diff --git a/map.py b/map.py
index b8ce5cc..4adee05 100644
--- a/map.py
+++ b/map.py
@@ -15,13 +15,17 @@ class Triangle:
         self.v1 = v1
         self.v2 = v2
         self.v3 = v3
+        # Sort triangle vertices so that so that the normal points "outward"
+        if np.dot(self.v1, np.cross(self.v2 - self.v1, self.v3 - self.v1)) < 0:
+            self.v3, self.v2 = self.v2, self.v3
         # Edges of the origin vertex and their L2 norms
-        self.e1 = v2 - v1
-        self.e2 = v3 - v1
+        self.e1 = self.v2 - self.v1
+        self.e2 = self.v3 - self.v1
         self.e1n = np.linalg.norm(self.e1)
         self.e2n = np.linalg.norm(self.e2)
         # Normal vector of the triangle's plane
         self.n = np.cross(self.e1 / self.e1n, self.e2 / self.e2n)
+        self.n = self.n / np.linalg.norm(self.n)
         # The vertex coordinates in plane coordinates
         self.v1p = self.plane_coords(self.v1)
         self.v2p = self.plane_coords(self.v2)