# scipy.spatial.transform: Differentiable Framework-Agnostic 3D Transformations in Python

arXiv: https://arxiv.org/abs/2511.18157 · HTML: https://mlsanity.com/paper/2511.18157/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 13 references that are in the map.
- First posted on arXiv 22 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Kornia: an Open Source Differentiable Computer Vision Library for PyTorch](https://mlsanity.com/paper/1910.02190/) (2019)
- [Model Predictive Contouring Control for Time-Optimal Quadrotor Flight](https://mlsanity.com/paper/2108.13205/) (2021)

## Built on by (most cited first, 2 of 2)

- [Crazyflow: An Accurate, GPU-Accelerated, Differentiable Drone Simulator in JAX](https://mlsanity.com/paper/2606.01478/) (2026)
- [RAM: Reachability Across Morphologies](https://mlsanity.com/paper/2606.09108/) (2026)

## Abstract (arXiv)

Three-dimensional rigid-body transforms, i.e. rotations and translations, are central to modern differentiable machine learning pipelines in robotics, vision, and simulation. However, numerically robust and mathematically correct implementations, particularly on SO(3), are error-prone due to issues such as axis conventions, normalizations, composition consistency and subtle errors that only appear in edge cases. SciPy's spatial.transform module is a rigorously tested Python implementation. However, it historically only supported NumPy, limiting adoption in GPU-accelerated and autodiff-based workflows. We present a complete overhaul of SciPy's spatial.transform functionality that makes it compatible with any array library implementing the Python array API, including JAX, PyTorch, and CuPy. The revised implementation preserves the established SciPy interface while enabling GPU/TPU execution, JIT compilation, vectorized batching, and differentiation via native autodiff of the chosen backend. We demonstrate how this foundation supports differentiable scientific computing through two case studies: (i) scalability of 3D transforms and rotations and (ii) a JAX drone simulation that leverages SciPy's Rotation for accurate integration of rotational dynamics. Our contributions have been merged into SciPy main and will ship in the next release, providing a framework-agnostic, production-grade basis for 3D spatial math in differentiable systems and ML.