v3d

v3d (Stands for Vector 3D) is a 3D vector library for basic Vector operations. It was inspired by: https://github.com/allelos/vectors

WHY?

A library was created by https://github.com/allelos/. However there was some missing parts(such as from_mag_and_dir).

Installation

pip install v3d

Documentation

Concept

This work inspired by https://github.com/allelos/vectors

V3D has no dependency other than standard math and logging module.

It consists of two parts, Point and Vector.

A point is a class with multiple operations. It is also a data carrier for Vector.

Operations:

• to_polar -> Converts from cartesian to polar
• from_polar -> Converts polar to cartesian
• add -> Calculates addition of two points
• subtract -> Calculates subtraction of two points. Uses add
• scale -> Calculates multiplication a point with a scalar
• divide -> Calculates division a point with a scalar. Uses scale
• dist -> Calculates distance between two points or a point and origin
• is_same -> Checks if two points are same

Vector is a module with multiple operations.

Operations:

• from_points -> Creates a Vector from two points
• add -> Calculates addition of two vectors. Uses Point.add
• subtract -> Calculates subtraction of two vectors. Uses add
• multiply -> Calculates cross product of two vectors or scales a vector with a scalar
• divide -> Scales a vector with 1/scalar. Uses multiply
• dot -> Calculates dot product of two vectors
• rotate -> Calculates a retated vector around given alpha, beta, gamma (alpha in x, beta in y and gamma in z axis)
• mag -> Calculates magnitude of a vector
• unit -> Calculates unit vector of a vector
• normal -> Calculates normal vector of a vector
• heading -> Calculates heading direction of a vector
• angle_between -> Calculates angle between two vectors
• is_parallel -> Checks if two vectors are parallel
• is_perpendicular -> Checks if two vectors are perpendicular
• is_non_parallel -> Checks if two vectors are neither parallel nor perpendicular
• is_same -> Checks if two vectors are same

Point

Creating a Point:

from v3d import Vector, Point

p1 = Point()# This will create a zero point. (0, 0, 0)
p2 = Point(1, 3, 1)# This will create a point at (1, 3, 1)

Converting between Polar and Cartesian:

p2.to_polar()# r, theta, phi (angles are in degrees)
# (3.3166247903554, 72.4515993862077, 71.56505117707799)
p1 = Point.from_polar(1, 45, 0)# Creates a cartesian point by given polar coordinates

Add/Subtract:

# Add
p1.add(p2)
# Point(x=1.7071067811865475, y=3.0, z=1.7071067811865475)
p2.add(p1)
# Point(x=1.7071067811865475, y=3.0, z=1.7071067811865475)
p1 + p2
# Point(x=1.7071067811865475, y=3.0, z=1.7071067811865475)
p2 + p1
# Point(x=1.7071067811865475, y=3.0, z=1.7071067811865475)

# Subtract
p1.subtract(p2)
# Point(x=-0.29289321881345254, y=-3.0, z=-0.2928932188134524)
p1 - p2
# Point(x=-0.29289321881345254, y=-3.0, z=-0.2928932188134524)

p2.subtract(p1)
# Point(x=0.29289321881345254, y=3.0, z=0.2928932188134524)
p2 - p1
# Point(x=0.29289321881345254, y=3.0, z=0.2928932188134524)

Multiply/Divide

p2.scale(2)
# Point(x=2, y=6, z=2)
p2 * 2
# Point(x=2, y=6, z=2)

p2.divide(2)
# Point(x=0.5, y=1.5, z=0.5)
p2 / 2
# Point(x=0.5, y=1.5, z=0.5)

Other Operations:

# Distance from origin:
p1.dist()
# 1.0

# Distance from other point:
p1.dist(p2)
# 3.028460479394408

# Check if two point are the same:
p1.is_same(p2)
# False
p1 == p2
# False

# Notice we made a copy of p2 as p3
p3 = p2.copy()

p2.is_same(p3)
# True
p2 == p3
# True

Vector

Creating a Vector:

# Notice p1 is a point type. It was created before.
v1 = Vector(p1)
# Vector(Point(x=0.7071067811865475, y=0.0, z=0.7071067811865476))

Magnitude, heading and unit vector:

v1.mag()
# 1.0
abs(v1)
# 1.0

v1.heading()
# (45.0, 0.0)

v1.unit()
# Vector(Point(x=0.7071067811865475, y=0.0, z=0.7071067811865476))

Rotate:

v1.rotate(alpha=45, beta=0, gamma=0)# alpha in x, beta in y and gamma in y axis
# Vector(Point(x=0.7071067811865475, y=-0.5, z=0.5000000000000001))

Rotate about another vector:

# Creating a new vector from p2
v2 = Vector(p2)

v1.rotate_about(v2, 30)
# Vector(Point(x=1.8625012984571216, y=0.5684060729445177, z=-0.2588190451025205))

Add/Subtract:

v1.add(v2)
# Vector(Point(x=1.7071067811865475, y=3.0, z=1.7071067811865475))
v1 + v2
# Vector(Point(x=1.7071067811865475, y=3.0, z=1.7071067811865475))

v1.subtract(v2)
# Vector(Point(x=-0.29289321881345254, y=-3.0, z=-0.2928932188134524))
v1 - v2
# Vector(Point(x=-0.29289321881345254, y=-3.0, z=-0.2928932188134524))

Multiply:

v1.multiply(2)
# Vector(Point(x=1.414213562373095, y=0.0, z=1.4142135623730951))
v1 * 2
# Vector(Point(x=1.414213562373095, y=0.0, z=1.4142135623730951))

# In case of two vector multiplication cross product will be calculated.
v1.multiply(v2)
# Vector(Point(x=-2.121320343559643, y=1.1102230246251565e-16, z=2.1213203435596424))
v1 * v2
# Vector(Point(x=-2.121320343559643, y=1.1102230246251565e-16, z=2.1213203435596424))

v1.divide(2)
# Vector(Point(x=0.35355339059327373, y=0.0, z=0.3535533905932738))
v1 / 2
# Vector(Point(x=0.35355339059327373, y=0.0, z=0.3535533905932738))

# These two lines will raise an error. Vector by Vector division is not possible
v1.divide(v2)
v1 / v2

Dot product:

v1.dot(v2)
# 1.414213562373095

Other operations:

# Angle between two vectors
v1.angle_between(v2)
# 64.7605981793211

# Check if two vector are same
v1.is_same(v2)
# False
v1 == v2
# False

# Noice Points p2 and p3 are the same so will the vectors be
v3 = Vector(p3)
v2.is_same(v3)
# True
v2 == v3
# True


# Check if two vectors are perpendicular
# We know cross product of two vectors will be a vector perpendicular to other two vectors

cross_product = v1 * v2
cross_product.is_perpendicular(v1) and cross_product.is_perpendicular(v2)
# True

# Check if two vectors are parallel
# We know cross product of two vectors will be a vector perpendicular to other two vectors

cross_product.is_parallel(v1) or cross_product.is_parallel(v2)
# False

# Check if two vectors are non_parallel
# We know cross product of two vectors will be a vector perpendicular to other two vectors

cross_product.is_non_parallel(v1) and cross_product.is_non_parallel(v2)
# False

Example

Example: https://github.com/mshemuni/V3D/blob/master/example.ipynb