Polygon 3英文作业代写、代写polygons程序
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).
1.1 Submission
Your programs will be stored in a file named polygons.py. After you have developed and tested your program,
upload your files using Ed. Assignments can be submitted more than once: the last version is marked. Your
assignment is due by May 7, 11:59pm.
1.2 Assessment
The assignment is worth 10 marks. the automarking script will allocate 30 seconds to each run of your program.
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.
The outputs of your programs should be exactly as indicated.
1.3 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.
1
2 Examples
2.1 First example
Given a file named polys_1.txt whose contents is
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
your program when run as python3 polygons.py --file polys_1.txt should output
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
2
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
3
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
4
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
and when run as python3 polygons.py -print --file polys_1.txt should produce some output saved in a file
named polys_1.tex, which can be given as argument to pdflatex to produce a file named polys_1.pdf that
views as follows.
5
2.2 Second example
Given a file named polys_2.txt whose contents is
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
your program when run as python3 polygons.py --file polys_2.txt should output
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:
6
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
7
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
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
8
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
9
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
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
10
and when run as python3 polygons.py -print --file polys_2.txt should produce some output saved in a file
named polys_2.tex, which can be given as argument to pdflatex to produce a file named polys_2.pdf that
views as follows.
11
2.3 Third example
Given a file named polys_3.txt whose contents is
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
your program when run as python3 polygons.py --file polys_3.txt should output
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
12
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
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
13
and when run as python3 polygons.py -print --file polys_3.txt should produce some output saved in a file
named polys_3.tex, which can be given as argument to pdflatex to produce a file named polys_3.pdf that
views as follows.
14
2.4 Fourth example
Given a file named polys_4.txt whose contents is
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
0100010001000100010000100010100010100011
100 1 0 0 0 10 0 0 1 00 0 1 00 01 010 000 0000 0 0 0 1 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
your program when run as python3 polygons.py --file polys_4.txt should output
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: 0.8 + 8*sqrt(.32)
Area: 1.92
Convex: yes
Nb of invariant rotations: 2
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
15
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
16
and when run as python3 polygons.py -print --file polys_4.txt should produce some output saved in a file
named polys_4.tex, which can be given as argument to pdflatex to produce a file named polys_4.pdf that
views as follows.
17
3 Detailed description
3.1 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.
3.2 Output
The program should be run as either
python3 polygons.py --file filename.txt
or as
python3 polygons.py -print --file filename.txt
(where filename.txt is the name of a file that stores the input). You can study the program ascii_art.py from
Lecture 7 to find out how this can be done.
If the input is incorrect, that is, does not satisfy the conditions spelled out in the previous section, then the program
should print out a single line that reads
Incorrect input.
and immediately exit.
3.2.1 When the program is run without -print as command-line argument
If the input is correct, then the program should output a first line that reads one of
Cannot get polygons as expected.
in case 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.
Otherwise, the program should output 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(.32)
Perimeter: a
Perimeter: b*sqrt(.32)
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
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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
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. Note that your program should output no blank line. For
a given test, the output of your program will be compared with the expected output; your program will pass the
test if and only if both outputs are absolutely identical, character for character, including spaces. For the provided
examples, the expected outputs are available in files that end in _output.txt. To check that the output of your
program on those examples is correct, you can redirect it to a file and compare the contents of that file with the
contents of the appropriate _output.txt file using the diff command. If diff silently exits then your program
passes the test; otherwise it fails it. For instance, run
python3 polygons.py --file polys_1.txt >polys_1_my_output.txt
and then
diff polys_1_my_output.txt polys_1_output.txt
to check whether your program succeeds on the first provided example.
3.2.2 When the program is run with -print as command-line argument
If the input is correct, then the program should output some lines saved in a file named filename.tex, that can
be given as an argument to pdflatex to produce a file named filename.pdf that depicts the maze. The provided
examples will show you what 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
contents of the file output by your program 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. For instance, rename
the provided file polys_1.tex to polys_1_expected.tex, and then run
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python3 polygons.py -print --file polys_1.txt
and then
diff polys_1.tex polys_1_expected.tex
to check whether your program succeeds on the first provided example.
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