Vectors

Vectors is a simple library toolkit dealing with common vector logic in the 3-dimensional space.

Installation

pip install vectors

Documentation

• Initialization
  • Position arguments
  • From list
  • From points
  • Spherical
  • Cylindrical
• To points
• Magnitude
• Addition
• Subtract
• Multiplication
• Dot Product
• Cross/Scalar Product
• Unit Vector
• Angle Theta
• Rotate
• Parallel, Perpendicular, Non-Parallel

Initialization

There are multiple ways to create our vector instances using the vectors module.

Position arguments

from vectors import  Vector

v1 = Vector(1, 2, 3) #=> Vector(1, 2, 3)

From list

from vectors import Vector
components = [1.2, 2.4, 3.8]

v = Vector.from_list(components) #=> Vector(1.2, 2.4, 3.8)

From points

Vectors package contains also Point class that allow to create vector from to points.

from vectors import Point, Vector
p1 = Point(1, 2, 6) #=> Point(1, 2, 6)
p2 = Point(2, 0, 2) #=> Point(2, 0, 2)

v = Vector.from_points(p1, p2) #=> Vector(1, -2, -4)

Spherical

Using spherical coordinates in the r, theta, phi space.

from vectors import Vector

r, theta, phi = 1, 0, 0
v = Vector.spherical(r, theta, phi) #=> Vector(0.0, 0.0, 1.0)

Cylindrical

Using cylindrical coordinates in the r, theta, z space.

from vectors import Vector

r, theta, z = 1, 0, 0
v = Vector.cylindrical(r, theta, z) #=> Vector(1.0, 0.0, 0)

To points

We can also get access to the vector array to use it with other libraries.

from vectors import Vector
v = Vector(1,2,3)

v.to_points() #=> [1, 2, 3]

Magnitude

We can get the magnitude of the vector easily.

from vectors import Vector
v = Vector(2,0,0)
v.magnitude() #==> 2.0

v1 = Vector(1,2,3)
v1.magnitude() #==> 3.7416573867739413

v2 = Vector(2,4,6)
v2.magnitude() #==> 7.483314773547883

Addition

We can add a real number to a vector or compute the vector sum of two vectors as follows.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.add(2)  #=> Vector(3.0, 4.0, 5.0)
v1 + 2     #=> Vector(3.0, 4.0, 5.0)

v1.sum(v2) #=> Vector(3.0, 6.0, 9.0)
v1 + v2    #=> Vector(3.0, 6.0, 9.0)

Both methods return a Vector instance.

Subtract

We can subtract a real number from a vector or compute the vector subtraction of two vectors as follows.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.subtract(2)  #=> Vector(-1, 0 ,-1)
v1 - 2          #=> Vector(-1, 0, -1)

v1.subtract(v2) #=> Vector(-1, -2, -3)
v1 - v2         #=> Vector(-1, -2, -3)

Both methods return a Vector instance.

Multiplication

We can multiply a vector by a real number.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.multiply(4) #=> Vector(4.0, 8.0, 12.0)
# TODO: add * operator for real numbers

The above returns a Vector instance.

Dot Product

We can find the dot product of two vectors.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.dot(v2) #=> 28

We can also use angle theta on the dot function.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

# TODO: This does not work
v1.dot(v2, 180)

Dot product returns a real number.

Cross/Scalar Product

We can find the cross product of two vectors.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.cross(v2) #=> Vector(0, 0, 0)

Cross product returns a Vector instance, which is always perpendicular to the other two vectors.

Unit Vector

We can find the unit vector of a given vector.

from vectors import Vector
v1 = Vector(1,2,3)

v1.unit() #=> Vector(0.267261241912, 0.534522483825, 0.801783725737)

Unit vector function returns a Vector instance that has a magnitude of 1.

Angle Theta

We can also find the angle theta between two vectors.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.angle(v2) #=> 0.0

Angle is a measured in degrees.

Rotate

We can also rotate vector by given angle.

from vectors import Vector
import math
v = Vector(1,0,0)

v1.angle(math.pi/2) #=> Vector(6.123233995736766e-17, 1.0, 0)

It does not correct problem of floating numbers.
Angle is provided in radians.

Parallel, Perpendicular, Non-Parallel

We can check if two vectors are parallel, perpendicular or non-parallel to each other.

from vectors import Vector
v1 = Vector(1,2,3)
v2 = Vector(2,4,6)

v1.parallel(v2) #=> True
v1.perpendicular(v2) #=> False
v1.non_parallel(v2) #=> False

All of the above return either True or False.

#TODO

• Change to named tuple?
• Implement sequence protocol
• Floating point fix
• Fix dot with theta value
• Tests
• Generalize methods so it is easier to inherit
• Vector2D? Vector4D?
• Allow for * operator in multiplication with real numbers
• Allow for initialization with key arguments
• x, y, z unit vectors
• visualization / demo ?
• Check for optimization without loosing simplicity
• Standardize for radians/degrees
• Logo?
• Force to update package in pip

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I'm looking for collaborators, so if you have something interesting, feel free to collaborate.