THE VISUAL-DISPLAY TRANSFORMATION FOR VIRTUAL-REALITY

The visual display transformation for virtual reality (VR) systems is typically much more complex than the standard viewing transformation d iscussed in the literature for conventional computer graphics. The pro cess can be represented as a series of transformations, some of which contain parameters that must match the physical configuration of the s ystem hardware and the user's body, Because of the number and complexi ty of the transformations, a systematic approach and a thorough unders tanding of the mathematical models involved are essential. This paper presents a complete model for the visual display transformation for a VR system; that is, the series of transformations used to map points f rom object coordinates to screen coordinates, Virtual objects are typi cally defined in an object-centered coordinate system (CS), but must b e displayed using the screen-centered CSs of the two screens of a head -mounted display (HMD). This particular algorithm for the VR display c omputation allows multiple users to independently change position, ori entation, and scale within the virtual world, allows users to pick up and move virtual objects, uses the measurements from a head tracker-to immerse the user in the virtual world, provides an adjustable eye sep aration for generating two stereoscopic images, uses the off-center pe rspective projection required by many HMDs, and compensates for the op tical distortion introduced by the lenses in an HMD. The implementatio n of this framework as the core of the UNC VR software is described, a nd the values of the UNC display parameters are given. We also introdu ce the vector-quaternion-scalar (VQS) representation for transformatio ns between 3D coordinate systems, which is specifically tailored to th e needs of a VR system, The transformations and CSs presented comprise a complete framework for generating the computer-graphic imagery requ ired in a typical VR system. The model presented here is deliberately abstract in order to be general purpose; thus, issues of system design and visual perception are not addressed. While the mathematical techn iques involved are already well known, there are enough parameters and pitfalls that a detailed description of the entire process should be a useful tool for someone interested in implementing a VR system.