can be kept in that form.
NOTE of June 28th: Here is an earlier SAMPLE QUIZ. Your quiz will be quite similar, with changes in the actual coordinates, the angles, etc.
IMPORTANT NOTE: Your diagnostic/preview exercise in class on Thursday, June 26, showed that a number of you have problems with the material and need to work hard to prepare for the quiz on Monday. See the section further down entitled, "Things many of you need to work on" for specific comments about what you need to pay careful attention to and what you need to practice.
Remember, you can use our mailing list to discuss any points you need clarified.
Here are excerpts from a guide for a former Midterm which applies quite well to our first quiz:
1. Trigonometry basics: Be able to plot sine and cosine reasonably accurately from -2π to +2π. Know conversions between radians and degrees for 45°, 90°, etc. Know the values of the sine and cosine of the most common angles, including π/4 and by extension, angles such as 5π/4.
2. 2x2 transformations: Be able to correctly write out a rotation matrix and scaling matrix.
3. Computations with 2D vectors and 2x2 matrices: Be able to
add vectors, multiply matrices together, in the correct order, and transform
vectors with matrices. All these computations are to be done manually with
numerical answers. Items such as
can be kept in that form.
4. Homogeneous coordinates. Be able to write down a scaling, rotation or translation matrix in 3x3 homogeneous coordinate form for 2D.
5. Compound matrix manipulations using homogeneous coordinates. Be able to show various relations and identities, such matrix multiplication that shows that a translation of -10,20 is the inverse of 10,-20.
6. Transformations that produce a given effect. Given two different positions and orientations of an object, figure out what simple matrix or simple product of matrices will produce one from the other.
Here's a question from a previous year: This question involves only 2x2 matrices, not ones using homogeneous coordinates.
Make sure you've studied the material in the book in Chapter 5, through page 206. Also, Sec. 5.3.
Since this is a closed book/notes quiz, you'll have to know various important things such as the sine and cosine of the basic positive and negative angles including 0, ±π/2 and ±π. You'll also have to know how to write down the rotation matrix and translation matrix in 3x3 homogeneous coordinates form.
Basic fact: A vector in 2D has an x and a y value, also called a point. If homogeneous coordinates are used, there's a third component, always = 1. Don't stick vector values in matrices; that doesn't make sense.
Always draw pictures corresponding to the examples you do or questions you answer. This is particularly useful when practicing to study for a test in this course. If you have a point at 10,10 and you translate it by tx = 5, it better end up at 15,10. Otherwise, you've done something wrong.
In two dimensions, you can do scaling and rotations with 2x2 matrices, but you cannot do translation with a 2x2. Translations require a 3x3 matrix in homogeneous coordinates. The vector (a point in 2D space) becomes a 3x1 vector with a 1 in the last, bottom element.
A matrix can be used to transform a vector by doing the multiplication with the vector on the right, yielding another vector. Be sure you can multiply matrices together. A good way to test yourself is to multiply a matrix by its inverse to make sure you get the right answer, the identity matrix. Simplest example, a +π rotation matrix times a -π rotation matrix. Or translate by 5,-10, then -5,10.