Continuous Offset-Based Coverage Paths for Planar Regions

Undergraduate research project, 2022

Key ideas explored

• A geometric distinction between local and global self-intersections in contour-parallel offset curves, and how they affect coverage continuity.
• Use of medial-axis width structure to reason about when offsetting causes a region to split, and how modifying width can prevent topological disconnection.
• A simple pre-processing technique that converts a family of offset loops into a single spiral-like continuous path.
• Identification of sharp-turn regions induced by offsetting and localized smoothing without globally altering equidistance.

Limitations and scope

• This work does not claim empirical superiority over existing infill or coverage strategies used in modern additive manufacturing.
• The approach prioritizes geometric continuity over material optimality, and is most relevant to contexts where uniform coverage and motion smoothness dominate.
• The algorithms are primarily geometric and exploratory; no large-scale benchmarking or hardware validation was performed.

In hindsight, this project shaped how I think about the relationship between geometric structure, modeling assumptions, and real-world relevance. Many of the limitations of this work informed my later focus on formally scoped, validated methods in safe learning and control.

Follow-up: Corner Smoothing for Additive Manufacturing Toolpaths (May 2021 — Aug 2021)

As a natural extension of the coverage-path work above, I later proposed a corner-smoothing method for additive manufacturing toolpaths, aiming to achieve uniform coating while constraining maximum curvature. I refined the original formulation into a convex optimization problem enforcing continuous curvature and even area coverage, implemented an iterative gradient-based solver in Python, and integrated it into the parallel-curve toolpath planner from the coverage-path project.

Research Assistant (May 2021 — Aug 2021)

• Proposed a corner smoothing method for additive manufacturing toolpaths to achieve uniform coating while constraining maximum curvature.
• Refined the original formulation into a convex optimization problem to enforce continuous curvature and even area coverage.
• Implemented an iterative solver (gradient-based) in Python and integrated it into a parallel-curve toolpath planner.

Tech: Convex optimization, Python.