Fluid Animation With Frequency Domain Analysis To Generate Detail

Fluid animation, as an important research branch in Computer Graphics, has been well-developed. It emphasizes on visual effect of fluid shapes drawn by traditional artists. It also regards laws of motion in Physics. In Computational Fluid Dynamics (CFD), motions of fluids are interpreted by solutions of Navier-Stokes equations. Combing these two emphases, physically-based fluid animation creates fluid motions based on physical laws with visually fine shapes. With the growing demand of huge scene, high-resolution and realistic effect, fluid detail simulation becomes more and more important in physically-based fluid animation. However, the main problem in detail simulation is that how to minimize the cost of computational resources and at the same time ensure a visually fine effect which obeys the laws of Physics.This paper starts with the analysis of the cause of detail losing in current fluid animation framework. It also points out several parts that lose details in this framework. For one of the parts, interpolation step in semi-Lagrangian advection, we theoretically analyze how it loses details and introduce detail enhancement to delay the speed of detail losing. This can preserve the remaining details after interpolation step. Detail enhancement is implemented by convolving fluid fields with a modified Laplace kernel.Besides, for overall parts that lose details in the whole framework, we derive a method called detail reconstruction whose concept comes from signal processing theory. It finds back the lost details and reseeds them into fluid fields that lack details. Detail reconstruction can be implemented by passing fluid fields through a general reconstruction filter which represents the difference between detail lacking fluid fields and detail abundant ones.In addition, Fourier Transform used in detail enhancement and reconstruction brings serious Gibbs Effect when dealing with fluid fields that have mutations. Boundary smoothing reduces the Gibbs Effect by extrapolating the mutational boundary into a smooth one.At last, we testify the effectiveness and efficiency of detail enhancement and reconstruction by experiments and data analyses and also illustrate the effectiveness of boundary smoothing.Compared with previous work, this paper does further research on applying signal processing to fluid animation. Our main innovations are: (1) for the first time, we analyze the cause of detail losing in semi-Lagrangian method from the perspective of frequency domain analysis and derive the principles of two solutions to it: detail enhancement and detail reconstruction; (2) we introduce filters to improve the existing framework of detail simulation and process fluid fields as signals in frequency domain; (3) by the implementation of these two solutions, we efficiently add details in fluid fields and make the new details more physical.