Unit vectors and normalization

In vector mathematics, a unit vector is a vector of any given direction with magnitude 1. Each vector on the following image is a unit vector:

The above example showed four simple unit vectors pointing at all directions of the graph, the following is a different example, of a unit vector with direction (1, 1):

A very important fact about unit vectors, is that a unit vector multiplied by any scalar will have the same direction. This property is essential for any algorithm dealing with geometrical calculations. A perfect real-life usage example of unit vectors is moving a character in video games along a given direction with some set speed.

The following example demonstrates finding different vectors with the use of unti vectors:

Vector normalization

A normalization operation is used to obtain a unit vector from any given vector. To normalize a vector means to divide each component of a vector with it's magnitude:

v1 = {
    'x': 3,
    'y': 5
}

magnitude = math.sqrt(v1.x * v1.x + v1.y * v1.y)
v1norm = {
    'x': v1.x / magnitude,
    'y': v1.y / magnitude
}
print(v1norm)

{'x': 0.514496, 'y': 0.857493}

This operation is implemented by GLM as simply:

v1 = glm.vec2(3, 5)
v1norm = glm.normalize(v1)