Geometry - shoelace formula (#12118)

* Compute the area of a polygon.

* updating DIRECTORY.md

* updating DIRECTORY.md

---------

Co-authored-by: simin75simin <simin75simin@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>
Co-authored-by: cclauss <cclauss@users.noreply.github.com>

Author: simin75simin

DIRECTORY.md

@@ -549,6 +549,7 @@
   * [Ramer Douglas Peucker](geometry/ramer_douglas_peucker.py)
   * [Rotating Calipers](geometry/rotating_calipers.py)
   * [Segment Intersection](geometry/segment_intersection.py)
+  * [Shoelace](geometry/shoelace.py)
   * Tests
     * [Test Graham Scan](geometry/tests/test_graham_scan.py)
     * [Test Jarvis March](geometry/tests/test_jarvis_march.py)
@@ -817,6 +818,7 @@
   * [Monte Carlo](maths/monte_carlo.py)
   * [Monte Carlo Dice](maths/monte_carlo_dice.py)
   * [Ncr Combinations](maths/ncr_combinations.py)
+  * [Next Prime Number](maths/next_prime_number.py)
   * [Number Of Digits](maths/number_of_digits.py)
   * Numerical Analysis
     * [Adams Bashforth](maths/numerical_analysis/adams_bashforth.py)

geometry/shoelace.py

@@ -0,0 +1,30 @@
+def area_of_polygon(xs: list[float], ys: list[float]) -> float:
+    """
+    Compute the area of a polygon. The polygon has to be planar and simple
+    (not self-intersecting). The vertices have to be ordered in the
+    counter-clockwise direction.
+    https://en.wikipedia.org/wiki/Shoelace_formula
+
+    Args:
+        xs: list of x coordinates of the polygon vertices in counter-clockwise order
+        ys: list of y coordinates of the polygon vertices in counter-clockwise order
+    Returns:
+        area of the polygon
+
+    >>> from math import isclose
+    >>> xs = [1, 3, 7, 4, 8]
+    >>> ys = [6, 1, 2, 4, 5]
+    >>> isclose(area_of_polygon(xs, ys), 16.5)
+    True
+    """
+
+    return 0.5 * sum(
+        (ys[i] + ys[(i + 1) % len(ys)]) * (xs[i] - xs[(i + 1) % len(xs)])
+        for i in range(len(xs))
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()