Add utility function to create change-of-basis matrices

src/algebra_utils.rs

@@ -0,0 +1,67 @@
+use nalgebra::{Matrix3, RealField, Vector3};
+
+pub fn try_change_of_basis_matrix<T: RealField>(
+    x: &Vector3<T>,
+    y: &Vector3<T>,
+    z: &Vector3<T>,
+) -> Option<Matrix3<T>> {
+    Some(Matrix3::from_rows(&[x.transpose(), y.transpose(), z.transpose()]))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[cfg(test)]
+    mod change_of_basis_matrix {
+        use super::*;
+        use quickcheck_macros::quickcheck;
+
+        #[test]
+        fn produces_isentity_when_passed_axes() {
+            let target: Matrix3<f32> = try_change_of_basis_matrix(
+                &Vector3::x_axis(),
+                &Vector3::y_axis(),
+                &Vector3::z_axis(),
+            )
+            .unwrap();
+            assert!(target == Matrix3::identity())
+        }
+
+        #[quickcheck]
+        fn swap_xy_does_not_change_z(v: Vector3<f32>) {
+            let target: Matrix3<f32> = try_change_of_basis_matrix(
+                &Vector3::y_axis(),
+                &Vector3::x_axis(),
+                &Vector3::z_axis(),
+            )
+            .unwrap();
+            let v2 = target * v;
+            assert!(v2.z == v.z)
+        }
+
+        #[quickcheck]
+        fn swap_xy_copies_y_to_x(v: Vector3<f32>) {
+            let target: Matrix3<f32> = try_change_of_basis_matrix(
+                &Vector3::y_axis(),
+                &Vector3::x_axis(),
+                &Vector3::z_axis(),
+            )
+            .unwrap();
+            let v2 = target * v;
+            assert!(v2.x == v.y)
+        }
+
+        #[quickcheck]
+        fn swap_xy_copies_x_to_y(v: Vector3<f32>) {
+            let target: Matrix3<f32> = try_change_of_basis_matrix(
+                &Vector3::y_axis(),
+                &Vector3::x_axis(),
+                &Vector3::z_axis(),
+            )
+            .unwrap();
+            let v2 = target * v;
+            assert!(v2.y == v.x)
+        }
+    }
+}