JMU CS Research

Systems and methods for generating a graded lattice structure and their application to additive manufacturing

Sat, 31 Oct 2026 12:00:00 +0000

Patent · Mar 14, 2023

U.S. Patent 11,602,898 B2

Seokpum Kim, John C. Bowers, Kenneth Stephenson, Vlastimil Kunc, Ahmed Arabi Hassen, Lonnie J. Love, and Gregory D. Dreifus

Systems and methods for generating graded lattice structures that can be used as infill for additively manufactured articles. Tailored sectioning and field-based smoothing are modified polygon, e.g., circle, packing algorithms that adjust the size of the circles based on physical field data to adapt the infill generation process to a field expected to be experienced by the article. Molecular dynamically generated lattice infill is based on force balancing a node distribution instead of a circle packing. Field data can be utilized to adjust the spacing of the node distribution according to a force balance equilibrium model that accounts for the field expected to be experienced by the article being additively manufactured. The resultant non-uniform honeycomb structures from tailored sectioning, field-based smoothing, and force-balancing robustly and efficiently address the connection issues with traditional non-uniform lattice structures.

Twoville

Fri, 30 Oct 2026 12:00:00 +0000

Project · Oct 30, 2026

Chris Johnson

A 2D design platform that supports bidirectional manipulation between code that generates a geometric design and the geometric objects themselves.

Praxly

Fri, 30 Oct 2026 12:00:00 +0000

Project · Sep 5, 2026

Chris Mayfield, Chris Johnson, and Michael Stewart

Students: Ben Saupp, Ellona Macmillan, Victor Del Carpio, Meghan Riordan, and Linnea Hellner

A visual programming environment that bridges the gap between pseudocode and standard programming languages.

Source code on GitHub: [Praxly v1](https://github.com/JMU-CS/praxly) and [Praxly v2](https://github.com/JMU-CS/praxly2).

Spanning Trees Minimizing Geometric Indices

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Nov 13, 2026 · to appear

33rd Annual Fall Workshop on Computational Geometry

John C. Bowers, Bradley McCoy, Dema Nasrawt, and Aidan Pawlak

Student co-authors: Dema Nasrawt and Aidan Pawlak

A topological index assigns a number to a graph, treating every edge as having unit length. Motivated by the work of Abu-Affash et al. on a geometric analogue of the Wiener index, we study geometric versions of two indices: the mean subtree order and the Hosoya index. Given $n$ points, the goal is a spanning tree minimizing the index. For the mean subtree order on a line, the sorted path is a tight $2$-approximation. In the plane, deciding whether there exists a spanning tree with mean subtree order at most $\mu_0$ is NP-hard. For the Hosoya index, the optimal star gives an aspect-ratio-sensitive approximation, and it is weakly NP-hard to decide whether a spanning tree has Euclidean Hosoya index at most $Z_0$ and total Euclidean length at most $L_0$.

Escher: An Engine for Exploring Hierarchical Combinatorial Tilings

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Jul 1, 2024

Proceedings of Bridges 2024: Mathematics, Art, Music, Architecture, Culture

John Bowers and Dakota Lawson

Student co-authors: Dakota Lawson

Almost all circle polyhedra are rigid

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Mar 15, 2019

Geometriae Dedicata

John C. Bowers, Philip L. Bowers, and Kevin Pratt

Graded Infill Structure of Wind Turbine Blade Accounting for Internal Stress in Big Area Additive Manufacturing

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Oct 15, 2018

CAMX Conference Proceedings (CAMX 2018), Dallas, Texas

Seokpum Kim, Gregory Dreifus, Bentley Beard, Andrew Glick, Andrew Messing, Ahmed Arabi Hassen, John Lindahl, Peng Liu, Tyler Smith, Jordan Failla, Brian Post, John C. Bowers, Kenneth Stephenson, Lonnie Love, and Vlastimil Kunc

Rigidity of circle polyhedra in the 2-sphere and of hyperideal polyhedra in hyperbolic 3-space

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Sep 25, 2018

Transactions of the American Mathematical Society

John Bowers, Philip Bowers, and Kevin Pratt

Ma–Schlenker c-Octahedra in the 2-Sphere

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Sep 7, 2017

Discrete & Computational Geometry

John C. Bowers and Philip L. Bowers

A Menger Redux: Embedding Metric Spaces Isometrically in Euclidean Space

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Aug 1, 2017

The American Mathematical Monthly

John C. Bowers and Philip L. Bowers

A framework for tool path optimization in fused filament fabrication

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Jun 12, 2017

Proceedings of the 1st Annual ACM Symposium on Computational Fabrication (SCF '17)

Gregory Dreifus, Ben Rapone, John Bowers, Xiang Chen, A. John Hart, and Bala Krishnamoorthy

Student co-authors: Xiang Chen

An Integrated Design Approach for Infill Patterning of Fused Deposition Modeling and its Application to an Airfoil

Fri, 30 Oct 2026 12:00:00 +0000

Paper · May 22, 2017

SAMPE Conference (SAMPE Seattle 2017)

Seokpum Kim, Xiang Chen, Gregory Dreifus, John Lindahl, Inseung Kang, Jung-Hyun Kim, Mohamed Selim, David Nuttall, Andrew Messing, Andrzej Nycz, Robert Minneci, John C. Bowers, Brittany Braswell, Byron Pipes, Ahmed Arabi Hassen, and Vlastimil Kunc

Student co-authors: Xiang Chen

Geodesic Universal Molecules

Fri, 30 Oct 2026 12:00:00 +0000

Paper · Mar 29, 2016

Mathematics in Computer Science

John C. Bowers and Ileana Streinu

Bowers and Taalman co-organize ICERM workshop on AI-assisted coding for mathematical exploration

Fri, 30 Oct 2026 12:00:00 +0000

News · Dec 11, 2026

John Bowers and Laura Taalman

John Bowers and Laura Taalman are co-organizing "AI-assisted coding for Mathematical Exploration", an ICERM Hot Topics workshop at Brown University, December 11–13, 2026, with Aaron Abrams (University of Virginia), David Bachman (Pitzer College) and Martin Skrodzki (TU Delft). The workshop explores how large language models and other AI tools can help mathematicians rapidly prototype, visualize and analyze mathematical concepts through custom-built applications, ending with a showcase of participant-created apps.