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https://github.com/open-space-collective/open-space-toolkit-mathematics
Geometry, curve fitting, optimization.
https://github.com/open-space-collective/open-space-toolkit-mathematics
cpp engineering mathematics python space toolkit
Last synced: 8 days ago
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Geometry, curve fitting, optimization.
- Host: GitHub
- URL: https://github.com/open-space-collective/open-space-toolkit-mathematics
- Owner: open-space-collective
- License: apache-2.0
- Created: 2018-06-10T18:35:03.000Z (over 6 years ago)
- Default Branch: main
- Last Pushed: 2024-12-11T19:32:14.000Z (14 days ago)
- Last Synced: 2024-12-11T20:34:51.948Z (14 days ago)
- Topics: cpp, engineering, mathematics, python, space, toolkit
- Language: C++
- Homepage: https://open-space-collective.github.io/open-space-toolkit-mathematics/
- Size: 18.2 MB
- Stars: 19
- Watchers: 7
- Forks: 4
- Open Issues: 9
-
Metadata Files:
- Readme: README.md
- Contributing: CONTRIBUTING.md
- License: LICENSE
Awesome Lists containing this project
README
# Open Space Toolkit ▸ Mathematics
[](https://github.com/open-space-collective/open-space-toolkit-mathematics/actions/workflows/build-test.yml)
[](https://github.com/open-space-collective/open-space-toolkit-mathematics/actions/workflows/release.yml)
[](https://codecov.io/gh/open-space-collective/open-space-toolkit-mathematics)
[](https://open-space-collective.github.io/open-space-toolkit-mathematics)
[](https://badge.fury.io/gh/open-space-collective%2Fopen-space-toolkit-mathematics)
[](https://badge.fury.io/py/open-space-toolkit-mathematics)
[](https://opensource.org/licenses/Apache-2.0)
Geometry, curve fitting, optimization.
## Getting Started
Want to get started? This is the simplest and quickest way:
[](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)
Structure
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
```
## 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
[](https://www.loftorbital.com/)
## License
Apache License 2.0