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Assignment 2, final version
COMP9021, Term 1, 2021
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 tangram.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 April 26, 10:00pm.
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.
Late assignments will be penalised: the mark for a late submission will be the minimum of the awarded mark
and 13 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.
1.4. 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.
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2. Background
The game of tangram consists in creating shapes out of pieces. We assume that each piece has its own colour,
different to the colour of any other piece in the set we are working with. Just for reference, here is the list of
colours that are available to us (you will not make use of this list):
https://www.w3.org/TR/2011/REC-SVG11-20110816/types.html#ColorKeywords
A representation of the pieces will be stored in an .xml file thanks to a simple, fixed syntax.
2.1. Pieces. Here is an example of the contents of the file pieces_A.xml, typical of the contents of any file of
this kind (so only the number of pieces, the colour names, and the various coordinates can differ from one such
file to another—we do not bother with allowing for variations, in the use of space in particular).









Opened in a browser, pieces_A.xml displays as follows:
Note that the coordinates are nonnegative integers. This means that the sets of pieces we consider rule out
those of the traditional game of tangram, where √
2 is involved everywhere...
We require every piece to be a convex polygon. An .xml file should represent a piece with n sides (n ≥ 3) by
an enumeration of n pairs of coordinates, those of consecutive vertices, the first vertex being arbitrary, and the
enumeration being either clockwise or anticlockwise.
The pieces can be flipped over horizontally, flipped over vertically, and rotated by 90 degrees. For instance, the
file pieces_AA.xml whose contents is
3









and which displays as
represents the same set of pieces (the fact that the latter appear as smaller than the former is just due to the
different scaling of the included pdf’s; the sizes of the pieces are actually the same in terms of the coordinates
of their vertices).
The pieces can overlap, but that does not concern us. In practice, we will just use representations where the
pieces do not overlap as that allows us to visualise the pieces properly when we open the corresponding .xml
file, but it is just for convenience and irrelevant to the tasks we tackle.
2.2. Shapes. A representation of a shape is provided thanks to an .xml file with the same structure, storing
the coordinates of the vertices of just one polygon.
The file shape_A_1.xml whose contents is



and which displays as
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is such an example. The file shape_A_2.xml whose contents is



and which displays as
is another such example.
Contrary to pieces, shapes are not assumed to be convex polygons. Still they are assumed to be simple polygons
(the boundary of a simple polygon does not cross itself; in particular, it cannot consist of at least 2 polygons
that are connected by letting two of them just “touch” each other at one of their vertices—e.g., two rectangles
such that the upper right corner of one rectangle is the lower left corner of the other rectangle; that is not
allowed).
Whereas you will have to check that the representation of the pieces in an .xml file satisfies our constraints,
you will not have to do so for the representation of a shape; you can assume that any shape we will be dealing
with satisfies our constraints.
2.3. Tangrams. The first shape can be built from our set of pieces, in many ways. Here is one, given by the
file tangram_A_1_a.xml whose contents is









and which displays as follows.
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Here is another one, given by the file tangram_A_1_b.xml whose contents is









and which displays as follows.
The second shape can also be built from our set of pieces, in many ways. Here is one, given by the file
tangram_A_2_a.xml whose contents is









and which displays as follows.
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Here is another one, given by the file tangram_A_2_b.xml whose contents is









and which displays as follows.
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3. First task (4 marks)
You have to check that the pieces represented in an .xml file satisfy our constraints. So you have to check
that each piece is convex, and if it represents a polygon with n sides (n ≥ 3) then the representation consists
of an enumeration of the n vertices, either clockwise or anticlockwise. Here is the expected behaviour of your
program.
$ python3
...
>>> from tangram import *
>>> TangramPieces('pieces_A.xml')

>>> TangramPieces('pieces_AA.xml')

>>> TangramPieces('incorrect_pieces_1.xml')
...
tangram.TangramPiecesError: At least one piece is invalid
>>> TangramPieces('incorrect_pieces_2.xml')
...
tangram.TangramPiecesError: At least one piece is invalid
>>> TangramPieces('incorrect_pieces_3.xml')
...
tangram.TangramPiecesError: At least one piece is invalid
>>> TangramPieces('incorrect_pieces_4.xml')
...
tangram.TangramPiecesError: At least one piece is invalid
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4. Second task (4 marks)
You have to check whether the sets of pieces represented in two .xml files are identical, allowing for pieces to
be flipped over horizontally, flipped over vertically, and rotated by 90 degrees. Here is the expected behaviour
of your program.
$ python3
...
>>> from tangram import *
>>> pieces_1 = TangramPieces('pieces_A.xml')
>>> pieces_2 = TangramPieces('pieces_AA.xml')
>>> pieces_1.are_identical_to(pieces_2)
True
>>> # Next line is OK as the shape in shape_A_1.xml, being convex, is a valid piece
>>> pieces_3 = TangramPieces('shape_A_1.xml')
>>> pieces_1.are_identical_to(pieces_3)
False
Note that the method are_identical_to() does not print out True or False, but returns True or False.
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5. Third task (5 marks)
You have to check whether the pieces represented in an .xml file are a solution to a tangram puzzle represented
in another .xml file. Here is the expected behaviour of your program.
$ python3
...
>>> from tangram import *
>>> shape = TangramShape('shape_A_1.xml')
>>> pieces = TangramPieces('tangram_A_1_a.xml')
>>> shape.has_as_solution(pieces)
True
>>> pieces = TangramPieces('tangram_A_1_b.xml')
>>> shape.has_as_solution(pieces)
True
>>> pieces = TangramPieces('tangram_A_2_a.xml')
>>> shape.has_as_solution(pieces)
False
>>> shape = TangramShape('shape_A_2.xml')
>>> pieces = TangramPieces('tangram_A_2_a.xml')
>>> shape.has_as_solution(pieces)
True
>>> pieces = TangramPieces('tangram_A_2_b.xml')
>>> shape.has_as_solution(pieces)
True
>>> pieces = TangramPieces('tangram_A_1_a.xml')
>>> shape.has_as_solution(pieces)
False
Note that the method shape.has_as_solution() does not print out True or False, but returns True or False.