3D Visualization and Exploration of Relationships and Constraints at the Example of Sudoku Games

In recent years, many systems for visualizing and exploring massive amounts of data have emerged. A topic that has not yet been investigated much, concerns the analysis of constraints that different objects impose on one another, regarding co-existence. In this paper, we present concepts toward visualizing mutual constraints between objects in a three-dimensional virtual and ARbased setting. We use 3x3 Sudoku games as suitable examples for investigating the underlying, more general concepts of helping users visualize and explore the constraints between different settings in rows, columns and blocks of matrix-like arrangements. Constraints are shown as repulsive and magnetic forces making objects keep their distance or seek proximity. We expect our concepts to be valuable beyond gaming – both as didactic tools for teaching and research, and in computational steering scenarios where problems are too complex to be solved by the computer alone in a reasonable amount of time. We are in the process of developing several prototypical visualization and interaction environments for Sudoku puzzles, allowing users to explore constraints in virtual 3D settings on a desktop and in an Augmented Reality-based environment. This paper reports on the underlying visualization principles.