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 constructor 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
Takesstart_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
.