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).
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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
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
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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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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.
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
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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
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
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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
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
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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
Nb of invariant rotations: 1
Depth: 7
Polygon 40:
Perimeter: 6.4 + 14*sqrt(.32)
Area: 8.96
Convex: yes
Nb of invariant rotations: 1
Depth: 8
Polygon 41:
Perimeter: 4.8 + 10*sqrt(.32)
Area: 4.80
Convex: yes
Nb of invariant rotations: 1
Depth: 9
Polygon 42:
Perimeter: 3.2 + 6*sqrt(.32)
Area: 1.92
Convex: yes
Nb of invariant rotations: 1
Depth: 10
Polygon 43:
Perimeter: 1.6 + 2*sqrt(.32)
Area: 0.32
Convex: yes
Nb of invariant rotations: 1
Depth: 11
>>> polys.display()
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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.
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3.3. Third example. The file polys_3.txt has the following contents:
0100000000111111111111111111110000000010 1011000000100000000110000000010000001101 0100100000100110001001000110010000010010 0100010000100110010000100110010000100010 0010010000100110100000010110010000100100 0010010000100101001111001010010000100100 0010100000100010010000100100010000010100 0001000000100100010000100010010000001000 0000000000101011001001001101010000000000 0000000000110011010000101100110000000000 1111111111100011001001001100011111111111 1101010100100011010000101100010010101011 1110101010100011001001001100010101010111 1100111010100011010000101100010101110011 1100101010100011001001001100010101010011 1100101010100011010000101100010101010011 1100101010100011001001001100010101010011 1110111010100011010000101100010101110111 1101010100100011001001001100010010101011 1111111111100011010000101100011111111111 0000000000110011001111001100110000000000 0000000000101011000000001101010000000000 0001000000100101111111111010010000001000 0010100000100010111111110100010000010100 0010010000100101000000001010010000100100 0010010000100110100000010110010000100100 0100010000100110010000100110010000100010 0100100000100110001001000110010000010010 1011000000100000000110000000010000001101 0100000000111111111111111111110000000010
Here is a possible interaction:
$ python3
…
>>> from polygons import *
>>> polys = Polygons(‘polys_3.txt’)
>>> polys.analyse()
Polygon 1:
Perimeter: 2.4 + 9*sqrt(.32)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 2:
Perimeter: 51.2 + 4*sqrt(.32)
Area: 117.28
Convex: no
Nb of invariant rotations: 2
Depth: 0
Polygon 3:
Perimeter: 2.4 + 9*sqrt(.32)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 4:
Perimeter: 17.6 + 40*sqrt(.32)
Area: 59.04
Convex: no
Nb of invariant rotations: 2
Depth: 1
Polygon 5:
Perimeter: 3.2 + 28*sqrt(.32)
Area: 9.76
Convex: no
Nb of invariant rotations: 1
Depth: 2
Polygon 6:
Perimeter: 27.2 + 6*sqrt(.32)
Area: 5.76
Convex: no
Nb of invariant rotations: 1
Depth: 2
Polygon 7:
Perimeter: 4.8 + 14*sqrt(.32)
Area: 6.72
Convex: no
Nb of invariant rotations: 1
Depth: 1
Polygon 8:
Perimeter: 4.8 + 14*sqrt(.32)
Area: 6.72
Convex: no
Nb of invariant rotations: 1
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Depth: 1
Polygon 9:
Perimeter: 3.2 + 2*sqrt(.32)
Area: 1.12
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 10:
Perimeter: 3.2 + 2*sqrt(.32)
Area: 1.12
Convex: yes
Nb of invariant rotations: 1
Depth: 2
Polygon 11:
Perimeter: 2.4 + 9*sqrt(.32)
Area: 2.80
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 12:
Perimeter: 2.4 + 9*sqrt(.32)
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.
3.4. Fourth example. The file polys_4.txt has the following contents:
1 1 101 11 0 1 1
01 01000100010001000100100 100 0010 0 0 1
1 0 1 1 1011 10 1 1 1 0 000
1 1 1 0 00 1 001 11 1
1000101010101010101000100101010100010000 0100010001000100010000100010100011100011
100 1 0 0 0 10 0 0 1
11101 1101110 1 000000000000000000000001100000011000100
1
110 01 0 1 1 0 001 1000011 10
00 0 1
00
01
00 0 1 0 00
110010010101001 100
01000 100 0 1 01 0001011
1
11
010 000 0000 0 0 0 0
0111011101100000001111000 0
010000
1011111100011111000000000001000 000000000 11111111111111111
00 01
1 111001100111111100000000111111000
1
00
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Here is a possible interaction:
$ python3
…
>>> from polygons import *
>>> polys = Polygons(‘polys_4.txt’)
>>> polys.analyse()
Polygon 1:
Perimeter: 11.2 + 28*sqrt(.32)
Area: 18.88
Convex: no
Nb of invariant rotations: 2
Depth: 0
Polygon 2:
Perimeter: 3.2 + 5*sqrt(.32)
Area: 2.00
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 3:
Perimeter: 1.6 + 6*sqrt(.32)
Area: 1.76
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 4:
Perimeter: 3.2 + 1*sqrt(.32)
Area: 0.88
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 5:
Perimeter: 4*sqrt(.32)
Area: 0.32
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 6:
Perimeter: 4*sqrt(.32)
Area: 0.32
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 7:
Perimeter: 4*sqrt(.32)
Area: 0.32
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 8:
Perimeter: 4*sqrt(.32)
Area: 0.32
Convex: yes
Nb of invariant rotations: 4
Depth: 1
Polygon 9:
Perimeter: 1.6 + 1*sqrt(.32)
Area: 0.24
Convex: yes
Nb of invariant rotations: 1
Depth: 0
Polygon 10:
Perimeter: 0.8 + 2*sqrt(.32)
Area: 0.16
Convex: yes
Nb of invariant rotations: 2
Depth: 0
Polygon 11:
Perimeter: 12.0 + 7*sqrt(.32)
Area: 5.68
Convex: no
Nb of invariant rotations: 1
Depth: 0
Polygon 12:
Perimeter: 2.4 + 3*sqrt(.32)
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(.32)
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.
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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 xth digit of the yth line with digits, with 0≤x