Final Exam Topics
CS145: Images and Imagination, Fall 2010

This will be a closed book exam. Material will be drawn from assigned readings, class lectures, and labs.

Topics

• The Final Exam will focus mostly on material covered since the Exam 1 and Exam 2. However, a few topics will be repeated and, keep in mind, that most of the material is cumulative, so you need to know the earlier material in order to do the new material.

• Image filters

  • What is the pixels[] array.
  • How does one use the pixels[] array, e.g. given a pixel in the image (i.e. row and column) where is this pixel stored in the pixels array.
  • How does one combine and/or modify an image by setting values in the pixels array. See Lab 7 for example.

• Trigonometry

  • How are the functions sin(θ) and cos(θ) defined. That is, how do they relate to points in a unit circle or a circle of raduius r.
  • What are the maximum and minumum values of sin(θ) and cos(θ) and for what angles to do they occur.
  • What are the values of sin(θ) and cos(θ) for θ=0, 90, 180, 270, and 360 degrees.
  • What do the graphs of sin and cos (as a function of θ) look like?
  • Given a function, e.g. func(θ) = A*sin(f*θ). How does varying A (the amplitude) and f (frequency) affect the graph of func?

• Complex Numbers

  • What is an imaginary number? What is i and how does one compute powers of i, e.g. i², i³, etc.
  • What is a complex number.
  • Know the standard form of a complex number: (a + b i).
  • How does one add, subtract, and multiply complex numbers and place the result in standard form.
  • What is the complex plane and how does one plot numbers in the complex plane .
  • What is the length (or modulus) of a complex number and how does one compute it.

• Other items

  • How does one use the map function to do rescaling (e.g. see the Mandelbrot code)
  • What is the Mandelbrot Set and what does it mean to iterate on a variable.
  • How/why is the break function used in a for-loop.
  • What is the syntax for using functions in a class (e.g. Complex.cAdd(c1, c2)) and how does one combine them to compute such things as z = z² + c (e.g. see your the Mandelbrot code for the syntax) .