TSP on a Euclidean plane is solved quite well by humans when the stimulus is orthogonal to the line of sight. In such a case, the retinal image is identical to the stimulus up to an overall scaling factor. As a result, the projection from the stimulus to the retina does not change the TSP problem because the lengths of all tours are changed by the same factor. We tested subjects under conditions involving perspective projection, which does change a TSP problem. Tennis balls were arranged on a floor within 55' by 55' area. The number of tennis balls (cities) was 5, 10 and 20. There were 10 instances of each problem. The instances were generated in such a way that perspective projection changed the optimal tours substantially. The experiment on a real floor was replicated in a VR environment (Cave). Performance in real space was very close to that on a computer monitor. However, performance in VR showed greater variability. There was an indication that subjects who had experience with VR performed better. Finally, we tested subjects with TSP in 3D space. Points were rendered in a volume of a VR space. Performance with 3D TSP was an order of magnitude lower than that with 2D TSP, suggesting that 2D representations have special status in human problem solving. |