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The growing popularity and demand for scientific visualization is due to the explosion in generating data as simulations and measurements using supercomputers. Scientific visualization facilitates visual interpretation of massive data sets. The dissertation focuses on the following: (a) visualization of two-dimensional tensor fields using topology, (b) a new algorithm to generate isosurfaces for visualizing volume data, (c) different schemes of interactive visualization of water-resource data. This article particularly brings out the use of duality of key aspects in three different areas for effective visualization.