Modeling and rendering waves: wave-tracing using beta-splines and reflective and refractive texture mapping.

The graphical simulation of a certain subset of hydrodynamics phenomena is examined. New algorithms for both modeling and rendering these complex phenomena are presented. The modeling algorithms deal with wave refraction in an ocean. Waves refract in much the same way as light. In both cases, the equation that controls the change in direction is Snell's law. Ocean waves are continuous but can be discretely decomposed into wave rays or wave orthogonals. These wave orthogonals are wave-traced in a manner similar to the rendering algorithm of ray-tracing. The refracted wave orthogonals are later traversed and their height contributions to the final surface are calculated using a sinusoidal shape approximation and the principle of wave superposition. The surface is then represented by Beta-splines, using the tension (or β2) shape parameter to easily add more complexity to the surface. The rendering algorithms are based on the use of texture maps and Fresnel's law of reflection. In each algorithm, two texture maps are used to simulate reflection and refraction. Based on surface normal orientation and Fresnel's law, a weighting is calculated that determines what fractions of reflected color and refracted color are assigned to a point. These algorithms are more efficient, though less accurate, alternatives to standard ray-tracing techniques.