Periodic Caustic Textures

Description

generating periodic caustics pattern in space and time

Algorithm Overview

random (fractal) surface profile by filtering three-dimensional noise by a power law-like filter in space and a Gaussian-like filter in time

1. random height field generation based on frequency synthesis

• create a random noise signal
• apply the fast Fourier transform to transfer the data into the frequency domain and apply the 1/f filter
• transform it back to the spatial domain with an inverse fast Fourier transform

2. smoothing in time with Gaussian filter
3. projection of the resulting surface to the ground plane – assuming directional light source pointing at this surface, computation of the intersection of the refracted rays with a plane at some depth – visualization with additive blending, triangle intensity is inversely proportional to the area of the projected triangle

References

• Periodic Caustic Textures by Jos Stam
• Frequency Synthesis of Landscapes (and clouds) by Paul Bourke