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Assignment 2

COMP9021, Trimester 3, 2023

General matter
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.
2. Submission. Your program will be stored in a file named polygons.py. After you have developed 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 20, 10:00am.
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.
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.
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 d0 < d, the set of polygons of depth d0 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
Examples
1. First example. The file polys_1.txt has the following contents:

11111111111111111111111111111111111111111111111111

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: 324.00

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

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

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()

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[SOLVED] COMP9021 Assignment 3

Aims. The purpose of the assignment is to:

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.

– 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.

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[SOLVED] COMP9021 Assignment 3

Aims. The purpose of the assignment is to:

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.

– 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.

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