CS0045 Module 6

A rectangular array of mathematical expressions, much like a two-dimensional array

Matrix

Example of a matrix displayed in the common square brackets form

Matrices values are indexed by (__) where is the row and _ is the column

i, j

Matrices values are indexed by (i, j) where i is the __ and j is the __

row, column

The only requirement is that the two operands have exactly the same row and column dimensions

Addition and Subtraction in Matrices

The product of a scalar and a matrix is as straightforward as addition and subtraction

Scalar Product

The product of a matrix with another matrix is quite a bit more involved in computer graphics

Matrix Vector Product

OpenGL uses ___ matrix for transformations

4 x 4

Until then, we only considered 3D vertices as a (___) triplet

x, y, z

Until then, we only considered __ __ as a (x, y, z) triplet

3D vertices

Let’s introduce _. We will now have (x, y, z, _) vectors

w

(x, y, z, w) vectors

The reason why we have glVertex4f

If w == 1, then the vector (x, y, z, 1) is a _____

position in space

If w == 0, then the vector (x, y, z, 0) is a ____

direction

A translation matrix looks like this:

where X, Y, Z are the values that you want to add to your position

If we want to translate the vector (10,10,10,1) of 10 units in the X direction, we get:

A Scaling Matrix looks like this:

If you want to scale a vector (position or direction, it doesn’t matter) by __ in all directions

2.0

Left-Hand

Right-Hand