open-space-toolkit-mathematics

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open-space-toolkit-mathematics

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Geometry, curve fitting, optimization.

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# Open Space Toolkit ▸ Mathematics

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Geometry, curve fitting, optimization.

## Getting Started

Want to get started? This is the simplest and quickest way:

[![Binder](https://mybinder.org/badge_logo.svg)](https://mybinder.org/v2/gh/open-space-collective/open-space-toolkit/main?urlpath=lab/tree/notebooks)

*Nothing to download or install! This will automatically start a [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) environment in your browser with Open Space Toolkit libraries and example notebooks ready to use.*

### Alternatives

#### Docker Images

[Docker](https://www.docker.com/) must be installed on your system.

##### iPython

The following command will start an [iPython](https://ipython.org/) shell within a container where the OSTk components are already installed:

```bash
docker run -it openspacecollective/open-space-toolkit-mathematics-development python3.11 -m IPython
```

Once the shell is up and running, playing with it is easy:

```py
import numpy
from ostk.mathematics.geometry import Angle
from ostk.mathematics.geometry.d3.transformation.rotation import Quaternion
from ostk.mathematics.geometry.d3.transformation.rotation import RotationVector

rv = RotationVector(numpy.array([[0.0], [0.0], [1.0]], dtype=float), Angle.degrees(15.0)) # Construct rotation vector

q_AB = Quaternion(1.0, 2.0, 3.0, 4.0, Quaternion.Format.XYZS).to_normalized() # Construct quaternion and normalize
q_BC = Quaternion.rotation_vector(rv) # Construct quaternion from rotation vector

q_AC = q_AB * q_BC # Multiply quaternions
```

*Tip: Use tab for auto-completion!*

##### JupyterLab

The following command will start a [JupyterLab](https://jupyterlab.readthedocs.io/en/stable/) server within a container where the OSTk components are already installed:

```bash
docker run --publish=8888:8888 openspacecollective/open-space-toolkit-mathematics-jupyter
```

Once the container is running, access [http://localhost:8888/lab](http://localhost:8888/lab) and create a Python 3 Notebook.

## Installation

### C++

The binary packages are hosted using [GitHub Releases](https://github.com/open-space-collective/open-space-toolkit-mathematics/releases):

- Runtime libraries: `open-space-toolkit-mathematics-X.Y.Z-1.x86_64-runtime`
- C++ headers: `open-space-toolkit-mathematics-X.Y.Z-1.x86_64-devel`
- Python bindings: `open-space-toolkit-mathematics-X.Y.Z-1.x86_64-python`

#### Debian / Ubuntu

After downloading the relevant `.deb` binary packages, install:

```bash
apt install open-space-toolkit-mathematics-*.deb
```

### Python

Install from [PyPI](https://pypi.org/project/open-space-toolkit-mathematics/):

```bash
pip install open-space-toolkit-mathematics
```

## Documentation

Documentation is available here:

- [C++](https://open-space-collective.github.io/open-space-toolkit-mathematics)
- [Python](./bindings/python/docs)

<details>
<summary>Structure</summary>
<p>

The library exhibits the following structure:

```txt
├── Object
│   ├── Vector
│   ├── Matrix
│   └── Interval
├── Geometry
│   ├── 2D
|   │   ├── Object
│   │   │   ├── Point
│   │   │   ├── Point Set
│   │   │   ├── Line
│   │   │   ├── Line String
│   │   │   ├── Multi Line String
│   │   │   └── Polygon
│   │   ├── Intersection
│   │   └── Transformation
│   │       ├── Identity
│   │       ├── Translation
│   │       ├── Rotation
│   │       ├── Reflection
│   │       ├── Scaling
│   │       └── Shear
│   ├── 3D
|   │   ├── Object
│   │   │   ├── Point
│   │   │   ├── Point Set
│   │   │   ├── Line
│   │   │   ├── Ray
│   │   │   ├── Segment
│   │   │   ├── Line String
│   │   │   ├── Polygon
│   │   │   ├── Plane
│   │   │   ├── Cuboid
│   │   │   ├── Sphere
│   │   │   ├── Ellipsoid
│   │   │   ├── Cone
│   │   │   ├── Pyramid
│   │   │   └── Composite
│   │   ├── Intersection
│   │   └── Transformation
│   │       ├── Identity
│   │       ├── Translation
│   │       ├── Rotation
│   │       │   ├── Quaternion
│   │       │   ├── Euler Angle
│   │       │   ├── Rotation Vector
│   │       │   └── Rotation Matrix
│   │       ├── Reflection
│   │       ├── Scaling
│   │       └── Shear
├── Dynamics
│   ├── State
│   ├── Solver
│   │   ├── Runge–Kutta 4 (RK4)
│   │   ├── Dormand–Prince 5 (DP5)
│   │   └── Runge–Kutta–Fehlberg 78 (F78)
│   └── Systems
├── Curve Fitting
│   ├── Interpolator
│   │   ├── Linear
│   │   ├── Barycentric Rational
│   │   ├── Cubic Spline
│   │   └── Lagrange
│   └── Smoothing
├── Optimization
│   ├── Problem
│   └── Algorithms
│       ├── Gradient Descent
│       └── Evolutionary
│           ├── Genetic
│           ├── Differential Evolution
│           └── Swarm
└── Statistics
```

</p>
</details>

## Tutorials

Tutorials are available here:

- [C++](./tutorials/cpp)
- [Python](./tutorials/python)

## Features

### Geometry Queries

- `○`: query only
- `✔`: query / intersection set
- ` `: to be implemented
- `-`: undefined

#### 3D

| Intersect       | Point | Point Set | Line | Ray | Segment | Line String | Polygon | Plane | Cuboid | Sphere | Ellipsoid | Cone | Pyramid | Composite |
| --------------- | ----- | --------- | ---- | --- | ------- | ----------- | ------- | ----- | ------ | ------ | --------- | ---- | ------- | --------- |
| **Point**       |       |           | ○    | ○   |         |             |         | ✔     | ○      | ○      | ○         |      |         |           |
| **Point Set**   |       |           |      |     |         |             |         | ✔     | ○      | ○      | ○         |      |         |           |
| **Line**        | ○     |           |      |     |         |             |         | ✔     | ○      | ○      | ✔         |      |         |           |
| **Ray**         | ○     |           |      |     |         |             |         | ✔     |        | ○      | ✔         |      |         |           |
| **Segment**     |       |           |      |     |         |             |         | ✔     |        | ○      | ✔         |      |         |           |
| **Line String** |       |           |      |     |         |             |         |       |        |        |           |      |         |           |
| **Polygon**     |       |           |      |     |         |             |         |       |        |        |           |      |         |           |
| **Plane**       | ✔     | ✔         | ✔    | ✔   | ✔       |             |         |       |        | ○      | ○         |      |         |           |
| **Cuboid**      | ○     | ○         | ○    |     |         |             |         |       |        |        |           |      |         |           |
| **Sphere**      | ○     | ○         | ○    | ○   | ○       |             |         | ○     |        |        |           |      | ○       |           |
| **Ellipsoid**   | ○     | ○         | ✔    | ✔   | ✔       |             |         | ○     |        |        |           | ✔    | ✔       |           |
| **Cone**        |       |           |      |     |         |             |         |       |        |        | ✔         |      |         |           |
| **Pyramid**     |       |           |      |     |         |             |         |       |        | ○      | ✔         |      |         |           |
| **Composite**   |       |           |      |     |         |             |         |       |        |        |           |      |         |           |

| Contain         | Point | Point Set | Line | Ray | Segment | Line String | Polygon | Plane | Cuboid | Sphere | Ellipsoid | Cone | Pyramid | Composite |
| --------------- | ----- | --------- | ---- | --- | ------- | ----------- | ------- | ----- | ------ | ------ | --------- | ---- | ------- | --------- |
| **Point**       |       |           | -    | -   | -       | -           | -       | -     | -      | -      | -         | -    | -       |           |
| **Point Set**   |       |           | -    | -   | -       | -           | -       | -     | -      | -      | -         | -    | -       |           |
| **Line**        | ✔     |           |      |     |         |             | -       | -     | -      | -      | -         | -    | -       |           |
| **Ray**         | ✔     | ✔         | -    |     |         |             | -       | -     | -      | -      | -         | -    | -       |           |
| **Segment**     | ✔     |           | -    | -   |         |             | -       | -     | -      | -      | -         | -    | -       |           |
| **Line String** |       |           | -    | -   |         |             | -       | -     | -      | -      | -         | -    | -       |           |
| **Polygon**     |       |           | -    | -   |         |             |         | -     | -      | -      | -         | -    | -       |           |
| **Plane**       | ✔     | ✔         | ✔    | ✔   | ✔       |             |         |       | -      | -      | -         | -    | -       |           |
| **Cuboid**      | ✔     | ✔         | -    | -   |         |             |         | -     |        |        |           |      |         |           |
| **Sphere**      | ✔     | ✔         | -    | -   | -       | -           | -       | -     |        |        |           |      |         |           |
| **Ellipsoid**   | ✔     | ✔         | -    | -   | -       | -           | -       | -     |        |        |           |      |         |           |
| **Cone**        |       |           |      |     |         | -           | -       | -     |        |        |           |      |         |           |
| **Pyramid**     | ✔     |           |      |     |         |             |         | -     |        |        |           |      |         |           |
| **Composite**   |       |           |      |     |         |             |         |       |        |        |           |      |         |           |

## Setup

### Development Environment

Using [Docker](https://www.docker.com) for development is recommended, to simplify the installation of the necessary build tools and dependencies.
Instructions on how to install Docker are available [here](https://docs.docker.com/install/).

To start the development environment:

```bash
make start-development
```

This will:

1. Build the `openspacecollective/open-space-toolkit-mathematics-development` Docker image.
2. Create a development environment container with local source files and helper scripts mounted.
3. Start a `bash` shell from the `./build` working directory.

If installing Docker is not an option, you can manually install the development tools (GCC, CMake) and all required dependencies,
by following a procedure similar to the one described in the [Development Dockerfile](./docker/development/Dockerfile).

### Build

From the `./build` directory:

```bash
cmake ..
make
```

*Tip: `ostk-build` simplifies building from within the development environment.*

### Test

To start a container to build and run the tests:

```bash
make test
```

Or to run them manually:

```bash
./bin/open-space-toolkit-mathematics.test
```

*Tip: `ostk-test` simplifies running tests from within the development environment.*

## Dependencies

| Name                   | Version  | License                | Link                                                                                                                         |
| ---------------------- | -------- | ---------------------- | ---------------------------------------------------------------------------------------------------------------------------- |
| Pybind11               | `2.12.0` | BSD-3-Clause           | [github.com/pybind/pybind11](https://github.com/pybind/pybind11)                                                             |
| Eigen                  | `3.3.7`  | MPL2                   | [eigen.tuxfamily.org](http://eigen.tuxfamily.org/index.php)                                                                  |
| Geometric Tools Engine | `3.28`   | Boost Software License | [geometrictools.com](https://www.geometrictools.com)                                                                         |
| Core                   | `main`   | Apache License 2.0     | [github.com/open-space-collective/open-space-toolkit-core](https://github.com/open-space-collective/open-space-toolkit-core) |

## Contribution

Contributions are more than welcome!

Please read our [contributing guide](CONTRIBUTING.md) to learn about our development process, how to propose fixes and improvements, and how to build and test the code.

## Special Thanks

[![Loft Orbital](https://github.com/open-space-collective/open-space-toolkit/blob/main/assets/thanks/loft_orbital.png)](https://www.loftorbital.com/)

## License

Apache License 2.0

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