scikit-spatial 9.0.1
Spatial objects and computations based on NumPy arrays.
License: BSD-3-Clause
Requires Python: >=3.8
Keywords: NumPy, linear algebra, matplotlib, spatial, visualization

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# 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.

```py
>>> from skspatial.objects import Vector

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

```

Behaviour inherited from NumPy:

```py
>>> vector.size
3

>>> vector.mean().round(3)
np.float64(0.667)

```

Additional methods from `scikit-spatial`:

```py
>>> vector.norm()
np.float64(2.0)

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

```

Because `Point` and `Vector` are both subclasses of `ndarray`, a `Vector` can be added to a `Point`. This produces a new `Point`.

```py
>>> from skspatial.objects import Point

>>> Point([1, 2]) + Vector([3, 4])
Point([4, 6])

```

`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 NumPy object,
instead of the spatial object class.

```py
>>> vector.sum()
np.int64(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.

```py
>>> 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`.

```py
>>> 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.

```bash
$ pip install scikit-spatial

```

It can also be installed with conda.

```bash
$ conda install scikit-spatial -c conda-forge

```

The `matplotlib` dependency is optional. To enable plotting, you can install scikit-spatial with the extra `plotting`.

```bash
   $ pip install 'scikit-spatial[plotting]'

```

# Example Usage

## Measurement

Measure the cosine similarity between two vectors.

```py
>>> from skspatial.objects import Vector

>>> Vector([1, 0]).cosine_similarity([1, 1]).round(3)
np.float64(0.707)

```

## Comparison

Check if multiple points are collinear.

```py
>>> 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.

```py
>>> 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.

```py
>>> 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.

```py
>>> 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.

```py
>>> 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.

```py
>>> 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](https://github.com/audreyr/cookiecutter) and the [audreyr/cookiecutter-pypackage](https://github.com/audreyr/cookiecutter-pypackage) project template.