diff --git a/src/size.rs b/src/size.rs
index a5c9fa7..60b3249 100644
--- a/src/size.rs
+++ b/src/size.rs
@@ -13,7 +13,7 @@ use scale_factor::ScaleFactor;
 use vector::{TypedVector2D, vec2};
 use num::*;
 
-use num_traits::NumCast;
+use num_traits::{NumCast, Signed};
 use std::fmt;
 use std::ops::{Add, Div, Mul, Sub};
 use std::marker::PhantomData;
@@ -245,6 +245,17 @@ impl<T: NumCast + Copy, Unit> TypedSize2D<T, Unit> {
     }
 }
 
+impl<T, U> TypedSize2D<T, U>
+where T: Signed {
+    pub fn abs(&self) -> Self {
+        size2(self.width.abs(), self.height.abs())
+    }
+
+    pub fn is_positive(&self) -> bool {
+        self.width.is_positive() && self.height.is_positive()
+    }
+}
+
 /// Shorthand for `TypedSize2D::new(w, h)`.
 pub fn size2<T, U>(w: T, h: T) -> TypedSize2D<T, U> {
     TypedSize2D::new(w, h)
diff --git a/src/vector.rs b/src/vector.rs
index 0fa3f08..51255e7 100644
--- a/src/vector.rs
+++ b/src/vector.rs
@@ -14,7 +14,7 @@ use point::{TypedPoint2D, TypedPoint3D, point2, point3};
 use size::{TypedSize2D, size2};
 use scale_factor::ScaleFactor;
 use num::*;
-use num_traits::{Float, NumCast};
+use num_traits::{Float, NumCast, Signed};
 use std::fmt;
 use std::ops::{Add, Neg, Mul, Sub, Div, AddAssign, SubAssign, MulAssign, DivAssign};
 use std::marker::PhantomData;
@@ -58,13 +58,15 @@ impl<T: fmt::Display, U> fmt::Display for TypedVector2D<T, U> {
     }
 }
 
-impl<T: Copy, U> TypedVector2D<T, U> {
+impl<T, U> TypedVector2D<T, U> {
     /// Constructor taking scalar values directly.
     #[inline]
     pub fn new(x: T, y: T) -> Self {
         TypedVector2D { x: x, y: y, _unit: PhantomData }
     }
+}
 
+impl<T: Copy, U> TypedVector2D<T, U> {
     /// Constructor taking properly typed Lengths instead of scalar values.
     #[inline]
     pub fn from_lengths(x: Length<T, U>, y: Length<T, U>) -> Self {
@@ -384,6 +386,13 @@ impl<T: Copy, U> From<[T; 2]> for TypedVector2D<T, U> {
     }
 }
 
+impl<T, U> TypedVector2D<T, U>
+where T: Signed {
+    pub fn abs(&self) -> Self {
+        vec2(self.x.abs(), self.y.abs())
+    }
+}
+
 define_matrix! {
     /// A 3d Vector tagged with a unit.
     pub struct TypedVector3D<T, U> {
@@ -423,13 +432,15 @@ impl<T: fmt::Display, U> fmt::Display for TypedVector3D<T, U> {
     }
 }
 
-impl<T: Copy, U> TypedVector3D<T, U> {
+impl<T, U> TypedVector3D<T, U> {
     /// Constructor taking scalar values directly.
     #[inline]
     pub fn new(x: T, y: T, z: T) -> Self {
         TypedVector3D { x: x, y: y, z: z, _unit: PhantomData }
     }
+}
 
+impl<T: Copy, U> TypedVector3D<T, U> {
     /// Constructor taking properly typed Lengths instead of scalar values.
     #[inline]
     pub fn from_lengths(x: Length<T, U>, y: Length<T, U>, z: Length<T, U>) -> TypedVector3D<T, U> {
@@ -753,16 +764,22 @@ impl<T: Copy, U> From<[T; 3]> for TypedVector3D<T, U> {
     }
 }
 
+impl<T, U> TypedVector3D<T, U>
+where T: Signed {
+    pub fn abs(&self) -> Self {
+        vec3(self.x.abs(), self.y.abs(), self.z.abs())
+    }
+}
 
 /// Convenience constructor.
 #[inline]
-pub fn vec2<T: Copy, U>(x: T, y: T) -> TypedVector2D<T, U> {
+pub fn vec2<T, U>(x: T, y: T) -> TypedVector2D<T, U> {
     TypedVector2D::new(x, y)
 }
 
 /// Convenience constructor.
 #[inline]
-pub fn vec3<T: Copy, U>(x: T, y: T, z: T) -> TypedVector3D<T, U> {
+pub fn vec3<T, U>(x: T, y: T, z: T) -> TypedVector3D<T, U> {
     TypedVector3D::new(x, y, z)
 }