Align concave polygon normals with boundary winding

AUTHORS.md

@@ -46,3 +46,4 @@
 - Eric Gozzi <<eric.gozzi@arch.ethz.ch>> [@ericgozzi](https://github.com/ericgozzi)
 - Daniel Nunes Locatelli <<nuneslocatelli@arch.ethz.ch>> [@daniel-locatelli](https://github.com/daniel-locatelli)
 - Mengxi He <<m.he@lekolabs.com>> [@mengxihex](https://github.com/mengxihex)
+- Arian Moeini <<arianmoeini11@gmail.com>> [@ArianMoeini](https://github.com/ArianMoeini)

src/compas/geometry/polygon.py

@@ -16,7 +16,7 @@
 from compas.geometry import earclip_polygon
 from compas.geometry import is_coplanar
 from compas.geometry import is_polygon_convex
-from compas.geometry import normal_triangle
+from compas.geometry import normal_polygon
 from compas.geometry import transform_points
 from compas.itertools import pairwise
 from compas.tolerance import TOL
@@ -180,15 +180,10 @@ def normal(self):
 
     @property
     def plane(self):
-        # by just taking the bestfit plane,
-        # the normal might not be aligned with the winding direciton of the polygon
-        # this can be solved by comparing the plane normal with the normal of one of the triangles of the polygon
-        # for convex polygons this is always correct
-        # in the case of concave polygons it may not be
-        # to be entirely correct, the check should be done with one of the polygon ears after earclipping
-        # however, this is costly
-        # and even then it is only correct if we assume th polygon is plat enough to have a consistent direction
-        normal = normal_triangle([self.centroid] + self.points[:2])
+        # Align the best-fit plane with the winding of the full boundary.
+        # A triangle formed from the centroid and first edge can point the
+        # wrong way when that edge lies on a concave part of the polygon.
+        normal = normal_polygon(self.points)
         plane = Plane.from_points(self.points)
         if plane.normal.dot(normal) < 0:
             plane.normal.flip()

tests/compas/geometry/test_polygon.py

@@ -99,6 +99,15 @@ def test_polygon_normal_direction():
     assert polygon.normal.dot([0, 0, 1]) < 0
 
 
+def test_concave_polygon_normal_follows_winding_for_any_starting_vertex():
+    points = [[3, 1, 0], [1, 1, 0], [1, 4, 0], [0, 4, 0], [0, 0, 0], [4, 0, 0], [4, 4, 0], [3, 4, 0]]
+
+    for index in range(len(points)):
+        rotated = points[index:] + points[:index]
+        assert Polygon(rotated).normal.dot([0, 0, 1]) > 0
+        assert Polygon(list(reversed(rotated))).normal.dot([0, 0, 1]) < 0
+
+
 @pytest.mark.parametrize(
     "points",
     [