PolytopAX Documentation

PolytopAX is a JAX-based computational geometry library for differentiable convex hull computation and polytope operations. It provides efficient, GPU-accelerated algorithms for convex hull approximation with automatic differentiation support.

Getting Started

User Guide

API Reference

Key Features

  • Differentiable Convex Hull: Approximate convex hull computation that maintains differentiability

  • JAX Integration: Full compatibility with JAX transformations (jit, grad, vmap, pmap)

  • GPU Acceleration: Efficient computation on GPU and TPU through XLA compilation

  • Object-Oriented API: Intuitive ConvexHull class with comprehensive methods

  • Functional API: Low-level functions for custom workflows

  • Batch Processing: Native support for batch operations

  • Geometric Predicates: Point inclusion, volume, surface area, and distance computations

Quick Example

import jax.numpy as jnp
import polytopax as ptx

# Create some 2D points
points = jnp.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]])

# Compute convex hull
hull = ptx.ConvexHull.from_points(points)

# Access properties
print(f"Volume: {hull.volume()}")
print(f"Surface area: {hull.surface_area()}")
print(f"Centroid: {hull.centroid()}")

# Test point inclusion
test_point = jnp.array([0.5, 0.5])
is_inside = hull.contains(test_point)

Installation

Install PolytopAX using pip:

pip install polytopax

Or install from source:

git clone https://github.com/your-org/polytopax.git
cd polytopax
pip install -e .

Requirements

  • Python 3.8+

  • JAX 0.4.0+

  • NumPy

  • SciPy (optional, for comparisons)

Indices and tables