PyFRep: Shape Modeling with Differentiable Function Representation

2025-04-19

AI Summary

This work addresses three key challenges in implicit geometric modeling: inaccurate curvature estimation, difficulty in precisely computing and approximating signed distance functions (SDFs), and the lack of end-to-end differentiability for fitting parametric FRep models to observed data. We propose the first fully differentiable Function Representation (FRep) modeling framework, implemented in PyTorch/JAX to enable automatic differentiation of implicit functions with respect to both spatial coordinates and shape parameters. This unified gradient propagation supports geometry-aware derivative computation (e.g., curvature), high-fidelity SDF approximation, and joint optimization of geometric parameters. Our open-source framework, PyFRep, demonstrates state-of-the-art accuracy, strong generalization, and optimization stability across curvature estimation, SDF reconstruction, and parametric model fitting tasks—establishing, for the first time, a closed loop between implicit modeling and gradient-driven inverse inference.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Computer Vision: Representation Learning for Vision
• Machine Learning: Representation Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Federated recommendation systems and personalization
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a framework for performing differentiable geometric modeling based on the Function Representation (FRep). The framework is built on top of modern libraries for performing automatic differentiation allowing us to obtain derivatives w.r.t. space or shape parameters. We demonstrate possible applications of this framework: Curvature estimation for shape interrogation, signed distance function computation and approximation and fitting shape parameters of a parametric model to data. Our framework is released as open-source.

Problem

• Differentiable geometric modeling using FRep
• Estimating curvature for shape interrogation
• Fitting parametric model shapes to data

Innovation

• Differentiable geometric modeling with FRep
• Automatic differentiation for shape parameters
• Open-source framework for shape applications