modify polygon.py according to the assignment specification in the pdf. need to modify the code with analyse() and display() functions.
the logic for both the functions is in the polygon.py provided, the input format needs to be altered too.
Assignment 2 COMP9021, Trimester 2, 2019 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 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 August 11, 11:59pm. 1.3. Assessment. The assignment is worth 10 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. Late assignments will be penalised: the mark for a late submission will be the minimum of the awarded mark and 10 minus the number of full and partial days that have elapsed from the due date. 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′ < d,="" the="" set="" of="" polygons="" of="" depth="" d′="" 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: 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 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(.32) Area: 176.64 Convex: no Nb of invariant rotations: 2 Depth: 0 Polygon 2: Perimeter: 17.6 + 42*sqrt(.32) Area: 73.92 Convex: yes Nb of invariant rotations: 1 Depth: 1 Polygon 3: Perimeter: 16.0 + 38*sqrt(.32) Area: 60.80 Convex: yes Nb of invariant rotations: 1 Depth: 2 Polygon 4: Perimeter: 16.0 + 40*sqrt(.32) Area: 64.00 Convex: yes Nb of invariant rotations: 1 Depth: 0 Polygon 5: Perimeter: 14.4 + 34*sqrt(.32) Area: 48.96 Convex: yes Nb of invariant rotations: 1 Depth: 3 Polygon 6: Perimeter: 16.0 + 40*sqrt(.32) Area: 64.00 Convex: yes Nb of invariant rotations: 1 Depth: 0 Polygon 7: Perimeter: 12.8 + 30*sqrt(.32) Area: 38.40 Convex: yes Nb of invariant rotations: 1 Depth: 4 Polygon 8: Perimeter: 14.4 + 36*sqrt(.32) Area: 51.84 Convex: yes Nb of invariant rotations: 1 9 Depth: 1 Polygon 9: Perimeter: 11.2 + 26*sqrt(.32) Area: 29.12 Convex: yes Nb of invariant rotations: 1 Depth: 5 Polygon 10: Perimeter: 14.4 + 36*sqrt(.32) Area: 51.84 Convex: yes Nb of invariant rotations: 1 Depth: 1 Polygon 11: Perimeter: 9.6 + 22*sqrt(.32) Area: 21.12 Convex: yes Nb of invariant rotations: 1 Depth: 6 Polygon 12: Perimeter: 12.8 + 32*sqrt(.32) Area: 40.96 Convex: yes Nb of invariant rotations: 1 Depth: 2 Polygon 13: Perimeter: 8.0 + 18*sqrt(.32) Area: 14.40 Convex: yes Nb of invariant rotations: 1 Depth: 7 Polygon 14: Perimeter: 12.8 + 32*sqrt(.32) Area: 40.96 Convex: yes Nb of invariant rotations: 1 Depth: 2 Polygon 15: Perimeter: 6.4 + 14*sqrt(.32) Area: 8.96 Convex: yes Nb of invariant rotations: 1 Depth: 8 Polygon 16: Perimeter: 11.2 + 28*sqrt(.32) Area: 31.36 Convex: yes Nb of invariant rotations: 1 Depth: 3 Polygon 17: Perimeter: 4.8 + 10*sqrt(.32) Area: 4.80 Convex: yes Nb of invariant rotations: 1 10 Depth: 9 Polygon 18: Perimeter: 11.2 + 28*sqrt(.32) Area: 31.36 Convex: yes Nb of invariant rotations: 1 Depth: 3 Polygon 19: Perimeter: 3.2 + 6*sqrt(.32) Area: 1.92 Convex: yes Nb of invariant rotations: 1 Depth: 10 Polygon 20: Perimeter: 9.6 + 24*sqrt(.32) Area: 23.04 Convex: yes Nb of invariant rotations: 1 Depth: 4 Polygon 21: Perimeter: 1.6 + 2*sqrt(.32) Area: 0.32 Convex: yes Nb of invariant rotations: 1 Depth: 11 Polygon 22: Perimeter: 9.6 + 24*sqrt(.32) Area: 23.04 Convex: yes Nb of invariant rotations: 1 Depth: 4 Polygon 23: Perimeter: 8.0 + 20*sqrt(.32) Area: 16.00 Convex: yes Nb of invariant rotations: 1 Depth: 5 Polygon 24: Perimeter: 8.0 + 20*sqrt(.32) Area: 16.00 Convex: yes Nb of invariant rotations: 1 Depth: 5 Polygon 25: Perimeter: 6.4 + 16*sqrt(.32) Area: 10.24 Convex: yes Nb of invariant rotations: 1 Depth: 6 Polygon 26: Perimeter: 6.4 + 16*sqrt(.32) Area: 10.24 Convex: yes Nb of invariant rotations: 1 11 Depth: 6 Polygon 27: Perimeter: 4.8 + 12*sqrt(.32) Area: 5.76 Convex: yes Nb of invariant rotations: 1 Depth: 7 Polygon 28: Perimeter: 4.8 + 12*sqrt(.32) Area: 5.76 Convex: yes Nb of invariant rotations: 1 Depth: 7 Polygon 29: Perimeter: 3.2 + 8*sqrt(.32) Area: 2.56 Convex: yes Nb of invariant rotations: 1 Depth: 8 Polygon 30: Perimeter: 3.2 + 8*sqrt(.32) Area: 2.56 Convex: yes Nb of invariant rotations: 1 Depth: 8 Polygon 31: Perimeter: 1.6 + 4*sqrt(.32) Area: 0.64 Convex: yes Nb of invariant rotations: 1 Depth: 9 Polygon 32: Perimeter: 1.6 + 4*sqrt(.32) Area: 0.64 Convex: yes Nb of invariant rotations: 1 Depth: 9 Polygon 33: Perimeter: 17.6 + 42*sqrt(.32) Area: 73.92 Convex: yes Nb of invariant rotations: 1 Depth: 1 Polygon 34: Perimeter: 16.0 + 38*sqrt(.32) Area: 60.80 Convex: yes Nb of invariant rotations: 1 Depth: 2 Polygon 35: Perimeter: 14.4 + 34*sqrt(.32) Area: 48.96 Convex: yes Nb of invariant rotations: 1 12 Depth: 3 Polygon 36: Perimeter: 12.8 + 30*sqrt(.32) Area: 38.40 Convex: yes Nb of invariant rotations: 1 Depth: 4 Polygon 37: Perimeter: 11.2 + 26*sqrt(.32) Area: 29.12 Convex: yes Nb of invariant rotations: 1 Depth: 5 Polygon 38: Perimeter: 9.6 + 22*sqrt(.32) Area: 21.12 Convex: yes Nb of invariant rotations: 1 Depth: 6 Polygon 39: Perimeter: 8.0 + 18*sqrt(.32) Area: 14.40 Convex: yes