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In many scientific simulations, the temporal variation and analysis of features are important. Visualization and visual analysis of time series data is still a significant challenge because of the large volume of data. Irregular and scattered time series data sets are even more problematic to visualize interactively. Previous work proposed functional representation using basis functions as one solution for interactively visualizing scattered data by harnessing the power of modern PC graphics boards. In this paper, we use the functional representation approach for time-varying data sets and develop an efficient encoding technique utilizing temporal similarity between time steps. Our system utilizes a graduated approach of three methods with increasing time complexity based on the lack of similarity of the evolving data sets. Using this system, we are able to enhance the encoding performance for the time-varying data sets, reduce the data storage by saving only changed or additional basis functions over time, and interactively visualize the time-varying encoding results. Moreover, we present efficient rendering of the functional representations using binary space partitioning tree textures to increase the rendering performance.