Rendering Falling Snow Using an Inverse Fourier Transform

The typical method for rendering falling snow in computer graphics is to use particle systems. Particle systems can be computationally expensive, however, since each snowflake is modelled. Here we introduce a new, less expensive method for rendering falling snow. The method is based on a global Fourier transform. It extends a well-known model in visual perception of motion that a pure translational image motion produces a plane of energy in the 3D frequency domain. We extend this translational image motion model to the case of motion parallax such as occurs in a falling snow image sequence. Specifically the 2D image speed and the size of each moving snowflake depends on its depth in 3D because of standard perspective effects. We show that this depth vs. speed vs. size relationship leads to a non-planar motion surface in the 3D frequency domain. By synthesizing such a surface in the frequency domain and taking the inverse Fourier transform, we obtain a motion parallax image sequence which has the appearance of falling snow. We treat this image sequence as an opacity function and use it to composite white falling snow over a single image frame. This creates visual effect that snow is falling within the scene.