InterpolatePy

Smooth trajectories, precise motion — one library. InterpolatePy brings together classic and modern interpolation techniques for robotics, animation, and scientific computing in a single, easy‑to‑use Python package.

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⭐️ Support the Project

If InterpolatePy saves you time or powers your research, please consider starring the repo – it helps others discover the project and motivates future development!

Have you built something cool on top of InterpolatePy? Open an issue or start a discussion – we’d love to showcase community projects.

Overview

InterpolatePy is a comprehensive collection of trajectory‑generation algorithms – from simple linear blends to high‑order B‑splines – with a consistent, NumPy‑friendly API. Designed for robotics, animation, path planning, and data smoothing, it lets you craft trajectories that respect position, velocity, acceleration and jerk constraints.

Key design goals:

• Breadth – one package for splines and motion profiles.
• Visualization‑ready – every spline exposes plot() helpers built on Matplotlib.
• Pure Python ≥ 3.10 – no compiled extensions; installs quickly everywhere.

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Roadmap

Upcoming features (✅ done, 🚧 planned):

Status	Feature
🚧	Bezier curves – arbitrary degree
🚧	Quaternion interpolation: LERP / SLERP / SQUAD & B‑spline‑quaternions
🚧	Linear blends with quintic/parabolic smoothing
🚧	Spherical paths & great‑circle splines

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Key Features

1 · Spline Interpolation

• B‑Splines – cubic, approximating, smoothing.
• Cubic Splines – with optional velocity/acceleration endpoint constraints.
• Global B‑Spline Interpolation – C², C³, C⁴ continuity (degree 3–5).

2 · Motion Profiles

• Double‑S (S‑curve) – bounded jerk.
• Trapezoidal – classic industrial profile.
• Polynomial – 3/5/7‑order with boundary conditions.

3 · Path Utilities

• Linear & Circular paths in 3‑D.
• Frenet frames helper for tool orientation along curves.

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Installation

InterpolatePy lives on PyPI. Install the latest stable release with:

pip install InterpolatePy

Development version (with test & dev extras):

git clone https://github.com/GiorgioMedico/InterpolatePy.git
cd InterpolatePy
pip install -e '.[all]'

Optional extras:

pip install InterpolatePy[test]   # testing only
pip install InterpolatePy[dev]    # linting & build tools

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Quick Start

from interpolatepy.cubic_spline import CubicSpline

t = [0, 5, 10]
q = [0, 2, 0]

spline = CubicSpline(t, q, v0=0.0, vn=0.0)
print(spline.evaluate(7.5))  # position at t = 7.5 s
spline.plot()                # visualize position/velocity/acceleration

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Usage Examples

Cubic spline with velocity constraints

from interpolatepy.cubic_spline import CubicSpline

t_points = [0.0, 5.0, 7.0, 10.0]
q_points = [1.0, 3.0, -1.0, 2.0]

s = CubicSpline(t_points, q_points, v0=1.0, vn=0.0)
position = s.evaluate(6.0)

Double‑S trajectory

from interpolatepy.double_s import DoubleSTrajectory, StateParams, TrajectoryBounds

state  = StateParams(q_0=0, q_1=10, v_0=0, v_1=0)
bounds = TrajectoryBounds(v_bound=5, a_bound=10, j_bound=30)
traj   = DoubleSTrajectory(state, bounds)

For more, see the examples folder or the full API docs (coming soon).

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Requirements

• Python ≥ 3.10
• NumPy ≥ 2.0
• SciPy ≥ 1.15
• Matplotlib ≥ 3.10

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Development

InterpolatePy uses modern Python tooling for development:

• Code Quality: Black and isort for formatting, Ruff and mypy for linting and type checking
• Testing: pytest for unit tests and benchmarks

To set up the development environment:

pip install -e '.[all]'
pre-commit install

Running Tests

python -m pytest tests

Contributing

We love pull requests — thanks for helping improve InterpolatePy!

1. Fork the repository and create a descriptive branch (feat/my-feature).

2. Install dev dependencies:

   pip install -e '.[all]'
   pre-commit install

3. Code your change, following our style (Black, isort, Ruff, mypy).

4. Test with pytest and run pre-commit run --all-files.

5. Open a pull request and explain why & how your change helps.

For larger ideas, open an issue first so we can discuss direction and scope.

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Acknowledgments

InterpolatePy implements algorithms and mathematical concepts primarily from the following authoritative textbooks:

• Biagiotti, L., & Melchiorri, C. (2008). Trajectory Planning for Automatic Machines and Robots. Springer.
• Siciliano, B., Sciavicco, L., Villani, L., & Oriolo, G. (2010). Robotics: Modelling, Planning and Control. Springer.

The library's implementation draws heavily from the theoretical frameworks, mathematical formulations, and algorithms presented in these works.

I express my gratitude to these authors for their significant contributions to the field of trajectory planning and robotics, which have made this library possible.

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License

InterpolatePy is released under the MIT License – do whatever you want, but please give credit.

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Citation

If InterpolatePy contributes to your academic work, consider citing it:

@misc{InterpolatePy,
  author       = {Giorgio Medico},
  title        = {InterpolatePy: Trajectory and Spline Library},
  year         = {2025},
  howpublished = {\url{https://github.com/GiorgioMedico/InterpolatePy}}
}