This branch

This branch adds some objects to the original functionality of skspatial.

New objects:

• Circle3D - a 2D circle on a plane in 3D space
• Elipse3D - a 2D elipse on a plane in 3D space

New functionality within existing objects:

• Sphere

  • Added sphere-plane intersection, which is a Circle3D
  • Added sphere-sphere intersection, which projects both spheres onto their shared plane of intersection, which is a Circle3D

• Cylinder

  • Added cylinder-plane intersection, which is a Elipse3D or Circle3D depending on the plane's orientation

New functionality, added into skspatial/geometric_functions.py

• extract_center_and_radius, from a sphere's equation, which can then be used to initialize Sphere object
• intersection_3_spheres, which is a Point
• ssc_intersect - Sphere, Sphere, Cylinder intersection - to find 2 points
• intersect_circle (intersects cylinder with 2D circle on a plane), to find 2 points
• plot_elipse - which is used for plotting 2D elipses in 3D space (Elipse3D)
• plot_triangle - which is used for plotting arrays of 2D triangles in 3D space
• mirror_triangles, rotate_triangles, mirror_point, translate_and_rotate etc.

Introduction

This package provides spatial objects based on NumPy arrays, as well as computations using these objects. The package includes computations for 2D, 3D, and higher-dimensional space.

The following spatial objects are provided:

• Point
• Points
• Vector
• Line
• LineSegment
• Plane
• Circle
• Sphere
• Triangle
• Cylinder

Most of the computations fall into the following categories:

• Measurement
• Comparison
• Projection
• Intersection
• Fitting
• Transformation

All spatial objects are equipped with plotting methods based on matplotlib. Both 2D and 3D plotting are supported. Spatial computations can be easily visualized by plotting multiple objects at once.

Why this instead of scipy.spatial or sympy.geometry?

This package has little to no overlap with the functionality of scipy.spatial. It can be viewed as an object-oriented extension.

While similar spatial objects and computations exist in the sympy.geometry module, scikit-spatial is based on NumPy rather than symbolic math. The primary objects of scikit-spatial (Point, Points, and Vector) are actually subclasses of the NumPy ndarray. This gives them all the regular functionality of the ndarray, plus additional methods from this package.

>>> from skspatial.objects import Vector

>>> vector = Vector([2, 0, 0])

Behaviour inherited from NumPy:

>>> vector.size
3
>>> vector.mean().round(3)
0.667

Additional methods from scikit-spatial:

>>> vector.norm()
2.0
>>> vector.unit()
Vector([1., 0., 0.])

Point and Vector are based on a 1D NumPy array, and Points is based on a 2D NumPy array, where each row represents a point in space. The Line and Plane objects have Point and Vector objects as attributes.

Note that most methods inherited from NumPy return a regular ndarray, instead of the spatial object class.

>>> vector.sum()
array(2)

This is to avoid getting a spatial object with a forbidden shape, like a zero dimension Vector. Trying to convert this back to a Vector causes an exception.

>>> Vector(vector.sum())
Traceback (most recent call last):
...
ValueError: The array must be 1D.

Because the computations of scikit-spatial are also based on NumPy, keyword arguments can be passed to NumPy functions. For example, a tolerance can be specified while testing for collinearity. The tol keyword is passed to numpy.linalg.matrix_rank.

>>> from skspatial.objects import Points

>>> points = Points([[1, 2, 3], [4, 5, 6], [7, 8, 8]])

>>> points.are_collinear()
False
>>> points.are_collinear(tol=1)
True

Installation

The package can be installed with pip.

$ pip install scikit-spatial

It can also be installed with conda.

$ conda install scikit-spatial -c conda-forge

Example Usage

Measurement

Measure the cosine similarity between two vectors.

>>> from skspatial.objects import Vector

>>> Vector([1, 0]).cosine_similarity([1, 1]).round(3)
0.707

Comparison

Check if multiple points are collinear.

>>> from skspatial.objects import Points

>>> points = Points([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]])

>>> points.are_collinear()
True

Projection

Project a point onto a line.

>>> from skspatial.objects import Line

>>> line = Line(point=[0, 0, 0], direction=[1, 1, 0])

>>> line.project_point([5, 6, 7])
Point([5.5, 5.5, 0. ])

Intersection

Find the intersection of two planes.

>>> from skspatial.objects import Plane

>>> plane_a = Plane(point=[0, 0, 0], normal=[0, 0, 1])
>>> plane_b = Plane(point=[5, 16, -94], normal=[1, 0, 0])

>>> plane_a.intersect_plane(plane_b)
Line(point=Point([5., 0., 0.]), direction=Vector([0, 1, 0]))

An error is raised if the computation is undefined.

>>> plane_b = Plane(point=[0, 0, 1], normal=[0, 0, 1])

>>> plane_a.intersect_plane(plane_b)
Traceback (most recent call last):
...
ValueError: The planes must not be parallel.

Fitting

Find the plane of best fit for multiple points.

>>> points = [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]]

>>> Plane.best_fit(points)
Plane(point=Point([0.5, 0.5, 0. ]), normal=Vector([0., 0., 1.]))

Transformation

Transform multiple points to 1D coordinates along a line.

>>> line = Line(point=[0, 0, 0], direction=[1, 2, 0])
>>> points = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

>>> line.transform_points(points).round(3)
array([ 2.236,  6.261, 10.286])

Acknowledgment

This package was created with Cookiecutter and the audreyr/cookiecutter-pypackage project template.