In this article, we introduce a new function visualization method and demonstrate that numerical integration and visualization of multi-dimensional functions are closely related. Adaptive numerical integration is utilized to reduce the number of function evaluations, and generate time series data. The integration region is partitioned into a uniform grid. A grid cell can be sampled many times, or is not sampled at all, depending on the function properties and the integration rule. Function properties are extracted during the process of function evaluation. An aging technique helps visualize functions by retaining the most recently sampled areas and making the older ones transparent. This also results in giving the non-smooth areas more attention than the smooth areas. The new function visualization method gives a view of the whole function while elaborating on important areas such as ridges and troughs, which are critical in many fields, including numerical integration. A Grid service, called Integration Service, is used to solve computationally intensive integration problems. Remote visualization based on the adaptive method helps monitor the progress of a computation, and can be utilized for computational steering. The data are filtered by the server and transferred to the client, which is responsible for visualization mapping and rendering.
Irregular Morphing for Real-Time Rendering of Large Terrain
