Many papers have presented rendering techniques and simplification ideas with the objective of speeding up image generation for irregular grid data sets. For large data sets, however, even the current fastest algorithms are known to require seconds to generate each image, making real-time analysis of such data sets very difficult, or even impossible, unless one has access to powerful and expensive computer hardware. In order to synthesize a system for handling very large data sets analysis, we have assembled algorithms for rendering, simplification and triangulation, and added to them some optimizations. We have made some improvements on one of the best current algorithms for rendering irregular grids, and added to it some simple approximation methods in both image and object space, resulting in a system that achieves high frame rates, even on slow computers without any specific graphic hardware. The algorithm adapts itself to the time budget it has available for each image generation, using hierarchical representations of the mesh for faster delivery of images when transformations are imposed to the data. When given additional time, the algorithm generates finer images, obtaining the precise final image if given sufficient time. We were able to obtain frame rates of the order of 5Hz for medium-sized data sets, which is about 20 times faster than previous rendering algorithms. With a trade-off between image accuracy and speed, similar frame rates can be achieved on different computers.