Abstract:
Realistic sprays for simulated fluids are created by adding a set of spray particles to a boundary region just below the fluid surface. The fluid surface is determined by solving a level set equation for a zero level corresponding to the fluid surface. Additionally, the boundary region is determined by solving the level set equation for a non-zero level corresponding to a surface at the specified depth from the fluid surface. The set of spray particles inherit an initial state, for example a velocity, from the fluid simulation. Subsequent motion of the spray particles is determined according to a ballistic simulation, rather than a fluid simulation, thereby substantially reducing the computational burden required to animate the fluid. Spray particles that sink below a specified depth from the fluid surface are removed.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 10/780,847 filed Feb. 17, 2004, and entitled “Water Particle Manipulation,” which issued as U.S. Pat. No. 7,349,832 on Mar. 25. 2008. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to the field of computer graphics, and in particular to methods and apparatus for realistically animating water and other fluids. The present invention relates to the field of computer graphics. Many computer graphic images are created by mathematically modeling the interaction of light with a three dimensional scene from a given viewpoint. This process, called rendering, generates a two-dimensional image of the scene from the given viewpoint, and is analogous to taking a photograph of a real-world scene. Animated sequences can be created by rendering a sequence of images of a scene as the scene is gradually changed over time. A great deal of effort has been devoted to making realistic looking rendered images and animations. 
     Realistically animating water and other fluids presents a particular challenge. The behavior of a fluid, for example a churning ocean, has a number of different characteristics that are difficult to animate by hand. To assist animators, simulations of fluid dynamics are often used to animate the fluid according to parameters defined by animators. In a typical fluid dynamics simulation, the fluid is modeled as a set of particles. The simulation solves a system of equations defining the dynamic behavior of the fluid to determine the motion of the set of particles. The result of the simulation is a set of particles imitating the behaviors of the fluid, such as waves, splashes, eddies, currents and ripples. 
     Although the set of particles animated by a typical simulation technique move, as a whole, like a fluid, it often does not look like a fluid if rendered directly. Typically, the number of particles in a set is too small to give the appearance of a continuous surface of a fluid. Some rendering techniques render particles as metaballs, which are “blobs” that stretch or deform themselves into a continuous “goo.” However, metaballs give the surface of the fluid a lumpy appearance, similar to rice pudding, which is unacceptable for representing fluids such as water. Another rendering technique creates an isosurface from the set of particles. The isosurface creates a smooth, spatially-continuous fluid surface; however, this surface is temporally discontinuous due to frame-to-frame noise. As a results, the motion of the isosurface appears jerky and discontinuous. 
     One rendering technique to create a smooth-looking fluid from the set of particles creates a level set representing the fluid surface from the set of particles. The level set is created from a signed distance function of the set of particles. The values of the level set are adjusted for each frame of animation from the velocities of the set of particles. This results in a fluid surface that is spatially continuous, i.e. smooth-looking, and temporally continuous, i.e. smoothly-animated. 
     Although level-sets provide a smooth-looking fluid, the relatively small number of particles used for the simulation does not allow for the fluid to form “sprays” as waves break or recede. The resulting fluid appears sterile and artificial. Increasing the number of particles in the fluid simulation may allow for a more realistic spray; however, this greatly increases the computational burden of the simulation. Additionally, the use of additional simulation particles is wasteful, as the majority of particles, such as those below the fluid surface, do not form sprays. 
     It is therefore desirable to have a system and method for creating realistic-looking sprays for simulated fluids. It is further desirable that the sprays do not increase the computational burden of the fluid simulation or rendering. 
     BRIEF SUMMARY OF THE INVENTION 
     An embodiment of the invention creates realistic sprays for simulated fluids by adding a set of spray particles to a boundary region just below the fluid surface. The set of spray particles inherit an initial state, for example a velocity, from the fluid simulation. Subsequent motion of the spray particles is determined according to a ballistic simulation, rather than a fluid simulation, thereby substantially reducing the computational burden required to animate the fluid. Spray particles that sink below a specified depth from the fluid surface are removed. 
     In an embodiment, a method of animating a fluid includes determining a state of a set of fluid particles at a first instance of time using a fluid simulation and defining a fluid surface from the state of the set of fluid particles. A boundary region is then defined between the fluid surface and a specified depth from the fluid surface. A plurality of spray particles are added to the boundary region. The plurality of spray particles is assigned a state based derived from the state of the set of fluid particles. The plurality of spray particles are moved according to at least the state of the plurality of spray particles, and a portion of the plurality of spray particles that are located below the specified depth from the fluid surface are removed. 
     In a further embodiment, a ballistic simulation moves the plurality of spray particles. In an additional embodiment, the method includes rendering the fluid surface and rendering a portion of the plurality of spray particles located above the fluid surface. 
     In another embodiment, the fluid surface is determined by solving a level set equation for a zero level corresponding to the fluid surface. Additionally, the boundary region is determined by solving the level set equation for a non-zero level corresponding to a surface at the specified depth from the fluid surface. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be described with reference to the drawings, in which: 
         FIG. 1  illustrates a general-purpose computing system suitable for implementing an embodiment of the invention; 
         FIGS. 2A and 2B  illustrate a prior technique for creating an animated fluid; 
         FIG. 3  illustrates a method for creating an animated fluid with sprays according to an embodiment of the invention; and 
         FIGS. 4A-4F  illustrate the creation of an animated fluid with sprays for an example fluid according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  illustrates an example computer system  100  capable of implementing an embodiment of the invention. Computer system  100  typically includes a monitor  110 , computer  120 , a keyboard  130 , a user input device  140 , and a network interface  150 . User input device  140  includes a computer mouse, a trackball, a track pad, graphics tablet, touch screen, and/or other wired or wireless input devices that allow a user to create or select graphics, objects, icons, and/or text appearing on the monitor  110 . Embodiments of network interface  150  typically provides wired or wireless communication with an electronic communications network, such as a local area network, a wide area network, for example the Internet, and/or virtual networks, for example a virtual private network (VPN). 
     Computer  120  typically includes components such as one or more general purpose processors  160 , and memory storage devices, such as a random access memory (RAM)  170 , disk drives  180 , and system bus  190  interconnecting the above components. RAM  170  and disk drive  180  are examples of tangible media for storage of data, audio/video files, computer programs, applet interpreters or compilers, virtual machines, embodiments of the herein described invention including geometric scene data, object data files, shader descriptors, a rendering engine, output image files, texture maps, and displacement maps. Further embodiments of computer  120  can include specialized audio and video subsystems for processing and outputting audio and graphics data. Other types of tangible media include floppy disks; removable hard disks; optical storage media such as DVD-ROM, CD-ROM, and bar codes; non-volatile memory devices such as flash memories; read-only-memories (ROMS); battery-backed volatile memories; and networked storage devices. 
       FIGS. 2A and 2B  illustrate a prior technique for creating an animated fluid.  FIG. 2A  illustrates a close-up view of a fluid simulation  200  over a small region of the fluid surface. Simulation  200  models the behavior of a fluid as a set of particles  205 . In  FIGS. 2A and 2B , the fluid is animated in two-dimensions for clarity; however, fluids are typically animated in three-dimensions. The simulation  200  solves a system of fluid dynamics equations to determine the forces on each particle in the set  205 , which in turn determines the acceleration, velocity, and position of each particle in the set  205 . For example, particles  215 ,  220 , and  225  each have a velocity, represented by a solid arrow, and an acceleration, represented by a dashed arrow. Together, these parameters represent at least a portion of the state of the set of particles  205 . The simulation  200  determines the state of the set of particles  205  for each frame of the animation. 
     As discussed above, although the set of particles  205  behaves, as a whole, like a fluid, the set of particles  205  do not create the smooth, continuous surface needed for rendering the fluid. To create a smooth fluid surface, a level set is created from the set of particles.  FIG. 2B  illustrates an example level set  250  created from the state of the set of particles  205 . Region  270  corresponds to the close up view of the particle simulation shown in  FIG. 2A  The level set  250  is a signed distance function giving a value corresponding to the distance from the surface of the fluid. Zero level lines  255 ,  260 , and  265  represent the surface of the fluid, which are the portions of the level set with a value of zero. In the example of  FIG. 2B , the zero level lines can be visualized as the outlines of drops of fluid resting on a flat sheet. 
       FIG. 3  illustrates a method  300  for creating an animated fluid with sprays according to an embodiment of the invention. At step  305 , the state of a set of fluid particles is determined for a given instant of time. In an embodiment, a fluid dynamics simulation using smooth particle hydrodynamics (SPH) is used to determine the forces on each one of the set of fluid particles, which in turn determines the state of the set of fluid particles at a given instant of time. In an example implementation, the fluid dynamics simulation determines the state of 10,000 to 1,000,000 fluid particles. Dynamic behaviours, such as waves, are initiated in the fluid dynamics simulation as pressure forces induced by collisions with boundary objects. 
     Following the determination of the state of the set of fluid particles, a fluid surface is defined from the state of the set of fluid particles at step  310 . The purpose of step  310  is to create a continuous surface for the fluid to be used during rendering. In an embodiment, the fluid surface is the zero level of a level set. The level set is initialized using a signed distance function that represents the distance from an arbitrary point in space to the fluid surface forms the level set. In the case of a two-dimensional fluid, as shown in the examples, the level set is a three dimensional surface. In the case of a three-dimensional fluid, the level set is a four dimensional surface. 
     A level set equation is solved to determine the location of the zero level of the level set at a given point in time, t. An example level set equation is:
 
φ t   F |∇φ|=0.
 
In this example equation, φ is the signed distance function to the zero level surface, which is a function of position and time, and the F represents the velocity of the zero level surface, which as discussed below is determined from the set of fluid particles. In an embodiment, the space around the set of fluid particles is discretized into a grid of points. The velocity values of fluid particles adjacent to grid points are weighted to determine an average velocity for each grid point. The average velocity of each grid point, in conjunction with the partial derivatives of the level set function are used to find the solution of the level set equation. In an example implementation, a “nudging” solver is used to solve the level set equation and to incrementally update the level set over time, allowing a solution that appears continuous over time but which does not diverge from the set of fluid particles. The solution of the level set equation defines the zero level surface at the given instant of time. In an embodiment, the surface of the fluid is created by trilinearly interpolating the position of zero level surface from the grid. The surface of the fluid can be rendered as a polygonal mesh using the values of the level set to determine surface normals.
 
       FIGS. 4A and 4B  illustrate an example implementation of steps  305  and  310  of method  300 .  FIG. 4A  illustrates a close-up view of a fluid simulation  400  over a small region of the fluid surface. Fluid simulation  400  models the behavior of a fluid as a set of particles  405 . Simulation  400  solves a system of fluid dynamics equations to determine the forces on each particle in the set  405 , which in turn determines the acceleration, velocity, and position of each particle in the set  405 . For example, particles  410 ,  415 , and  420  each have a velocity, represented by a solid arrow. 
     A level set  430  defining the surface of the fluid is created by weighting the velocities of particles adjacent to grid points to determine a velocity for each grid point. The velocity of the grid points, along with the partial derivatives of the level set function, are used to find the solution of the level set equation and thus the location of the zero level of the level set function at a given point of time. The zero level  430  corresponds to the surface of the fluid.  FIG. 4B  illustrates example level set  430  view from above. Contour lines  440 ,  445 , and  450  indicate the portions of the level set  430  at the zero level. Region  470  corresponds to the close up view of the particle simulation shown in  FIG. 4A . 
     Following step  310 , in which a fluid surface is defined at a given instant of time, step  315  determines a boundary region to be used in the creation of spray. The boundary region is a region of the space just beneath the fluid surface. In an embodiment, the boundary region is determined from the level set function previously used to determine the fluid surface. In this embodiment, the level set equation is modified to solve for a non-zero level, for example one centimeter below the surface. An example level set equation for finding the desired non-zero level might be:
 
φ t   +F |∇φ|=−0.01
 
Because the level set function is based on the signed distance function, a boundary region any thickness can be defined by solving the level set equation for the desired thickness value. The resulting non-zero level corresponds to the inner surface of the boundary region, with the outer surface of the boundary region being the fluid surface.
 
     Once the boundary region is defined, a set of spray particles is added, or seeded to the boundary region. The spray particles are assigned a velocity based on the weighted velocity of adjacent grid points. In an example implementation, the density of spray particles added to the boundary region ranges from ten to 100 times the density of the set of simulation particles. 
       FIGS. 4C and 4D  illustrate an example implementation of step  315 .  FIG. 4C  illustrates an example level set  480 . The level set  480  includes zero level boundaries  488 ,  490 , and  492 , representing the surface of the fluid. The boundary regions  482 ,  484 , and  486  are formed in this example by finding a non-zero level of the level set function. Once the boundary region is defined, a set of spray particles are seeded into the boundary region. 
       FIG. 4D  illustrates a close-up view of region  494  of  FIG. 4C , showing the seeding of spray particles within the boundary region. Zero level  500 , defining the surface of the fluid, and non-zero level  505  define the boundary region  503 . Within the boundary region  503 , a number of spray particles, shown in gray, have been added. Each spray particle is assigned a velocity based on the weighted average of the velocity of adjacent grid points. For example, spray particles  507 ,  509 ,  511 ,  513 , and  515  have each been assigned a velocity, shown with an arrow. 
     At step  320 , the zero level and the spray particles are rendered to create an output image. In an embodiment, spray particles are only rendered if they are above the surface of the fluid. Although initially all of the spray particles will be found within the boundary region underneath the fluid surface, eventually some spray particles will travel above the surface of the fluid, as discussed below. Rendering can be performed using any technique, for example ray-tracing or scanline rendering, in combination with lighting, shading, texture mapping, and any other image processing information to create a final image or frame. As it is often desirable to animate a fluid in the context of other entities, step  320  may also integrate unrelated objects, images, and other entities into the rendering. In an alternate embodiment, the location of the zero level and the spray particles is stored and rendering is deferred until a later time. 
     At step  325 , the motion of the spray particles is simulated in preparation for the next frame of animation. Unlike the fluid particles, which are moved according to a complex fluid simulation, the spray particles are moved according to a ballistic simulation. For example, each spray particle is displaced by a distance equal to the product of its velocity and the time increment between frames. Each spray particle&#39;s velocity is then added to an acceleration vector, representing the force of gravity, with the result stored as the spray particle&#39;s new velocity. The acceleration vector, which determines how long a spray “floats,” can be changed in value to achieve the desired aesthetic effect. Because the spray particles are not animated with a computationally expensive fluid simulation, the addition of the spray particles does not adversely effect the performance of the overall fluid animation. As discussed below, method  300  is repeated for each frame of fluid animation. It should be noted that step  325  simulates the motion of all of the spray particles in the system, including any remaining from previous iterations of the method  300 . 
       FIG. 4E  illustrates an example implementation of step  325 . In  FIG. 4E , some of the spray particles, such as spray particles  522 ,  524 , and  526 , have traveled outside the boundary region  520  and above the fluid surface  521 . Similarly, spray particles  528 ,  530 , and  532  have sunk below the inner surface  527  of the boundary region  520 . 
     In an embodiment, it is assumed that spray particles that sink below the boundary region will never rise above the fluid surface to become visible again. Thus, step  330  removes from the simulation the spray particles that have moved below the boundary region.  FIG. 4F  illustrates an example implementation of step  330 , in which the spray particles  552 ,  554 , and  556  have sunk below the boundary region  550  and have been removed. In  FIG. 4F , the removed spray particles are shown in outline. In an embodiment, the same boundary region is used both for seeding new spray particles and removing old spray particles. However, alternate embodiments can define separate boundary regions for seeding new spray particles and removing old spray particles. 
     Further embodiments can be envisioned to one of ordinary skill in the art after reading the attached documents. In other embodiments, combinations or sub-combinations of the above disclosed invention can be advantageously made. The block diagrams of the architecture and flow charts are grouped for ease of understanding. However it should be understood that combinations of blocks, additions of new blocks, re-arrangement of blocks, and the like are contemplated in alternative embodiments of the present invention. 
     The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense. It will, however, be evident that various modifications and changes may be made thereunto without departing from the broader spirit and scope of the invention as set forth in the claims.