Abstract
We present a simple model for the surface of the ocean, suitable for the modeling and rendering of most common waves where the disturbing force is from the wind and the restoring force from gravity.It is based on the Gerstner, or Rankine, model where particles of water describe circular or elliptical stationary orbits. The model can easily produce realistic waves shapes which are varied according to the parameters of the orbits. The surface of the ocean floor affects the refraction and the breaking of waves on the shore. The model can also determine the position, direction, and speed of breakers.The ocean surface is modeled as a parametric surface, permitting the use of traditional rendering methods, including ray-tracing and adaptive subdivision. Animation is easy, since time is built into the model. The foam generated by the breakers is modeled by particle systems whose direction, speed and life expectancy is given by the surface model.To give designers control over the shape of the ocean, the model of the overall surface includes multiple trains of waves, each with its own set of parameters and optional stochastic elements. The overall "randomness" and "short-crestedness" of the ocean is achieved by a combination of small variations within a train and large variations between trains.Rendered examples of oceans waves generated by the model are given and a 10 second animation is described.
- Bies52 Biesel, F., "Study of Wave Propagation in Wa~r of Gradually Varying Depth," in Gravity Waves, U.S. National Bureau of Standards Circular 521, (1952), pp. 243-253.]]Google Scholar
- Blin78 Blinn, J. F., "Simulation of Wrinkled Surfaces," in Proceedings of SIGGRAPH '78, also published as Comput. Graphics, 12, 3, (Aug 1978), pp. 286-292.]] Google ScholarDigital Library
- Cook84 Cook, R. L., "'Shade trees," in Proceedings of SIGGRAPH '84, also published as Comput. Graphics, 18, 3, (july 1984), pp. 223-231.]] Google ScholarDigital Library
- Cook86 Cook, R. L., "Antialiasing by Stochastic Sampling," accepted to appear in Transactions on Graphics, (summer 1986).]]Google Scholar
- Crap84 Crapper, G. D., Introduction to Water Waves (Chichester, West Sussex, England : 1984).]]Google Scholar
- FeLS65 Feynman, R. P., Leighton, R. B. and Sands, M., The Feynman Lecture Notes on Physics, (Addison-Wesley, 1965).]] Google ScholarDigital Library
- Gers1802 Gcrstner, F. J. v, "Theorie der Wellen," Abh. d. k. bohm. Ges. d. Wiss. Also reprinted in Ann. der Physik, 32, (1809), pp. 412-440.]]Google ScholarCross Ref
- Kins65 Kinsman, Blair, Wind Waves (Prentice-Hail, 1965).]]Google Scholar
- Kins84 Kinsman, Blair, Wind Waves (Dover, 1984), reprint of preceding.]]Google Scholar
- LeBl78 LeBIond, Paul H., Waves in the Ocean (Amsterdam, 1978.)]]Google Scholar
- LeMe76 Le Mehaute, Bernard, An Introduction to Hydrodynamics and Water Waves (New York, Springer-Verlag, 1976)]]Google ScholarCross Ref
- Long76 Longuet-Higgins, M. S., "On Breaking Waves," in Waves on Water of Variable Depth, Provis, D. G. and Radok, R., Eds, Springer-Verlag Lecture Notes in Physics, (1976), pp. 129- 130.]]Google Scholar
- Max81a Max, N., "Vectorized. Procedural Models for Natural Terrains: Waves and Islands in the Sunset," in Proceedings of SIGGRAPH 81, also published as Comput. Graphics, 15, 3, (Aug 81), pp. 317-324.]] Google ScholarDigital Library
- Max81b Max, N., "Carla's Island," appeared in Issue #5 of the SIGGRAPH Video Review, (1981).]]Google Scholar
- Mei83 Mei, Chiang C., The Applied Dynamics of Ocean Surface Waves (New York, c 1983.)]]Google Scholar
- NoRS82 Norton, A., Rockwtxxt, A. P. and Skolmoski, P. T., "Clamping: A Method of Antialiasing Textured Surfaces by Bandwidth Limiting in Object Space," in Proceedings of SIGGRAPH 82, also published as Comput. Graphics, 16, 3, (July 82), pp. 1-8.]] Google ScholarDigital Library
- Ogde85 Ogden, L, "Generation of Fractals Using the Burt Pyramid," presented at the 1985 Optical Society of America Annual Meeting, Washington, DC, (October 1985).]]Google Scholar
- Peac86 Peachy, D., "Modeling Waves and Surf", these Proceedings.]] Google ScholarDigital Library
- Perl85 Perlin, K., "'An Image Synthetizer," in Proceedings of SIGGRAPH 85, also published as Comput. Graphics, 19, 3, (July 85), pp. 287-296.]] Google ScholarDigital Library
- Rank1863 Rarddne, W. J. W., "On the Exact Form of Waves near the Surfaces of Deep Water," Phil. Trans. Roy. Soc., A 153, (1863), pp. 127-138.]]Google ScholarCross Ref
- Reev83 Reeves, W. T., "Particle Systerns-A Technique for Modeling a Class of Fuzzy Objects," Transactions on Graphics, 2, 2, (April 83), pp. 91-108.]] Google ScholarDigital Library
- Scha80 Schachter, B., "Long crested wave models," Computer Graphics and Image Processing, 12, (1980), pp. 187-201.]]Google ScholarCross Ref
- Shep64 Shepard, D., "A two-dimensional interpolation function for irregularly spaced data," in Proceedings 1964 ACM National Conference, (1964), pp. 517-524.]] Google ScholarDigital Library
- TsBa86 Ts'o, P. Y. and Barsky, B. A., "Modeling and Rendering Waves: Wave-tracing using Beta-splines and Reflective and Refractive Texture Mapping", submitted for publication.]]Google Scholar
Index Terms
- A simple model of ocean waves
Recommendations
A simple model of ocean waves
SIGGRAPH '86: Proceedings of the 13th annual conference on Computer graphics and interactive techniquesWe present a simple model for the surface of the ocean, suitable for the modeling and rendering of most common waves where the disturbing force is from the wind and the restoring force from gravity.It is based on the Gerstner, or Rankine, model where ...
Interactive animation of ocean waves
SCA '02: Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animationWe present an adaptive scheme for the interactive animation and display of ocean waves far from the coast. Relying on a procedural wave model, the method restricts computations to the visible part of the ocean surface, adapts the geometric resolution to ...
Modeling ocean waves and interaction between objects and ocean water for cartoon animation
We present a scheme for the animation of ocean waves in a recognizable drawn animation cartoon style. This consists principally of two parts: the first part is the ocean surface generated by a procedural model which governs the dynamics of the ocean ...
Comments