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Book Excerpt: 18.2.5 Rendering Local Perturbations Sometimes it is desirable to render local choppiness caused by buoyant objects or by objects falling into the water. This is especially important for games, where it is necessary to generate explosions, ship trails, or the like. Because it is hard to integrate physically correct methods in our height-map-based model of the water surface, we discuss simpler methods, based on heuristics. Analytical Deformation Model The simplest way to achieve local choppiness is to disturb displaced vertex positions analytically, by combining them with the computed vertex position in the vertex shader. For explosions, we can use the following formula:
where r is the distance from the explosion center in the water plane and b is a decimation constant. The values of I0, w, and k are chosen according to a given explosion and its parameters. For rendering, we can use the same radial grid as the one used for regular water rendering, but centered at the explosion location. Dynamic Displacement Mapping Another option is to render all of the locally generated displacements directly into the vertex texture, essentially implementing a general-purpose programming on the GPU (GPGPU) type of approach. That way, we generate a vertex texture in the first pass and then use it in a subsequent pass for the actual water rendering. As an additional benefit, we can offload some work from the vertex shaders by filtering the base height map and summing “octaves” in the pixel shader. To calculate displacements, we can either employ the above-mentioned analytical model or try using a cellular-automata approach, by evolving local displacements from frame to frame. Wind effects can also be taken into account by blurring the texture along the appropriate direction. However, to cover 1 km of water surface with 50 cm resolution, it would be necessary to use a texture about 2048 × 2048 in size, which would create additional pressure on texture memory and shader execution speed. Also, quick transitions of the viewpoint would be problematic. Nevertheless, we encourage the reader to experiment with these approaches. Foam Generation When choppiness is strong enough, we can generate foam to further increase realism. The simplest way to do this is to blend in a precreated foam texture at vertices displaced above a certain height H0. Transparency of the foam texture is calculated according to the following formula:
where H max is the height at which the foam is at maximum, H0 is the base height, and H is the current height. The foam texture can be animated to show the evolution of foam creation and dissipation. The animation sequence can be either created manually by artists or generated programmatically 18.3 ConclusionBy combining the flexibility of vertex texture fetch and the performance-saving features of dynamic branching, we were able to develop a practical method for rendering realistic-looking water surfaces at interactive speeds. The approach described here was successfully applied in the title Pacific Fighters, and it allowed us to create a realistic water surface across a significant range of distances—from 10 cm up to 40 km. This is acceptable for modern flight simulators. We were able to eliminate tiling artifacts across the whole visible region of the water surface. Future hardware is likely to enable even more robust implementations of the technique, in particular eliminating the need to manually perform filtering of the texture values, as well as providing even more vertex shader performance. The quality of our approach can be increased even further by employing advanced shading techniques, such as parallax mapping, to provide fine-grained details and bumps on the water surface. See Chapter 8, “Per-Pixel Displacement Mapping with Distance Functions,” for one approach like this. Finally, lighting calculations could greatly benefit from high-dynamic-range techniques, because highly reflective water surfaces can exhibit huge brightness variations. 18.4 ReferencesFournier, Alain, and William T. Reeves. 1986. “A Simple Model of Ocean Waves.” In Computer Graphics (Proceedings of SIGGRAPH 86), pp. 75-84. Kryachko, Yuri. 2004. “Modelling Sea and River Water with Pixel Shader 2.0.” Presentation. Available online at Tessendorf, Jerry. 2001. “Simulating Ocean Water.” In “Simulating Nature: Realistic and Interactive Techniques,” SIGGRAPH 2001 course notes, course 47. _____________________________________________________ |
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