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zxAdufNxMVt?luZqlD9m;uqRkkYTM)aYnzoD&@$vB) zXVCRlenLV*X-FheZ7P$B>QVEaVC5ruNu1Kr(UC$_YAZQ($Hcr%|G7kFc1){|;nhd8 z=LO^Nc)a~Vn-zj%%3Xk$t1byYrvy-d7Zyxli_J$70Rg6vyLZ1$PTJJ>e}6Qj&=DLJ z9-hQH-__N1oA6~)I7;)WMT)rLzQbS%+~5DKA;ZUmw6wH!3BzaI4V9IZf#Kl-l78nl zU2V^b<yu8f*i=U4#KHv;D&q7B= x and point.x <= x+w and point.y>=y and point.y<=y+h: + pts.append(point) + return pts + + +def find_children(node): + if not node.children: + return [node] + else: + children = [] + for child in node.children: + children += (find_children(child)) + return children +``` +The QTree class is used to tie together all the data associated with creating a quadtree. +This class is also used to generate dummy data and graph it using matplotlib. + +```python +import random +import matplotlib.pyplot as plt # plotting libraries +import matplotlib.patches as patches + +class QTree(): + def __init__(self, k, n): + self.threshold = k + self.points = [Point(random.uniform(0, 10), random.uniform(0, 10)) for x in range(n)] + self.root = Node(0, 0, 10, 10, self.points) + + def add_point(self, x, y): + self.points.append(Point(x, y)) + + def get_points(self): + return self.points + + def subdivide(self): + recursive_subdivide(self.root, self.threshold) + + def graph(self): + fig = plt.figure(figsize=(12, 8)) + plt.title("Quadtree") + c = find_children(self.root) + print("Number of segments: %d" %len(c)) + areas = set() + for el in c: + areas.add(el.width*el.height) + print("Minimum segment area: %.3f units" %min(areas)) + for n in c: + plt.gcf().gca().add_patch(patches.Rectangle((n.x0, n.y0), n.width, n.height, fill=False)) + x = [point.x for point in self.points] + y = [point.y for point in self.points] + plt.plot(x, y, 'ro') # plots the points as red dots + plt.show() + return +``` + +Creating a quadtree where each cell can only contain at the most section will produce a lot of cells. + +![png](media/quad-tree/output_4_1.png) + +If we change the hyperparameter to split until there is at most two objects per cell, we 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