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Multiresolution streamline placement is useful for interactive visualization of flow fields. In this paper, a new method is proposed to build placements of streamlines in different resolutions for 2D and 3D flow fields. This method is developed from a basic streamline placement algorithm that takes control grids to place streamlines in 2D flow fields. The process of multiresolution analysis starts from a sparse placement, which is obtained with a coarse grid according to the basic placement algorithm. The sparse placement is then iteratively refined by elongating all existing streamlines and adding new streamlines under the control of a finer grid. By this means, a series of placements can be built in different resolutions, each of which reuses its previously placed streamlines at increasing density levels. This multiresolution placement for 2D flow fields is further extended to 3D flow fields by changing the basic placement algorithm to fit 3D space. Test results show that the basic streamline placement algorithm is very fast, so the proposed multiresolution analysis can be done for both 2D and 3D flow fields efficiently.