Description
1 Objectives
1. Gain familiarity with the Python programming language
2. Use the OOP aspects of Python
3. Do some basic data plotting and visualization
2 Tasks
1. Write a Python class called Vector to represent a 2-dimensional point/vector, with x and y coordinates
(a) Include methods to overload addition and subtraction with other vectors
(b) Include a method to compute the dot product with another vector
(c) Include a method to compute the distance to another vector
2. Write a Python class called Geometry that represents a polygon with several vertices and faces, given
by vectors.
(a) You will add a face to the geometry by adding both of its constituent vectors. So when you add
a face, check to see if you’re connecting to a vertex that is already present!
i. One way to make the “bookkeeping” simple is to store the vertices and faces separately:
maintain a list or dictionary of vertices and then a list of pairs of those vertices, where a pair
represents a face.
ii. Include a method to add a face to the geometry. You do not need to worry about removing
or “splitting” faces
iii. Include a method to check that the geometry is “closed” – the faces create a cycle that start
and end at the same vertex.
(b) Write a method to draw the outline of the shape with matplotlib.
(c) Write a method to determine if a given point is inside the geometry.
i. To do this, there is a nice simple geometric algorithm:
ii. Consider the query point, then “cast a ray” outward from that point in any direction (straight
to the right will the be the easiest to program).
iii. Count the number of faces that the ray passes through: if it is odd, the point is inside the
shape; if even, it lies outside.
iv. Two special cases to consider:
A. If the ray passes along a face (the body must be non-convex for this), don’t count it as
an intersection;.
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B. If the ray passes through a vertex exactly, only count it as a single intersection (not both
faces that meet at that vertex).
3. Test your Geometry class and its methods on various shapes: triangle, rectangle, star, etc. Be creative!
Show some examples of the interior/exterior testing (you do not have to illustrate/visualize the raycasting process).
3 Submission
Zip your source files and upload them to the assignment page on MyClasses. Be sure to include all source
files, properly documented, a README file to describe the program and how it works, along with answers to
any above discussion questions.
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