Make look_at, perspective, and orthographic projection matrices conform to computer-graphics convensions.

The `look_at` method itself has been split into a right-handed and a left-handed variant:
`look_at_rh` and `look_at_lh`.

Fix #171, #158, #88, #79.

src/structs/iso.rs

@@ -16,7 +16,7 @@ use structs::rot::{Rot2, Rot3};
 use quickcheck::{Arbitrary, Gen};
 
 
-/// Two dimensional isometry.
+/// Two dimensional **direct** isometry.
 ///
 /// This is the composition of a rotation followed by a translation. Vectors `Vec2` are not
 /// affected by the translational component of this transformation while points `Pnt2` are.
@@ -30,7 +30,7 @@ pub struct Iso2<N> {
     pub translation: Vec2<N>
 }
 
-/// Three dimensional isometry.
+/// Three dimensional **direct** isometry.
 ///
 /// This is the composition of a rotation followed by a translation. Vectors `Vec3` are not
 /// affected by the translational component of this transformation while points `Pnt3` are.
@@ -62,20 +62,40 @@ impl<N: Clone + BaseFloat> Iso3<N> {
         Iso3::new_with_rotmat(eye.as_vec().clone(), new_rotmat)
     }
 
-    /// Builds a look-at view matrix.
+    /// Builds a right-handed look-at view matrix.
     ///
-    /// This conforms to the common notion of "look-at" matrix from the computer graphics
+    /// This conforms to the common notion of right handed look-at matrix from the computer
-    /// community. Its maps the view direction `target - eye` to the **negative** `z` axis and the
+    /// graphics community.
-    /// `eye` to the origin.
     ///
     /// # Arguments
     ///   * eye - The eye position.
     ///   * target - The target position.
-    ///   * up - The vertical view direction. It must not be to collinear to `eye - target`.
+    ///   * up - A vector approximately aligned with required the vertical axis. The only
+    ///   requirement of this parameter is to not be collinear to `target - eye`.
     #[inline]
-    pub fn new_look_at(eye: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
+    pub fn look_at_rh(eye: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
-        let new_rotmat = Rot3::new_look_at(&(*target - *eye), up);
+        let rot   = Rot3::look_at_rh(&(*target - *eye), up);
-        Iso3::new_with_rotmat(new_rotmat * (-*eye.as_vec()), new_rotmat)
+        let trans = rot * (-*eye);
+
+        Iso3::new_with_rotmat(trans.to_vec(), rot)
+    }
+
+    /// Builds a left-handed look-at view matrix.
+    ///
+    /// This conforms to the common notion of left handed look-at matrix from the computer
+    /// graphics community.
+    ///
+    /// # Arguments
+    ///   * eye - The eye position.
+    ///   * target - The target position.
+    ///   * up - A vector approximately aligned with required the vertical axis. The only
+    ///   requirement of this parameter is to not be collinear to `target - eye`.
+    #[inline]
+    pub fn look_at_lh(eye: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
+        let rot   = Rot3::look_at_lh(&(*target - *eye), up);
+        let trans = rot * (-*eye);
+
+        Iso3::new_with_rotmat(trans.to_vec(), rot)
     }
 }
 

src/structs/ortho.rs

@@ -7,18 +7,24 @@ use quickcheck::{Arbitrary, Gen};
 
 /// A 3D orthographic projection stored without any matrix.
 ///
-/// Reading or modifying its individual properties is cheap but applying the transformation is costly.
+/// This flips the `z` axis and maps a axis-aligned cube to the unit cube with corners varying from
+/// `(-1, -1, -1)` to `(1, 1, 1)`. Reading or modifying its individual properties is cheap but
+/// applying the transformation is costly.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
 pub struct Ortho3<N> {
-    width:  N,
+    left:   N,
-    height: N,
+    right:  N,
+    bottom: N,
+    top:    N,
     znear:  N,
     zfar:   N
 }
 
 /// A 3D orthographic projection stored as a 4D matrix.
 ///
-/// Reading or modifying its individual properties is costly but applying the transformation is cheap.
+/// This flips the `z` axis and maps a axis-aligned cube to the unit cube with corners varying from
+/// `(-1, -1, -1)` to `(1, 1, 1)`. Reading or modifying its individual properties is costly but
+/// applying the transformation is cheap.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
 pub struct OrthoMat3<N> {
     mat: Mat4<N>
@@ -26,14 +32,16 @@ pub struct OrthoMat3<N> {
 
 impl<N: BaseFloat> Ortho3<N> {
     /// Creates a new 3D orthographic projection.
-    pub fn new(width: N, height: N, znear: N, zfar: N) -> Ortho3<N> {
+    pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> Ortho3<N> {
         assert!(!::is_zero(&(zfar - znear)));
-        assert!(!::is_zero(&width));
+        assert!(!::is_zero(&(left - right)));
-        assert!(!::is_zero(&height));
+        assert!(!::is_zero(&(top - bottom)));
 
         Ortho3 {
-            width:  width,
+            left:   left,
-            height: height,
+            right:  right,
+            bottom: bottom,
+            top:    top,
             znear:  znear,
             zfar:   zfar
         }
@@ -41,37 +49,51 @@ impl<N: BaseFloat> Ortho3<N> {
 
     /// Builds a 4D projection matrix (using homogeneous coordinates) for this projection.
     pub fn to_mat(&self) -> Mat4<N> {
-        self.to_ortho_mat().mat
+        self.to_persp_mat().mat
     }
 
     /// Build a `OrthoMat3` representing this projection.
-    pub fn to_ortho_mat(&self) -> OrthoMat3<N> {
+    pub fn to_persp_mat(&self) -> OrthoMat3<N> {
-        OrthoMat3::new(self.width, self.height, self.znear, self.zfar)
+        OrthoMat3::new(self.left, self.right, self.bottom, self.top, self.znear, self.zfar)
     }
 }
 
 #[cfg(feature="arbitrary")]
 impl<N: Arbitrary + BaseFloat> Arbitrary for Ortho3<N> {
     fn arbitrary<G: Gen>(g: &mut G) -> Ortho3<N> {
-        let width = reject(g, |x| !::is_zero(x));
+        let left   = Arbitrary::arbitrary(g);
-        let height = reject(g, |x| !::is_zero(x));
+        let right  = reject(g, |x: &N| *x > left);
+        let bottom = Arbitrary::arbitrary(g);
+        let top    = reject(g, |x: &N| *x > bottom);
         let znear  = Arbitrary::arbitrary(g);
-        let zfar = reject(g, |&x: &N| !::is_zero(&(x - znear)));
+        let zfar   = reject(g, |x: &N| *x > znear);
         Ortho3::new(width, height, znear, zfar)
     }
 }
 
 impl<N: BaseFloat + Clone> Ortho3<N> {
-    /// The width of the view cuboid.
+    /// The smallest x-coordinate of the view cuboid.
     #[inline]
-    pub fn width(&self) -> N {
+    pub fn left(&self) -> N {
-        self.width.clone()
+        self.left.clone()
     }
 
-    /// The height of the view cuboid.
+    /// The largest x-coordinate of the view cuboid.
     #[inline]
-    pub fn height(&self) -> N {
+    pub fn right(&self) -> N {
-        self.height.clone()
+        self.right.clone()
+    }
+
+    /// The smallest y-coordinate of the view cuboid.
+    #[inline]
+    pub fn bottom(&self) -> N {
+        self.bottom.clone()
+    }
+
+    /// The largest y-coordinate of the view cuboid.
+    #[inline]
+    pub fn top(&self) -> N {
+        self.top.clone()
     }
 
     /// The near plane offset of the view cuboid.
@@ -86,27 +108,45 @@ impl<N: BaseFloat + Clone> Ortho3<N> {
         self.zfar.clone()
     }
 
-    /// Sets the width of the view cuboid.
+    /// Sets the smallest x-coordinate of the view cuboid.
     #[inline]
-    pub fn set_width(&mut self, width: N) {
+    pub fn set_left(&mut self, left: N) {
-        self.width = width
+        assert!(left < self.right, "The left corner must be farther than the right corner.");
+        self.left = left 
     }
 
-    /// Sets the height of the view cuboid.
+    /// Sets the largest x-coordinate of the view cuboid.
     #[inline]
-    pub fn set_height(&mut self, height: N) {
+    pub fn set_right(&mut self, right: N) {
-        self.height = height
+        assert!(right > self.left, "The left corner must be farther than the right corner.");
+        self.right = right
+    }
+
+    /// Sets the smallest y-coordinate of the view cuboid.
+    #[inline]
+    pub fn set_bottom(&mut self, bottom: N) {
+        assert!(bottom < self.top, "The top corner must be higher than the bottom corner.");
+        self.bottom = bottom
+    }
+
+    /// Sets the largest y-coordinate of the view cuboid.
+    #[inline]
+    pub fn set_top(&mut self, top: N) {
+        assert!(top > self.bottom, "The top corner must be higher than the left corner.");
+        self.top = top
     }
 
     /// Sets the near plane offset of the view cuboid.
     #[inline]
     pub fn set_znear(&mut self, znear: N) {
+        assert!(znear < self.zfar, "The far plane must be farther than the near plane.");
         self.znear = znear
     }
 
     /// Sets the far plane offset of the view cuboid.
     #[inline]
     pub fn set_zfar(&mut self, zfar: N) {
+        assert!(zfar > self.znear, "The far plane must be farther than the near plane.");
         self.zfar = zfar
     }
 
@@ -114,34 +154,47 @@ impl<N: BaseFloat + Clone> Ortho3<N> {
     #[inline]
     pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
         // FIXME: optimize that
-        self.to_ortho_mat().project_pnt(p)
+        self.to_persp_mat().project_pnt(p)
     }
 
     /// Projects a vector.
     #[inline]
     pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
         // FIXME: optimize that
-        self.to_ortho_mat().project_vec(p)
+        self.to_persp_mat().project_vec(p)
     }
 }
 
 impl<N: BaseFloat> OrthoMat3<N> {
-    /// Creates a new orthographic projection matrix from the width, heihgt, znear and zfar planes of the view cuboid.
+    /// Creates a new orthographic projection matrix.
-    pub fn new(width: N, height: N, znear: N, zfar: N) -> OrthoMat3<N> {
+    pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> OrthoMat3<N> {
-        assert!(!::is_zero(&(zfar - znear)));
+        assert!(left < right, "The left corner must be farther than the right corner.");
-        assert!(!::is_zero(&width));
+        assert!(bottom < top, "The top corner must be higher than the bottom corner.");
-        assert!(!::is_zero(&height));
+        assert!(znear < zfar, "The far plane must be farther than the near plane.");
 
         let mat: Mat4<N> = ::one();
 
         let mut res = OrthoMat3 { mat: mat };
-        res.set_width(width);
+        res.set_left_and_right(left, right);
-        res.set_height(height);
+        res.set_bottom_and_top(bottom, top);
         res.set_znear_and_zfar(znear, zfar);
 
         res
     }
 
+    /// Creates a new orthographic projection matrix from an aspect ratio and the vertical field of view.
+    pub fn new_with_fov(aspect: N, vfov: N, znear: N, zfar: N) -> OrthoMat3<N> {
+        assert!(znear < zfar, "The far plane must be farther than the near plane.");
+        assert!(!::is_zero(&aspect));
+
+        let _1: N = ::one();
+        let _2 = _1 + _1;
+        let width  = zfar * (vfov / _2).tan();
+        let height = width / aspect;
+
+        OrthoMat3::new(-width / _2, width / _2, -height / _2, height / _2, znear, zfar)
+    }
+
     /// Creates a new orthographic matrix from a 4D matrix.
     ///
     /// This is unsafe because the input matrix is not checked to be a orthographic projection.
@@ -158,42 +211,68 @@ impl<N: BaseFloat> OrthoMat3<N> {
         &self.mat
     }
 
-    /// The width of the view cuboid.
+    /// The smallest x-coordinate of the view cuboid.
     #[inline]
-    pub fn width(&self) -> N {
+    pub fn left(&self) -> N {
-        <N as Cast<f64>>::from(2.0) / self.mat.m11
+        (-::one::<N>() - self.mat.m14) / self.mat.m11
     }
 
-    /// The height of the view cuboid.
+    /// The largest x-coordinate of the view cuboid.
     #[inline]
-    pub fn height(&self) -> N {
+    pub fn right(&self) -> N {
-        <N as Cast<f64>>::from(2.0) / self.mat.m22
+        (::one::<N>() - self.mat.m14) / self.mat.m11
+    }
+
+    /// The smallest y-coordinate of the view cuboid.
+    #[inline]
+    pub fn bottom(&self) -> N {
+        (-::one::<N>() - self.mat.m24) / self.mat.m22
+    }
+
+    /// The largest y-coordinate of the view cuboid.
+    #[inline]
+    pub fn top(&self) -> N {
+        (::one::<N>() - self.mat.m24) / self.mat.m22
     }
 
     /// The near plane offset of the view cuboid.
     #[inline]
     pub fn znear(&self) -> N {
-        (self.mat.m34 + ::one()) / self.mat.m33
+        (::one::<N>() + self.mat.m34) / self.mat.m33
     }
 
     /// The far plane offset of the view cuboid.
     #[inline]
     pub fn zfar(&self) -> N {
-        (self.mat.m34 - ::one()) / self.mat.m33
+        (-::one::<N>() + self.mat.m34) / self.mat.m33
     }
 
-    /// Sets the width of the view cuboid.
+    /// Sets the smallest x-coordinate of the view cuboid.
     #[inline]
-    pub fn set_width(&mut self, width: N) {
+    pub fn set_left(&mut self, left: N) {
-        assert!(!::is_zero(&width));
+        let right = self.right();
-        self.mat.m11 = <N as Cast<f64>>::from(2.0) / width;
+        self.set_left_and_right(left, right);
     }
 
-    /// Sets the height of the view cuboid.
+    /// Sets the largest x-coordinate of the view cuboid.
     #[inline]
-    pub fn set_height(&mut self, height: N) {
+    pub fn set_right(&mut self, right: N) {
-        assert!(!::is_zero(&height));
+        let left = self.left();
-        self.mat.m22 = <N as Cast<f64>>::from(2.0) / height;
+        self.set_left_and_right(left, right);
+    }
+
+    /// Sets the smallest y-coordinate of the view cuboid.
+    #[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.
+    #[inline]
+    pub fn set_top(&mut self, top: N) {
+        let bottom = self.bottom();
+        self.set_bottom_and_top(bottom, top);
     }
 
     /// Sets the near plane offset of the view cuboid.
@@ -210,6 +289,22 @@ impl<N: BaseFloat> OrthoMat3<N> {
         self.set_znear_and_zfar(znear, zfar);
     }
 
+    /// Sets the view cuboid coordinates along the `x` axis.
+    #[inline]
+    pub fn set_left_and_right(&mut self, left: N, right: N) {
+        assert!(left < right, "The left corner must be farther than the right corner.");
+        self.mat.m11 = <N as Cast<f64>>::from(2.0) / (right - left);
+        self.mat.m14 = -(right + left) / (right - left);
+    }
+
+    /// Sets the view cuboid coordinates along the `y` axis.
+    #[inline]
+    pub fn set_bottom_and_top(&mut self, bottom: N, top: N) {
+        assert!(bottom < top, "The top corner must be higher than the bottom corner.");
+        self.mat.m22 = <N as Cast<f64>>::from(2.0) / (top - bottom);
+        self.mat.m24 = -(top + bottom) / (top - bottom);
+    }
+
     /// Sets the near and far plane offsets of the view cuboid.
     #[inline]
     pub fn set_znear_and_zfar(&mut self, znear: N, zfar: N) {
@@ -222,8 +317,8 @@ impl<N: BaseFloat> OrthoMat3<N> {
     #[inline]
     pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
         Pnt3::new(
-            self.mat.m11 * p.x,
+            self.mat.m11 * p.x + self.mat.m14,
-            self.mat.m22 * p.y,
+            self.mat.m22 * p.y + self.mat.m24,
             self.mat.m33 * p.z + self.mat.m34
         )
     }
@@ -251,7 +346,7 @@ impl<N: BaseFloat + Clone> OrthoMat3<N> {
 impl<N: Arbitrary + BaseFloat> Arbitrary for OrthoMat3<N> {
     fn arbitrary<G: Gen>(g: &mut G) -> OrthoMat3<N> {
         let x: Ortho3<N> = Arbitrary::arbitrary(g);
-        x.to_ortho_mat()
+        x.to_persp_mat()
     }
 }
 

src/structs/persp.rs

@@ -7,18 +7,22 @@ use quickcheck::{Arbitrary, Gen};
 
 /// A 3D perspective projection stored without any matrix.
 ///
-/// Reading or modifying its individual properties is cheap but applying the transformation is costly.
+/// This maps a frustrum cube to the unit cube with corners varying from `(-1, -1, -1)` to
+/// `(1, 1, 1)`. Reading or modifying its individual properties is cheap but applying the
+/// transformation is costly.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
 pub struct Persp3<N> {
     aspect: N,
-    fov:    N,
+    fovy:    N,
     znear:  N,
     zfar:   N
 }
 
 /// A 3D perspective projection stored as a 4D matrix.
 ///
-/// Reading or modifying its individual properties is costly but applying the transformation is cheap.
+/// This maps a frustrum to the unit cube with corners varying from `(-1, -1, -1)` to
+/// `(1, 1, 1)`. Reading or modifying its individual properties is costly but applying the
+/// transformation is cheap.
 #[derive(Eq, PartialEq, RustcEncodable, RustcDecodable, Clone, Debug, Copy)]
 pub struct PerspMat3<N> {
     mat: Mat4<N>
@@ -26,13 +30,13 @@ pub struct PerspMat3<N> {
 
 impl<N: BaseFloat> Persp3<N> {
     /// Creates a new 3D perspective projection.
-    pub fn new(aspect: N, fov: N, znear: N, zfar: N) -> Persp3<N> {
+    pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Persp3<N> {
         assert!(!::is_zero(&(zfar - znear)));
         assert!(!::is_zero(&aspect));
 
         Persp3 {
             aspect: aspect,
-            fov:    fov,
+            fovy:    fovy,
             znear:  znear,
             zfar:   zfar
         }
@@ -45,7 +49,7 @@ impl<N: BaseFloat> Persp3<N> {
 
     /// Build a `PerspMat3` representing this projection.
     pub fn to_persp_mat(&self) -> PerspMat3<N> {
-        PerspMat3::new(self.aspect, self.fov, self.znear, self.zfar)
+        PerspMat3::new(self.aspect, self.fovy, self.znear, self.zfar)
     }
 }
 
@@ -66,10 +70,10 @@ impl<N: BaseFloat + Clone> Persp3<N> {
         self.aspect.clone()
     }
 
-    /// Gets the field of view of the view frustrum.
+    /// Gets the y field of view of the view frustrum.
     #[inline]
-    pub fn fov(&self) -> N {
+    pub fn fovy(&self) -> N {
-        self.fov.clone()
+        self.fovy.clone()
     }
 
     /// Gets the near plane offset of the view frustrum.
@@ -92,12 +96,12 @@ impl<N: BaseFloat + Clone> Persp3<N> {
         self.aspect = aspect;
     }
 
-    /// Sets the field of view of the view frustrum.
+    /// Sets the y field of view of the view frustrum.
     ///
     /// This method does not build any matrix.
     #[inline]
-    pub fn set_fov(&mut self, fov: N) {
+    pub fn set_fovy(&mut self, fovy: N) {
-        self.fov = fov;
+        self.fovy = fovy;
     }
 
     /// Sets the near plane offset of the view frustrum.
@@ -132,19 +136,19 @@ impl<N: BaseFloat + Clone> Persp3<N> {
 }
 
 impl<N: BaseFloat> PerspMat3<N> {
-    /// Creates a new persepctive matrix from the aspect ratio, field of view, and near/far planes.
+    /// Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.
-    pub fn new(aspect: N, fov: N, znear: N, zfar: N) -> PerspMat3<N> {
+    pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> PerspMat3<N> {
         assert!(!::is_zero(&(znear - zfar)));
         assert!(!::is_zero(&aspect));
 
         let mat: Mat4<N> = ::one();
 
         let mut res = PerspMat3 { mat: mat };
-        res.set_fov(fov);
+        res.set_fovy(fovy);
         res.set_aspect(aspect);
         res.set_znear_and_zfar(znear, zfar);
         res.mat.m44 = ::zero();
-        res.mat.m43 = ::one();
+        res.mat.m43 = -::one::<N>();
 
         res
     }
@@ -168,12 +172,12 @@ impl<N: BaseFloat> PerspMat3<N> {
     /// Gets the `width / height` aspect ratio of the view frustrum.
     #[inline]
     pub fn aspect(&self) -> N {
-        -self.mat.m22 / self.mat.m11
+        self.mat.m22 / self.mat.m11
     }
 
-    /// Gets the field of view of the view frustrum.
+    /// Gets the y field of view of the view frustrum.
     #[inline]
-    pub fn fov(&self) -> N {
+    pub fn fovy(&self) -> N {
         let _1: N = ::one();
         let _2 = _1 + _1;
 
@@ -185,7 +189,7 @@ impl<N: BaseFloat> PerspMat3<N> {
     pub fn znear(&self) -> N {
         let _1: N = ::one();
         let _2 = _1 + _1;
-        let ratio = (self.mat.m33 + _1) / (self.mat.m33 - _1);
+        let ratio = (-self.mat.m33 + _1) / (-self.mat.m33 - _1);
 
         self.mat.m34 / (_2 * ratio) - self.mat.m34 / _2
     }
@@ -195,29 +199,29 @@ impl<N: BaseFloat> PerspMat3<N> {
     pub fn zfar(&self) -> N {
         let _1: N = ::one();
         let _2 = _1 + _1;
-        let ratio = (self.mat.m33 + _1) / (self.mat.m33 - _1);
+        let ratio = (-self.mat.m33 + _1) / (-self.mat.m33 - _1);
 
         (self.mat.m34 - ratio * self.mat.m34) / _2
     }
 
-    // FIXME: add a method to retriev znear and zfar at once ?
+    // FIXME: add a method to retrieve znear and zfar simultaneously?
 
     /// Updates this projection matrix with a new `width / height` aspect ratio of the view
     /// frustrum.
     #[inline]
     pub fn set_aspect(&mut self, aspect: N) {
         assert!(!::is_zero(&aspect));
-        self.mat.m11 = -self.mat.m22 / aspect;
+        self.mat.m11 = self.mat.m22 / aspect;
     }
 
-    /// Updates this projection with a new field of view of the view frustrum.
+    /// Updates this projection with a new y field of view of the view frustrum.
     #[inline]
-    pub fn set_fov(&mut self, fov: N) {
+    pub fn set_fovy(&mut self, fovy: N) {
         let _1: N = ::one();
         let _2 = _1 + _1;
 
         let old_m22  = self.mat.m22.clone();
-        self.mat.m22 = _1 / (fov / _2).tan();
+        self.mat.m22 = _1 / (fovy / _2).tan();
         self.mat.m11 = self.mat.m11 * (self.mat.m22 / old_m22);
     }
 
@@ -241,7 +245,7 @@ impl<N: BaseFloat> PerspMat3<N> {
         let _1: N = ::one();
         let _2 = _1 + _1;
 
-        self.mat.m33 = -(zfar + znear) / (znear - zfar);
+        self.mat.m33 = (zfar + znear) / (znear - zfar);
         self.mat.m34 = zfar * znear * _2 / (znear - zfar);
     }
 
@@ -249,7 +253,7 @@ impl<N: BaseFloat> PerspMat3<N> {
     #[inline]
     pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
         let _1: N = ::one();
-        let inv_denom = _1 / p.z;
+        let inv_denom = -_1 / p.z;
         Pnt3::new(
             self.mat.m11 * p.x * inv_denom,
             self.mat.m22 * p.y * inv_denom,
@@ -261,7 +265,7 @@ impl<N: BaseFloat> PerspMat3<N> {
     #[inline]
     pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
         let _1: N = ::one();
-        let inv_denom = _1 / p.z;
+        let inv_denom = -_1 / p.z;
         Vec3::new(
             self.mat.m11 * p.x * inv_denom,
             self.mat.m22 * p.y * inv_denom,

src/structs/rot.rs

@@ -218,19 +218,36 @@ impl<N: Clone + BaseFloat> Rot3<N> {
         }
     }
 
-    /// Builds a look-at view matrix with no translational component.
+
+    /// Builds a right-handed look-at view matrix without translation.
     ///
-    /// This conforms to the common notion of "look-at" matrix from the computer graphics community.
+    /// This conforms to the common notion of right handed look-at matrix from the computer
-    /// Its maps the view direction `dir` to the **negative** `z` axis.
+    /// graphics community.
     ///
     /// # Arguments
-    ///   * dir - The view direction.
+    ///   * eye - The eye position.
-    ///   * up - The vertical direction. The only requirement of this parameter is to not be
+    ///   * target - The target position.
-    ///   collinear to `dir`.
+    ///   * up - A vector approximately aligned with required the vertical axis. The only
+    ///   requirement of this parameter is to not be collinear to `target - eye`.
     #[inline]
-    pub fn new_look_at(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
+    pub fn look_at_rh(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
         Rot3::new_observer_frame(&(-*dir), up).inv().unwrap()
     }
+
+    /// Builds a left-handed look-at view matrix without translation.
+    ///
+    /// This conforms to the common notion of left handed look-at matrix from the computer
+    /// graphics community.
+    ///
+    /// # Arguments
+    ///   * eye - The eye position.
+    ///   * target - The target position.
+    ///   * up - A vector approximately aligned with required the vertical axis. The only
+    ///   requirement of this parameter is to not be collinear to `target - eye`.
+    #[inline]
+    pub fn look_at_lh(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
+        Rot3::new_observer_frame(&(*dir), up).inv().unwrap()
+    }
 }
 
 impl<N: Clone + BaseFloat + Cast<f64>>

tests/transforms.rs

@@ -2,8 +2,8 @@ extern crate nalgebra as na;
 extern crate rand;
 
 use rand::random;
-use na::{Pnt2, Pnt3, Vec2, Vec3, Vec1, Rot2, Rot3, Persp3, PerspMat3, Ortho3, OrthoMat3, Iso2,
+use na::{Pnt2, Pnt3, Vec2, Vec3, Vec1, Rot2, Rot3, Persp3, PerspMat3, Ortho3, OrthoMat3,
-         Iso3, Sim2, Sim3, BaseFloat, Transform};
+         Iso2, Iso3, Sim2, Sim3, BaseFloat, Transform};
 
 #[test]
 fn test_rotation2() {
@@ -71,25 +71,27 @@ fn test_rot2_angle_between() {
 
 
 #[test]
-fn test_look_at_iso3() {
+fn test_look_at_rh_iso3() {
     for _ in 0usize .. 10000 {
         let eye     = random::<Pnt3<f64>>();
         let target  = random::<Pnt3<f64>>();
         let up      = random::<Vec3<f64>>();
-        let viewmat = Iso3::new_look_at(&eye, &target, &up);
+        let viewmat = Iso3::look_at_rh(&eye, &target, &up);
 
-        assert_eq!(&(viewmat * eye), &na::orig());
+        let origin: Pnt3<f64> = na::orig();
+        assert_eq!(&(viewmat * eye), &origin);
         assert!(na::approx_eq(&na::normalize(&(viewmat * (target - eye))), &-Vec3::z()));
     }
 }
 
 #[test]
-fn test_look_at_rot3() {
+fn test_look_at_rh_rot3() {
     for _ in 0usize .. 10000 {
         let dir     = random::<Vec3<f64>>();
         let up      = random::<Vec3<f64>>();
-        let viewmat = Rot3::new_look_at(&dir, &up);
+        let viewmat = Rot3::look_at_rh(&dir, &up);
 
+        println!("found: {}", viewmat * dir);
         assert!(na::approx_eq(&na::normalize(&(viewmat * dir)), &-Vec3::z()));
     }
 }
@@ -124,16 +126,16 @@ fn test_persp() {
     let mut pm = PerspMat3::new(42.0f64, 0.5, 1.5, 10.0);
     assert!(p.to_mat() == pm.to_mat());
     assert!(p.aspect() == 42.0);
-    assert!(p.fov()    == 0.5);
+    assert!(p.fovy()   == 0.5);
     assert!(p.znear()  == 1.5);
     assert!(p.zfar()   == 10.0);
     assert!(na::approx_eq(&pm.aspect(), &42.0));
-    assert!(na::approx_eq(&pm.fov(),    &0.5));
+    assert!(na::approx_eq(&pm.fovy(),   &0.5));
     assert!(na::approx_eq(&pm.znear(),  &1.5));
     assert!(na::approx_eq(&pm.zfar(),   &10.0));
 
-    p.set_fov(0.1);
+    p.set_fovy(0.1);
-    pm.set_fov(0.1);
+    pm.set_fovy(0.1);
     assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
 
     p.set_znear(24.0);
@@ -149,52 +151,60 @@ fn test_persp() {
     assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
 
     assert!(p.aspect() == 23.0);
-    assert!(p.fov()    == 0.1);
+    assert!(p.fovy()   == 0.1);
     assert!(p.znear()  == 24.0);
     assert!(p.zfar()   == 61.0);
     assert!(na::approx_eq(&pm.aspect(), &23.0));
-    assert!(na::approx_eq(&pm.fov(),    &0.1));
+    assert!(na::approx_eq(&pm.fovy(),   &0.1));
     assert!(na::approx_eq(&pm.znear(),  &24.0));
     assert!(na::approx_eq(&pm.zfar(),   &61.0));
 }
 
 #[test]
 fn test_ortho() {
-    let mut p  = Ortho3::new(42.0f64, 0.5, 1.5, 10.0);
+    let mut p  = Ortho3::new(-0.3, 5.2, -3.9, -1.0, 1.5, 10.0);
-    let mut pm = OrthoMat3::new(42.0f64, 0.5, 1.5, 10.0);
+    let mut pm = OrthoMat3::new(-0.3, 5.2, -3.9, -1.0, 1.5, 10.0);
     assert!(p.to_mat() == pm.to_mat());
-    assert!(p.width()  == 42.0);
+    assert!(p.left()   == -0.3);
-    assert!(p.height() == 0.5);
+    assert!(p.right()  == 5.2);
+    assert!(p.bottom() == -3.9);
+    assert!(p.top()    == -1.0);
     assert!(p.znear()  == 1.5);
     assert!(p.zfar()   == 10.0);
-    assert!(na::approx_eq(&pm.width(),  &42.0));
+    assert!(na::approx_eq(&pm.left(),   &-0.3));
-    assert!(na::approx_eq(&pm.height(), &0.5));
+    assert!(na::approx_eq(&pm.right(),  &5.2));
+    assert!(na::approx_eq(&pm.bottom(), &-3.9));
+    assert!(na::approx_eq(&pm.top(),    &-1.0));
     assert!(na::approx_eq(&pm.znear(),  &1.5));
     assert!(na::approx_eq(&pm.zfar(),   &10.0));
 
-    p.set_width(0.1);
+    p.set_left(0.1);
-    pm.set_width(0.1);
+    pm.set_left(0.1);
     assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
 
-    p.set_znear(24.0);
+    p.set_right(10.1);
-    pm.set_znear(24.0);
+    pm.set_right(10.1);
+    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+
+    p.set_top(24.0);
+    pm.set_top(24.0);
+    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+
+    p.set_bottom(-23.0);
+    pm.set_bottom(-23.0);
     assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
 
     p.set_zfar(61.0);
     pm.set_zfar(61.0);
     assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
 
-    p.set_height(23.0);
+    p.set_znear(21.0);
-    pm.set_height(23.0);
+    pm.set_znear(21.0);
     assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
 
-    assert!(p.height() == 23.0);
+    assert!(p.znear()  == 21.0);
-    assert!(p.width()  == 0.1);
-    assert!(p.znear()  == 24.0);
     assert!(p.zfar()   == 61.0);
-    assert!(na::approx_eq(&pm.height(), &23.0));
+    assert!(na::approx_eq(&pm.znear(),  &21.0));
-    assert!(na::approx_eq(&pm.width(),  &0.1));
-    assert!(na::approx_eq(&pm.znear(),  &24.0));
     assert!(na::approx_eq(&pm.zfar(),   &61.0));
 }