Skip to main content

Convert to Spherical Coordination or Rectangular Coordination in Python

Project description

n_sphere

Spherical Coordinate system, Rectangular coordinate system and Stereographic Projection in N-sphere (Using Python)

https://pypi.org/project/n-sphere/

  1. Spherical Coordinate (Show Image)

    r = math.sqrt( (x_n)^2 + ((x_n-1)^2) + ... + (x_1)^2 )
    Phi_1 = math.acos( x_1 / math.sqrt((x_n)^2 + (x_n-1)^2 + ... + (x_1)^2 ))
    Phi_2 = math.acos( x_2 / math.sqrt((x_n)^2 + (x_n-1)^2 + ... + (x_2)^2 ))
    ...
    Phi_n-2 = math.acos( x_n-2 / math.sqrt((x_n)^2 + (x_n-1)^2 ))
    Phi_n-1 = math.acos( x_n-1 / math.sqrt((x_n)^2 + (x_n-1)^2 )) (x_n >= 0)
          = 2 * Pi - math.acos( x_n-1 / math.sqrt((x_n)^2 + (x_n-1)^2 )) (x_n < 0) 
    
    • R = radius
    • n - 1 angular coordinates Phi_1, Phi_2, ... , Phi_n-1 in n-dimensional Euclidean Space
    • Phi_1 , Phi_2 , ... , Phi_n-2 range over [0, Pi] radians
    • Phi_n-1 range over [0, 2 * Pi) radians
  2. Rectangular Coordinate (Show Image)

    x_1 = r * math.cos(Phi_1)
    x_2 = r * math.sin(Phi_1) * math.cos(Phi_2)
    x_3 = r * math.sin(Phi_1) * math.sin(Phi_2) * math.cos(Phi_3)
    ...
    x_n-1 = r * math.sin(Phi_1) * ... * math.sin(Phi_n-2) * math.cos(Phi_n-1)
    x_n = r * math.sin(Phi_1) * ... * math.sin(Phi_n-2) * math.sin(Phi_n-1)
    
  3. Stereographic Projection (incomplete)

    • In 3-dimension
    [x,y,z] -> [x/1-z, y/1-z]
    
    • In N-dimension
    [x_1 , x_2 , ... , x_n] -> [ x_1 / 1-x_n , x_2 / 1-x_n , ... , x_n-1 / 1-x_n] 
    
  4. Generating random points (Plan)

Project Object

https://en.wikipedia.org/wiki/N-sphere

How to Use

pip install n-sphere
  • Tensor (Using Torch)
> python
Python 3.7.2 (tags/v3.7.2:9a3ffc0492, Dec 23 2018, 23:09:28) [MSC v.1916 64 bit (AMD64)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import torch
>>> import n_sphere
>>> x = torch.randint(10, size(5,3,))
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
NameError: name 'size' is not defined
>>> x = torch.randint(10, size=(5,3,))
>>> x
tensor([[1, 0, 4],
        [2, 7, 9],
        [1, 8, 6],
        [4, 9, 3],
        [0, 8, 1]])
>>> c_x = n_sphere.convert_spherical(x)
>>> c_x
tensor([[ 4.1231,  1.3258,  1.5708],
        [11.5758,  1.3972,  0.9098],
        [10.0499,  1.4711,  0.6435],
        [10.2956,  1.1718,  0.3218],
        [ 8.0623,  1.5708,  0.1244]], dtype=torch.float64)
>>> r_x = n_sphere.convert_rectangular(c_x)
>>> r_x
tensor([[1.0000e+00, 2.4493e-16, 4.0000e+00],
        [2.0000e+00, 7.0000e+00, 9.0000e+00],
        [1.0000e+00, 8.0000e+00, 6.0000e+00],
        [4.0000e+00, 9.0000e+00, 3.0000e+00],
        [2.6347e-06, 8.0000e+00, 1.0000e+00]], dtype=torch.float64)
  • List
>>> list = [
... [2,3,4,5,6],
... [4,1,3,6,7],
... [2,2,2,2,2],
... [4,9,1,2,8]]
>>> c_list = n_sphere.convert_spherical(list)
>>> c_list
array([[ 9.48683298,  1.358384  ,  1.241372  ,  1.097478  ,  0.87605805],
       [10.53565375,  1.181364  ,  1.468018  ,  1.256207  ,  0.86217005],
       [ 4.47213595,  1.107149  ,  1.047198  ,  0.955317  ,  0.78539816],
       [12.88409873,  1.255119  ,  0.745355  ,  1.450118  ,  1.32581766]])
>>> r_list = n_sphere.convert_rectangular(c_list)
>>> r_list
array([[2.000001, 3.      , 4.      , 5.      , 6.      ],
       [4.000001, 0.999996, 2.999996, 6.000001, 7.000001],
       [1.999999, 1.999999, 2.      , 2.000001, 2.000001],
       [4.000002, 9.000003, 0.999998, 1.999999, 7.999996]])
>>>
  • Number of digits can be changed in Round Function (default = 6)
>>> list = [
... [2,3,4,5,6],
... [4,1,3,6,7],
... [2,2,2,2,2],
... [4,9,1,2,8]]
>>> c_list = n_sphere.convert_spherical(list,10)
>>> c_list
array([[ 9.48683298,  1.35838411,  1.24137205,  1.097478  ,  0.87605805],
       [10.53565375,  1.18136412,  1.46801764,  1.25620658,  0.86217005],
       [ 4.47213595,  1.10714872,  1.04719755,  0.95531662,  0.78539816],
       [12.88409873,  1.2551192 ,  0.74535537,  1.45011777,  1.32581766]])
>>> r_list = n_sphere.convert_rectangular(c_list,10)
>>> r_list
array([[2., 3., 4., 5., 6.],
       [4., 1., 3., 6., 7.],
       [2., 2., 2., 2., 2.],
       [4., 9., 1., 2., 8.]])
>>>

Contact Us

yunseong14@naver.com

Reference

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distributions

No source distribution files available for this release.See tutorial on generating distribution archives.

Built Distribution

n_sphere-1.2.0-py3-none-any.whl (5.3 kB view details)

Uploaded Python 3

File details

Details for the file n_sphere-1.2.0-py3-none-any.whl.

File metadata

  • Download URL: n_sphere-1.2.0-py3-none-any.whl
  • Upload date:
  • Size: 5.3 kB
  • Tags: Python 3
  • Uploaded using Trusted Publishing? No
  • Uploaded via: twine/2.0.0 pkginfo/1.5.0.1 requests/2.22.0 setuptools/40.6.2 requests-toolbelt/0.9.1 tqdm/4.37.0 CPython/3.7.2

File hashes

Hashes for n_sphere-1.2.0-py3-none-any.whl
Algorithm Hash digest
SHA256 9c2ad1514c13d47f75230d481659851e443d4e44fb073ef9b33f8303a6df548f
MD5 a6a5b16046cf96ea1b364a6df92d4d89
BLAKE2b-256 6f7aa9f3efeb4a56636f6ec9c891526e371af24dd69533b235e58036ce0dacd3

See more details on using hashes here.

Supported by

AWS Cloud computing and Security Sponsor Datadog Monitoring Fastly CDN Google Download Analytics Pingdom Monitoring Sentry Error logging StatusPage Status page