Polygons

python_geometry/polygon_utilities.py

@@ -0,0 +1,49 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+"""docstring"""
+import numpy as np
+
+
+def area_of_polygon_2D(polygon, *args):
+    """
+    Computes the signed area of an arbitrary convex polygon as described in
+    http://paulbourke.net/geometry/polygonmesh/.
+    The signed area is positive for counter clockwise ordering otherwise
+    negative.
+
+    Parameters
+    ----------
+     polygon:
+        np.ndarray, list
+            The polygon as a list of consecutive 2D points.
+
+    Returns
+    -------
+    float
+        Area of the polygon. The area is negativ for clockwise point ordering
+    """
+
+    if args:
+        poly = [polygon]
+
+        for pt in args:
+            if pt.shape != (2,):
+                for sp in pt:
+                    poly.append(sp)
+            else:
+                poly.append(pt)
+        polygon = np.array(poly)
+
+    area = 0.
+    for i in range(len(polygon) - 1):
+        area += (polygon[i][0] * polygon[i + 1][1]
+                 - polygon[i + 1][0] * polygon[i][1])
+
+    # close the loop with the last crossproduct
+    area += (polygon[-1][0] * polygon[0][1] - polygon[-1][1] * polygon[0][0])
+
+    area /= 2.
+    if area == 0:
+        raise ValueError('Calculated Area is 0!')
+    return area

tests/test_polygon_utilities.py

@@ -0,0 +1,38 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+
+"""docstring"""
+from unittest import TestCase
+from numpy.testing import assert_equal
+from numpy import array
+
+from python_geometry.polygon_utilities import area_of_polygon_2D
+
+
+class TestArea_of_polygon2D(TestCase):
+    def test_rectangles(self):
+        ## square
+        quad1 = ([0, 0], [1, 0], [1, 1], [0, 1])
+        quad2 = ([0, 0], [0, 1], [1, 1], [1, 0])
+        quad1_np = array([[0, 0], [1, 0], [1, 1], [0, 1]])
+        quad2_np = array([[0, 0], [0, 1], [1, 1], [1, 0]])
+
+        assert_equal(area_of_polygon_2D(quad1), 1)
+        assert_equal(area_of_polygon_2D(quad2), -1)
+        assert_equal(area_of_polygon_2D(quad1_np), 1)
+        assert_equal(area_of_polygon_2D(quad2_np), -1)
+
+
+        # rectangles
+        quad3 = ([0, 0], [5, 0], [5, 1], [0, 1])
+        assert_equal(area_of_polygon_2D(quad3), 5)
+
+    def test_triangles(self):
+        tria1 = ([0, 0], [1, 0], [1, 1])
+        tria1_np = array([[0, 0], [1, 0], [1, 1]])
+        tria2 = ([0, 0], [1, 1], [1, 0])
+        tria3 = ([0, 0], [5, 10], [2, 5])
+        assert_equal(area_of_polygon_2D(tria1), 0.5)
+        assert_equal(area_of_polygon_2D(tria1_np), 0.5)
+        assert_equal(area_of_polygon_2D(tria2), -0.5)
+        assert_equal(area_of_polygon_2D(tria3), 2.5)