Assignment 2
CPTG1405, Trimester 3, 2024
1. General matter
1.1. Aims. The purpose of the assignment is to:
• design and implement an interface based on the desired behaviour of an application program;
• practice the use of Python syntax;
• develop problem solving skills.
1.2. Submission. Your program will be stored in a file n amed p olygons.py. A fter y ou h ave d eveloped and
tested your program, upload it using Ed (unless you worked directly in Ed). Assignments can be submitted
more than once; the last version is marked. Your assignment is due by November 11, 9:00am.
1.3. Assessment. The assignment is worth 13 marks. It is going to be tested against a number of input files.
For each test, the automarking script will let your program run for 30 seconds.
Assignments can be submitted up to 5 days after the deadline. The maximum mark obtainable reduces by
5% per full late day, for up to 5 days. Thus if students A and B hand in assignments worth 12 and 11, both
two days late (that is, more than 24 hours late and no more than 48 hours late), then the maximum mark
obtainable is 11.7, so A gets min(11.7, 11) = 11 and B gets min(11.7, 11) = 11. The outputs of your programs
should be exactly as indicated.
1.4. Reminder on plagiarism policy. You are permitted, indeed encouraged, to discuss ways to solve the
assignment with other people. Such discussions must be in terms of algorithms, not code. But you must
implement the solution on your own. Submissions are routinely scanned for similarities that occur when students
copy and modify other people’s work, or work very closely together on a single implementation. Severe penalties
apply.
2. General presentation
You will design and implement a program that will
• extract and analyse the various characteristics of (simple) polygons, their contours being coded and
stored in a file, and
• – either display those characteristics: perimeter, area, convexity, number of rotations that keep the
polygon invariant, and depth (the length of the longest chain of enclosing polygons)
– or output some Latex code, to be stored in a file, from which a pictorial representation of the
polygons can be produced, coloured in a way which is proportional to their area.
Call encoding any 2-dimensional grid of size between between 2 × 2 and 50 × 50 (both dimensions can be
different) all of whose elements are either 0 or 1.
Call neighbour of a member m of an encoding any of the at most eight members of the grid whose value is 1
and each of both indexes differs from m’s corresponding index by at most 1. Given a particular encoding, we
inductively define for all natural numbers d the set of polygons of depth d (for this encoding) as follows. Let a
natural number d be given, and suppose that for all d
0 < d, the set of polygons of depth d
0 has been defined.
Change in the encoding all 1’s that determine those polygons to 0. Then the set of polygons of depth d is
defined as the set of polygons which can be obtained from that encoding by connecting 1’s with some of their
neighbours in such a way that we obtain a maximal polygon (that is, a polygon which is not included in any
other polygon obtained from that encoding by connecting 1’s with some of their neighbours).
1
2
3. Examples
3.1. First example. The file polys_1.txt has the following contents:
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
11111111111111111111111111111111111111111111111111
3
Here is a possible interaction:
$ python3
...
>>> from polygons import *
>>> polys = Polygons('polys_1.txt')
>>> polys.analyse()
Polygon 1:
Perimeter: 78.4
Area: 384.16
Convex: yes
Nb of invariant rotations: 4
Depth: 0
Polygon 2:
Perimeter: 75.2
Area: 353.44
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 3:
Perimeter: 72.0
Area: **4.00
Convex: yes
Nb of invariant rotations: 4
Depth: 2
Polygon 4:
Perimeter: 68.8
Area: 295.84
Convex: yes
Nb of invariant rotations: 4
Depth: 3
Polygon 5:
Perimeter: 65.6
Area: 268.96
Convex: yes
Nb of invariant rotations: 4
Depth: 4
Polygon 6:
Perimeter: 62.4
Area: 243.36
Convex: yes
Nb of invariant rotations: 4
Depth: 5
Polygon 7:
Perimeter: 59.2
Area: 219.04
Convex: yes
Nb of invariant rotations: 4
Depth: 6
Polygon 8:
Perimeter: 56.0
Area: 196.00
Convex: yes
Nb of invariant rotations: 4
4
Depth: 7
Polygon 9:
Perimeter: 52.8
Area: 174.24
Convex: yes
Nb of invariant rotations: 4
Depth: 8
Polygon 10:
Perimeter: 49.6
Area: 153.76
Convex: yes
Nb of invariant rotations: 4
Depth: 9
Polygon 11:
Perimeter: 46.4
Area: 134.56
Convex: yes
Nb of invariant rotations: 4
Depth: 10
Polygon 12:
Perimeter: 43.2
Area: 116.64
Convex: yes
Nb of invariant rotations: 4
Depth: 11
Polygon 13:
Perimeter: 40.0
Area: 100.00
Convex: yes
Nb of invariant rotations: 4
Depth: 12
Polygon 14:
Perimeter: 36.8
Area: 84.64
Convex: yes
Nb of invariant rotations: 4
Depth: 13
Polygon 15:
Perimeter: 33.6
Area: 70.56
Convex: yes
Nb of invariant rotations: 4
Depth: 14
Polygon 16:
Perimeter: 30.4
Area: 57.76
Convex: yes
Nb of invariant rotations: 4
Depth: 15
Polygon 17:
Perimeter: 27.2
Area: 46.24
Convex: yes
Nb of invariant rotations: 4
5
Depth: 16
Polygon 18:
Perimeter: 24.0
Area: 36.00
Convex: yes
Nb of invariant rotations: 4
Depth: 17
Polygon 19:
Perimeter: 20.8
Area: 27.04
Convex: yes
Nb of invariant rotations: 4
Depth: 18
Polygon 20:
Perimeter: 17.6
Area: 19.36
Convex: yes
Nb of invariant rotations: 4
Depth: 19
Polygon 21:
Perimeter: 14.4
Area: 12.96
Convex: yes
Nb of invariant rotations: 4
Depth: 20
Polygon 22:
Perimeter: 11.2
Area: 7.84
Convex: yes
Nb of invariant rotations: 4
Depth: 21
Polygon 23:
Perimeter: 8.0
Area: 4.00
Convex: yes
Nb of invariant rotations: 4
Depth: 22
Polygon 24:
Perimeter: 4.8
Area: 1.44
Convex: yes
Nb of invariant rotations: 4
Depth: 23
Polygon 25:
Perimeter: 1.6
Area: 0.16
Convex: yes
Nb of invariant rotations: 4
Depth: 24
>>> polys.display()
6
The effect of executing polys.display() is to produce a file named polys_1.tex that can be given as
argument to pdflatex to produce a file named polys_1.pdf that views as follows.
7
3.2. Second example. The file polys_2.txt has the following contents:
00000000000000000000000000000000000000000000000000
01111111111111111111111111111111111111111111111110
00111111111111111111111111111111111111111111111100
00011111111111111111111111111111111111111111111000
01001111111111111111111111111111111111111111110010
01100111111111111111111111111111111111111111100110
01110011111111111111111111111111111111111111001110
01111001111111111111111111111111111111111110011110
01111100111111111111111111111111111111111100111110
01111110011111111111111111111111111111111001111110
01111111001111111111111111111111111111110011111110
01111111100111111111111111111111111111100111111110
01111111110011111111111111111111111111001111111110
01111111111001111111111111111111111110011111111110
01111111111100111111111111111111111100111111111110
01111111111110011111111111111111111001111111111110
01111111111111001111111111111111110011111111111110
01111111111111100111111111111111100111111111111110
01111111111111110011111111111111001111111111111110
01111111111111111001111111111110011111111111111110
01111111111111111100111111111100111111111111111110
01111111111111111110011111111001111111111111111110
01111111111111111111001111110011111111111111111110
01111111111111111111100111100111111111111111111110
01111111111011111111110011001111111111011111111110
01111111111111111111100111100111111111111111111110
01111111111111111111001111110011111111111111111110
01111111111111111110011111111001111111111111111110
01111111111111111100111111111100111111111111111110
01111111111111111001111111111110011111111111111110
01111111111111110011111111111111001111111111111110
01111111111111100111111111111111100111111111111110
01111111111111001111111111111111110011111111111110
01111111111110011111111111111111111001111111111110
01111111111100111111111111111111111100111111111110
01111111111001111111111111111111111110011111111110
01111111110011111111111111111111111111001111111110
01111111100111111111111111111111111111100111111110
01111111001111111111111111111111111111110011111110
01111110011111111111111111111111111111111001111110
01111100111111111111111111111111111111111100111110
01111001111111111111111111111111111111111110011110
01110011111111111111111111111111111111111111001110
01100111111111111111111111111111111111111111100110
01001111111111111111111111111111111111111111110010
00011111111111111111111111111111111111111111111000
00111111111111111111111111111111111111111111111100
01111111111111111111111111111111111111111111111110
00000000000000000000000000000000000000000000000000
8
Here is a possible interaction:
$ python3
...
>>> from polygons import *
>>> polys = Polygons('polys_2.txt')
>>> polys.analyse()
Polygon 1:
Perimeter: 37.6 + 92*sqrt(.**)
Area: 176.64
Convex: no
Nb of invariant rotations: 2
Depth: 0
Polygon 2:
Perimeter: 17.6 + 42*sqrt(.**)
Area: **.92
Convex: yes
Nb of invariant rotations: 1
Depth: 1
Polygon 3:
Perimeter: 16.0 + 38*sqrt(.**)
Area: 60.80
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 4:
Perimeter: 16.0 + 40*sqrt(.**)
Area: 64.00
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 5:
Perimeter: 14.4 + 34*sqrt(.**)
Area: 48.96
Convex: yes
Nb of invariant rotations: 1
Depth: 3
Polygon 6:
Perimeter: 16.0 + 40*sqrt(.**)
Area: 64.00
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 7:
Perimeter: 12.8 + 30*sqrt(.**)
Area: 38.40
Convex: yes
Nb of invariant rotations: 1
Depth: 4
Polygon 8:
Perimeter: 14.4 + 36*sqrt(.**)
Area: 51.84
Convex: yes
Nb of invariant rotations: 1
9
Depth: 1
Polygon 9:
Perimeter: 11.2 + 26*sqrt(.**)
Area: 29.12
Convex: yes
Nb of invariant rotations: 1
Depth: 5
Polygon 10:
Perimeter: 14.4 + 36*sqrt(.**)
Area: 51.84
Convex: yes
Nb of invariant rotations: 1
Depth: 1
Polygon 11:
Perimeter: 9.6 + 22*sqrt(.**)
Area: 21.12
Convex: yes
Nb of invariant rotations: 1
Depth: 6
Polygon 12:
Perimeter: 12.8 + ***sqrt(.**)
Area: 40.96
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 13:
Perimeter: 8.0 + 18*sqrt(.**)
Area: 14.40
Convex: yes
Nb of invariant rotations: 1
Depth: 7
Polygon 14:
Perimeter: 12.8 + ***sqrt(.**)
Area: 40.96
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 15:
Perimeter: 6.4 + 14*sqrt(.**)
Area: 8.96
Convex: yes
Nb of invariant rotations: 1
Depth: 8
Polygon 16:
Perimeter: 11.2 + 28*sqrt(.**)
Area: 31.36
Convex: yes
Nb of invariant rotations: 1
Depth: 3
Polygon 17:
Perimeter: 4.8 + 10*sqrt(.**)
Area: 4.80
Convex: yes
Nb of invariant rotations: 1
10
Depth: 9
Polygon 18:
Perimeter: 11.2 + 28*sqrt(.**)
Area: 31.36
Convex: yes
Nb of invariant rotations: 1
Depth: 3
Polygon 19:
Perimeter: 3.2 + 6*sqrt(.**)
Area: 1.92
Convex: yes
Nb of invariant rotations: 1
Depth: 10
Polygon 20:
Perimeter: 9.6 + 24*sqrt(.**)
Area: 23.04
Convex: yes
Nb of invariant rotations: 1
Depth: 4
Polygon 21:
Perimeter: 1.6 + 2*sqrt(.**)
Area: 0.**
Convex: yes
Nb of invariant rotations: 1
Depth: 11
Polygon 22:
Perimeter: 9.6 + 24*sqrt(.**)
Area: 23.04
Convex: yes
Nb of invariant rotations: 1
Depth: 4
Polygon 23:
Perimeter: 8.0 + 20*sqrt(.**)
Area: 16.00
Convex: yes
Nb of invariant rotations: 1
Depth: 5
Polygon 24:
Perimeter: 8.0 + 20*sqrt(.**)
Area: 16.00
Convex: yes
Nb of invariant rotations: 1
Depth: 5
Polygon 25:
Perimeter: 6.4 + 16*sqrt(.**)
Area: 10.24
Convex: yes
Nb of invariant rotations: 1
Depth: 6
Polygon 26:
Perimeter: 6.4 + 16*sqrt(.**)
Area: 10.24
Convex: yes
Nb of invariant rotations: 1
11
Depth: 6
Polygon 27:
Perimeter: 4.8 + 12*sqrt(.**)
Area: 5.76
Convex: yes
Nb of invariant rotations: 1
Depth: 7
Polygon 28:
Perimeter: 4.8 + 12*sqrt(.**)
Area: 5.76
Convex: yes
Nb of invariant rotations: 1
Depth: 7
Polygon 29:
Perimeter: 3.2 + 8*sqrt(.**)
Area: 2.56
Convex: yes
Nb of invariant rotations: 1
Depth: 8
Polygon 30:
Perimeter: 3.2 + 8*sqrt(.**)
Area: 2.56
Convex: yes
Nb of invariant rotations: 1
Depth: 8
Polygon 31:
Perimeter: 1.6 + 4*sqrt(.**)
Area: 0.64
Convex: yes
Nb of invariant rotations: 1
Depth: 9
Polygon **:
Perimeter: 1.6 + 4*sqrt(.**)
Area: 0.64
Convex: yes
Nb of invariant rotations: 1
Depth: 9
Polygon 33:
Perimeter: 17.6 + 42*sqrt(.**)
Area: **.92
Convex: yes
Nb of invariant rotations: 1
Depth: 1
Polygon 34:
Perimeter: 16.0 + 38*sqrt(.**)
Area: 60.80
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 35:
Perimeter: 14.4 + 34*sqrt(.**)
Area: 48.96
Convex: yes
Nb of invariant rotations: 1
12
Depth: 3
Polygon 36:
Perimeter: 12.8 + 30*sqrt(.**)
Area: 38.40
Convex: yes
Nb of invariant rotations: 1
Depth: 4
Polygon 37:
Perimeter: 11.2 + 26*sqrt(.**)
Area: 29.12
Convex: yes
Nb of invariant rotations: 1
Depth: 5
Polygon 38:
Perimeter: 9.6 + 22*sqrt(.**)
Area: 21.12
Convex: yes
Nb of invariant rotations: 1
Depth: 6
Polygon 39:
Perimeter: 8.0 + 18*sqrt(.**)
Area: 14.40
Convex: yes
Nb of invariant rotations: 1
Depth: 7
Polygon 40:
Perimeter: 6.4 + 14*sqrt(.**)
Area: 8.96
Convex: yes
Nb of invariant rotations: 1
Depth: 8
Polygon 41:
Perimeter: 4.8 + 10*sqrt(.**)
Area: 4.80
Convex: yes
Nb of invariant rotations: 1
Depth: 9
Polygon 42:
Perimeter: 3.2 + 6*sqrt(.**)
Area: 1.92
Convex: yes
Nb of invariant rotations: 1
Depth: 10
Polygon 43:
Perimeter: 1.6 + 2*sqrt(.**)
Area: 0.**
Convex: yes
Nb of invariant rotations: 1
Depth: 11
>>> polys.display()
13
The effect of executing polys.display() is to produce a file named polys_2.tex that can be given as
argument to pdflatex to produce a file named polys_2.pdf that views as follows.
14
3.3. Third example. The file polys_3.txt has the following contents:
0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0
1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1
0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0
0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0
0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0
0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0
0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1
1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1
1 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 1 1
1 1 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 0 1 1
1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1
1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1
1 1 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1
1 1 1 0 1 1 1 0 1 0 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 1 1 0 1 1 1
1 1 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 1
1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 1 1 1
0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0
0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0
0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0
0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 0 0 1 0 0
0 1 0 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0
0 1 0 0 1 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0
1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1
0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0
15
Here is a possible interaction:
$ python3
...
>>> from polygons import *
>>> polys = Polygons('polys_3.txt')
>>> polys.analyse()
Polygon 1:
Perimeter: 2.4 + 9*sqrt(.**)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 2:
Perimeter: 51.2 + 4*sqrt(.**)
Area: 117.28
Convex: no
Nb of invariant rotations: 2
Depth: 0
Polygon 3:
Perimeter: 2.4 + 9*sqrt(.**)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 4:
Perimeter: 17.6 + 40*sqrt(.**)
Area: 59.04
Convex: no
Nb of invariant rotations: 2
Depth: 1
Polygon 5:
Perimeter: 3.2 + 28*sqrt(.**)
Area: 9.76
Convex: no
Nb of invariant rotations: 1
Depth: 2
Polygon 6:
Perimeter: 27.2 + 6*sqrt(.**)
Area: 5.76
Convex: no
Nb of invariant rotations: 1
Depth: 2
Polygon 7:
Perimeter: 4.8 + 14*sqrt(.**)
Area: 6.72
Convex: no
Nb of invariant rotations: 1
Depth: 1
Polygon 8:
Perimeter: 4.8 + 14*sqrt(.**)
Area: 6.72
Convex: no
Nb of invariant rotations: 1
16
Depth: 1
Polygon 9:
Perimeter: 3.2 + 2*sqrt(.**)
Area: 1.12
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 10:
Perimeter: 3.2 + 2*sqrt(.**)
Area: 1.12
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 11:
Perimeter: 2.4 + 9*sqrt(.**)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 12:
Perimeter: 2.4 + 9*sqrt(.**)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
>>> polys.display()
The effect of executing polys.display() is to produce a file named polys_3.tex that can be given as
argument to pdflatex to produce a file named polys_3.pdf that views as follows.
17
3.4. Fourth example. The file polys_4.txt has the following contents:
1 1 101 11 0 1 1 1 0 1 1 1011 10 1 1 1 0 000 1 1 1 0 00 1 001 11 1
01 01000100010001000100100 110010010101001
100 0010 0 0 1 00 0 1 0 00 100 01000 100 0 1 01 0001011 1
1000101010101010101000100101010100010000
0100010001000100010000100010100011100011
100 1 0 0 0 10 0 0 1 00 0 1 00 01 010 000 0000 0 0 0 0 00 01 11
11101 1101110 1 1 1 0111011101100000001111000
000000000000000000000001100000011000100 0
1 111001100111111100000000111111000 010000
110 01 0 1 1 0 1011111100011111000000000001000
001 1000011 10 000000000 11111111111111111 00
18
Here is a possible interaction:
$ python3
...
>>> from polygons import *
>>> polys = Polygons('polys_4.txt')
>>> polys.analyse()
Polygon 1:
Perimeter: 11.2 + 28*sqrt(.**)
Area: 18.88
Convex: no
Nb of invariant rotations: 2
Depth: 0
Polygon 2:
Perimeter: 3.2 + 5*sqrt(.**)
Area: 2.00
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 3:
Perimeter: 1.6 + 6*sqrt(.**)
Area: 1.76
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 4:
Perimeter: 3.2 + 1*sqrt(.**)
Area: 0.88
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 5:
Perimeter: 4*sqrt(.**)
Area: 0.**
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 6:
Perimeter: 4*sqrt(.**)
Area: 0.**
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 7:
Perimeter: 4*sqrt(.**)
Area: 0.**
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 8:
Perimeter: 4*sqrt(.**)
Area: 0.**
Convex: yes
Nb of invariant rotations: 4
19
Depth: 1
Polygon 9:
Perimeter: 1.6 + 1*sqrt(.**)
Area: 0.24
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 10:
Perimeter: 0.8 + 2*sqrt(.**)
Area: 0.16
Convex: yes
Nb of invariant rotations: 2
Depth: 0
Polygon 11:
Perimeter: 12.0 + 7*sqrt(.**)
Area: 5.68
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 12:
Perimeter: 2.4 + 3*sqrt(.**)
Area: 0.88
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 13:
Perimeter: 1.6
Area: 0.16
Convex: yes
Nb of invariant rotations: 4
Depth: 0
Polygon 14:
Perimeter: 5.6 + 3*sqrt(.**)
Area: 1.36
Convex: no
Nb of invariant rotations: 1
Depth: 0
>>> polys.display()
The effect of executing polys.display() is to produce a file named polys_4.tex that can be given as
argument to pdflatex to produce a file named polys_4.pdf that views as follows.
20
4. Detailed description
4.1. Input. The input is expected to consist of ydim lines of xdim 0’s and 1’s, where xdim and ydim are at
least equal to 2 and at most equal to 50, with possibly lines consisting of spaces only that will be ignored and
with possibly spaces anywhere on the lines with digits. If n is the x
th digit of the y
th line with digits, with
0 ≤ x < xdim and 0 ≤ y < ydim , then n is to be associated with a point situated x × 0.4 cm to the right and
y × 0.4 cm below an origin.
4.2. Output. Consider executing from the Python prompt the statement from polygons import * followed
by the statement polys = Polygons(some_filename). In case some_filename does not exist in the working
directory, then Python will raise a FileNotFoundError exception, that does not need to be caught. Assume
that some_filename does exist (in the working directory). If the input is incorrect in that it does not contain
only 0’s and 1’a besides spaces, or in that it contains either too few or too many lines of digits, or in that
some line of digits contains too many or too few digits, or in that two of its lines of digits do not contain the
same number of digits, then the effect of executing polys = Polygons(some_filename) should be to generate
a PolygonsError exception that reads
Traceback (most recent call last):
...
polygons.PolygonsError: Incorrect input.
If the previous conditions hold but it is not possible to use all 1’s in the input and make them the contours
of polygons of depth d, for any natural number d, as defined in the general presentation, then the effect of
executing polys = Polygons(some_filename) should be to generate a PolygonsError exception that reads
Traceback (most recent call last):
...
polygons.PolygonsError: Cannot get polygons as expected.
If the input is correct and it is possible to use all 1’s in the input and make them the contours of polygons
of depth d, for any natural number d, as defined in the general presentation, then executing the statement
polys = Polygons(some_filename) followed by polys.analyse() should have the effect of outputting a first
line that reads
Polygon N:
with N an appropriate integer at least equal to 1 to refer to the N’th polygon listed in the order of polygons
with highest point from smallest value of y to largest value of y, and for a given value of y, from smallest value
of x to largest value of x, a second line that reads one of
Perimeter: a + b*sqrt(.**)
Perimeter: a
Perimeter: b*sqrt(.**)
with a an appropriate strictly positive floating point number with 1 digit after the decimal point and b an
appropriate strictly positive integer, a third line that reads
Area: a
with a an appropriate floating point number with 2 digits after the decimal point, a fourth line that reads one
of
Convex: yes
Convex: no
a fifth line that reads
Nb of invariant rotations: N
21
with N an appropriate integer at least equal to 1, and a sixth line that reads
Depth: N
with N an appropriate positive integer (possibly 0).
Pay attention to the expected format, including spaces.
If the input is correct and it is possible to use all 1’s in the input and make them the contours of poly gons of depth d, for any natural number d, as defined in the general presentation, then executing the state ment polys = Polygons(some_filename) followed by polys.display() should have the effect of produc ing a file named some_filename.tex that can be given as argument to pdflatex to generate a file named
some_filename.pdf. The provided examples will show you what some_filename.tex should contain.
• Polygons are drawn from lowest to highest depth, and for a given depth, the same ordering as previously
described is used.
• The point that determines the polygon index is used as a starting point in drawing the line segments
that make up the polygon, in a clockwise manner.
• A polygons’s colour is determined by its area. The largest polygons are yellow. The smallest polygons
are orange. Polygons in-between mix orange and yellow in proportion of their area. For instance, a
polygon whose size is 25% the difference of the size between the largest and the smallest polygon will
receive 25% of orange (and 75% of yellow). That proportion is computed as an integer. When the value
is not an integer, it is rounded to the closest integer, with values of the form z.5 rounded up to z + 1.
Pay attention to the expected format, including spaces and blank lines. Lines that start with % are comments.
The output of your program redirected to a file will be compared with the expected output saved in a file (of a
different name of course) using the diff command. For your program to pass the associated test, diff should
silently exit, which requires that the contents of both files be absolutely identical, character for character,
including spaces and blank lines. Check your program on the provided examples using the associated .tex files,
renaming them as they have the names of the files expected to be generated by your program.

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