INFO 206B

INFO 206B, Assignment 8. Submit your Jupyter notebook (.ipynb file) that contains your well-commented code. Please name your file that you submit {firstname_lastname}_A8.ipynb.

YouTube is littered with fake videos of purportedly amazing basketball shots. In this assignment, you will write some code to analyze the trajectory of ballistic or projectile motion in a video to determine if it is real or not. Ballistic motion occurs when the only significant force on an object is gravity (e.g., a basketball free-throw).
Here is a sample video of a ballistic motion.
I have extracted for you 25 evenly spaced frames from this video as well as the x-y coordinates of the ball on each of these frames. The frames are stored as standard PNG images and the coordinates are stored as a CSV file in which each row corresponds to the x- and y-coordinates. Download this data.
Load the CSV file into a 25 x 2 numpy matrix.
Load and display each of the 25 frames into a figure with 5 x 5 subplots. Overlay onto each figure, the corresponding coordinate to make sure that your loaded coordinates correspond to the position of the ball. Your code should generate a figure that looks something like this.
Fit a parabola y = ax^2 + bx + c to the coordinates using least-squares estimation (do not use any libraries or pre-packaged code, you must build the linear system and solve directly for the least-squares estimate of the parameters a,b,c).
To help you visually assess how well the parabola fits the underlying data, plot the least-squares curve overlaid atop the 25 selected points. Because our sampling of the coordinates is pretty sparse, you'll want to plot this curve with a denser sampling of x- and y- coordinates. Remember that the origin in most plots is in the bottom left corner, whereas it is in the upper left corner for images. As such, make sure to reverse the vertical axis in your plot so that the origin is in top left corner. Your code should generate a figure that looks something like this.
It is always good to verify your solutions by going back to the original data, in our case, the video frames. Write some code to display each video frame. Overlay on each frame the user-selected position of the ball and the full parabolic trajectory to make sure that the ball in each frame follows the expected ballistic trajectory. Your code should generate an animation that looks something like this.

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