class Vector

• Read the guideline before start

In order to get information about vectors follow this:

• Vectors on coordinate plane
• Vector by two points
• Adding vectors
• Normalized vector
• Vectors dot product
• Angle between two vectors
• Rotating vectors

You recently got a job at a game development company as a graphic engineer. You have to calculate light tracing, but it is impossible without using vectors.

Vector on coordinate plane is directed line segment, that always starts in (0, 0) and ends in coordinates (x, y).

Implement Vector class, its __init__ method takes and stores two coordinates: x, y - coordinates of end of the vector, rounded to two decimals.

vector = Vector(-2.343, 8.008)
vector.x == -2.34
vector.y == 8.0

Vector class should have such magic methods:

• __add__

Addition of two Vectors should return Vector.

vector1 = Vector(2, 4)
vector2 = Vector(-1, 3)
vector3 = vector1 + vector2

isinstance(vector3, Vector) is True
vector3.x == 1
vector3.y == 7

• __sub__

Subtraction of two Vectors should return Vector.

vector1 = Vector(2, 4)
vector2 = Vector(-1, 3)
vector3 = vector1 - vector2

isinstance(vector3, Vector) is True
vector3.x == 3
vector3.y == 1

• __mul__

Multiplying Vector on a number should return another Vector.

vector1 = Vector(2, 4)
vector2 = vector1 * 3.743
isinstance(vector2, Vector) is True
vector2.x == 7.49
vector2.y == 14.97

Multiplying Vector on Vector should return their dot product.

vector1 = Vector(2.11, 4.55)
vector2 = Vector(-3.51, 10.33)
dot_product = vector1 * vector2
dot_product == 39.5954

Also, Vector class should have such methods:

• create_vector_by_two_points Takes start_point - tuple of point coordinates, start of the vector, end_point - tuple of point coordinates, end of the vector. It returns Vector.

start_point = (5.2, 2.6)
end_point = (10.7, 6)

vector = Vector.create_vector_by_two_points(start_point, end_point)
isinstance(vector, Vector) is True
vector.x == 5.5
vector.y == 3.4

NOTE: create_vector_by_two_points should be a classmethod

• get_length

Returns length of the vector.

vector = Vector(2, 4)
vector.get_length() == 4.47213595499958

• get_normalized

Returns normalized copy of vector.

vector1 = Vector(13, -4)
vector1.get_length() == 13.6

vector2 = vector1.get_normalized()

vector2.x == 0.96
vector2.y == -0.29
vector2.get_length() == 1.0

• angle_between

Takes vector and returns angle between current vector and vector in integer degrees.

vector1 = Vector(13, -4)
vector2 = Vector(-6, -11)
vector1.angle_between(vector2) == 102

Most likely you get cosine of the angle. To correct calculate angle use math library. For your cosine cos_a use math.degrees(math.acos(cos_a)) in order to get degrees.

NOTE: In this method round only returning degrees.

• get_angle

Returns angle between current vector and positive Y axis.

vector = Vector(33, 8)
vector.get_angle() == 76

• rotate

Takes degrees that is integer rotation degrees. It returns rotated Vector by degrees.

vector = Vector(33, 8)
vector2 = vector.rotate(45)

vector2.x == 17.68
vector2.y == 28.99

You may use math.cos, math.sin here, but they use radians. In order to convert degrees to radians use math.radians.