Description
This assignment has one part: Part I – Analytical geometry (14 marks) Part I – Analytical Geometry You will create a small graphical Python 3 program that draws a few shapes using the turtle library and information taken from the user. You will also use the Python math library to do calculations. Your TA will introduce you to these libraries and their intricate details during tutorials. You can start learning about turtle graphics here. You can also find documentation about Turtle graphics here. The assignment generally revises your concepts regarding constants, variables, expressions, as well as importing and using libraries, getting input from users, casting variables to different types, problemsolving. It will also help you to develop an interactive application using graphics and drawing in a coordinate system. Your program will present an 800×600 pixel window with (0,0) being the bottom left corner point and (800,600) being the top right corner point. Within this coordinate system, your program will draw an x and y axes that identify the centre of the window. Your program will prompt the user for values that define a circle and a line in this coordinate system and draw them. Finally, your program will perform calculations to determine whether the line and circle intersect. You can think of this assignment as a series of stages to complete. First, you import some libraries. Next, you define constants (all upper case). Some of these are obvious like the window size. You will likely identify more constants as you write the rest of the program. Then setup your window and carry out the rest of the assignment requirements. This code should get you started. With your window ready, draw your axis. This axis should cross through the middle point of the screen, i.e. (400,300). Remember to use your constants here and later on. Then prompt the user for input, cast it to the proper type, and store it in variables. Remember to use descriptive variable names. Draw your circle and your line. Calculate the number of intersection points between the circle and line. Then, produce a conditional statement that lets you display a message indicating the number of intersection points to the user. Drawing in Turtle: You can imagine the turtle drawing system as a turtle carrying a pen. The turtle starts at some default location within the window and has its pen pressed down and ready to draw. To draw a line from the turtle’s location to a new point, tell the turtle to move to the new location. It will drag the pen along as it moves to the new location effectively drawing a line. If you tell the turtle to lift up the pen then tell it to move to a new point, it will go to this new point without drawing the line. For this assignment, you must know how to position the turtle in a specific location (a point in the coordinate system, also known as pixel location), how to start and stop drawing, and how to change drawing colors. Draw the axis in black, the circle in red, the line in blue, and the intersect/text in green. You can use the circle command to draw the circle. The circle command, by default, draws circles from the middle of the bottom edge. Therefore, to draw a circle around a centre point, you must determine where the proper start location is (hint: adjust from the centre using the radius). Getting Input: Read the input from the user from command line (no command line argument). Display a prompt in the terminal window with a print statement, or by providing a parameter to the input function. Note that the user will enter their input in the terminal window, not in the graphics window. You will need to prompt for 7 and only 7 inputs. You will need an integer xc and integer yc for the centre (xc,yc) of the circle and a float r for the radius. You will need an integer x1 and integer y1 for the start (x1,y1) of the line and an integer x2 and integer y2 for the end (x2,y2) of the line. These are pixel locations in the window. A circle with middle (400,300) and radius 300 would be drawn in the middle of the window touching the top and bottom of the window. Analytical Geometry: We have 7 values that you should have stored as input: xc, yc, r, x1, y1, x2, y2. We will use these in our calculations. We will make use of 3 intermediate calculations to determine intersections. These fulfill the parameters of the quadratic We can solve this quadratic to determine intersections alpha ( ). However, we will not do this directly, but instead using the quadratic formula. Before we jump directly to using this to calculate alpha ( ) we can look at the value under the root to determine the number of intersections. Note that an alpha value greater than 1 or less than 0, indicates that the intersection occurs outside the end points of the line segment. These intersections should not be drawn. If then there are no intersections. We cannot use the imaginary number from square rooting a negative number in this situation. If then there is 1 intersection. The square root value is the root of 0. The result of adding and subtracting 0 is the same number. So there is only one result to the alpha. If then there are 2 intersections. Since the value is positive when add or subtract the result of rooting it, we will produce two different alphas; one for each intersection. After making a decision based on this value, we need to draw the result of the intersections. If there are no intersections, you should draw the words “No Intersect!” in the centre of the window. If there is one, or two intersections, you will should then calculate the alpha of the quadratic formula for each. With each alpha, we can calculate the coordinates of the intersection point using the following two formulas With this coordinate, you should draw a circle around this location. Using a radius of 5 (constant) is a good size. In effect the alpha is a ratio spot along the line between (x1,y1) and (x2,y2). An alpha of 0 is the point (y1,x1) and an alpha of one is the point (x2,y2). One final and very important point: although we may calculate an alpha that indicates that there is an intersection, this intersection may not be between the two points of the line. The calculation we have used so far also gives us intersections if line continue into infinity off either end. To ensure we only plot intersections between the two points we need to make sure that the alpha greater than or equal to zero and less than or equal to 1. Additional Specifications: Ensure that your program meets all the following requirements: You should have the class, your name, your tutorial, your student id, the date, and a description at the top of your code file in comments. Marks are given for these. The code file should be .py Import the necessary libraries Use constants appropriately. Use descriptive naming of variables. The use of variables that follow the math descriptions given are fine for those purposes. Draw your axis black, your circle red, your line blue, and your intersection circles/text green. Use descriptive prompts for input and cast input to the indicated types. Use in-line comments to indicate blocks of code and describe decisions or complex expressions. You do not have to worry about making sure input is of the correct type. Your program should crash if the values given cannot be cast from strings into the request types. So don’t worry about input validation. Example: Example input in the terminal window may looks as follow: Enter circle x coordinate: 400 Enter circle y coordinate:300 Enter radius of circle:200 Enter line start x coordinate:100 Enter line start y coordinate:200 Enter line end x coordinate:700 Enter line end y coordinate: 200 The output looks like: Submission: After you have completed this assignment, you should have written a total of one Python programs, saved as .py files. Use the University of Calgary Desire2Learn system (http://d2l.ucalgary.ca) to submit your assignment work online. Log in using your UofC eID and password and find our course, CPSC 231 L01 and L02, in the list. Then navigate to Assessments -> Dropbox Folders, and find the folder for Assignment #4 here. Collaboration Discussing the assignment requirements with others is a reasonable thing to do, and an excellent way to learn. However, the work you hand-in must ultimately be your work. This is essential for you to benefit from the learning experience, and for the instructors and TAs to grade you fairly. Handing in work that is not your original work, but is represented as such, is plagiarism and academic misconduct. Penalties for academic misconduct are outlined in the university calendar. Here are some tips to avoid plagiarism in your programming assignments. 1. Cite all sources of code that you hand-in that are not your original work. You can put the citation into comments in your program. For example, if you find and use code found on a web site, include a comment that says, for example: # the following code is from https://www.quackit.com/python/tutorial/python_hello_world.cfm. Use the complete URL so that the marker can check the source. 2. Citing sources avoids accusations of plagiarism and penalties for academic misconduct. However, you may still get a low grade if you submit code that is not primarily developed by yourself. 3. Discuss and share ideas with other programmers as much as you like, but make sure that when you write your code that it is your own. A good rule of thumb is to wait 20 minutes after talking with somebody before writing your code. If you find yourself exchanging code by electronic means, writing code while sitting and discussing with a fellow student, typing what you see on another person’s console, then you can be sure that “your” code is not substantially your own, and your sources must then be cited to avoid plagiarism. 4. Collaborative coding is strictly prohibited. Your assignment submission must be strictly your code. Discussing anything beyond assignment requirements and ideas is a strictly forbidden form of collaboration. This includes sharing code, discussing code itself, or modeling code after another student’s algorithm. You cannot use (even with citation) another student’s code. 5. We will be looking for plagiarism in all code submissions, possibly using automated software designed for the task. For example, see Measures of Software Similarity (MOSS – https://theory.stanford.edu/~aiken/moss/). Remember, if you are having trouble with an assignment, it is always better to go to your TA and/or instructor to get help, than it is to plagiarize. Grading for Part I: 14 – Fulfilled assignment specification and solved the problems completely 12 – Appears to fulfill assignment part 1 spec 9 – Code has part of intersection work done, but obvious errors/incomplete 6 – Code draws axis, gets input, draws circle/line 3 – Code draws axis and gets input 1 – 2 Syntax error or barely written any code. Credits: A few problems were derived from problems originally posted by Dr. Jonathan Hudson from University of Calgary.
