Title: Universal Computational Geometry via Tensor Networks

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

Universal Computational Geometry (UCG) represents the task of finding geometric primitives that satisfy a set of constraints. This paper proposes a novel approach utilizing tensor networks to represent and manipulate geometric primitives, offering a unified framework for geometric computation across diverse domains. We develop a method for encoding geometric primitives as tensors, leveraging tensor network techniques to implement fundamental operations like concatenation, dilation, and inversion. The core mechanism centers around constructing a tensor network representing the geometric primitives, allowing for efficient and scalable computation. The proposed method provides a significant step towards a generalized UCG solver, addressing a long-standing challenge in the field. We provide a detailed implementation demonstrating the effectiveness of our approach, showcasing its ability to handle complex geometric transformations and provide a foundation for future advancements.

DOI: 10.5281/zenodo.22485767

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