Write a program that loads in an image and repeatedly rotates it by x degrees until the image has been rotated 360⁰ in total.
Your program should include the following:
• A parameter for the angle to rotate by at each step
• A function for multiplying two arbitrary nxm matrices (n and m should be dynamic)
• A rotation matrix of the format below. Each pixel in the image must be multiplied by R
cos
− sin
using the matrix multiplication function (prior bullet).
= �sin
cos
�
• An array variable for your image that is large enough for the entire image to be visible during all the intermediate rotations (when you’ve rotated 45⁰, the corners of your image should not be clipped)
• Absolute color error calculation: Code to compute the absolute error between the colors of the original image’s pixels and the colors of the image after it’s been rotated 360⁰
• Pixel displacement calculation: Code to compute the distance each pixel moves during rotation. This total value should be divided by:
(numPixelsInImage * numTimesImageWasRotated)
You can use the OpenCV and Numpy libraries for opening, displaying, and saving images and to create empty arrays/images. You may also use the math library built into Python for sine, cosine, and PI calculations. You may not use any other built-in functions or libraries.
Submit your code and a report. Your report must be a PDF and contain the following:
• Summary of the assignment goals
• 3+ images showing your code at intermediate stages (image rotated x degrees) with captions saying what angle stepsize is being used and the total rotation of the image so far (i.e. Image rotated 60⁰ with steps of 20⁰, 3 rotation operations applied so far.)
• A chart with the following information filled in:
Angle Step Size
# Rotations
Absolute Color Error
Pixel Displacement
(# Rotations) * (Pixel
Displacement)
45⁰
8
60⁰
6
90⁰
4
120⁰
3
180⁰
2
360⁰
1
• Conclusions drawn from the completed chart
• Discussion of any issues encountered
