Remove over-restrictive assertions on Orthographic3 construction + add doc-tests.

Fix #365

src/geometry/orthographic.rs

@@ -63,21 +63,50 @@ impl<'a, N: Real + Deserialize<'a>> Deserialize<'a> for Orthographic3<N> {
 
 impl<N: Real> Orthographic3<N> {
     /// Creates a new orthographic projection matrix.
+    ///
+    /// This follows the OpenGL convention, so this will flip the `z` axis.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::{Orthographic3, Point3};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// // Check this projection actually transforms the view cuboid into the double-unit cube.
+    /// // See https://www.nalgebra.org/projections/#orthographic-projection for more details.
+    /// let p1 = Point3::new(1.0, 2.0, -0.1);
+    /// let p2 = Point3::new(1.0, 2.0, -1000.0);
+    /// let p3 = Point3::new(1.0, 20.0, -0.1);
+    /// let p4 = Point3::new(1.0, 20.0, -1000.0);
+    /// let p5 = Point3::new(10.0, 2.0, -0.1);
+    /// let p6 = Point3::new(10.0, 2.0, -1000.0);
+    /// let p7 = Point3::new(10.0, 20.0, -0.1);
+    /// let p8 = Point3::new(10.0, 20.0, -1000.0);
+    ///
+    /// assert_relative_eq!(proj.project_point(&p1), Point3::new(-1.0, -1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p2), Point3::new(-1.0, -1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p3), Point3::new(-1.0,  1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p4), Point3::new(-1.0,  1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p5), Point3::new( 1.0, -1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p6), Point3::new( 1.0, -1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p7), Point3::new( 1.0,  1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p8), Point3::new( 1.0,  1.0,  1.0));
+    ///
+    /// // This also works with flipped axis. In other words, we allow that
+    /// // `left > right`, `bottom > top`, and/or `znear > zfar`.
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    ///
+    /// assert_relative_eq!(proj.project_point(&p1), Point3::new( 1.0,  1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p2), Point3::new( 1.0,  1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p3), Point3::new( 1.0, -1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p4), Point3::new( 1.0, -1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p5), Point3::new(-1.0,  1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p6), Point3::new(-1.0,  1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p7), Point3::new(-1.0, -1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p8), Point3::new(-1.0, -1.0, -1.0));
+    /// ```
     #[inline]
     pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Self {
-        assert!(
-            left < right,
-            "The left corner must be farther than the right corner."
-        );
-        assert!(
-            bottom < top,
-            "The top corner must be higher than the bottom corner."
-        );
-        assert!(
-            znear < zfar,
-            "The far plane must be farther than the near plane."
-        );
-
         let matrix = Matrix4::<N>::identity();
         let mut res = Self::from_matrix_unchecked(matrix);
 
@@ -92,6 +121,19 @@ impl<N: Real> Orthographic3<N> {
     ///
     /// It is not checked whether or not the given matrix actually represents an orthographic
     /// projection.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Orthographic3, Point3, Matrix4};
+    /// let mat = Matrix4::new(
+    ///     2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
+    ///     0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
+    ///     0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
+    ///     0.0,       0.0,        0.0,         1.0
+    /// );
+    /// let proj = Orthographic3::from_matrix_unchecked(mat);
+    /// assert_eq!(proj, Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0));
+    /// ```
     #[inline]
     pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
         Orthographic3 { matrix: matrix }
@@ -101,8 +143,8 @@ impl<N: Real> Orthographic3<N> {
     #[inline]
     pub fn from_fov(aspect: N, vfov: N, znear: N, zfar: N) -> Self {
         assert!(
-            znear < zfar,
+            znear != zfar,
-            "The far plane must be farther than the near plane."
+            "The far plane must not be equal to the near plane."
         );
         assert!(
             !relative_eq!(aspect, N::zero()),
@@ -124,6 +166,23 @@ impl<N: Real> Orthographic3<N> {
     }
 
     /// Retrieves the inverse of the underlying homogeneous matrix.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::{Orthographic3, Point3, Matrix4};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// let inv = proj.inverse();
+    ///
+    /// assert_relative_eq!(inv * proj.as_matrix(), Matrix4::identity());
+    /// assert_relative_eq!(proj.as_matrix() * inv, Matrix4::identity());
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// let inv = proj.inverse();
+    /// assert_relative_eq!(inv * proj.as_matrix(), Matrix4::identity());
+    /// assert_relative_eq!(proj.as_matrix() * inv, Matrix4::identity());
+    /// ```
     #[inline]
     pub fn inverse(&self) -> Matrix4<N> {
         let mut res = self.to_homogeneous();
@@ -144,66 +203,187 @@ impl<N: Real> Orthographic3<N> {
     }
 
     /// Computes the corresponding homogeneous matrix.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Orthographic3, Point3, Matrix4};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// let expected = Matrix4::new(
+    ///     2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
+    ///     0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
+    ///     0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
+    ///     0.0,       0.0,        0.0,         1.0
+    /// );
+    /// assert_eq!(proj.to_homogeneous(), expected);
+    /// ```
     #[inline]
     pub fn to_homogeneous(&self) -> Matrix4<N> {
         self.matrix
     }
 
     /// A reference to the underlying homogeneous transformation matrix.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::{Orthographic3, Point3, Matrix4};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// let expected = Matrix4::new(
+    ///     2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
+    ///     0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
+    ///     0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
+    ///     0.0,       0.0,        0.0,         1.0
+    /// );
+    /// assert_eq!(*proj.as_matrix(), expected);
+    /// ```
     #[inline]
     pub fn as_matrix(&self) -> &Matrix4<N> {
         &self.matrix
     }
 
     /// A reference to this transformation seen as a `Projective3`.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_eq!(proj.as_projective().to_homogeneous(), proj.to_homogeneous());
+    /// ```
     #[inline]
     pub fn as_projective(&self) -> &Projective3<N> {
         unsafe { mem::transmute(self) }
     }
 
     /// This transformation seen as a `Projective3`.
+    ///
+    /// # Example
+    /// ```
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_eq!(proj.to_projective().to_homogeneous(), proj.to_homogeneous());
+    /// ```
     #[inline]
     pub fn to_projective(&self) -> Projective3<N> {
         Projective3::from_matrix_unchecked(self.matrix)
     }
 
     /// Retrieves the underlying homogeneous matrix.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::{Orthographic3, Point3, Matrix4};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// let expected = Matrix4::new(
+    ///     2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
+    ///     0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
+    ///     0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
+    ///     0.0,       0.0,        0.0,         1.0
+    /// );
+    /// assert_eq!(proj.unwrap(), expected);
+    /// ```
     #[inline]
     pub fn unwrap(self) -> Matrix4<N> {
         self.matrix
     }
 
-    /// The smallest x-coordinate of the view cuboid.
+    /// The left offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_relative_eq!(proj.left(), 1.0, epsilon = 1.0e-6);
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// assert_relative_eq!(proj.left(), 10.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn left(&self) -> N {
         (-N::one() - self.matrix[(0, 3)]) / self.matrix[(0, 0)]
     }
 
-    /// The largest x-coordinate of the view cuboid.
+    /// The right offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_relative_eq!(proj.right(), 10.0, epsilon = 1.0e-6);
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// assert_relative_eq!(proj.right(), 1.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn right(&self) -> N {
         (N::one() - self.matrix[(0, 3)]) / self.matrix[(0, 0)]
     }
 
-    /// The smallest y-coordinate of the view cuboid.
+    /// The bottom offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_relative_eq!(proj.bottom(), 2.0, epsilon = 1.0e-6);
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// assert_relative_eq!(proj.bottom(), 20.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn bottom(&self) -> N {
         (-N::one() - self.matrix[(1, 3)]) / self.matrix[(1, 1)]
     }
 
-    /// The largest y-coordinate of the view cuboid.
+    /// The top offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_relative_eq!(proj.top(), 20.0, epsilon = 1.0e-6);
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// assert_relative_eq!(proj.top(), 2.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn top(&self) -> N {
         (N::one() - self.matrix[(1, 3)]) / self.matrix[(1, 1)]
     }
 
     /// The near plane offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_relative_eq!(proj.znear(), 0.1, epsilon = 1.0e-6);
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// assert_relative_eq!(proj.znear(), 1000.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn znear(&self) -> N {
         (N::one() + self.matrix[(2, 3)]) / self.matrix[(2, 2)]
     }
 
     /// The far plane offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// assert_relative_eq!(proj.zfar(), 1000.0, epsilon = 1.0e-6);
+    ///
+    /// let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
+    /// assert_relative_eq!(proj.zfar(), 0.1, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn zfar(&self) -> N {
         (-N::one() + self.matrix[(2, 3)]) / self.matrix[(2, 2)]
@@ -211,6 +391,32 @@ impl<N: Real> Orthographic3<N> {
 
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a point. Faster than matrix multiplication.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::{Orthographic3, Point3};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    ///
+    /// let p1 = Point3::new(1.0, 2.0, -0.1);
+    /// let p2 = Point3::new(1.0, 2.0, -1000.0);
+    /// let p3 = Point3::new(1.0, 20.0, -0.1);
+    /// let p4 = Point3::new(1.0, 20.0, -1000.0);
+    /// let p5 = Point3::new(10.0, 2.0, -0.1);
+    /// let p6 = Point3::new(10.0, 2.0, -1000.0);
+    /// let p7 = Point3::new(10.0, 20.0, -0.1);
+    /// let p8 = Point3::new(10.0, 20.0, -1000.0);
+    ///
+    /// assert_relative_eq!(proj.project_point(&p1), Point3::new(-1.0, -1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p2), Point3::new(-1.0, -1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p3), Point3::new(-1.0,  1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p4), Point3::new(-1.0,  1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p5), Point3::new( 1.0, -1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p6), Point3::new( 1.0, -1.0,  1.0));
+    /// assert_relative_eq!(proj.project_point(&p7), Point3::new( 1.0,  1.0, -1.0));
+    /// assert_relative_eq!(proj.project_point(&p8), Point3::new( 1.0,  1.0,  1.0));
+    /// ```
     #[inline]
     pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
         Point3::new(
@@ -221,6 +427,32 @@ impl<N: Real> Orthographic3<N> {
     }
 
     /// Un-projects a point. Faster than multiplication by the underlying matrix inverse.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::{Orthographic3, Point3};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    ///
+    /// let p1 = Point3::new(-1.0, -1.0, -1.0);
+    /// let p2 = Point3::new(-1.0, -1.0,  1.0);
+    /// let p3 = Point3::new(-1.0,  1.0, -1.0);
+    /// let p4 = Point3::new(-1.0,  1.0,  1.0);
+    /// let p5 = Point3::new( 1.0, -1.0, -1.0);
+    /// let p6 = Point3::new( 1.0, -1.0,  1.0);
+    /// let p7 = Point3::new( 1.0,  1.0, -1.0);
+    /// let p8 = Point3::new( 1.0,  1.0,  1.0);
+    ///
+    /// assert_relative_eq!(proj.unproject_point(&p1), Point3::new(1.0, 2.0, -0.1), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p2), Point3::new(1.0, 2.0, -1000.0), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p3), Point3::new(1.0, 20.0, -0.1), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p4), Point3::new(1.0, 20.0, -1000.0), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p5), Point3::new(10.0, 2.0, -0.1), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p6), Point3::new(10.0, 2.0, -1000.0), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p7), Point3::new(10.0, 20.0, -0.1), epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.unproject_point(&p8), Point3::new(10.0, 20.0, -1000.0), epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn unproject_point(&self, p: &Point3<N>) -> Point3<N> {
         Point3::new(
@@ -232,6 +464,24 @@ impl<N: Real> Orthographic3<N> {
 
     // FIXME: when we get specialization, specialize the Mul impl instead.
     /// Projects a vector. Faster than matrix multiplication.
+    ///
+    /// Vectors are not affected by the translation part of the projection.
+    ///
+    /// # Example
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::{Orthographic3, Vector3};
+    /// let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    ///
+    /// let v1 = Vector3::x();
+    /// let v2 = Vector3::y();
+    /// let v3 = Vector3::z();
+    ///
+    /// assert_relative_eq!(proj.project_vector(&v1), Vector3::x() * 2.0 / 9.0);
+    /// assert_relative_eq!(proj.project_vector(&v2), Vector3::y() * 2.0 / 18.0);
+    /// assert_relative_eq!(proj.project_vector(&v3), Vector3::z() * -2.0 / 999.9);
+    /// ```
     #[inline]
     pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
     where SB: Storage<N, U3> {
@@ -242,28 +492,80 @@ impl<N: Real> Orthographic3<N> {
         )
     }
 
-    /// Sets the smallest x-coordinate of the view cuboid.
+    /// Sets the left offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_left(2.0);
+    /// assert_relative_eq!(proj.left(), 2.0, epsilon = 1.0e-6);
+    ///
+    /// // It is OK to set a left offset greater than the current right offset.
+    /// proj.set_left(20.0);
+    /// assert_relative_eq!(proj.left(), 20.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_left(&mut self, left: N) {
         let right = self.right();
         self.set_left_and_right(left, right);
     }
 
-    /// Sets the largest x-coordinate of the view cuboid.
+    /// Sets the right offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_right(15.0);
+    /// assert_relative_eq!(proj.right(), 15.0, epsilon = 1.0e-6);
+    ///
+    /// // It is OK to set a right offset smaller than the current left offset.
+    /// proj.set_right(-3.0);
+    /// assert_relative_eq!(proj.right(), -3.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_right(&mut self, right: N) {
         let left = self.left();
         self.set_left_and_right(left, right);
     }
 
-    /// Sets the smallest y-coordinate of the view cuboid.
+    /// Sets the bottom offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_bottom(8.0);
+    /// assert_relative_eq!(proj.bottom(), 8.0, epsilon = 1.0e-6);
+    ///
+    /// // It is OK to set a bottom offset greater than the current top offset.
+    /// proj.set_bottom(50.0);
+    /// assert_relative_eq!(proj.bottom(), 50.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_bottom(&mut self, bottom: N) {
         let top = self.top();
         self.set_bottom_and_top(bottom, top);
     }
 
-    /// Sets the largest y-coordinate of the view cuboid.
+    /// Sets the top offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_top(15.0);
+    /// assert_relative_eq!(proj.top(), 15.0, epsilon = 1.0e-6);
+    ///
+    /// // It is OK to set a top offset smaller than the current bottom offset.
+    /// proj.set_top(-3.0);
+    /// assert_relative_eq!(proj.top(), -3.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_top(&mut self, top: N) {
         let bottom = self.bottom();
@@ -271,6 +573,19 @@ impl<N: Real> Orthographic3<N> {
     }
 
     /// Sets the near plane offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_znear(8.0);
+    /// assert_relative_eq!(proj.znear(), 8.0, epsilon = 1.0e-6);
+    ///
+    /// // It is OK to set a znear greater than the current zfar.
+    /// proj.set_znear(5000.0);
+    /// assert_relative_eq!(proj.znear(), 5000.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_znear(&mut self, znear: N) {
         let zfar = self.zfar();
@@ -278,39 +593,97 @@ impl<N: Real> Orthographic3<N> {
     }
 
     /// Sets the far plane offset of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_zfar(15.0);
+    /// assert_relative_eq!(proj.zfar(), 15.0, epsilon = 1.0e-6);
+    ///
+    /// // It is OK to set a zfar smaller than the current znear.
+    /// proj.set_zfar(-3.0);
+    /// assert_relative_eq!(proj.zfar(), -3.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_zfar(&mut self, zfar: N) {
         let znear = self.znear();
         self.set_znear_and_zfar(znear, zfar);
     }
 
-    /// Sets the view cuboid coordinates along the `x` axis.
+    /// Sets the view cuboid offsets along the `x` axis.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_left_and_right(7.0, 70.0);
+    /// assert_relative_eq!(proj.left(), 7.0, epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.right(), 70.0, epsilon = 1.0e-6);
+    ///
+    /// // It is also OK to have `left > right`.
+    /// proj.set_left_and_right(70.0, 7.0);
+    /// assert_relative_eq!(proj.left(), 70.0, epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.right(), 7.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_left_and_right(&mut self, left: N, right: N) {
         assert!(
-            left < right,
+            left != right,
-            "The left corner must be farther than the right corner."
+            "The left corner must not be equal to the right corner."
         );
         self.matrix[(0, 0)] = ::convert::<_, N>(2.0) / (right - left);
         self.matrix[(0, 3)] = -(right + left) / (right - left);
     }
 
-    /// Sets the view cuboid coordinates along the `y` axis.
+    /// Sets the view cuboid offsets along the `y` axis.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_bottom_and_top(7.0, 70.0);
+    /// assert_relative_eq!(proj.bottom(), 7.0, epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.top(), 70.0, epsilon = 1.0e-6);
+    ///
+    /// // It is also OK to have `bottom > top`.
+    /// proj.set_bottom_and_top(70.0, 7.0);
+    /// assert_relative_eq!(proj.bottom(), 70.0, epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.top(), 7.0, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_bottom_and_top(&mut self, bottom: N, top: N) {
         assert!(
-            bottom < top,
+            bottom != top,
-            "The top corner must be higher than the bottom corner."
+            "The top corner must not be equal to the bottom corner."
         );
         self.matrix[(1, 1)] = ::convert::<_, N>(2.0) / (top - bottom);
         self.matrix[(1, 3)] = -(top + bottom) / (top - bottom);
     }
 
     /// Sets the near and far plane offsets of the view cuboid.
+    ///
+    /// ```
+    /// # #[macro_use] extern crate approx;
+    /// # extern crate nalgebra;
+    /// # use nalgebra::Orthographic3;
+    /// let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
+    /// proj.set_znear_and_zfar(50.0, 5000.0);
+    /// assert_relative_eq!(proj.znear(), 50.0, epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.zfar(), 5000.0, epsilon = 1.0e-6);
+    ///
+    /// // It is also OK to have `znear > zfar`.
+    /// proj.set_znear_and_zfar(5000.0, 0.5);
+    /// assert_relative_eq!(proj.znear(), 5000.0, epsilon = 1.0e-6);
+    /// assert_relative_eq!(proj.zfar(), 0.5, epsilon = 1.0e-6);
+    /// ```
     #[inline]
     pub fn set_znear_and_zfar(&mut self, znear: N, zfar: N) {
         assert!(
-            !relative_eq!(zfar - znear, N::zero()),
+            zfar != znear,
             "The near-plane and far-plane must not be superimposed."
         );
         self.matrix[(2, 2)] = -::convert::<_, N>(2.0) / (zfar - znear);