Every one of us uses matrices nearly everyday in our lives and probably unaware of it. Matrices are commonly used in computers for their 3D graphics. Most of the matrices that are used are either 3x3 or 4x4 matrices and are computed by either rotation matrices or translation matrices. The matrices that are used are an array that holds numbers, commonly called a 3x3 array or 4x4 array.
Or .
Examples of 3x3 and 4x4 matrices.
The reason that matrices are used is because matrices have some very interesting properties. One of these is the ability to concatenate many mathematical operations into one single matrix. This means that with just one matrix it is possible to perform the task of literally hundreds of operations within that one single matrix. Another reason that matrices are used is because they are very easy to use and a matrix multiply routine is really all you need to get all the desired results. The algebra involved is also fairly well hidden from the programmer of the graphics, which, therefore, makes the code much easier to read and thus easier to understand. Another good characteristic of matrices is that they are very intuitive. This means that someone can look at a matrix and be able to actually visualize something as complex as its rotation, just by the way the numbers are arranged in the matrix. .
In computer programming of its graphics the matrices are simply used a multidimensional array. The only thing that is even the least bit complicated, in theory, is how to multiply the matrix and what to multiply it. This is how they are able to concentrate multiple matrices into one single matrix. The following is how you would use matrix multiplication on a 4x4 matrix to another 4x4 matrix: .
X =.
Although this may look complicated at first glance, it really isn't. If you look closely at it and you'll see that it is really just a simple pattern. Here are some of the matrices that are used in computer graphics in order to make the objects they represent turn into 3D objects.
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