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# Vectors¶

The Vec2, Vec3, Vec4 classes implement vectors in 2, 3 and four dimensions. They support basic arithmetic via overloaded operators. Essentially, the following basic operations are available:

• adding and subtracting two vectors
• negation
• multiplying and dividing by scalar value

This is shown in the following example:

vec_a=geom.Vec2(1, 0)
vec_b=geom.Vec2(0, 1)
print(vec_a, vec_b)
print(vec_a+vec_b)
print(vec_a*3-vec_b)


The standard vector operations are implemented as free standing functions:

vec_a=geom.Vec3(1, 0, 0)
vec_b=geom.Vec3(0, 1, 0)

print(geom.Dot(vec_a, vec_b))
print(geom.Cross(vec_a, vec_b))

print(geom.Normalize(geom.Vec3(1, 1, 0)))

print(geom.Length(geom.Vec3(1, 1, 1)))


## Vector Classes¶

class Vec2([x=0.0, y=0.0, z=0.0])
class Vec2(vec)

Real-valued vector in 2 dimensions.

Parameters: x (float or int) – x coordinate y (float or int) – y coordinate vec (Vec2, Vec3 or Vec4) – the coordinates are set to the coordinates of vec. If vec is a Vec2, the coordinates are copied directly, If vec is a Vec3, the x and y coordinates are set to the coordinates of vec and z is silently swallowed. If vec is of type Vec4, x and y are divided by the homogenous coordinate w, raising a DivideByZeroException when w is zero.
x

The x-coordinate of the vector.

Type: float
y

The y-coordinate of the vector.

class Vec3([x=0.0, y=0.0, z=0.0])
class Vec3(vec)

Real-valued vector in 3 dimensions.

Parameters: x – x coordinate y – y coordinate z – z coordinate vec (Vec2, Vec3 or Vec4) – the coordinates are set to the coordinates of vec. If vec is a Vec3, the coordinates are copied directly, If vec is a Vec2, the x and y coordinates are set to the coordinates of vec and z is initialized to zero. If vec is of type Vec4, x, y and z are divided by homogenous coordinate w, raising a DivideByZeroException when w is zero.
x

The x-coordinate of the vector.

Type: float or int
y

The y-coordinate of the vector.

Type: float or int
z

The z-coordinate of the vector.

Type: float or int
class Vec4([x=0.0, y=0.0, z=0.0, w=1.0])
class Vec4(vec)

Real-valued vector in 4 dimensions.

Parameters: x (float or int) – x coordinate y (float or int) – y coordinate z (float or int) – z coordinate w (float or int) – w (homogenous) coordinate vec – the coordinates are set to the coordinates of vec. If vec is a Vec4, the coordinates are copied directly, If vec is a Vec2, the x and y coordinates are set to the coordinates of vec and z and w are initialized to 0 and 1, respectively. If vec is of type Vec4, x, y and z are divided by homogenous coordinate w, raising a DivideByZeroException when w is zero.
x

The x-coordinate of the vector.

Type: float or int
y

The y-coordinate of the vector.

Type: float or int
z

The z-coordinate of the vector.

Type: float or int
w

The homogenous coordinate.

Type: float or int

## Functions Operating on Vectors¶

Cross(vec_a, vec_b)

Cross product of vec_a and vec_b

Dot(vec_a, vec_b)

Dot (scalar) product of vec_a and vec_b

Parameters: vec_a (Vec3) – first vector vec_b (Vec3) – second vector
Length(vec)

Length of vector

Parameters: vec (Vec2, Vec3 or Vec4) –
Length2(vec)

Returns the squared length of vec

Parameters: vec (Vec2, Vec3 or Vec4) –
Normalize(vec)

Returns a normalized version of vec

Parameters: vec (Vec2, Vec3 or Vec4) – Vector to be normalized

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## Previous topic

geom – vectors, matrices and geometrical objects

Matrices