COMP9021 Principles of Programming Assignment 2: Polygons
Assignment 2 COMP9021, Trimester 3, 2023
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 November 20, 10:00am.
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′ < 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
3
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 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:
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
Area: a
with a an appropriate floating point number with 2 digits after the decimal point, a fourth line that reads one
of
a fifth line that reads
Convex: yes
Convex: no
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.
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.
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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.
