def jarvis(points: List) -> List[Point]: """ In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. Complexity: O(nh) :return: the set of points which span the convex hull """ # Take the leftmost point as the starting point of the hull leftmost_point = last_point = min(points, key=lambda point: point.x) current_point = max(points, key=lambda x: get_polar_angle(last_point, x)) result = [leftmost_point] # Keep tracking the convex hull clockwise while current_point != leftmost_point: result.append(current_point) # Choose the point which result in the largest inner angle new_point = max( points, key=lambda x: get_internal_angle(last_point, current_point, x) if x != current_point else 0) last_point, current_point = current_point, new_point return result
def jarvis(points: List) -> List[Point]: """ In computational geometry, the gift wrapping algorithm is an algorithm for computing the convex hull of a given set of points. Complexity: O(nh) :return: the set of points which span the convex hull """ # Take the leftmost point as the starting point of the hull leftmost_point = last_point = min(points, key=lambda point: point.x) current_point = max(points, key=lambda x: get_polar_angle(last_point, x)) result = [leftmost_point] # Keep tracking the convex hull clockwise while current_point != leftmost_point: result.append(current_point) # Choose the point which result in the largest inner angle new_point = max(points, key=lambda x: get_internal_angle(last_point, current_point, x) if x != current_point else 0) last_point, current_point = current_point, new_point return result
def graham(points: List) -> List: """ Graham's scan is a method of finding the convex hull of a finite set of points in the plane with time complexity O(n log n). It is named after Ronald Graham, who published the original algorithm in 1972.The algorithm finds all vertices of the convex hull ordered along its boundary. """ # Find the bottom left point and remove it from the set bottom_left_point = min(points, key=lambda x: (x[1], x[0])) # Put the points on a min heap by polar angle polar_points = [(get_polar_angle(bottom_left_point, x), x) for x in points if x != bottom_left_point] point_heap = BinomialHeap(polar_points) # Push the first 3 elements on a stack stack = Stack() stack.push(bottom_left_point) stack.push(point_heap.pop()[1]) stack.push(point_heap.pop()[1]) for _ in range(len(point_heap)): _, p3 = point_heap.pop() while is_counterclockwise(stack.peek(1), stack.peek(), p3) < 0: stack.pop() stack.push(p3) return stack.to_array()