In Euclidean geometry, a vector is an object that represents a physical quantity that has both the magnitude and direction. Kivy library includes Vector class and provides functionality to perform 2D vector operations.

The Vector class is defined in kivy.vector module. Kivy”s Vector class inherits Python”s builtin list class. A Vector object is instantiated by passing x and y coordinate values in a cartesian coordinate system.

from kivy.vector import Vector
v=vector(10,10)

The two parameters are accessible either by the subscript operator. First parameter is v[0], and second parameter is v[1].

print (v[0], v[1])

They are also identified as x and y properties of a Vector object.

print (v.x, v.y)

You can also initialize a vector by passing a two value list or a tuple to the constructor.

vals = [10,10]
v = Vector(vals)

Example

The Vector class in Kivy supports vector operations represented by the usual arithmetic operations +, −, /

The addition of two vectors (a,b)+(c,d) results in a vector (a+c, b+d). Similarly, “(a,b) – (c,d)” is equal to “(a − c, b − d)”.

from kivy.vector import Vector

a = (10, 10)
b = (87, 34)
print ("addition:",Vector(1, 1) + Vector(9, 5))
print ("Subtraction:",Vector(9, 5) - Vector(5, 5))
print ("Division:",Vector(10, 10) / Vector(2., 4.))
print ("division:",Vector(10, 10) / 5.)

Output

addition: [10, 6]
Subtraction: [4, 0]
Division: [5.0, 2.5]
division: [2.0, 2.0]

Methods in Vector Class

Following methods are defined in Kivy”s Vector class −

angle()

It computes the angle between a vector and an argument vector, and returns the angle in degrees.

Mathematically, the angle between vectors is calculated by the formula −

$$theta =cos^{-1}left [ frac{xcdot y}{left| xright|left|y right|} right ]$$

The Kivy code to find angle is −

Example

a=Vector(100, 0)
b=(0, 100)
print ("angle:",a.angle(b))

Output

angle: -90.0

distance()

It returns the distance between two points. The Euclidean distance between two vectors is computed by the formula −

$$dleft ( p,q right )=sqrt{left ( q_{1}-p_{1} right )^{2}+left ( q_{2}-p_{2} right )^{2}}$$

The distance() method is easier to use.

Example

a = Vector(90, 33)
b = Vector(76, 34)
print ("Distance:",a.distance(b))

Output

Distance: 14.035668847618199

distance2()

It returns the distance between two points squared. The squared distance between two vectors x = [ x1, x2 ] and y = [ y1, y2 ] is the sum of squared differences in their coordinates.

Example

a = (10, 10)
b = (5,10)
print ("Squared distance:",Vector(a).distance2(b))

Output

Squared distance: 25

dot(a)

Computes the dot product of “a” and “b”. The dot product (also called the scalar product) is the magnitude of vector b multiplied by the size of the projection of “a” onto “b”. The size of the projection is $costheta $(where $theta$ is the angle between the 2 vectors).

Example

print ("dot product:",Vector(2, 4).dot((2, 2)))

Output

dot product: 12

length()

It returns the length of a vector. length2() method Returns the length of a vector squared.

Example

pos = (10, 10)
print ("length:",Vector(pos).length())
print ("length2:",Vector(pos).length2())

Output

length: 14.142135623730951
length2: 200

rotate(angle)

Rotate the vector with an angle in degrees.

Example

v = Vector(100, 0)
print ("rotate:",v.rotate(45))

Output

rotate: [70.71067811865476, 70.71067811865476]