Computer Graphics Matrices Tutorial

Matrices are fundamental in computer graphics, providing a way to represent transformations and other operations. This tutorial will guide you through the basics of matrices in computer graphics.

What are Matrices?

In mathematics, a matrix is a rectangular array of numbers. In computer graphics, matrices are used to transform objects, such as scaling, rotating, and translating them.

Types of Matrices

Transformation Matrices: Used to transform objects in space.
Projection Matrices: Used to project 3D objects onto a 2D plane.
Model-View-Projection Matrices: Combines model and view transformations with projection.

Matrix Operations

Multiplication: Matrices can be multiplied to combine transformations.
Inverse: Every matrix has an inverse, which can be used to reverse a transformation.

Example

Here's a simple example of a 3x3 matrix:

[ 1  0  0 ]
[ 0  1  0 ]
[ 0  0  1 ]

This matrix represents a translation of (0, 0, 0).

Applications

Matrices are used in various applications, such as:

Rendering 3D scenes: To transform objects and project them onto the screen.
Animation: To create smooth and realistic animations.
Computer Vision: To analyze and process images.