Matrices

In computer graphics, matrices are used to calculate object transforms like translation which is movement, scaling in X,Y and Z axis, and rotation around the X,Y and Z axis. We will also be changing the position of objects from one coordinate system to the other, which are called space transforms. We will see how matrices work and how they help in simplifying the mathematics.

Matrices are represented as having rows and columns. A matrix with m number of rows and n number of columns is said to be a matrix of size m × n. Each element of a matrix is represented as indices ij where i specifies the row number and j represents the column number.

So, a matrix M of size 3 × 2 is represented as as follows:

Here, matrix M has three rows and two columns and each element is represented as m11, m12 and so on until m32, which is the size of the matrix.

In 3D graphics programming, we will be mostly dealing with a 4×4 matrix. So, let us look at another matrix of size 4x4.

Matrix A with numbers in it is:

Here, the element A₁₁ = 3, A₃₂ = 1 and A₄₄ = 1 and the dimension of the matrix is 4×4.

We can also have a single-dimension matrix like vector B as follows which is called the row vector or a column vector as shown as follows ad vector C:

• Two matrices are equal if the number of rows and columns are the same and if the corresponding elements are of the same value.
• Two matrices can be added if they have the same number of rows and columns. We add each element of the corresponding location on both matrices to get a third matrix of the same dimension as the added matrices.