From ea9bbbeda7494ba67b1d8d07910599a6f9ffca11 Mon Sep 17 00:00:00 2001
From: "Navid C. Constantinou" <navidcy@users.noreply.github.com>
Date: Tue, 5 Sep 2023 15:16:13 +1000
Subject: [PATCH] simplify angle_between

---
 regional_mom6/regional_mom6.py | 25 +++++++------------------
 tests/test_grid_generation.py  |  7 +++++++
 2 files changed, 14 insertions(+), 18 deletions(-)

diff --git a/regional_mom6/regional_mom6.py b/regional_mom6/regional_mom6.py
index 0818c14a..f5719a24 100644
--- a/regional_mom6/regional_mom6.py
+++ b/regional_mom6/regional_mom6.py
@@ -261,7 +261,6 @@ def dz(npoints, ratio, target_depth, min_dz=0.0001, tolerance=1):
 
     Returns:
         numpy.array: An array containing the thickness profile.
-
     """
 
     profile = min_dz + 0.5 * (np.abs(ratio) * min_dz - min_dz) * (
@@ -279,24 +278,14 @@ def dz(npoints, ratio, target_depth, min_dz=0.0001, tolerance=1):
     return dz(npoints, ratio, target_depth, min_dz * err_ratio)
 
 
-# Borrowed from grid tools (GFDL)
 def angle_between(v1, v2, v3):
-    """Returns angle v2-v1-v3 i.e betweeen v1-v2 and v1-v3."""
-
-    # vector product between v1 and v2
-    px = v1[1] * v2[2] - v1[2] * v2[1]
-    py = v1[2] * v2[0] - v1[0] * v2[2]
-    pz = v1[0] * v2[1] - v1[1] * v2[0]
-    # vector product between v1 and v3
-    qx = v1[1] * v3[2] - v1[2] * v3[1]
-    qy = v1[2] * v3[0] - v1[0] * v3[2]
-    qz = v1[0] * v3[1] - v1[1] * v3[0]
-
-    ddd = (px * px + py * py + pz * pz) * (qx * qx + qy * qy + qz * qz)
-    ddd = (px * qx + py * qy + pz * qz) / np.sqrt(ddd)
-    angle = np.arccos(ddd)
-
-    return angle
+    """Returns angle v2-v1-v3 that is between the vectors v1-v2 and v1-v3."""
+
+    v1xv2 = np.cross(v1, v2)
+    v1xv3 = np.cross(v1, v3)
+    cosangle = np.dot(v1xv2, v1xv3) / np.sqrt(np.dot(v1xv2, v1xv2) * np.dot(v1xv3, v1xv3))
+
+    return np.arccos(cosangle)
 
 
 # Borrowed from grid tools (GFDL)
diff --git a/tests/test_grid_generation.py b/tests/test_grid_generation.py
index d39bed9e..b0b63a9e 100644
--- a/tests/test_grid_generation.py
+++ b/tests/test_grid_generation.py
@@ -5,6 +5,13 @@
 from regional_mom6 import rectangular_hgrid
 import xarray as xr
 
+def random_unit_vector():
+    """Return a random unit vector on the unit sphere."""
+    z = 2 * np.random.rand(1)[0] - 1; z
+    θ = 2 * np.pi * np.random.rand(1)[0]
+    return [np.sqrt(1 - z**2) * np.cos(θ), np.sqrt(1 - z**2) * np.sin(θ), z]
+
+
 
 @pytest.mark.parametrize(
     ("v1", "v2", "v3", "true_angle"),