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Ranxiao Frances Wang, Christopher Widdowson; Spatial Representation for a Non-Euclidean Virtual Maze. Journal of Vision 2017;17(10):986. doi: 10.1167/17.10.986.
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One of the basic properties of space is its curvature, i.e. whether it is Euclidean (flat) or not (curved). The present study examined how people represent non-Euclidean space using two virtual tunnel mazes. One maze formed a square shape (Euclidean space), while the other contained a shortened path segment using a portal so that the overall maze violated the principles of Euclidean geometry. Each segment contained two landmarks. Participants learned the mazes by freely traversing the paths using a virtual reality HMD, and completed a pointing task and map-drawing task. Items in the pointing task were separated into local and global landmark pairs and tested independently. The local landmark pairs were adjacent but in different segments. The global landmark pairs were in opposite segments. The pointing responses for each landmark pair were compared to the corresponding directions indicated in each participant's drawn map and three hypothetical Euclidean maps that preserve the maximum amount of spatial relations by lengthening the shortened segment. They differ in how the two landmarks were placed in the lengthened segment. One placed the landmarks at the same distance from their nearest corner (corner map), one placed them proportionally in the lengthened segment (scale map), and one placed them in the mean position relative to the two corners (mean position map). The mean errors of the pointing directions relative to each of these four maps were calculated to assess the underlying representation guiding the pointing responses. The data showed that the egocentric pointing judgments were most similar to the corner map, with errors comparable to those of the regular square maze, and significantly different from their own drawn map, especially for the local landmark pairs, suggesting people's pointing judgments in a globally non-Euclidean maze resemble an underlying Euclidean map that preserves landmark distance from the nearest corners.
Meeting abstract presented at VSS 2017
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