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Item The Priority Face Determination Tree for Hidden Surface Removal(Blackwell Publishers Ltd and the Eurographics Association, 1998) James, A.; Day, A. M.Many virtual environments are built from a set of polygons that form the basis of objects in the scene. Using priority-list algorithms, the sequence in which these polygons are drawn is dependent upon the location of an observer; the polygons must be ordered correctly before a realistic image can be displayed. It is necessary for a scene to be drawn correctly in real time from all locations before the observer can move interactively around the scene with complete freedom.The binary-space partitioning (BSP) tree developed by Fuchs, Kedem and Naylor in 1980 stores the view independent priority of a set of polygons which can be used to obtain the correct order for any given view-point. However, the number of polygons grows significantly due to the BSP splitting stage, increasing the number of nodes in the tree. This affects linearly the number of tests necessary to traverse the tree to obtain the priority of the set of polygons.The algorithm presented here is built using its associated BSP tree, but attempts to reduce the number of tests to, log4/3n, at the cost of a tree of size of O(N1.5log4/3n?1), where n is the initial number of polygons in the scene, and N the resulting number after BSP splitting. To achieve the increase in run-time efficiency, a height plane is used to restrict the view point of the observer to a fixed height, but the key to the efficiency of the algorithm is in the use of polygonal dependencies. In the scene; if we know our location relative to the front or back of a polygon, then our position relative to one-quarter of the remaining polygons, in the expected worst-case, can be determined.Item Five-dimensional Adaptive Subdivision for Ray Tracing(Blackwell Science Ltd and the Eurographics Association, 1994) Simiakakis, G.; Day, A. M.This paper presents a directional subdivision method for speeding up ray tracing. This method is easy to use, because it automatically adapts the subdivision to the scene relieving the user from having to set parameters for the subdivision. It also attempts a balance between 5D and spatial subdivision in order to benefit from both methods. A memory saving scheme is introduced and experimental results are presented.Item Planar Convex Hull Algorithms in Theory and Practice(Blackwell Publishing Ltd and the Eurographics Association, 1988) Day, A. M.Sequential and parallel planar convex hull algorithms, their applications and some of the problems encountered on implementations are described. Details of Pascal implementations are given for three of the sequential algorithms: Graham s, Floyd-Eddy and the Approximation method. The programs are compared experimentally.Item Erratum: Conflict Neutralization on Binary Space Partitioning(Blackwell Publishers Ltd and the Eurographics Association., 2001) James, A.; Day, A. M.Item Haptic Device Control - Will it Fit Standardized Input Models?(Blackwell Publishers Ltd and the Eurographics Association, 2001) Arnold, D. B.; Day, A. M.; Jennings, V.; Courtenay, A.; Duce, D. A.Over recent years a wide variety of interaction devices involving haptic feedback have been brought to the market, but they vary widely in terms of input measures recorded. These range from one dimensional input on a haptic feedback steering wheel to a six degree of freedom position and orientation device and further, to assemblies of such devices. On the surface most of the variations can be accommodated logically with standardized input models combining existing logical input devices and haptic feedback processes as acknowledgement/echos. However it is very uncertain whether such a model can adequately model the system requirements for effective haptic feedback.In this paper we review the input models that have developed over the past 20 years and ask "Is it the end of the road for the conceptual model of input incorporated into the early graphics standards and elaborated over the years?" In addition, to highlight the problems of implementation with haptic interaction, we describe a typical application, the simulation of a collision with a virtual wall.