## Python: Circle Packing

**Circle Packing Project **

** Subject: Draw, circles, Turtle **

**Definition**: In geometry, circle packing is the study of the arrangement of circles on a given surface such that no overlapping occurs and so that all circles touch one another. *Wikipedia*

So, we have a canvas size (w,h) and we want to write a code to draw X number of circles in this area without any overlapping or intersecting between circles. We will write some functions to do this task, thous functions are:

1. __c_draw (x1,y1,di)__: This function will take three arguments x1,y1 for circle position and di as circle diameter.

2. __draw_fram()__: This function will draw the frame on the screen, we set the frame_w and frame_h as variables in the setup area in the code.

3. __c_generator (max_di)__: c_generator is the circles generating function, and takes one argument max_di presenting the maximum circles diameter. To generate a circle we will generate three random numbers for x position, y position and for circle diameter (max_di is the upper limit),also with each generating a while loop will make sure that the circle is inside the frame, if not regenerate another one.

4. __can_we_draw_it (q1,di1)__: This is very important, to make sure that the circle is not overlapping with any other we need to use a function call (hypot) from math library hypot return the distance between two points, then if the distance between two circles is less than the total of there diameters then the two circles are not overlaps.

So, lets start coding …

First: the import and setup variables:

from turtle import * import random import math # Create a turtle named t: t =Turtle() t.speed(0) t.hideturtle() t.setheading(0) t.pensize(0.5) t.penup() # frame size frame_w = 500 frame_h = 600 di_list = [] # To hold the circles x,y and diameters

Now, Drawing the frame function:

def draw_fram () :t.penup()

t.setheading(0)

t.goto(-frame_w/2,frame_h/2)

t.pendown()

t.forward(frame_w)

t.right(90)

t.forward(frame_h)

t.right(90)

t.forward(frame_w)

t.right(90)

t.forward(frame_h)

t.penup()

t.goto(0,0)

Now, Draw circle function:

def c_draw (x1,y1,di):t.goto(x1,y1)

t.setheading(-90)

t.pendown()

t.circle(di)

t.penup()

This is Circles generator, we randomly select x,y and diameter then checks if it is in or out the canvas.

def c_generator (max_di):falls_out_frame = True

while falls_out_frame :

x1 = random.randint(-(frame_w/2),(frame_w/2))

y1 = random.randint(-(frame_h/2),(frame_h/2))

di = random.randint(3,max_di)

# if true circle is in canvas

if (x1-di > ((frame_w/2)*-1)) and (x1-di < ((frame_w/2)-(di*2))) :

if (y1 ((frame_h/2)-(di))*-1) :

falls_out_frame = False

di_list.append([x1-di,y1,di])

With each new circle we need to check the distances and the diameter between new circle and all circles we have in the list, if there is an overlap then we delete the new circle data (using di_list.pop()) and generate a new circle. So to get the distances and sum of diameters we use this code ..

# get circles distance cs_dis = math.hypot(((last_cx + last_cdi) - (c_n_list_x + c_n_list_di)) , (last_cy - c_n_list_y)) di_total = last_cdi + c_n_list_di

To speed up the generation of right size of circles I use a method of counting the trying times of wrong sizes, that’s mean if the circles is not fit, and we pop it’s details from the circles list we count pops, if we reach certain number then we reduce the upper limits of random diameter of the new circles we generate. Say we start with max_di = 200, then if we pop for a number that divide by 30 (pop%30) then we reduce the max_di with (-1) and if we reach max_di less then 10 then max_di = 60. and we keep doing this until we draw 700 circles.

# if di_list pops x time then we reduce the randomization upper limits if (total_pop % 30) == 0: max_di = max_di - 1 if max_di < 10 : max_di = 60

Here are some output circles packing ..

With current output we reach the goal we are looking for, although there is some empty spaces, but if we increase the number of circles then there will be more time finding those area with random (x,y,di) generator, I am thinking in another version of this code that’s will cover:

1. Coloring the circles based on the diameter size.

2. A method to fill the spaces.

## Python: Numpay – P3

**Learning : Python Numpy – P3 **

** Subject: numpy array and some basic commands **

The numpy lessons and basic commands will take us to plotting the data and presenting the numbers using the numpy and plot packages, but first we need to do more practices on arrays and functions in the numpy.

To get a row or a column from the array we use:

# Generate a 5x5 random array: ar = np.random.randint(10,60, size=(5,5)) print('\n A random generated array 5x5 is: \n',ar) # get the rows from 1 to 3 (rows 1 and 2): print('\n The rows from 1 to 3 is: \n',ar[1:3]) # get row 1 and row 3: print('\n The row 1 and row 2 is: \n',ar[1],ar[3]) # get the column 1 and column 3: print('\n The column 1 and column 3: \n',ar[:,[1,3]]) [Output]: A random generated array 5x5 is: [[59 43 46 44 39] [16 15 14 19 22] [59 16 33 59 19] [21 15 51 41 28] [48 46 58 33 19]] The rows from 1 to 3 is: [[16 15 14 19 22] [59 16 33 59 19]] The row 1 and row 2 is: [16 15 14 19 22] [21 15 51 41 28] The column 1 and column 3: [[43 44] [15 19] [16 59] [15 41] [46 33]]

To change a value in the array we give the position and new value as:

# Generate a 5x5 random array: ar = np.random.randint(10,60, size=(5,5)) print('\n A random generated array 5x5 is: \n',ar) print('\n Value in position (1,1):',ar[1][1]) # Re-set the value in position (1,1) to 55 ar[1][1] = 55 print('\n The array ar\n',ar) code [Output]: A random generated array 5x5 is: [[39 53 34 59 30] [33 10 42 20 36] [10 37 20 35 28] [26 18 14 41 24] [48 22 19 18 44]] Value in position (1,1): 10 The array ar [[39 53 34 59 30] [33 55 42 20 36] [10 37 20 35 28] [26 18 14 41 24] [48 22 19 18 44]]

If we have a one dimension array with values, and we want to create another array with values after applying a certain conditions, such as all values grater than 7.

# Create 1D array of range 10 ar = np.arange(10) print(ar) # ar_g7 is a sub array from ar of values grater then 7 ar_g7= np.where(ar >7) print('ar_g7:'ar_g7) [Output]: [0 1 2 3 4 5 6 7 8 9] ar_g7:(array([8, 9]),)

If we want to pass a 3×3 array and then we want the values to be changed to (1) if it is grater than 7 and to be (0) if it is less than 7.

# Generate a 3x3 array of random numbers. ar2 = np.random.randint(1,10, size =(3,3)) print(ar2) # Change any value grater than 7 to 1 and if less than 7 to 0. ar_g7= np.where(ar2 >7, 1 ,0) print('ar_g7:',ar_g7) [Output]: [[6 4 2] [8 5 1] [5 2 8]] ar_g7: [[0 0 0] [1 0 0] [0 0 1]]

Also we can say if, the value in the array is equal to 6 or 8 then change it to -1.

# Generate array of 3x3 ar2 = np.random.randint(1,10, size =(3,3)) print(ar2) # If the = 6 or 8 change it to (-1) ar_get_6_8_value= np.where((ar2 == 6) |( ar2==8), -1 ,ar2) print('ar_get_6_8_value:',ar_get_6_8_value) [Output]: [[3 4 8] [1 9 3] [5 6 6]] ar_get_6_8_value: [[ 3 4 -1] [ 1 9 3] [ 5 -1 -1]]

We can get the index location of the certain conditions values, and then we can print it out.

# # Generate array of 3x3 ar_less_6= np.where((ar2 < 6) ) print('ar_less_6 locations:',ar_less_6) # print out the values on those locations. print('ar_less_6 values: ',ar2[ar_less_6]) [Output]: [[6 1 9] [1 8 6] [6 9 2]] ar_less_6 locations: (array([0, 1, 2]), array([1, 0, 2])) ar_less_6 values :[1 1 2]

**:: numpy Sessions ::**

Sessions 1 | Sessions 2 | Sessions 3 | Sessions 4 |

## Python: Numpay – P1

**Learning : Python Numpy – P1 **

** Subject: Numpay and some basic commands **

In coming several posts I will talk about the numpay library and how to use some of its functions. So first what is numpy? **Definition:** NumPy is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. Also known as powerful package for scientific computing and data manipulation in python. As any library or package in python we need to install it on our device (we will not go through this process)

Basic commands in numpy: First of all we need to import it in our code. so we will use

import numpy as np

To create a 1 dimensional array we can use verey easy way as:

# create an array using numpy array function. my_array = np.array([1, 2, 3,4,5])

Later we will create a random array of numbers in a range.

Now, to get the length of the array we can use **len** command as

len(my_array) Output: 5

To get the sum of all elements in the array we use..

np.sum(my_array)

And to get the maximum and minimum numbers in the array we use ..

# Get the maximum and minimum numbers in the array my_array = np.array([1, 2, 3,4,5]) np.max(my_array) [Output]: 5 np.min(my_array) [Output]: 1

Some time we may need to create an array with certain Number of elements only one’s, to do this we can use this commands:

#create array of 1s (of length 5) np.ones(5) Output: [ 1., 1., 1., 1., 1.]

The default data type will be float, if we want to change it we need to pass the the ‘dtype’ to the command like this :

#create array of 1s (of length 5) as integer: np.ones(5, dtype = np.int) Output: [ 1, 1, 1, 1, 1]

Code output:

So far we work on a one dimensional array, in the next post we will cover some commands that will help us in the arrays with multiple dimensions.

**:: numpy Commands::**

Command |
comment |

my_array = np.array([1,2,3,4,5]) | Create an array with 1 to 5 integer |

len(my_array) | Get the array length |

np.sum(my_array) | get the sum of the elements in the array my_array = np.array([1,2,3,4,5]) print(np.sum(my_array)) [Output]: 15 |

np.max(my_array) | # Get the maximum number in the array my_array = np.array([1, 2, 3,4,5]) max_num = np.max(my_array) [Output]: 5 |

np.min(my_array) | # Get the minimum number in the array my_array = np.array([1, 2, 3,4,5]) min_num = np.min(my_array) [Output]: 1 |

my_array = np.ones(5) Output: [ 1., 1., 1., 1., 1.] |
create array of 1s (of length 5) np.ones(5) Output: [ 1., 1., 1., 1., 1.] |

**:: numpy Sessions ::**

Sessions 1 | Sessions 2 | Sessions 3 | Sessions 4 |

## Python and Lindenmayer System – P1

**Learning : Lindenmayer System P1**

** Subject: Drawing with python using L-System**

First What is **Lindenmayer System** or L-System? **L-System** is a system consists of an alphabet of symbols (A, B, C ..) that can be used to make strings, and a collection of rules that expand each symbol into larger string of symbols.

L-system structure: We can put it as Variables, Constants, Axiom, Rules

**Variables (V):** A, B, C …

**constants **: We define a symbols that present some movements, such as ‘+’ mean rotate right x degree, ‘F’ mean move forward and so on ..

**Axiom **: Axiom or Initiator is a string of symbols from Variable (V ) defining the initial state of the system.

**Rules **: Defining the way variables can be replaced with combinations of constants and other variables.

__Sample:__

Variables : A, B {we have two variables A and B}

Constants : none

Axiom : A {Start from A}

Rules : (A → AB), (B → A) {convert A to AB, and convert B to A}

So if we start running the Nx is the number the time we run the rules (Iteration).

N0 : A

N1 : AB

N2 : AB A

N3 : AB A AB

N4 : AB A AB AB A

N5 : AB A AB A AB A AB .. an so-on

So in this example after 5 Iteration we will have this pattern (AB A AB A AB A AB)

In this post we will write two functions, one to **generate the pattern** based on the Variables and Rules we have. Another function to **draw the pattern** using Python Turtle and based on the Constants we have within the patterns.

The __constants__ that we may use and they are often used as standard are:

F means “Move forward and draw line”.

f means “Move forward Don’t draw line”.

+ means “turn left by ang_L°”.

− means “turn right ang_R°”.

[ means “save position and angle”.

] means “pop position and angle”.

X means “Do nothing”

and sometime you may add your own symbols and and rules.

**First Function**: Generate the Pattern will take the Axiom (Start symbol) and apply the rules that we have (as our AB sample above). The tricky point here is that the function is changing with each example, so nothing fixed here. In the coming code i am using only one variable F mean (move forward) and + – to left and right rotations. Other patterns may include more variables. once we finished the function will return the new string list.

**Generate the Pattern**

# Generate the patern def l_system(s) : new_s = [] for each in s : if each == ‘F’: new_s.append(‘F+F+FF-F’) else : new_s.append(each) return new_s |

**The second function**: Draw the Pattern will take the string we have and draw it based on the commands and rules we have such as if it read ‘F’ then it will move forward and draw line, and if it reads ‘-‘ then it “turn right ang_R°”.

here is the code ..

**Draw the Pattern**

def draw_l_system(x,y,s,b,ang_L,ang_R):

cp = [] # Current position

t.goto(x,y)

t.setheading(90)

t.pendown()

for each in s:

if each == ‘F’ :

t.forward(b)

if each == ‘f’ :

t.penup()

t.forward(b)

t.pendown()

elif each == ‘+’:

t.left(ang_L)

elif each == ‘-‘:

t.right(ang_R)

elif each == ‘[‘:

cp.append((t.heading(),t.pos()))

elif each == ‘]’:

heading, position = cp.pop()

t.penup()

t.goto(position)

t.setheading(heading)

t.pendown()

t.penup()

Now we will just see a one example of what we may get out from all this, and in the next post P2, we will do more sample of drawing using L-System.

In the image bellow, left side showing the Rules, angles and iterations and on the right side the output after drawing the patters.

## Python: Date Validation Function

**Learning : Date Validation Function**

** Subject: Dll’s and Function **

In late of 90’s, I start writing **DLL **files, Dll file or Dynamic Link Library is a file that contain instructions or function that can be used and reused with/by other applications. So if we have a function that we keep using it in most of our programs then we write it in a **dll **file and re-call it any time we want to.

Writing a function that can be added to a **Dll **file and will be used by all the team is not a simple as it appeared to be, **Dll **files often contains more than one functions so we may find __ten or twenty__ functions in there most are related so a **DLL **file need to be a very well documented and each function has it’s own comments, variables, version number and summary of its task and what it will return back.

In this post we will write Python code for a date validation function, the function will take one argument and will return values as :

1. Function will return False and error message if the passed argument is not a valid date.

2. Function will return True and the date if the date is valid.

**Date Validation Function:**

# Date validation function

# Variables: This function will take one argument as a user input date.

# Returns: This dunction will return Fals and error_message each itme the user enter a not valid date.

# The functin will return True and the date in case it was correnct.

# The function will returns value as a list.

def valid_date(my_date):

# get the separator

the_separator = []

for each in my_date :

if not each.isdigit():

the_separator.append(each)

# If the user inter other that two separators then the date is invalid.

if len (the_separator) != 2 or (the_separator[0] != the_separator[1]):

error_message = “Date is not valid.”

return False, error_message

d,m,y = (my_date.split(the_separator[0]))

if not d.isdigit() or (int(d) > 31 or int(d) < 1 ):

error_message = ‘Day must be number and between (1-31).’

return False, error_message

if not m.isdigit() or (int(m) > 12 or int(m) < 1 ) :

error_message= ‘Mounth must be number and between (1-12).’

return False, error_message

if not y.isdigit() or len(y) != 4 or int(y) < 1:

error_message = ‘Year must be a 4-digit positive number. ‘

return False, error_message

# convert the days and month to two digits numbers

if len(d) == 1: d =’0′ + d

if len(m) == 1: m =’0′ + m

my_date = d + ‘/’ + m + ‘/’ + y

return True, my_date

So now if we want to call the function and pass the user input to it then examine the returns, we may use the While loop as here..

vd=[False,0]

while vd[0] == False :

my_date = input(‘\n Enter the date as dd/mm/yyyy :’)

vd = valid_date(my_date)

if not vd[0] : print(‘ ‘,vd[1])

print(“\n we have a valid date, it is .. “, vd[1])

… Have fun …

## Python: Drawing Shapes

**Learning : Drawing Shapes **

** Subject: New shapes function**

To Draw a Square shape, we need to know the width ( W ) of the square side, and then we draw a line and moving in 90 degree and drawing another line and so on until we finished the 4 side of the square. In the same principle if we want to draw a triangle (equilateral one), we need to know length of its sides and in mathematics we know that in equilateral triangles the angles (corners) are 120 degree, so we draw a line and move in 120 degree and drawing another two sides.

In coming code, we will write a general function in Python to pass the number on sides we want to draw (triangle =3, Square=4,Pentagon = 5, Hexagon =6 .. and so on), the width (size) of the shape and the position (x,y) of the first angle or point.

**The Codes:**

def d_shape(s_heads,w,x1,y1):

t.goto(x1,y1)

# To get t.right angle

rang = 360 / s_heads

t.pendown()

for x in range (s_heads +1) :

t.forward(w)

t.right(-rang)

t.penup()

__Results__ after using the new function we can pass any number of sides and the function will draw the shape, here are a sample execution of it. .. *.. Click to enlarge ..*

Now if we call the function number of times equal to it’s heads what we will get ? let’s see . *.. Click to enlarge ..*

And take a look when we set the numbers to 20. *.. Click to enlarge ..*

## Python: Orders Manager P4

**Learning : Orders Management System using Python and Pandas **

** Subject: File Exists and Adding new Record**

In the last post of our system, we develop the file_exists function, the function is checking if the file not exists then will create ond and enter a dummy data. Now we need to add a code to the application body that call this function and if the file exists the application will run without applying the or creating any file. Here is the code in the application body:

**Header here**

if file_exists() != ‘exit’ :

# calling the menu

user_enter = the_menu()

”’

Validation: If the user enter any thing else than numbers

or (q for quit) nothing will happen.

”’

while user_enter !=’q’ or ‘Q’ :

if user_enter in [‘q’,’Q’] :

print(‘\n You select to Exit the application.’)

save_it = input(‘\n Do your want to save your work/changes [y or n] ? ‘)

if save_it in [‘y’,’Y’]:

save_the_df (df)

break

elif user_enter not in [‘1′,’2′,’3′,’4′,’5′,’6′,’7′,’8′,’9’] :

user_enter = the_menu()

else:

user_choice(user_enter)

user_enter = the_menu()

In this post we will talk about the Adding new record function, since we may start from new file we need to enter some records in our data file. Here is the **def add_new_record()** that will help us to enter our data.

**Add New Record Function**

def add_new_record(old_df):

clear() # To clear the terminal.

app_header()

# First we will fetch the columns from the df

col_list = []

for each in old_df.columns :

col_list.append(each)

print(col_list)

# Get max id and increase it by 1

next_id = old_df[‘order_no’].max()+1

new_row={}

# let user enter the new record.

print(‘\n Enter the data for each field then press Enter.\n’ )

print(‘ If you just press Enter NaN will be entered.’)

for each in col_list:

if each !=’order_no’:

print(‘ Enter data for ‘,each)

new_row.update({each:(input(‘ : ‘))})

new_row.update({‘order_no’:next_id})

old_df = old_df.append([new_row])

for each in col_list :

if (old_df.loc[old_df[‘order_no’] == next_id, each][0]) ==”:

(old_df.loc[old_df[‘order_no’] == next_id,[each]]) = float(‘NaN’)

print(‘\n New Record added successfully..\n’)

# print out last 5 rows to show the new record.

print(‘\n The new record in the df..\n ‘,old_df.tail(5))

global df # Reset the df as global variable

df = old_df

input(‘\n\n\n\n ** Press any key to continue .. . . ‘)

In the coming post, we will work on the date validation function also the user choice loop so we can run the application and test it.