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Graph Constructive Geometric Constraint Solving: Challenges and Machine Learning

Graph Constructive Geometric Constraint Solving: Challenges and Machine Learning

I. Fudos and V. Stamati

CAD Conference, Computer Aided Design and Applications Journal, 2024

Computer-aided design (CAD) places significant emphasis on crafting precise and durable models that seamlessly adhere to constraints set forth by designers and/or specific application domains. Geometric constraint solving (GCS) plays a pivotal role in ensuring the fulfillment of these criteria. This paper delves into the contemporary research problems encountered within traditional GCS methodologies, particularly when combining graph algorithms (termed graph constructive GCS) and machine learning. Specifically, it investigates challenges about well-constrainedness in both 2D and 3D GCS scenarios. Furthermore, it proposes and scrutinizes an AI-assisted root navigation approach for graph-based constructive constraint-solving problems.

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Abstract

Computer-aided design (CAD) places significant emphasis on crafting precise and durable models that seamlessly adhere to constraints set forth by designers and/or specific application domains. Geometric constraint solving (GCS) plays a pivotal role in ensuring the fulfillment of these criteria. This paper delves into the contemporary research problems encountered within traditional GCS methodologies, particularly when combining graph algorithms (termed graph constructive GCS) and machine learning. Specifically, it investigates challenges about well-constrainedness in both 2D and 3D GCS scenarios. Furthermore, it proposes and scrutinizes an AI-assisted root navigation approach for graph-based constructive constraint-solving problems.

BibTeX Citation

@article{fudos2025graph,
  title={Graph Constructive Geometric Constraint Solving: Challenges and Machine Learning.},
  author={Fudos, Ioannis and Stamati, Vasiliki},
  journal={Computer-Aided Design \& Applications},
  volume={22},
  number={6},
  year={2025}
}