# CAD Adjacency Computation Using Validated Numerics

## TL;DR

This paper introduces an algorithm that computes cell adjacencies in cylindrical algebraic decomposition using validated numerics, enabling efficient topological analysis and applications like visualization and path planning.

## Contribution

The paper presents a novel validated numerics-based algorithm for cell adjacency computation in CAD, achieving efficiency comparable to CAD construction without adjacency info.

## Key findings

- Algorithm successfully computes cell adjacencies in CAD.
- Implementation demonstrates practical efficiency.
- Empirical data supports effectiveness of the method.

## Abstract

We present an algorithm for computation of cell adjacencies for well-based cylindrical algebraic decomposition. Cell adjacency information can be used to compute topological operations e.g. closure, boundary, connected components, and topological properties e.g. homology groups. Other applications include visualization and path planning. Our algorithm determines cell adjacency information using validated numerical methods similar to those used in CAD construction, thus computing CAD with adjacency information in time comparable to that of computing CAD without adjacency information. We report on implementation of the algorithm and present empirical data.