I am attempting to, given two dimensions (width and height) which represent a quadrilateral, partition that quad in to N
parts where each part is as proportionally similar to the other as possible.
For example, imagine a sheet of paper. It consists of 4 points A
, B
, C
, D
. Now consider that the sheet of paper has the dimensions 800 x 800 and the points:
A: {0, 0}
B: {0, 800}
C: {800, 800}
D: {800, 0}
Plotting that will give you 4 points, or 3 lines with a line plot. Add an additional point E: {0, 0}
to close the cell.
To my surprise, I've managed to do this programatically, for N
number of cells.
How can I improve this code to make it more readable, pythonic, and as performant as possible?
from math import floor, ceil
import matplotlib.pyplot as plt
class QuadPartitioner:
@staticmethod
def get_factors(number):
'''
Takes a number and returns a list of factors
:param number: The number for which to find the factors
:return: a list of factors for the given number
'''
facts = []
for i in range(1, number + 1):
if number % i == 0:
facts.append(i)
return facts
@staticmethod
def get_partitions(N, quad_width, quad_height):
'''
Given a width and height, partition the area into N parts
:param N: The number of partitions to generate
:param quad_width: The width of the quadrilateral
:param quad_height: The height of the quadrilateral
:return: a list of a list of cells where each cell is defined as a list of 5 verticies
'''
# We reverse only because my brain feels more comfortable looking at a grid in this way
factors = list(reversed(QuadPartitioner.get_factors(N)))
# We need to find the middle of the factors so that we get cells
# with as close to equal width and heights as possible
factor_count = len(factors)
# If even number of factors, we can partition both horizontally and vertically.
# If not even, we can only partition on the X axis
if factor_count % 2 == 0:
split = int(factor_count/2)
factors = factors[split-1:split+1]
else:
factors = []
split = ceil(factor_count/2)
factors.append(split)
factors.append(split)
# The width and height of an individual cell
cell_width = quad_width / factors[0]
cell_height = quad_height / factors[1]
number_of_cells_in_a_row = factors[0]
rows = factors[1]
row_of_cells = []
# We build just a single row of cells
# then for each additional row, we just duplicate this row and offset the cells
for n in range(0, number_of_cells_in_a_row):
cell_points = []
for i in range(0, 5):
cell_y = 0
cell_x = n * cell_width
if i == 2 or i == 3:
cell_x = n * cell_width + cell_width
if i == 1 or i == 2:
cell_y = cell_height
cell_points.append((cell_x, cell_y))
row_of_cells.append(cell_points)
rows_of_cells = [row_of_cells]
# With that 1 row of cells constructed, we can simply duplicate it and offset it
# by the height of a cell multiplied by the row number
for index in range(1, rows):
new_row_of_cells = [[ (point[0],point[1]+cell_height*index) for point in square] for square in row_of_cells]
rows_of_cells.append(new_row_of_cells)
return rows_of_cells
if __name__ == "__main__":
QP = QuadPartitioner()
partitions = QP.get_partitions(56, 1980,1080)
for row_of_cells in partitions:
for cell in row_of_cells:
x, y = zip(*cell)
plt.plot(x, y, marker='o')
plt.show()
Output: