Fournier, A. and Reeves, W. T. (1986). A simple model of ocean waves. SIGGRAPH Computer Graphics, 20(4):75--84.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....WORK In a recent survey, Adabala and Manohar [Ada02] identify three major types of fluid models for computer graphics: texture based (2 D, fractal, or 3 D) combining textures and particles (blobs, grids, or particle maps) and completely particle based. The seminal works of Fournier and Reeves [Fou86] as well as Peachey [Pea86] can be seen as forerunners of the 2 D texture based category. A wide spread approach to the dynamics of height fields uses finitedifference methods, as described by Kass and Miller [Kas90] On modern hardware, such an approach easily runs in real time even with a high ....

....reflections at boundaries which notably includes ship walls, an effect neglected in the presented simulation. Further topics include the refraction of water waves over depth variations in the ground (e.g. in front of a shore) the simulation of which has been studied thoroughly starting with [Fou86, Pea86]. Further investigation can be spent on the diffraction at barriers and how to model additional effects caused by the non linearity of the hydrodynamical equations. If the elevation and wavelength are of comparable size, the linear approximation can hardly be justified mathematically while still ....

Fournier, A., Reeves, T. A Simple Model of Ocean Waves. Proc. of SIGGRAPH '86, Vol. 20, Nr. 4, pp. 75--84, 1986.

....virtual environments and computer games (also because simple collision detection is possible) as well as multimedia applications (think about a fly over an infinite large ocean surf scene) 2. RELATED WORK Early approaches in the field of ocean modelling and visualizing by Max [Max81] Fournier [Fou86], Peachey [Pea86] and Tso [Tso87] were able to produce fairly realistic results for relatively quiet ocean surfaces (also called deep water waves ) but plunged breaking waves could not be modelled correctly due to the sinusoidal assumption in the parametric surface and or the use of a high field ....

Fournier, A., and Reeves, W.T. A Simple Model of Ocean Waves. In ACM SIGGRAPH Proceedings, Vol.20, No.4, pp.75-84, 1986.

....tend to lose persistent features (e.g. eddies) and that a good model accounting for static distribution (e.g. for clouds density) doesn t trivially yield a good animated model. Among the mentioned papers, only [13, 24] deal with water (ocean waves) Empirical or phenomenological animations [8, 15, 27, 28, 10] rely on simplified analytical models: trochoids for ocean waves [8, 15, 10] Laplace fields for wind [27] hydraulics for rivers [28] Some were introduced in early CG at a time where CFD wasn t affordable. New models are also proposed regularly since they offer a good appearance cost ratio. ....

....for static distribution (e.g. for clouds density) doesn t trivially yield a good animated model. Among the mentioned papers, only [13, 24] deal with water (ocean waves) Empirical or phenomenological animations [8, 15, 27, 28, 10] rely on simplified analytical models: trochoids for ocean waves [8, 15, 10]; Laplace fields for wind [27] hydraulics for rivers [28] Some were introduced in early CG at a time where CFD wasn t affordable. New models are also proposed regularly since they offer a good appearance cost ratio. Note that spectrum controlled signals such as Perlin noise [16, 17] are a ....

Alain Fournier and William T. Reeves. A simple model of ocean waves. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 75--84, August 1986.

....these familiar opacities and colors. Minnaert describes many of these effects [1] Perlin has used a noise synthesis approach [2] to simulate the appearance of the ocean surface seen from a distance. More in depth discussion of water waves in computer graphics was presented by Fournier and Reeves [3], Peachey [4] and Ts o and Barsky [5] who modeled shallow water waves using different basis shapes. Mastin et al. 6] described a technique long in use by the oceanography community for modeling deep ocean waves. The Eurographics Association and Blackwell Publishers Ltd 2001. Published by ....

A. Fournier and W. T. Reeves. A simple model of ocean waves. In D. C. Evans and R. J. Athay (eds), Computer Graphics (SIGGRAPH '86 Proceedings). volume 20, pages 75--84. August 1986.

....in a real time simulator. All of them are devoted to photo realistic wave generation and produce animations in a non applicable time for a common maritime simulator. Let us introduce the main works in the domain. The first and well known theory was put forward by Fournier and Reeves in 1986 [8]. The authors enhanced the Gerstner and Biesel models by simplifying the various parametric equations. Their method does not take in account refraction, reflection and diffraction phenomena which are common in a port for instance. A similar model based on the Z Buffer algorithm for the wave ....

....refraction is computed by the change of the wave velocity according to the depth. In order to preserve the precision, we send a new ray between two consecutive rays when they diverge too much (Figure 4) The waveshape is computed along these rays by an improved version of the Fournier Reeves wave [8]. The model of waveshape is done in equation 2. The details of this model are done in [10] Rapidly, our waveshape model controls efficiently the arrival of wave on the beach and simulate the beginning of breakers phenomenon. The system coordinate used is presented in figure 8. A tessellation is ....

A. Fournier and W. T. Reeves. A simple model of ocean waves. In SIGGRAPH'86, volume 20, pages 75--84, 1986.

....and amplitudes that are computed by utilizing an FFT algorithm. A variety of different shapes can be simulated quite efficiently using this approach (see [3] for a good overview) but the complexity of the employed algorithm doesn t allow for interactive frame rates in general. Particle models [5, 11], on the other hand, are based upon the separate displacement of particles with respect to physics based constraints. By simulating the circular motion of particles during wave propagation effects like shoreline waves or wave loops can be modeled. Beta splines were employed for wave simulation in ....

A. Fournier and W.T. Reeves. A simple model of ocean waves. Computer Graphics, 20(4):75--84, 1986.

....how water reflection above and below the surface can be modeled using backward beam tracing. All of this work was done in order to render large bodies of water having no contact with the ground. A few papers had taken into account shoreline and cresting water models: Peachey [8] and Fournier[1] simultaneously created images of seashores in 1986 by modeling the movement of explicit waves over the surface of a fluid with additional fog and sea foam elements. Most recently O Brien and Hodgins [3] presented a system designed to simulate the dynamics of splashing liquids using a deformable ....

Alain Fournier and William Reeves. A simple model of ocean waves. SIGGRAPH '86 Conference Proceedings, 20(4):75--84, August, 1986.

....by means of a dynamic spline curve and a dynamic surface has been used to represent the water surface. Considering the Lagrangian method to model the fluid motion, each particle (i.e. each point) on the water surface describes a circular trajectory around its rest position (x 0 ; y 0 ; z 0 ) [4]. If we assume that the XY plane is the plane of the water at rest, the equation of the particle motion is then: ae x = x 0 r sin(kx 0 Gamma t) z = z 0 Gamma r cos(kx 0 Gamma t) 1) where k is the wave number, r is the radius of orbit, and is the angular speed. We denote the phase ....

....3 we can observe 5 time steps of animation considering the resulting perturbation due to both the wave trains. Effect of wind on the top of the wave crest In order to represent the effect of wind on the top of the wave crest, so called kludge phenomenon, equations (1) are changed as follows [4]: ae x = x 0 r sin(kx 0 Gamma t Gamma fi Deltaz Deltat) z = z 0 Gamma r cos(kx 0 Gamma t Gamma fi Deltaz Deltat) where the quantity fi Deltaz Deltat has been subtracted to the phase angle OE, fi is the coefficient of proportionality, Deltaz = z Gamma z 0 and Deltat is ....

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Fournier A., Reeves W.T., "A Simple Model of Ocean Waves", ACM SIGGRAPH '86, Vol.20, N.4, 1986, pp. 75-84. 9

....space efficient because a relatively compact description of the world can be used to generate animation of arbitrarily long duration. The computer graphics literature contains techniques for dynamically simulating a wide range of phenomena, including humans [14, 43] creatures [57, 59, 86] fluids [27, 28, 48, 70, 79, 92], rigid and deformable bodies [4, 62, 85, 97] and recently fractures [71] and explosions [68] In principle, anything that can be described by a solvable system of equations or a set of rules can be simulated. In practice, however, two major technological problems prevent us from building a ....

Alain Fournier and William T. Reeves. A simple model of ocean waves. In Computer Graphics: Proceedings of SIGGRAPH 86, volume 20(4), pages 75--84, 1986. Dallas, TX, August 18-22. 145

....the interested reader to Abbot and Basco [1] which covers some of the important principles without being too mathematically dense. Early graphics work concentrated on modeling just the surface of a body of water as a parametric function that could be animated over time to simulate wave transport [12, 22, 23]. Kass and Miller [17] approximated the 2D shallow water equations to get a dynamic height field surface that interacted with a static ground object . Chen and Lobo [4] extended the height field approach by using the pressure arising from a 2D solution of the NavierStokes equations to modulate ....

Fournier, A. and Reeves, W.T., "A Simple Model of Ocean Waves", ACM SIGGRAPH 86, 75-84 (1986).

....effects of the reflection and refraction of light on the water surface: shafts of light, caustics. Shnyi89a] WattM90a] Nishi94a] Great effort has been taken in studying atmospheric conditions to know how much sunlight and skylight reaches the water surface and the problem of wave generation [Fourn86a], TsoPY87a] Peach86a] However, realistic rendering of water scenes requires the transport of light within the water body to be properly handled. Due its complexity, when considering light transport in water strong simplifications are usually made (single scattering, isotropy, homogeneous ....

Fournier, A., Reeves, W.T.: A simple model of ocean waves, Computer Graphics, Annual Conferences Series (SIGGRAPH'86), Vol. 20, No.4, pp.75-84, 1986.

....few others rely on deterministic structural models [12, 41] Another distinction is that some work directly on the pixel values while others project the image intensity function onto a basis of functions 3 . There have been many physically based algorithms which target specific dynamic textures [11, 13, 29, 38]. Some simulations have also done by particle systems [32, 37] These methods are computationally intensive, customized for particular textures and allow no parameters to control the simulation once formulated. There has been comparatively little work in the specific area of dynamic textures or ....

A. Fournier and W. Reeves. A simple model of ocean waves. In ACM SIGGRAPH Proceedings, pages 75--84, 1986.

....real world ground materials. Other environmental effects that have been animated include water, clouds, and gases[5, 23, 7] fire[2, 23] lightning[18] and leaves blowing in the wind[26] Among these, water has received the most attention. Early work by Peachey[17] and by Fournier and Reeves[8] used procedural models based on specially designed wave functions to model ocean waves as they travel and break on a beach. Later work by Kass and Miller[10] developed a more general approach using shallow water equations to model the behavior of water under more general of conditions. Their ....

A. Fournier and W. T. Reeves. A simple model of ocean waves. In SIGGRAPH '86 Conference Proceedings, pages 75--84. ACM SIGGRAPH, 1986.

....ways. One of the most accurate is to solve the 3D Navier Stokes equations that describe the fluid body[7] This approach is well suited for simulations requiring a high level of detail, but has a high computational cost. Particle systems have been used to model waterfalls[13] Fournier and Reeves[4] and Peachey[10] have implemented other techniques that model the movement of explicit waves over the surface of a fluid. Kass and Miller[6] used shallow water equations for real time simulation of water under conditions that did not involve splashing. DIVER SIMULATION AND CONTROL SYSTEM We have ....

Fournier, A. and Reeves, W., "A Simple Model of Ocean Waves," Proceedings of SIGGRAPH `86, (August 1986), In Computer Graphics, Vol. 20, No. 4, pp. 75-84, 1986.

....be modeled with interacting particles, the number of particles needed to fill a volume will grow with the cube of the resolution of the model, and despite the simplified equations for the dynamics this method can be computationally expensive for a large volume of particles. Fournier and Reeves [2] and Peachey [7] implemented techniques that model the movement of explicit waves over the surface of a fluid. They used functions that describe the shape of a wave to displace a model representing the free surface of the fluid. Spray from the top of the wave crests is modeled using a particle ....

Fournier, A. and Reeves, W., "A Simple Model of Ocean Waves," Proceedings of SIGGRAPH `86, in Computer Graphics, Vol. 20, No. 4, pp. 75-84, 1986.

.... For example, steam, fog, smoke, and fire have been simulated in this manner [15, 13, 27, 28] Explosions, fire, and waterfalls have been successfully simulated by animated particle systems [23, 24, 26] Simplified physically based models have also been used to produce synthetic waves and surf [17, 21]. While the techniques mentioned above have been able to generate impressive results of compelling realism, a custom tailored model must be developed for each type of simulated phenomena. Furthermore, such simulations are for the most part expensive and, more importantly, the resulting animations ....

Alain Fournier and William T. Reeves. A simple model of ocean waves. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings) , volume 20(4), pages 75--84, August 1986.

.... For example, steam, fog, smoke, and fire have been simulated in this manner [16, 14, 30, 31] Explosions, fire, and waterfalls have been successfully simulated by animated particle systems [25, 26, 28] Simplified physically based models have also been used to produce synthetic waves and surf [18, 23]. While the techniques mentioned above have been able to generate impressive results of compelling realism, a custom tailored model must be developed for each type of simulated phenomena. Furthermore, such simulations are for the most part expensive and, more importantly, the resulting animations ....

Alain Fournier and William T. Reeves. A simple model of ocean waves. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings) , volume 20(4), pages 75--84, August 1986.

....must be approximated to enough accuracy to recreate these familiar opacities and colors. Perlin has used noise synthesis approach [14] to simulate the appearance of the ocean surface seen from a distance. More in depth discussion of water waves in computer graphics was done by Fournier and Reeves [3], Peachey [13] and Tso and Barsky [23] 1 Fig. 1. Photograph of the ocean (left) and rendering (right) of ocean using technique described in the paper. who modeled shallow water waves using different basis shapes. Mastin et al. 9] described a technique long in use by oceanography community for ....

Alain Fournier and William T. Reeves. A simple model of ocean waves. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 75--84, August 1986.

....These approaches solve the problem for particular kinds of scenes, either by procedurally describing the objects, or by providing a specific representation and the mean to render it. The first category concerns L systems, fractals, botanical and physical models [Smi84, PLH88, dREF 88, FR86] which generate polygons. The second category mostly concerns particle systems and some landscape specialized models [Ree83, RB85, WP95] which use specific representations and rendering techniques. Procedural geometric models do not address the rendering aspect of the problem, and specific ....

Alain Fournier and William T. Reeves. A simple model of ocean waves. In David C. Evans and Russell J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 75--84, August 1986.

....flow effects. 2 To appear in the SIGGRAPH conference proceedings evolution is determined by applying certain rules to the particles. Particle motion may follow either deterministic or stochastic laws of motion. Particle systems have been used to model trees, grass, fog, waterfalls, and fire [5, 16, 23]. In a related work, Small described a parallel approach to the problem of modeling watercolor by predicting the actions of pigment and water when applied to paper fibers [19] This model was cast as a complex cellular automata on the Connection Machine II. Small s model produces nice results, ....

FOURNIER, A., AND REEVES, W. T. A simple model of ocean waves. Computer Graphics 20, 4 (Aug. 1986), 75--84.

....Systems were first used in computer graphics by Reeves in 1983 [36] He defined a particle system model as a cloud of primitive particles, where each particle is generated into the system, moves, ages, and then dies. This work was later extended by Reeves and Blau [37] Fournier and Reeves [20], Sims [42] and many others to model such diverse phenomena as trees and grass, ocean spray, fireworks, waterfalls, fire, snowstorms and explosions. Reynolds [38] in his work on flocking behavior, greatly enhanced the power of the particle system as a modeling tool. He proposed the idea of ....

Fournier, A. and W. Reeves, "A Simple Model of Ocean Waves," Computer Graphics (Proc. SIGGRAPH) , Vol. 20, No. 4, pp. 75-84, August 1986.

....to realistic shapes and rendering, Computer Animation techniques try to generate consistent motion and deformations. A wide range of natural phenomena have been animated over the past few years. They include gaseous phenomena such as fire or smoke [13, 18, 8] liquids from waves to droplets [9, 12, 16, 7, 10], and the simulation of soft terrains, from footprints to landslides [4, 19, 11] This paper addresses another complex problem: the animation of lava flows. Our aim is to provide visual realism in both motion and rendering. In order to generate complex trajectories due to the interactions between ....

A. Fournier and W.T. Reeves. A simple model of ocean waves. In SIGGRAPH '86 Conference Proceedings, pages 75--84, August 1986.

....many particles are simulated and viewed simultaneously, can effectively recreate complex visual phenomena. Reeves (1983) introduced the first particle set animations, modeling phenomena such as fire and clouds. This model has also been used to animate the spray of crashing waves (Peachey, 1986; Fournier, 1986). Reynolds extended the behaviors of individual particles to take into account the activity of neighboring particles. Using this technique, he generated convincing group behaviors, including flocks of birds and schools of fish (Reynolds, 1987) 7 The analogy to rendering is clear: research in ....

Fournier, A. 1986. A simple model of ocean waves. Proceedings of SIGGRAPH `86, pages 75-84. ACM SIGGRAPH.

....in the real sea. The ocean surface was graphically modeled as a set of bicubic patches. Again, this model was not meant to approach real time graphics speed, as the rendering of these patches in a single frame took as little as two to as many as ten hours on a Computer Consoles Power 6 32 computer [FOUR86]. C. VIRTUAL WORLD SIZE VERSUS POLYGON COUNT In every field of research, decisions must be made which involve trade offs between two or more desired goals. In the field of economics this is referred to as the opportunity cost of a capital expenditure. And in computer science there have been ....

Fournier, A., "A Simple Model of Ocean Waves," Computer Graphics, 20(4), 75-84, (Proc. SIGGRAPH `86).

....be modeled with interacting particles, the number of particles needed to fill a volume will grow with the cube of the resolution of the model, and despite the simplified equations for the dynamics this method can be computationally expensive for a large volume of particles. Fournier and Reeves [2] and Peachey [7] implemented techniques that model the movement of explicit waves over the surface of a fluid. They used functions that describe the shape of a wave to displace a model representing the free surface of the fluid. Spray from the top of the wave crests is modeled using a particle ....

Fournier, A. and Reeves, W., "A Simple Model of Ocean Waves," Proceedings of SIGGRAPH `86, in Computer Graphics, Vol. 20, No. 4, pp. 75-84, 1986.

....ripples to a surface [Musgr93] together with a renderer which uses bump or displacement mapping to convey the surface detail. The method may be extended to incorporate effects due to underwater topography, diffraction and reflection around obstacles and the formation of surf in breaking waves [Peach85, FouRe86]. Wcilso et al. WciKi98] have developed a method to model displacement behaviours in a settled body of liquid. The simulation space is decomposed uniformly into a number of cubic cells which record the location of the settled liquid within the scene. Dropping a solid object into the liquid body ....

Fournier, A., Reeves, W.T., A Simple Model of Ocean Waves, ACM Computer Graphics (SIGGRAPH '86 Proceedings) , pp.75--84, 1986.

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A. Fournier and W.T. Reeves. A simple model of ocean waves. In SIGGRAPH '86 Conference Proceedings, pages 75--84, Aug. 1986.

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Fournier, A. and Reeves, W. T. (1986). A simple model of ocean waves. SIGGRAPH Computer Graphics, 20(4):75--84.

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A. Fournier and W. T. Reeves. A simple model of ocean waves. In SIGGRAPH 1986.

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Fournier, A., Reeves, W.T., A simple model of ocean waves, in D.C Evans & R.J. Athay, eds., "Computer Graphics (SIGGRAPH '86 Proceedings)", vol 20, pp371-384, 1986.

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A Fournier and W T Reeves. A simple model of ocean waves. Computer Graphics, 20(4):75--84, 1986.

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FOURNIER, A. and REEVES, W. T., "A simple model of ocean waves," Computer Graphics, vol. 20, pp. 75--84, Aug. 1986.

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A. Fournier, " A Simple Model of Ocean Waves," Computer Graphics, Vol. 20, No. 4, (1986),pp. 75-84.

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A. Fournier, \ A Simple Model of Ocean Waves," Computer Graphics, Vol. 20, No. 4,(1986),pp. 75-84.

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Alain Fournier and William T. Reeves. A simple model of ocean waves. In Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 75--84, 1986.

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FOURNIER A., REEVES W. T.: A simple model of ocean waves. In Computer Graphics (Proc. of SIGGRAPH 86) (1986), vol. 20, pp. 75--84.

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A. Fournier and W. T. Reeves. A simple model of ocean waves. In D. C. Evans and R. J. Athay, editors, Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 75--84, Aug. 1986.

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A. Fournier and W.T. Reeves, "A Simple Model of Ocean Waves," Comp.Graphics, Vol. 20, No. 4, Aug. 1986, pp. 7584.

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A. Fournier and W. T. Reeves. A simple model of ocean waves. In SIGGRAPH 1986.

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Alain Fournier and William T. Reeves. A simple model of ocean waves. In Computer Graphics (SIGGRAPH '86 Proceedings), volume 20, pages 75--84, 1986.

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A. Fournier and W.T. Reeves. "A Simple Model of Ocean Waves". Computer Graphics (SIGGRAPH '86 Proceedings), Vol. 20, No. 4, pp. 75--84, August 1986.

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A. Fournier, W.T. Reeves, "A Simple Model of Ocean Waves," Proc. SIGGRAPH'86, 1986, pp.75-84.

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A. Fournier and W. Reeves. A simple model of ocean waves. ACM Siggraph 86, pages 75--84, 1986.

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A. Fournier and W. Reeves. A simple model of ocean waves. ACM Siggraph 86, pages 7584, 1986. 204

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Fournier, Alain, and Reeves, William. A Simple Model for Ocean Waves. Proceedings of SIGGRAPH'86 (Dallas, Texas, August 18-22,

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Fournier, A. and Reeves, W., (1986) "A Simple Model of Ocean Waves," Proceedings of SIGGRAPH '86, in Computer Graphics, 20(3), pp. 75--84.

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