd(0.0,  0.0, 1.0, 1.0);
 
-        assert_eq!(p0.intersection_3pl(&p1, &p2).unwrap(), Point3::new(1.0, -2.0, 1.0));
+        assert_eq!(p0.intersection_3pl(&p1, &p2), Some(Point3::new(1.0, -2.0, 1.0)));
     }
 
     #[test]
diff --git a/src/geom/point.rs b/src/geom/point.rs
index 6294dcd..160281f 100644
--- a/src/geom/point.rs
+++ b/src/geom/point.rs
@@ -13,31 +13,55 @@
 // See the License for the specific language governing permissions and
 // limitations under the License.
 
+use std::cast;
+
 use core::{Vec2, Vec3};
 
 /// A geometric point
 pub trait Point<T,V>: Eq + ApproxEq<T> + ToStr {
+    pub fn from_vec(vec: V) -> Self;
+    pub fn as_vec<'a>(&'a self) -> &'a V;
+    pub fn as_mut_vec<'a>(&'a mut self) -> &'a mut V;
+
     pub fn translate(&self, offset: &V) -> Self;
     pub fn distance(&self, other: &Self) -> T;
 }
 
 /// A two-dimensional point
 #[deriving(Clone, Eq)]
-pub struct Point2<T>(Vec2<T>);
+pub struct Point2<T> { x: T, y: T }
 
 impl<T> Point2<T> {
+    #[inline]
     pub fn new(x: T, y: T) -> Point2<T> {
-        Point2(Vec2::new(x, y))
+        Point2 { x: x, y: y }
     }
 }
 
-impl<T:Clone + Real> Point<T,Vec2<T>> for Point2<T> {
-    pub fn translate(&self, offset: &Vec2<T>) -> Point2<T> {
-        Point2(self.add_v(offset))
+impl<T:Clone + Float> Point<T,Vec2<T>> for Point2<T> {
+    #[inline]
+    pub fn from_vec(vec: Vec2<T>) -> Point2<T> {
+        unsafe { cast::transmute(vec) }
     }
 
+    #[inline]
+    pub fn as_vec<'a>(&'a self) -> &'a Vec2<T> {
+        unsafe { cast::transmute(self) }
+    }
+
+    #[inline]
+    pub fn as_mut_vec<'a>(&'a mut self) -> &'a mut Vec2<T> {
+        unsafe { cast::transmute(self) }
+    }
+
+    #[inline]
+    pub fn translate(&self, offset: &Vec2<T>) -> Point2<T> {
+        Point::from_vec(self.as_vec().add_v(offset))
+    }
+
+    #[inline]
     pub fn distance(&self, other: &Point2<T>) -> T {
-        (**self).distance(&**other)
+        self.as_vec().distance(other.as_vec())
     }
 }
 
@@ -54,7 +78,8 @@ impl<T:Clone + Eq + ApproxEq<T>> ApproxEq<T> for Point2<T> {
 
     #[inline]
     pub fn approx_eq_eps(&self, other: &Point2<T>, epsilon: &T) -> bool {
-        (**self).approx_eq_eps(&**other, epsilon)
+        self.x.approx_eq_eps(&other.x, epsilon) &&
+        self.y.approx_eq_eps(&other.y, epsilon)
     }
 }
 
@@ -76,21 +101,39 @@ mod test_point2 {
 
 /// A three-dimensional point
 #[deriving(Clone, Eq)]
-pub struct Point3<T>(Vec3<T>);
+pub struct Point3<T> { x: T, y: T, z: T }
 
 impl<T> Point3<T> {
+    #[inline]
     pub fn new(x: T, y: T, z: T) -> Point3<T> {
-        Point3(Vec3::new(x, y, z))
+        Point3 { x: x, y: y, z: z }
     }
 }
 
-impl<T:Clone + Real> Point<T,Vec3<T>> for Point3<T> {
-    pub fn translate(&self, offset: &Vec3<T>) -> Point3<T> {
-        Point3(self.add_v(offset))
+impl<T:Clone + Float> Point<T,Vec3<T>> for Point3<T> {
+    #[inline]
+    pub fn from_vec(vec: Vec3<T>) -> Point3<T> {
+        unsafe { cast::transmute(vec) }
     }
 
+    #[inline]
+    pub fn as_vec<'a>(&'a self) -> &'a Vec3<T> {
+        unsafe { cast::transmute(self) }
+    }
+
+    #[inline]
+    pub fn as_mut_vec<'a>(&'a mut self) -> &'a mut Vec3<T> {
+        unsafe { cast::transmute(self) }
+    }
+
+    #[inline]
+    pub fn translate(&self, offset: &Vec3<T>) -> Point3<T> {
+        Point::from_vec(self.as_vec().add_v(offset))
+    }
+
+    #[inline]
     pub fn distance(&self, other: &Point3<T>) -> T {
-        (**self).distance(&**other)
+        self.as_vec().distance(other.as_vec())
     }
 }
 
@@ -107,7 +150,9 @@ impl<T:Clone + Eq + ApproxEq<T>> ApproxEq<T> for Point3<T> {
 
     #[inline]
     pub fn approx_eq_eps(&self, other: &Point3<T>, epsilon: &T) -> bool {
-        (**self).approx_eq_eps(&**other, epsilon)
+        self.x.approx_eq_eps(&other.x, epsilon) &&
+        self.y.approx_eq_eps(&other.y, epsilon) &&
+        self.z.approx_eq_eps(&other.z, epsilon)
     }
 }
 
diff --git a/src/world/frustum.rs b/src/world/frustum.rs
index 26e6ca1..2c1e4ef 100644
--- a/src/world/frustum.rs
+++ b/src/world/frustum.rs
@@ -41,7 +41,7 @@ pub struct FrustumPoints<T> {
     far_bottom_right:  Point3<T>,
 }
 
-impl<T:Clone + Real> Frustum<T> {
+impl<T:Clone + Float> Frustum<T> {
     /// Constructs a frustum
     pub fn from_planes(left:   Plane<T>, right:  Plane<T>,
                        bottom: Plane<T>, top:    Plane<T>,
@@ -80,7 +80,7 @@ impl<T:Clone + Real> Frustum<T> {
     }
 }
 
-impl<T:Clone + Real + ApproxEq<T>> Frustum<T> {
+impl<T:Clone + Float> Frustum<T> {
     /// Computes where the frustum planes intersect to form corners and returns
     /// a struct containing the eight resulting position vectors.
     pub fn to_points(&self) -> FrustumPoints<T> {
diff --git a/src/world/projection.rs b/src/world/projection.rs
index d372324..c0f692f 100644
--- a/src/world/projection.rs
+++ b/src/world/projection.rs
@@ -28,7 +28,7 @@ mod num_macros;
 /// This is the equivalent of the gluPerspective function, the algorithm of which
 /// can be found [here](http://www.opengl.org/wiki/GluPerspective_code).
 ///
-pub fn perspective<T:Clone + Real>(fovy: T, aspectRatio: T, near: T, far: T) -> Mat4<T> {
+pub fn perspective<T:Clone + Float>(fovy: T, aspectRatio: T, near: T, far: T) -> Mat4<T> {
     let ymax = near * (fovy / two!(T)).to_radians().tan();
     let xmax = ymax * aspectRatio;
 
@@ -41,7 +41,7 @@ pub fn perspective<T:Clone + Real>(fovy: T, aspectRatio: T, near: T, far: T) ->
 /// This is the equivalent of the now deprecated [glFrustrum]
 /// (http://www.opengl.org/sdk/docs/man2/xhtml/glFrustum.xml) function.
 ///
-pub fn frustum<T:Clone + Real>(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Mat4<T> {
+pub fn frustum<T:Clone + Float>(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Mat4<T> {
     let c0r0 = (two!(T) * near) / (right - left);
     let c0r1 = zero!(T);
     let c0r2 = zero!(T);
@@ -74,7 +74,7 @@ pub fn frustum<T:Clone + Real>(left: T, right: T, bottom: T, top: T, near: T, fa
 /// This is the equivalent of the now deprecated [glOrtho]
 /// (http://www.opengl.org/sdk/docs/man2/xhtml/glOrtho.xml) function.
 ///
-pub fn ortho<T:Clone + Real>(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Mat4<T> {
+pub fn ortho<T:Clone + Float>(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Mat4<T> {
     let c0r0 = two!(T) / (right - left);
     let c0r1 = zero!(T);
     let c0r2 = zero!(T);
@@ -116,7 +116,7 @@ pub struct PerspectiveFOV<T> {
     far:    T,
 }
 
-impl<T:Clone + Real> PerspectiveFOV<T> {
+impl<T:Clone + Float> PerspectiveFOV<T> {
     pub fn to_perspective(&self) -> Result<Perspective<T>, ~str> {
         do self.if_valid {
             let angle = self.fovy / two!(T);
@@ -135,7 +135,7 @@ impl<T:Clone + Real> PerspectiveFOV<T> {
     }
 }
 
-impl<T:Clone + Real> Projection<T> for PerspectiveFOV<T> {
+impl<T:Clone + Float> Projection<T> for PerspectiveFOV<T> {
     pub fn if_valid<U:Clone>(&self, f: &fn() -> U) -> Result<U, ~str> {
         let frac_pi_2: T = Real::frac_pi_2();
         cond! (
@@ -169,7 +169,7 @@ pub struct Perspective<T> {
     far:    T,
 }
 
-impl<T:Clone + Real> Projection<T> for Perspective<T> {
+impl<T:Clone + Float> Projection<T> for Perspective<T> {
     pub fn if_valid<U:Clone>(&self, f: &fn() -> U) -> Result<U, ~str> {
         cond! (
             (self.left   > self.right) { Err(fmt!("`left` cannot be greater than `right`, found: left: %? right: %?", self.left, self.right)) }
@@ -275,7 +275,7 @@ pub struct Ortho<T> {
     far:    T,
 }
 
-impl<T:Clone + Real> Projection<T> for Ortho<T> {
+impl<T:Clone + Float> Projection<T> for Ortho<T> {
     pub fn if_valid<U:Clone>(&self, f: &fn() -> U) -> Result<U, ~str> {
         cond! (
             (self.left   > self.right) { Err(fmt!("`left` cannot be greater than `right`, found: left: %? right: %?", self.left, self.right)) }