Beyond A level · 2 exercises

Python geometry

Points as (x, y) pairs. The cross product of two vectors says which way they turn: positive left, negative right, zero in line.

The shoelace formula gives a polygon's area from its corners in order.

pts = [(0, 0), (4, 0), (4, 3)]
area = 0
for i in range(len(pts)):
    x1, y1 = pts[i]
    x2, y2 = pts[(i + 1) % len(pts)]
    area += x1 * y2 - x2 * y1
print(abs(area) / 2)  # 6.0

Watch for: Decimals add up small errors: keep whole numbers as long as you can and compare with care.

Exercises

Area of a polygonCompute the area of a simple polygon from its corners (in order around the edge)Expert
Fence around the treesBuild the smallest convex fence around all the trees (the convex hull).Expert

Start with “Area of a polygon”