Fix look_at matrices + implement Display for statically sized structures.

src/structs/iso.rs

@@ -1,3 +1,4 @@
+use std::fmt;
 use std::ops::{Add, Sub, Mul, Neg};
 
 use rand::{Rand, Rng};
@@ -44,33 +45,37 @@ pub struct Iso3<N> {
 }
 
 impl<N: Clone + BaseFloat> Iso3<N> {
-    /// Reorient and translate this transformation such that its local `x` axis points to a given
+    /// Creates an isometry that corresponds to the local frame of an observer standing at the
-    /// direction.  Note that the usually known `look_at` function does the same thing but with the
+    /// point `eye` and looking toward `target`.
-    /// `z` axis. See `look_at_z` for that.
+    ///
+    /// It maps the view direction `target - eye` to the positive `z` axis and the origin to the
+    /// `eye`.
     ///
     /// # Arguments
-    ///   * eye - The new translation of the transformation.
+    ///   * eye - The observer position.
-    ///   * at - The point to look at. `at - eye` is the direction the matrix `x` axis will be
+    ///   * target - The target position.
-    ///   aligned with.
+    ///   * up - Vertical direction. The only requirement of this parameter is to not be collinear
-    ///   * up - Vector pointing up. The only requirement of this parameter is to not be colinear
+    ///   to `eye - at`. Non-collinearity is not checked.
-    ///   with `at`. Non-colinearity is not checked.
     #[inline]
-    pub fn look_at(eye: &Pnt3<N>, at: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
+    pub fn new_observer_frame(eye: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
-        Iso3::new_with_rotmat(eye.as_vec().clone(), Rot3::look_at(&(*at - *eye), up))
+        let new_rotmat = Rot3::new_observer_frame(&(*target - *eye), up);
+        Iso3::new_with_rotmat(eye.as_vec().clone(), new_rotmat)
     }
 
-    /// Reorient and translate this transformation such that its local `z` axis points to a given
+    /// Builds a look-at view matrix.
-    /// direction.
+    ///
+    /// This conforms to the common notion of "look-at" matrix from the computer graphics
+    /// community. Its maps the view direction `target - eye` to the **negative** `z` axis and the
+    /// `eye` to the origin.
     ///
     /// # Arguments
-    ///   * eye - The new translation of the transformation.
+    ///   * eye - The eye position.
-    ///   * at - The point to look at. `at - eye` is the direction the matrix `x` axis will be
+    ///   * target - The target position.
-    ///   aligned with
+    ///   * up - The vertical view direction. It must not be to collinear to `eye - target`.
-    ///   * up - Vector pointing `up`. The only requirement of this parameter is to not be colinear
-    ///   with `at`. Non-colinearity is not checked.
     #[inline]
-    pub fn look_at_z(eye: &Pnt3<N>, at: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
+    pub fn new_look_at(eye: &Pnt3<N>, target: &Pnt3<N>, up: &Vec3<N>) -> Iso3<N> {
-        Iso3::new_with_rotmat(eye.as_vec().clone(), Rot3::look_at_z(&(*at - *eye), up))
+        let new_rotmat = Rot3::new_look_at(&(*target - *eye), up);
+        Iso3::new_with_rotmat(new_rotmat * (-*eye.as_vec()), new_rotmat)
     }
 }
 
@@ -95,6 +100,7 @@ pnt_mul_iso_impl!(Iso2, Pnt2);
 iso_mul_vec_impl!(Iso2, Vec2);
 vec_mul_iso_impl!(Iso2, Vec2);
 arbitrary_iso_impl!(Iso2);
+iso_display_impl!(Iso2);
 
 iso_impl!(Iso3, Rot3, Vec3, Vec3);
 rotation_matrix_impl!(Iso3, Rot3, Vec3, Vec3);
@@ -117,3 +123,4 @@ pnt_mul_iso_impl!(Iso3, Pnt3);
 iso_mul_vec_impl!(Iso3, Vec3);
 vec_mul_iso_impl!(Iso3, Vec3);
 arbitrary_iso_impl!(Iso3);
+iso_display_impl!(Iso3);

src/structs/iso_macros.rs

@@ -403,3 +403,26 @@ macro_rules! arbitrary_iso_impl(
         }
     )
 );
+
+macro_rules! iso_display_impl(
+    ($t: ident) => (
+        impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                try!(writeln!(f, "Isometry {{"));
+
+                if let Some(precision) = f.precision() {
+                    try!(writeln!(f, "... translation: {:.*}", precision, self.translation));
+                    try!(writeln!(f, "... rotation matrix:"));
+                    try!(write!(f, "{:.*}", precision, *self.rotation.submat()));
+                }
+                else {
+                    try!(writeln!(f, "... translation: {}", self.translation));
+                    try!(writeln!(f, "... rotation matrix:"));
+                    try!(write!(f, "{}", *self.rotation.submat()));
+                }
+
+                writeln!(f, "}}")
+            }
+        }
+    )
+);

src/structs/mat.rs

@@ -2,6 +2,7 @@
 
 #![allow(missing_docs)] // we allow missing to avoid having to document the mij components.
 
+use std::fmt;
 use std::ops::{Add, Sub, Mul, Div, Index, IndexMut};
 use std::mem;
 use std::slice::{Iter, IterMut};
@@ -82,6 +83,7 @@ eigen_qr_impl!(Mat1, Vec1);
 arbitrary_impl!(Mat1, m11);
 rand_impl!(Mat1, m11);
 mean_impl!(Mat1, Vec1, 1);
+mat_display_impl!(Mat1, 1);
 
 /// Square matrix of dimension 2.
 #[repr(C)]
@@ -136,6 +138,7 @@ eigen_qr_impl!(Mat2, Vec2);
 arbitrary_impl!(Mat2, m11, m12, m21, m22);
 rand_impl!(Mat2, m11, m12, m21, m22);
 mean_impl!(Mat2, Vec2, 2);
+mat_display_impl!(Mat2, 2);
 
 /// Square matrix of dimension 3.
 #[repr(C)]
@@ -233,6 +236,7 @@ rand_impl!(Mat3,
     m31, m32, m33
 );
 mean_impl!(Mat3, Vec3, 3);
+mat_display_impl!(Mat3, 3);
 
 /// Square matrix of dimension 4.
 #[repr(C)]
@@ -353,6 +357,7 @@ rand_impl!(Mat4,
   m41, m42, m43, m44
 );
 mean_impl!(Mat4, Vec4, 4);
+mat_display_impl!(Mat4, 4);
 
 /// Square matrix of dimension 5.
 #[repr(C)]
@@ -490,6 +495,7 @@ rand_impl!(Mat5,
   m51, m52, m53, m54, m55
 );
 mean_impl!(Mat5, Vec5, 5);
+mat_display_impl!(Mat5, 5);
 
 /// Square matrix of dimension 6.
 #[repr(C)]
@@ -632,3 +638,4 @@ rand_impl!(Mat6,
   m61, m62, m63, m64, m65, m66
 );
 mean_impl!(Mat6, Vec6, 6);
+mat_display_impl!(Mat6, 6);

src/structs/mat_macros.rs

@@ -749,3 +749,56 @@ macro_rules! mean_impl(
         }
     )
 );
+
+macro_rules! mat_display_impl(
+    ($t: ident, $dim: expr) => (
+        impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
+            // XXX: will will not always work correctly due to rounding errors.
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                fn integral_length<N: BaseFloat>(val: &N) -> usize {
+                    let mut res = 1;
+                    let mut curr: N = ::cast(10.0f64);
+
+                    while curr <= *val {
+                        curr = curr * ::cast(10.0f64);
+                        res = res + 1;
+                    }
+
+                    if val.is_sign_negative() {
+                        res + 1
+                    }
+                    else {
+                        res
+                    }
+                }
+
+                let mut max_decimal_length = 0;
+                let mut decimal_lengths: $t<usize> = ::zero();
+                for i in 0 .. $dim {
+                    for j in 0 .. $dim {
+                        decimal_lengths[(i, j)] = integral_length(&self[(i, j)].clone());
+                        max_decimal_length = ::max(max_decimal_length, decimal_lengths[(i, j)]);
+                    }
+                }
+
+                let precision = f.precision().unwrap_or(3);
+                let max_number_length = max_decimal_length + precision + 1;
+
+                try!(writeln!(f, "  ┌ {:>width$} ┐", "", width = max_number_length * $dim + $dim - 1));
+
+                for i in 0 .. $dim {
+                    try!(write!(f, "  │"));
+                    for j in 0 .. $dim {
+                        let number_length = decimal_lengths[(i, j)] + precision + 1;
+                        let pad = max_number_length - number_length;
+                        try!(write!(f, " {:>thepad$}", "", thepad = pad));
+                        try!(write!(f, "{:.*}", precision, (*self)[(i, j)]));
+                    }
+                    try!(writeln!(f, " │"));
+                }
+
+                writeln!(f, "  └ {:>width$} ┘", "", width = max_number_length * $dim + $dim - 1)
+            }
+        }
+    )
+);

src/structs/ortho.rs

@@ -41,11 +41,11 @@ 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_persp_mat().mat
+        self.to_ortho_mat().mat
     }
 
     /// Build a `OrthoMat3` representing this projection.
-    pub fn to_persp_mat(&self) -> OrthoMat3<N> {
+    pub fn to_ortho_mat(&self) -> OrthoMat3<N> {
         OrthoMat3::new(self.width, self.height, self.znear, self.zfar)
     }
 }
@@ -114,14 +114,14 @@ impl<N: BaseFloat + Clone> Ortho3<N> {
     #[inline]
     pub fn project_pnt(&self, p: &Pnt3<N>) -> Pnt3<N> {
         // FIXME: optimize that
-        self.to_persp_mat().project_pnt(p)
+        self.to_ortho_mat().project_pnt(p)
     }
 
     /// Projects a vector.
     #[inline]
     pub fn project_vec(&self, p: &Vec3<N>) -> Vec3<N> {
         // FIXME: optimize that
-        self.to_persp_mat().project_vec(p)
+        self.to_ortho_mat().project_vec(p)
     }
 }
 
@@ -251,7 +251,7 @@ 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_persp_mat()
+        x.to_ortho_mat()
     }
 }
 

src/structs/pnt.rs

@@ -1,6 +1,7 @@
 //! Points with dimension known at compile-time.
 
 use std::mem;
+use std::fmt;
 use std::slice::{Iter, IterMut};
 use std::iter::{Iterator, FromIterator, IntoIterator};
 use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut};
@@ -57,6 +58,7 @@ pnt_from_homogeneous_impl!(Pnt1, Pnt2, y, x);
 num_float_pnt_impl!(Pnt1, Vec1);
 arbitrary_pnt_impl!(Pnt1, x);
 rand_impl!(Pnt1, x);
+pnt_display_impl!(Pnt1);
 
 /// Point of dimension 2.
 ///
@@ -102,6 +104,7 @@ pnt_from_homogeneous_impl!(Pnt2, Pnt3, z, x, y);
 num_float_pnt_impl!(Pnt2, Vec2);
 arbitrary_pnt_impl!(Pnt2, x, y);
 rand_impl!(Pnt2, x, y);
+pnt_display_impl!(Pnt2);
 
 /// Point of dimension 3.
 ///
@@ -149,6 +152,7 @@ pnt_from_homogeneous_impl!(Pnt3, Pnt4, w, x, y, z);
 num_float_pnt_impl!(Pnt3, Vec3);
 arbitrary_pnt_impl!(Pnt3, x, y, z);
 rand_impl!(Pnt3, x, y, z);
+pnt_display_impl!(Pnt3);
 
 /// Point of dimension 4.
 ///
@@ -198,6 +202,7 @@ pnt_from_homogeneous_impl!(Pnt4, Pnt5, a, x, y, z, w);
 num_float_pnt_impl!(Pnt4, Vec4);
 arbitrary_pnt_impl!(Pnt4, x, y, z, w);
 rand_impl!(Pnt4, x, y, z, w);
+pnt_display_impl!(Pnt4);
 
 /// Point of dimension 5.
 ///
@@ -249,6 +254,7 @@ pnt_from_homogeneous_impl!(Pnt5, Pnt6, b, x, y, z, w, a);
 num_float_pnt_impl!(Pnt5, Vec5);
 arbitrary_pnt_impl!(Pnt5, x, y, z, w, a);
 rand_impl!(Pnt5, x, y, z, w, a);
+pnt_display_impl!(Pnt5);
 
 /// Point of dimension 6.
 ///
@@ -300,3 +306,4 @@ iterable_mut_impl!(Pnt6, 6);
 num_float_pnt_impl!(Pnt6, Vec6);
 arbitrary_pnt_impl!(Pnt6, x, y, z, w, a, b);
 rand_impl!(Pnt6, x, y, z, w, a, b);
+pnt_display_impl!(Pnt6);

src/structs/pnt_macros.rs

@@ -155,3 +155,24 @@ macro_rules! arbitrary_pnt_impl(
         }
     )
 );
+
+macro_rules! pnt_display_impl(
+    ($t: ident) => (
+        impl<N: fmt::Display> fmt::Display for $t<N> {
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                // FIXME: differenciate them from vectors ?
+                try!(write!(f, "("));
+
+                let mut it = self.iter();
+
+                try!(write!(f, "{}", *it.next().unwrap()));
+
+                for comp in it {
+                    try!(write!(f, ", {}", *comp));
+                }
+
+                write!(f, ")")
+            }
+        }
+    )
+);

src/structs/quat.rs

@@ -1,5 +1,6 @@
 //! Quaternion definition.
 
+use std::fmt;
 use std::mem;
 use std::slice::{Iter, IterMut};
 use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut};
@@ -154,6 +155,12 @@ impl<N: ApproxEq<N> + BaseFloat> Div<Quat<N>> for Quat<N> {
     }
 }
 
+impl<N: fmt::Display> fmt::Display for Quat<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "Quaternion {} − ({}, {}, {})", self.w, self.i, self.j, self.k)
+    }
+}
+
 rand_impl!(Quat, w, i, j, k);
 
 
@@ -505,6 +512,12 @@ impl<N: BaseNum + Neg<Output = N>> Transform<Pnt3<N>> for UnitQuat<N> {
     }
 }
 
+impl<N: fmt::Display> fmt::Display for UnitQuat<N> {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        write!(f, "Unit quaternion {} − ({}, {}, {})", self.q.w, self.q.i, self.q.j, self.q.k)
+    }
+}
+
 #[cfg(feature="arbitrary")]
 impl<N: Arbitrary + BaseFloat> Arbitrary for UnitQuat<N> {
     fn arbitrary<G: Gen>(g: &mut G) -> UnitQuat<N> {

src/structs/rot.rs

@@ -1,5 +1,6 @@
 //! Rotations matrices.
 
+use std::fmt;
 use std::ops::{Mul, Neg, Index};
 use rand::{Rand, Rng};
 use num::{Zero, One};
@@ -193,48 +194,43 @@ impl<N: Clone + BaseFloat> Rot3<N> {
 }
 
 impl<N: Clone + BaseFloat> Rot3<N> {
-    /// Create a new matrix and orient it such that its local `x` axis points to a given point.
+    /// Creates a rotation that corresponds to the local frame of an observer standing at the
-    /// Note that the usually known `look_at` function does the same thing but with the `z` axis.
+    /// origin and looking toward `dir`.
-    /// See `look_at_z` for that.
+    ///
+    /// It maps the view direction `dir` to the positive `z` axis.
     ///
     /// # Arguments
-    ///   * at - The point to look at. It is also the direction the matrix `x` axis will be aligned
+    ///   * dir - The look direction, that is, direction the matrix `z` axis will be aligned with.
-    ///   with
+    ///   * up - The vertical direction. The only requirement of this parameter is to not be
-    ///   * up - Vector pointing `up`. The only requirement of this parameter is to not be colinear
+    ///   collinear
-    ///   with `at`. Non-colinearity is not checked.
+    ///   to `dir`. Non-collinearity is not checked.
-    pub fn look_at(at: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
+    #[inline]
-        let xaxis = Norm::normalize(at);
+    pub fn new_observer_frame(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
-        let zaxis = Norm::normalize(&Cross::cross(up, &xaxis));
+        let zaxis = Norm::normalize(dir);
-        let yaxis = Cross::cross(&zaxis, &xaxis);
-
-        unsafe {
-            Rot3::new_with_mat(Mat3::new(
-                xaxis.x.clone(), yaxis.x.clone(), zaxis.x.clone(),
-                xaxis.y.clone(), yaxis.y.clone(), zaxis.y.clone(),
-                xaxis.z        , yaxis.z        , zaxis.z)
-            )
-        }
-    }
-
-    /// Create a new matrix and orient it such that its local `z` axis points to a given point.
-    ///
-    /// # Arguments
-    ///   * at - The look direction, that is, direction the matrix `y` axis will be aligned with
-    ///   * up - Vector pointing `up`. The only requirement of this parameter is to not be colinear
-    ///   with `at`. Non-colinearity is not checked.
-    pub fn look_at_z(at: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
-        let zaxis = Norm::normalize(at);
         let xaxis = Norm::normalize(&Cross::cross(up, &zaxis));
-        let yaxis = Cross::cross(&zaxis, &xaxis);
+        let yaxis = Norm::normalize(&Cross::cross(&zaxis, &xaxis));
 
         unsafe {
             Rot3::new_with_mat(Mat3::new(
                 xaxis.x.clone(), yaxis.x.clone(), zaxis.x.clone(),
                 xaxis.y.clone(), yaxis.y.clone(), zaxis.y.clone(),
-                xaxis.z        , yaxis.z        , zaxis.z)
+                xaxis.z        , yaxis.z        , zaxis.z))
-            )
         }
     }
+
+    /// Builds a look-at view matrix with no translational component.
+    ///
+    /// This conforms to the common notion of "look-at" matrix from the computer graphics community.
+    /// Its maps the view direction `dir` to the **negative** `z` axis.
+    ///
+    /// # Arguments
+    ///   * dir - The view direction.
+    ///   * up - The vertical direction. The only requirement of this parameter is to not be
+    ///   collinear to `dir`.
+    #[inline]
+    pub fn new_look_at(dir: &Vec3<N>, up: &Vec3<N>) -> Rot3<N> {
+        Rot3::new_observer_frame(&(-*dir), up).inv().unwrap()
+    }
 }
 
 impl<N: Clone + BaseFloat + Cast<f64>>
@@ -368,6 +364,7 @@ inv_impl!(Rot2);
 transpose_impl!(Rot2);
 approx_eq_impl!(Rot2);
 diag_impl!(Rot2, Vec2);
+rot_display_impl!(Rot2);
 
 submat_impl!(Rot3, Mat3);
 rotate_impl!(Rot3, Vec3, Pnt3);
@@ -390,3 +387,4 @@ inv_impl!(Rot3);
 transpose_impl!(Rot3);
 approx_eq_impl!(Rot3);
 diag_impl!(Rot3, Vec3);
+rot_display_impl!(Rot3);

src/structs/rot_macros.rs

@@ -326,3 +326,17 @@ macro_rules! absolute_impl(
         }
     )
 );
+
+macro_rules! rot_display_impl(
+    ($t: ident) => (
+        impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                let precision = f.precision().unwrap_or(3);
+
+                try!(writeln!(f, "Rotation matrix {{"));
+                try!(write!(f, "{:.*}", precision, self.submat));
+                writeln!(f, "}}")
+            }
+        }
+    )
+);

src/structs/sim.rs

@@ -1,3 +1,4 @@
+use std::fmt;
 use std::ops::{Mul, Neg};
 
 use rand::{Rand, Rng};
@@ -64,6 +65,7 @@ sim_to_homogeneous_impl!(Sim2, Mat3);
 sim_approx_eq_impl!(Sim2);
 sim_rand_impl!(Sim2);
 sim_arbitrary_impl!(Sim2);
+sim_display_impl!(Sim2);
 
 sim_impl!(Sim3, Iso3, Rot3, Vec3, Vec3);
 dim_impl!(Sim3, 3);
@@ -81,3 +83,4 @@ sim_to_homogeneous_impl!(Sim3, Mat4);
 sim_approx_eq_impl!(Sim3);
 sim_rand_impl!(Sim3);
 sim_arbitrary_impl!(Sim3);
+sim_display_impl!(Sim3);

src/structs/sim_macros.rs

@@ -118,7 +118,7 @@ macro_rules! sim_mul_sim_impl(
             #[inline]
             fn mul(self, right: $t<N>) -> $t<N> {
                 $t::new_with_rotmat(
-                    self.isometry.translation + self.isometry.rotation * (right.isometry.translation * right.scale),
+                    self.isometry.translation + self.isometry.rotation * (right.isometry.translation * self.scale),
                     self.isometry.rotation * right.isometry.rotation,
                     self.scale * right.scale)
             }
@@ -174,10 +174,11 @@ macro_rules! sim_inv_impl(
             fn inv_mut(&mut self) -> bool {
                 self.scale = ::one::<N>() / self.scale;
                 self.isometry.inv_mut();
-                // We multiply by self.scale because the scale has been inverted on the previous line.
+                // We multiply (instead of dividing) by self.scale because it has already been
+                // inverted.
                 self.isometry.translation = self.isometry.translation * self.scale;
 
-                // always succeed
+                // Always succeed.
                 true
             }
 
@@ -186,7 +187,7 @@ macro_rules! sim_inv_impl(
                 let mut res = *self;
                 res.inv_mut();
 
-                // always succeed
+                // Always succeed.
                 Some(res)
             }
         }
@@ -243,7 +244,12 @@ macro_rules! sim_rand_impl(
         impl<N: Rand + BaseFloat> Rand for $t<N> {
             #[inline]
             fn rand<R: Rng>(rng: &mut R) -> $t<N> {
-                $t::new_with_iso(rng.gen(), rng.gen())
+                let mut scale: N = rng.gen();
+                while scale.is_zero() {
+                    scale = rng.gen();
+                }
+
+                $t::new_with_iso(rng.gen(), scale)
             }
         }
     )
@@ -262,3 +268,28 @@ macro_rules! sim_arbitrary_impl(
         }
     )
 );
+
+macro_rules! sim_display_impl(
+    ($t: ident) => (
+        impl<N: fmt::Display + BaseFloat> fmt::Display for $t<N> {
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                try!(writeln!(f, "Similarity transformation {{"));
+
+                if let Some(precision) = f.precision() {
+                    try!(writeln!(f, "... scale factor: {:.*}", precision, self.scale));
+                    try!(writeln!(f, "... translation: {:.*}", precision, self.isometry.translation));
+                    try!(writeln!(f, "... rotation matrix:"));
+                    try!(write!(f, "{:.*}", precision, *self.isometry.rotation.submat()));
+                }
+                else {
+                    try!(writeln!(f, "... scale factor: {}", self.scale));
+                    try!(writeln!(f, "... translation: {}", self.isometry.translation));
+                    try!(writeln!(f, "... rotation matrix:"));
+                    try!(write!(f, "{}", *self.isometry.rotation.submat()));
+                }
+
+                writeln!(f, "}}")
+            }
+        }
+    )
+);

src/structs/vec.rs

@@ -4,6 +4,7 @@ use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut};
 use std::mem;
 use std::slice::{Iter, IterMut};
 use std::iter::{Iterator, FromIterator, IntoIterator};
+use std::fmt;
 use rand::{Rand, Rng};
 use num::{Zero, One};
 use traits::operations::{ApproxEq, POrd, POrdering, Axpy, Absolute, Mean};
@@ -71,6 +72,7 @@ absolute_vec_impl!(Vec1, x);
 arbitrary_impl!(Vec1, x);
 rand_impl!(Vec1, x);
 mean_impl!(Vec1);
+vec_display_impl!(Vec1);
 
 /// Vector of dimension 2.
 ///
@@ -128,6 +130,7 @@ absolute_vec_impl!(Vec2, x, y);
 arbitrary_impl!(Vec2, x, y);
 rand_impl!(Vec2, x, y);
 mean_impl!(Vec2);
+vec_display_impl!(Vec2);
 
 /// Vector of dimension 3.
 ///
@@ -187,6 +190,7 @@ absolute_vec_impl!(Vec3, x, y, z);
 arbitrary_impl!(Vec3, x, y, z);
 rand_impl!(Vec3, x, y, z);
 mean_impl!(Vec3);
+vec_display_impl!(Vec3);
 
 
 /// Vector of dimension 4.
@@ -249,6 +253,7 @@ absolute_vec_impl!(Vec4, x, y, z, w);
 arbitrary_impl!(Vec4, x, y, z, w);
 rand_impl!(Vec4, x, y, z, w);
 mean_impl!(Vec4);
+vec_display_impl!(Vec4);
 
 /// Vector of dimension 5.
 ///
@@ -312,6 +317,7 @@ absolute_vec_impl!(Vec5, x, y, z, w, a);
 arbitrary_impl!(Vec5, x, y, z, w, a);
 rand_impl!(Vec5, x, y, z, w, a);
 mean_impl!(Vec5);
+vec_display_impl!(Vec5);
 
 /// Vector of dimension 6.
 ///
@@ -375,3 +381,4 @@ absolute_vec_impl!(Vec6, x, y, z, w, a, b);
 arbitrary_impl!(Vec6, x, y, z, w, a, b);
 rand_impl!(Vec6, x, y, z, w, a, b);
 mean_impl!(Vec6);
+vec_display_impl!(Vec6);

src/structs/vec_macros.rs

@@ -820,3 +820,25 @@ macro_rules! mean_impl(
         }
     )
 );
+
+macro_rules! vec_display_impl(
+    ($t: ident) => (
+        impl<N: fmt::Display> fmt::Display for $t<N> {
+            fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+                try!(write!(f, "("));
+
+                let mut it = self.iter();
+
+                let precision = f.precision().unwrap_or(8);
+
+                try!(write!(f, "{:.*}", precision, *it.next().unwrap()));
+
+                for comp in it {
+                    try!(write!(f, ", {:.*}", precision, *comp));
+                }
+
+                write!(f, ")")
+            }
+        }
+    )
+);

tests/mat.rs

@@ -2,8 +2,8 @@ extern crate nalgebra as na;
 extern crate rand;
 
 use rand::random;
-use na::{Vec1, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, Rot2, Rot3, Persp3, PerspMat3, Ortho3,
+use na::{Rot2, Rot3, Iso2, Iso3, Sim2, Sim3, Vec3, Mat1, Mat2, Mat3, Mat4, Mat5, Mat6, DMat, DVec,
-         OrthoMat3, DMat, DVec, Row, Col, BaseFloat, Diag, Transpose, RowSlice, ColSlice, Shape};
+         Row, Col, Diag, Transpose, RowSlice, ColSlice, Shape};
 
 macro_rules! test_inv_mat_impl(
   ($t: ty) => (
@@ -12,7 +12,9 @@ macro_rules! test_inv_mat_impl(
 
       match na::inv(&randmat) {
           None    => { },
-          Some(i) => assert!(na::approx_eq(&(i * randmat), &na::one()))
+          Some(i) => {
+              assert!(na::approx_eq(&(i * randmat), &na::one()))
+          }
       }
     }
   );
@@ -183,13 +185,33 @@ fn test_inv_mat6() {
 }
 
 #[test]
-fn test_rotation2() {
+fn test_inv_rot2() {
-    for _ in 0usize .. 10000 {
+    test_inv_mat_impl!(Rot2<f64>);
-        let randmat: na::Rot2<f64> = na::one();
-        let ang    = Vec1::new(na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
-
-        assert!(na::approx_eq(&na::rotation(&na::append_rotation(&randmat, &ang)), &ang));
 }
+
+#[test]
+fn test_inv_rot3() {
+    test_inv_mat_impl!(Rot3<f64>);
+}
+
+#[test]
+fn test_inv_iso2() {
+    test_inv_mat_impl!(Iso2<f64>);
+}
+
+#[test]
+fn test_inv_iso3() {
+    test_inv_mat_impl!(Iso3<f64>);
+}
+
+#[test]
+fn test_inv_sim2() {
+    test_inv_mat_impl!(Sim2<f64>);
+}
+
+#[test]
+fn test_inv_sim3() {
+    test_inv_mat_impl!(Sim3<f64>);
 }
 
 #[test]
@@ -199,59 +221,6 @@ fn test_index_mat2() {
   assert!(mat[(0, 1)] == na::transpose(&mat)[(1, 0)]);
 }
 
-#[test]
-fn test_inv_rotation3() {
-    for _ in 0usize .. 10000 {
-        let randmat: Rot3<f64> = na::one();
-        let dir:     Vec3<f64> = random();
-        let ang            = na::normalize(&dir) * (na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
-        let rot            = na::append_rotation(&randmat, &ang);
-
-        assert!(na::approx_eq(&(na::transpose(&rot) * rot), &na::one()));
-    }
-}
-
-#[test]
-fn test_rot3_rotation_between() {
-    let r1: Rot3<f64> = random();
-    let r2: Rot3<f64> = random();
-
-    let delta = na::rotation_between(&r1, &r2);
-
-    assert!(na::approx_eq(&(delta * r1), &r2))
-}
-
-#[test]
-fn test_rot3_angle_between() {
-    let r1: Rot3<f64> = random();
-    let r2: Rot3<f64> = random();
-
-    let delta = na::rotation_between(&r1, &r2);
-    let delta_angle = na::angle_between(&r1, &r2);
-
-    assert!(na::approx_eq(&na::norm(&na::rotation(&delta)), &delta_angle))
-}
-
-#[test]
-fn test_rot2_rotation_between() {
-    let r1: Rot2<f64> = random();
-    let r2: Rot2<f64> = random();
-
-    let delta = na::rotation_between(&r1, &r2);
-
-    assert!(na::approx_eq(&(delta * r1), &r2))
-}
-
-#[test]
-fn test_rot2_angle_between() {
-    let r1: Rot2<f64> = random();
-    let r2: Rot2<f64> = random();
-
-    let delta = na::rotation_between(&r1, &r2);
-    let delta_angle = na::angle_between(&r1, &r2);
-
-    assert!(na::approx_eq(&na::norm(&na::rotation(&delta)), &delta_angle))
-}
 
 #[test]
 fn test_mean_dmat() {
@@ -755,86 +724,6 @@ fn test_row_3() {
     assert!(second_col == Vec3::new(1.0, 4.0, 7.0));
 }
 
-#[test]
-fn test_persp() {
-    let mut p  = Persp3::new(42.0f64, 0.5, 1.5, 10.0);
-    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.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.znear(),  &1.5));
-    assert!(na::approx_eq(&pm.zfar(),   &10.0));
-
-    p.set_fov(0.1);
-    pm.set_fov(0.1);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
-
-    p.set_znear(24.0);
-    pm.set_znear(24.0);
-    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_aspect(23.0);
-    pm.set_aspect(23.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
-
-    assert!(p.aspect() == 23.0);
-    assert!(p.fov()    == 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.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 pm = OrthoMat3::new(42.0f64, 0.5, 1.5, 10.0);
-    assert!(p.to_mat() == pm.to_mat());
-    assert!(p.width()  == 42.0);
-    assert!(p.height() == 0.5);
-    assert!(p.znear()  == 1.5);
-    assert!(p.zfar()   == 10.0);
-    assert!(na::approx_eq(&pm.width(),  &42.0));
-    assert!(na::approx_eq(&pm.height(), &0.5));
-    assert!(na::approx_eq(&pm.znear(),  &1.5));
-    assert!(na::approx_eq(&pm.zfar(),   &10.0));
-
-    p.set_width(0.1);
-    pm.set_width(0.1);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
-
-    p.set_znear(24.0);
-    pm.set_znear(24.0);
-    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);
-    pm.set_height(23.0);
-    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
-
-    assert!(p.height() == 23.0);
-    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.width(),  &0.1));
-    assert!(na::approx_eq(&pm.znear(),  &24.0));
-    assert!(na::approx_eq(&pm.zfar(),   &61.0));
-}
-
 #[test]
 fn test_cholesky_const() {
     

tests/transforms.rs

@@ -0,0 +1,220 @@
+extern crate nalgebra as na;
+extern crate rand;
+
+use rand::random;
+use na::{Pnt3, Vec3, Vec1, Rot2, Rot3, Persp3, PerspMat3, Ortho3, OrthoMat3, Iso2, Iso3, BaseFloat,
+         Sim2, Sim3};
+
+macro_rules! test_transform_inv_transform_impl(
+  ($t: ty, $p: ty) => (
+    for _ in 0usize .. 10000 {
+      let randmat: $t = random();
+      let randvec: $p = random();
+
+      let tvec = randmat.transform(&randvec);
+      let original = randmat.inv_transform(&randvec);
+
+      assert!(na::approx_eq(&randvec, &original));
+    }
+  );
+);
+
+test_transform_inv_transform_impl!(Rot2, Pnt2);
+test_transform_inv_transform_impl!(Rot3, Pnt3);
+test_transform_inv_transform_impl!(Iso2, Pnt2);
+test_transform_inv_transform_impl!(Iso3, Pnt3);
+test_transform_inv_transform_impl!(Sim2, Pnt2);
+test_transform_inv_transform_impl!(Sim3, Pnt3);
+
+#[test]
+fn test_rotation2() {
+    for _ in 0usize .. 10000 {
+        let randmat: na::Rot2<f64> = na::one();
+        let ang    = Vec1::new(na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
+
+        assert!(na::approx_eq(&na::rotation(&na::append_rotation(&randmat, &ang)), &ang));
+    }
+}
+
+#[test]
+fn test_inv_rotation3() {
+    for _ in 0usize .. 10000 {
+        let randmat: Rot3<f64> = na::one();
+        let dir:     Vec3<f64> = random();
+        let ang            = na::normalize(&dir) * (na::abs(&random::<f64>()) % <f64 as BaseFloat>::pi());
+        let rot            = na::append_rotation(&randmat, &ang);
+
+        assert!(na::approx_eq(&(na::transpose(&rot) * rot), &na::one()));
+    }
+}
+
+#[test]
+fn test_rot3_rotation_between() {
+    let r1: Rot3<f64> = random();
+    let r2: Rot3<f64> = random();
+
+    let delta = na::rotation_between(&r1, &r2);
+
+    assert!(na::approx_eq(&(delta * r1), &r2))
+}
+
+#[test]
+fn test_rot3_angle_between() {
+    let r1: Rot3<f64> = random();
+    let r2: Rot3<f64> = random();
+
+    let delta = na::rotation_between(&r1, &r2);
+    let delta_angle = na::angle_between(&r1, &r2);
+
+    assert!(na::approx_eq(&na::norm(&na::rotation(&delta)), &delta_angle))
+}
+
+#[test]
+fn test_rot2_rotation_between() {
+    let r1: Rot2<f64> = random();
+    let r2: Rot2<f64> = random();
+
+    let delta = na::rotation_between(&r1, &r2);
+
+    assert!(na::approx_eq(&(delta * r1), &r2))
+}
+
+#[test]
+fn test_rot2_angle_between() {
+    let r1: Rot2<f64> = random();
+    let r2: Rot2<f64> = random();
+
+    let delta = na::rotation_between(&r1, &r2);
+    let delta_angle = na::angle_between(&r1, &r2);
+
+    assert!(na::approx_eq(&na::norm(&na::rotation(&delta)), &delta_angle))
+}
+
+
+#[test]
+fn test_look_at_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);
+
+        assert_eq!(&(viewmat * eye), &na::orig());
+        assert!(na::approx_eq(&na::normalize(&(viewmat * (target - eye))), &-Vec3::z()));
+    }
+}
+
+#[test]
+fn test_look_at_rot3() {
+    for _ in 0usize .. 10000 {
+        let dir     = random::<Vec3<f64>>();
+        let up      = random::<Vec3<f64>>();
+        let viewmat = Rot3::new_look_at(&dir, &up);
+
+        assert!(na::approx_eq(&na::normalize(&(viewmat * dir)), &-Vec3::z()));
+    }
+}
+
+#[test]
+fn test_observer_frame_iso3() {
+    for _ in 0usize .. 10000 {
+        let eye      = random::<Pnt3<f64>>();
+        let target   = random::<Pnt3<f64>>();
+        let up       = random::<Vec3<f64>>();
+        let observer = Iso3::new_observer_frame(&eye, &target, &up);
+
+        assert_eq!(&(observer * na::orig::<Pnt3<f64>>()), &eye);
+        assert!(na::approx_eq(&(observer * Vec3::z()), &na::normalize(&(target - eye))));
+    }
+}
+
+#[test]
+fn test_observer_frame_rot3() {
+    for _ in 0usize .. 10000 {
+        let dir      = random::<Vec3<f64>>();
+        let up       = random::<Vec3<f64>>();
+        let observer = Rot3::new_observer_frame(&dir, &up);
+
+        assert!(na::approx_eq(&(observer * Vec3::z()), &na::normalize(&dir)));
+    }
+}
+
+#[test]
+fn test_persp() {
+    let mut p  = Persp3::new(42.0f64, 0.5, 1.5, 10.0);
+    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.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.znear(),  &1.5));
+    assert!(na::approx_eq(&pm.zfar(),   &10.0));
+
+    p.set_fov(0.1);
+    pm.set_fov(0.1);
+    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+
+    p.set_znear(24.0);
+    pm.set_znear(24.0);
+    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_aspect(23.0);
+    pm.set_aspect(23.0);
+    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+
+    assert!(p.aspect() == 23.0);
+    assert!(p.fov()    == 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.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 pm = OrthoMat3::new(42.0f64, 0.5, 1.5, 10.0);
+    assert!(p.to_mat() == pm.to_mat());
+    assert!(p.width()  == 42.0);
+    assert!(p.height() == 0.5);
+    assert!(p.znear()  == 1.5);
+    assert!(p.zfar()   == 10.0);
+    assert!(na::approx_eq(&pm.width(),  &42.0));
+    assert!(na::approx_eq(&pm.height(), &0.5));
+    assert!(na::approx_eq(&pm.znear(),  &1.5));
+    assert!(na::approx_eq(&pm.zfar(),   &10.0));
+
+    p.set_width(0.1);
+    pm.set_width(0.1);
+    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+
+    p.set_znear(24.0);
+    pm.set_znear(24.0);
+    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);
+    pm.set_height(23.0);
+    assert!(na::approx_eq(&p.to_mat(), pm.as_mat()));
+
+    assert!(p.height() == 23.0);
+    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.width(),  &0.1));
+    assert!(na::approx_eq(&pm.znear(),  &24.0));
+    assert!(na::approx_eq(&pm.zfar(),   &61.0));
+}

tests/vec.rs

@@ -1,10 +1,16 @@
 extern crate rand;
+#[cfg(feature="generic_sizes")]
 extern crate typenum;
 extern crate nalgebra as na;
 
 use rand::random;
+use na::{Vec1, Vec2, Vec3, Vec4, Vec5, Vec6, Mat3, Rot2, Rot3, Iterable, IterableMut};
+
+#[cfg(feature="generic_sizes")]
 use typenum::U10;
-use na::{VecN, Vec1, Vec2, Vec3, Vec4, Vec5, Vec6, Mat3, Rot2, Rot3, Iterable, IterableMut};
+#[cfg(feature="generic_sizes")]
+use na::VecN;
+
 
 macro_rules! test_iterator_impl(
     ($t: ty, $n: ty) => (
@@ -295,6 +301,7 @@ fn test_outer_vec3() {
             12.0, 15.0, 18.0));
 }
 
+#[cfg(feature="generic_sizes")]
 #[test]
 fn test_vecn10_add_mul() {
     for _ in 0usize .. 10000 {