cst 325 w3

This week, we learned how vectors and matrices are connected. We also learned how matrices are used to manipulate space and how to solve problems with matrix operations. We also created and combined matrix transformations.

Unfortunately, I did not have very much time to work on the lab because I went out of town and only had my laptop which is horrible. In the future, I think I’ll only go out of town on holidays and everyone else is going to have to deal with the fact that I have school, which is a priority and doing construction work all weekend on a condo I have no equity in is not really my priority.

A matrix describes the relationship between 2 coordinate spaces. It is a rectangular grid of numbers arranged into rows and columns defined in rows first then columns. A matrix may have 1 row or 1 column and are called row vectors and column vectors. A transposed matrix is where the column and rows are flipped. A diagonal matrix is equal to its transpose matrix. A scalar is a regular number and you just multiply the scalar by every element in the matrix. When you multiply two matrices, the columns in A must be the same amount of rows in B, if not it is not defined.

Rotation is about a point in 2D or about the origin based on the angle value. Scale is used to make matrices larger or smaller b a factor of k. There is uniform and nonuniform scale. In uniform scale, it dilates about the origin and preserves angles and proportions, the lengths change by k units, areas change by k squared, and volumes by k cubed. Nonuniform scale has different scale factors. The absolute value of k is shorter when less than 0. When k is 0, it has orthographic projection. Is reflected when k is negative and scales (?) when k is positive. It scales along the x axis when applied about the perpendicular axis. The basis vectors are independently affected by scale vectors so one can make a big y and small x object. In reflection, it is flipped about a line 2D or plane 3D. Shear is a transformation that skews the coordinate space, stretching nonuniformly. The angles are not preserved, but the areas and volumes are preserved.