Spatial problem solving: assembling three-dimensional puzzles in real and virtual environments

Abstract

There exist many varieties of puzzles, which are in continuous evolution. They are usually classified as ‘‘mechanical puzzles’’ (e.g., 14-15 Puzzle, 15 Puzzle, Rubik’s Cube, Rubik’s Magic), ‘‘wire puzzles’’ (e.g., Heart and Arrow Puzzle, Chinese Rings Puzzle), or ‘‘dissection puzzles’’, which require assembling objects in two dimensions (e.g., Tangram) or three dimensions (e.g., Soma Cubes, Bedlham Cube). With the development of informatics, new sorts of puzzles have been introduced, such as the ‘‘maze type puzzles’’ (e.g., Pacman, Rogue (Hack), Doom, Counter Strike). In fact, there are no ‘‘strict’’ rules for classifying puzzles in these categories. For instance, Tetris shares characteristics of several of them. It is based on the concept of assembling pieces (as the dissection puzzles), but it is also a computerized puzzle with time constraints. We are interested in the assembling of three-dimensional (3D) puzzles. We have selected a puzzle similar to the Soma Cubes. It is made of seven blocks of various shapes which have to be assembled to form a cube. Our objective was first to conduct an empirical study, and then to develop an experiment in a virtual environment. We were interested in the cognitive processes involved in solving the problem, with the objective of proposing methods of assistance for tasks involving the manipulation of 3D puzzles in virtual environments. The tasks of assembling 3D objects belong to the wider class of problem solving tasks. The operating agent has to build an anticipatory representation of a to-be-attained state of affairs, while generating strategies to reach that objective. Problem solving is illustrated by every situation where from the outset an agent does not have an obvious already available procedure to reach the final objective (cf. Newell and Simon 1972). One thus distinguishes between two sets of processes: the processes by which an agent builds a representation of the goal, and those by which a plan of action for attaining the goal is built and implemented. Two broad classes of space-related problems are typically contrasted: those involving large-scale environments calling for navigation (e.g., Denis and Loomis 2007) and those involving the perception and manipulation of smallscale configurations of objects, such as those where individual elements must be combined to form larger configurations (e.g., Butler 1994). In the tasks that belong to the first class, the agents have to typically control the movements of an object (a person moving in space) through a set of objects whose topography is fixed. On the contrary, in the tasks of the second class, the agents have to control and modify the spatial arrangement of the objects relative to one another. Previous research has shown that the users of virtual reality systems experience difficulty in operating within these systems and have poor performance when manipulating the objects displayed by the virtual reality devices. The current approaches to provide users with interactive tools are focusing on the realism of the perceptual or motor experiences, or on the use of metaphors for interaction (e.g., Bowman et al. 2002, 2005). This is why we propose an analytical approach based on the activity in the real world before moving to virtual worlds. Different interfaces can have different affordances and differently impact the S. Abbasi J.-M. Burkhardt ECI, Universite Paris Descartes, Paris, France