Self-animating image of flow through repeated asymmetric patterns (RAPs) is an innovative approach for creating illusory motion using a single image. In this paper, we present a smooth cyclic variable-speed RAP animation model that emulates orthogonal advancing waves from a geometry-based flow representation. It enables dense, accurate visualization of complex real-world flows using animated streamlines of an elegant placement coupled with visually appealing orthogonal advancing waves. The animation model first performs velocity (magnitude) integral luminance transition on individual streamlines. Then, inter-streamline synchronization in luminance varying along the tangential direction is imposed. Next, tangential flow streaks are constructed using evenly spaced hue differing in the orthogonal direction. In addition, an energy-decreasing strategy is proposed that adopts an iterative yet efficient procedure for determining the luminance phase and hue of each streamline in HSL (hue, saturation, and lightness or brightness) color space. To increase the contrast between flow streaks, adaptive luminance interleaving in the direction perpendicular to the flow is further applied. We demonstrate the effectiveness of the animation model using some synthetic and real flows. Color figures, images, and accompanying animations are available at http://graphics.csie.ncku. edu.tw/ flowvis.
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