Function-based flow modeling and animation

This paper summarizes a function-based approach to model and animate 2D and 3D flows. We use periodic functions to create cyclical animations that represent 2D and 3D flows. These periodic functions are constructed with an extremely simple algorithm from a set of oriented lines. The speed and orientation of the flow are described directly by the orientation and the lengths of these oriented lines. The resulting cyclical animations are then obtained by sampling the constructed periodic functions. Our approach is independent of dimension, i.e. for 2D and 3D flow the same types of periodic functions are used. Rendering images for 2D and 3D flows are slightly different. In 2D function values directly are mapped to color values. On the other hand, in 3D function values first mapped to color and opacity and then the volume is rendered by our volume renderer. Modeled and animated flows are used to improve the visualization of operations of rolling piston and rotary vane compressors.