Fix Matrix2::look_at, add look_at_stable

Fix bug in look_at

Use the up vector to determine turn direction

Add look_at_stable

Matrix2::look_at calls look_at_stable

src/matrix.rs

@@ -99,11 +99,23 @@ impl<S> Matrix2<S> {
 }
 
 impl<S: BaseFloat> Matrix2<S> {
-    /// Create a transformation matrix that will cause a vector to point at
-    /// `dir`, using `up` for orientation.
+    /// Create a transformation matrix that will cause `unit_x()` to point at
+    /// `dir`. `unit_y()` will be perpendicular to `dir`, and the closest to `up`.
     pub fn look_at(dir: Vector2<S>, up: Vector2<S>) -> Matrix2<S> {
-        //TODO: verify look_at 2D
-        Matrix2::from_cols(up, dir).transpose()
+        Matrix2::look_at_stable(dir, up.x * dir.y >= up.y * dir.x)
+    }
+
+    /// Crate a transformation that will cause `unit_x()` to point at
+    /// `dir`. This is similar to `look_at`, but does not take an `up` vector.
+    /// This will not cause `unit_y()` to flip when `dir` crosses over the `up` vector.
+    pub fn look_at_stable(dir: Vector2<S>, flip: bool) -> Matrix2<S> {
+        let basis1 = dir.normalize();
+        let basis2 = if flip {
+            Vector2::new(basis1.y, -basis1.x)
+        } else {
+            Vector2::new(-basis1.y, basis1.x)
+        };
+        Matrix2::from_cols(basis1, basis2)
     }
 
     #[inline]

src/rotation.rs

@@ -146,6 +146,14 @@ pub struct Basis2<S> {
     mat: Matrix2<S>,
 }
 
+impl<S: BaseFloat> Basis2<S> {
+    pub fn look_at_stable(dir: Vector2<S>, flip: bool) -> Basis2<S> {
+        Basis2 {
+            mat: Matrix2::look_at_stable(dir, flip),
+        }
+    }
+}
+
 impl<S: BaseFloat> AsRef<Matrix2<S>> for Basis2<S> {
     #[inline]
     fn as_ref(&self) -> &Matrix2<S> {

tests/matrix.rs

@@ -175,6 +175,27 @@ pub mod matrix2 {
         let rot3: Matrix2<f64> = Matrix2::from_angle(Rad(f64::consts::PI));
         assert_ulps_eq!(rot3 * Vector2::new(1.0, 1.0), &Vector2::new(-1.0, -1.0));
     }
+
+    #[test]
+    fn test_look_at() {
+        // rot should rotate unit_x() to look at the input vector
+        let rot = Matrix2::look_at(V, Vector2::unit_y());
+        assert_eq!(rot * Vector2::unit_x(),
+                   V.normalize());
+        let new_up = Vector2::new(-V.y, V.x).normalize();
+        assert_eq!(rot * Vector2::unit_y(),
+                   new_up);
+
+        let rot_down = Matrix2::look_at(V, -1.0 * Vector2::unit_y());
+        assert_eq!(rot_down * Vector2::unit_x(),
+                   V.normalize());
+        assert_eq!(rot_down * Vector2::unit_y(),
+                   -1.0 * new_up);
+
+        let rot2 = Matrix2::look_at(-V, Vector2::unit_y());
+        assert_eq!(rot2 * Vector2::unit_x(),
+                   (-V).normalize());
+    }
 }
 
 pub mod matrix3 {