Haptic Rendering of Data on Irregular Grids

Haptic rendering of data on irregular grids requires additional data storage and real time computation compared to the same size data sets on regular grids. At the same time, it is important to keep computation time small to avoid noticeable artifacts in haptic rendering. When the rendering algorithm is implemented on DSP processors, memory is often much smaller than on contemporary general purpose computers. By appropriate partitioning of algorithms between preprocessing and real time computation, and by quantizing and packing data, we show how scientific visualization of data sets on the order of 1 million elements by real time haptic rendering can be accomplished. INTRODUCTION In scientific visualization applications of haptic interfaces, forces are applied to the user’s hand which depend on values of data associated with physical locations in a data field. See e.g. [1]. As the user moves their hand, a corresponding virtual position in the data field changes. Data at that new position is then converted into (possibly different) forces to help the user understand the meaning of the data via changes in the “feel” generated by applied forces. For example, a vector field of fluid velocity data in an aerodynamics model can be converted into forces on the hand which cause a stylus in the user’s hand to orient itself along the local vector field direction. Translating the hand to another location interrogates another part of the vector field, and the hand orientation changes to correspond to the new data at that location. The scientific visualization of volume data is quite THIS WORK WAS SUPPORTED BY THE NATIONAL SCIENCE FOUNDATION (IIS-9711936) AND THE OFFICE OF NAVAL RESEARCH (N0001497-1-0354). different than surface rendering applications, e.g. [2, 3, 4], where two-dimensional meshes define a virtual surface which is traced with the haptic interface. It is important that the forces applied to the hand follow the changes in the data quickly and smoothly. Haptic rendering differs in this respect from visual (graphics) rendering, where the entire data field must be rendered, but substantial delays are acceptable [2]. Haptic rendering must be updated at rates exceeding several hundred Hz to avoid annoying edges and delays which corrupt the information that is to be conveyed by the data. Fast, smooth rendering is relatively easy when the data exists as an explicit function of position. This function is simply evaluated at each new hand position, and the data is converted directly to forces. In most applications, however, the data field is generated by finite element models, and no simple function describes data variation with position. This data exists as values (scalar, vector, tensor) specified at each node in a three-dimensional grid. Smooth data rendering is accomplished by interpolating the data grid. If the grid is structured (all elements in the grid have the same topology, e.g. cubes), and if the grid is regular (element edges all have equal lengths), then it is easy to interpolate directly from the (x;y;z) coordinates. Unfortunately, most data sets use irregular and/or unstructured meshes. This makes the interpolation problem more difficult, especially when it must be done quickly to avoid delays in real time haptic rendering. One solution is to resample the data onto a regular mesh, but this can cause artifacts unless an extremely fine mesh is used, and this requires storage and real time access of much larger sets of data. Instead, we wish to interpolate data on the original irregular mesh (to limit the size of the data set) and to do it efficiently (to minimize computation delays for high-fidelity haptic rendering).