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We introduce a novel flow visualization method called flow charts, which uses a texture atlas approach for the visualization of flows defined over curved surfaces. In this scheme the surface and its associated flow are segmented into overlapping patches which are then parameterized and packed in the texture domain. This scheme allows accurate particle advection across multiple charts in the texture domain, providing a flexible framework that supports various flow visualization techniques. The use of surface parameterization enables flow visualization techniques requiring the global view of the surface over long time spans, such as unsteady flow LIC (UFLIC), particle-based Unsteady flow advection-convolution (UFAC), or dye advection. It also prevents visual artifacts normally associated with view-dependent methods. Represented as textures, flow charts can be naturally integrated into GPU flow visualization techniques for interactive performance.