Abstract:
Systems and methods for rendering a gaseous display. The distance from a user&#39;s reference point to each pixel through the gas is determined. The distance is then converted into an attenuation factor that is used to blend the scene color with the gas color. The result can then be used to simulate patchy fog, clouds, or other gases of more or less constant density and colors.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     The present application is a continuation of and claims priority to U.S. patent application Ser. No. 09/990,085 filed Nov. 21, 2001 which, in turn, claims priority to U.S. Provisional Application No. 60/252,094, filed Nov. 21, 2000, the disclosures of which are incorporated by reference herein.  
         [0002]     This patent application is related to the following four co-pending and commonly-owned applications:  
         [0003]     1. R. Mech, et al., “Rendering Volumetric Fog and Other Gaseous Phenomena” (MS1-1031US), U.S. patent application Ser. No. 09/990,085, now pending issuance (incorporated in its entirety herein by reference);  
         [0004]     2. R. Mech, et al., “Rendering Volumetric Fog and Other Gaseous Phenomena” (MS1-1031USC1), filed concurrently herewith (incorporated in its entirety herein by reference);  
         [0005]     3. R. Mech, et al., “Rendering Volumetric Fog and Other Gaseous Phenomena Using an Alpha Channel” (MS1-1032US), now U.S. Pat. No. 6,940,504 (incorporated in its entirety herein by reference); and  
         [0006]     4. R. Mech, “Method, System, and Computer Program Product for Rendering Multicolored Layered Fog with Self-Shadowing and Scene Shadowing” (MS1-1033US), U.S. patent application Ser. No. 09/990,082, now abandoned (incorporated in its entirety herein by reference). 
     
    
     BACKGROUND  
       [0007]     Computer graphics systems are used in many game and simulation applications. For example, flight simulators use graphics systems to present scenes that a pilot would be expected to see if he or she were flying in an actual aircraft cockpit. Several key techniques used to achieve visual realism include antialiasing, blending, polygon offset, lighting, texturizing, and atmospheric effects. Atmospheric effects such as fog, smoke, smog, and other gaseous phenomena are particularly useful because they create the effect of objects appearing and fading at a distance. This effect is what one would expect as a result of movement. Gaseous phenomena are especially important in flight simulation applications because they help to train pilots to operate in and respond to conditions of limited visibility.  
         [0008]     Quite a few methods for creating realistic images of fog, clouds and other gaseous phenomena have been developed in the past. Most of these techniques focus on computing the light distribution through the gas and present various methods of simulating the light scattering from the particles of the gas. Some resolve multiple scattering of light in the gas and others consider only first order scattering (the scattering of light in the view direction) and approximate the higher order scattering by an ambient light. A majority of the techniques use ray-tracing, voxel-traversal, or other time-consuming algorithms to render the images. Taking advantage of the current graphics hardware some of the techniques are approaching interactive frame rates.  
         [0009]     Another approach renders clouds and light shafts by blending a set of billboards, representing metaballs. The rendering times range from 10 to 30 seconds for relatively small images. Another approach renders gases by blending slices of the volume in the view direction. Using 3D textures, a near real-time frame rate is achieved. This is especially true for smaller images. Unfortunately, both these techniques are fill-limited, i.e., the number and the size of the rendered semi-transparent polygons is limited by the number of pixels hardware can render per second. Even on the fastest machines, it is not possible to render too many full-screen polygons per frame. The techniques may be suitable for rendering smaller local objects, e.g., a smoke column or a cloud, but even then the performance can suffer when the viewer comes too close to the object and the semitransparent polygons fill the whole screen. In the case of a patchy fog that can be spread across a large part of the scene, the number of slices would be simply too large.  
         [0010]     In real-time animations, smoke and clouds are usually simulated by mapping transparent textures on a polygonal object that approximates the boundary of the gas. Although the texture may simulate different densities of the gas inside the 3D boundary and compute even the light scattering inside the gas, it does not change, when viewed from different directions, and it does not allow movement through the gas without sharp transitions. Consequently, these techniques are suitable for rendering very dense gases or gasses viewed from a distance. Other methods simplify their task by assuming constant density of the gas at a given elevation, thereby making it possible to use 3D textures to render the gas in real time. The assumption, however, prevents using the algorithm to render patchy fog. What is needed is a way to render in real-time, complex scenes that include patchy fog and other gaseous phenomena such that efficiency and high quality visual realism are achieved.  
       SUMMARY  
       [0011]     A system, method, and computer program product for rendering a realistic displays of a gaseous phenomenon in a scene. In one implementation, the distance from a user reference point to each pixel traveled through the gas is determined by subtracting the distances to the front faces of the gas boundary from the distances to the back faces of the gas boundary. The travel distance is then converted into an attenuation factor which is used to blend the scene color with the gas color. The result can then be used to simulate patchy fog, clouds, or other gases of more or less constant density and color. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]      FIG. 1  is a block diagram illustrating an exemplary computer architecture.  
         [0013]      FIG. 2  illustrates an exemplary host and graphics subsystem.  
         [0014]      FIG. 3  illustrates an example of a computer system.  
         [0015]      FIG. 4  is a flowchart illustrating a routine for rendering volumetric fog or other gaseous phenomena.  
         [0016]      FIG. 5  is a flowchart illustrating a routine for determining the distance traveled through fog from a reference point to a pixel.  
         [0017]      FIG. 6  is a flowchart diagram showing further detail of a routine for determining the distance traveled through fog from a reference point to a pixel.  
         [0018]      FIG. 7  is an illustration of a linear fog equation used to render a scene including fog or other gaseous phenomena.  
         [0019]      FIG. 8  is a flowchart diagram describing an OPENGL implementation of a routine for resetting pixel colors located outside of a fog region.  
         [0020]      FIG. 9  is a flowchart diagram describing an OPENGL implementation of a routine for determining travel distance through fog from a reference point to a pixel.  
         [0021]      FIG. 10  is a flowchart diagram of a routine for rendering a scene based on a final fog factor.  
         [0022]      FIG. 11  is an illustration of an equation used to determine a final fog factor.  
         [0023]      FIG. 12  is a flowchart diagram of a routine for rendering a scene including fog and other gaseous phenomena based on a final fog factor.  
         [0024]      FIG. 13A  is an illustration of a routine for rendering volumetric fog or other gaseous phenomena.  
         [0025]      FIG. 13B  is an illustration of a routine for determining the distance from a reference point to a pixel.  
         [0026]      FIG. 13C  is an illustration of resetting pixel colors located outside of a fog region.  
         [0027]      FIG. 13D  is an illustration showing further detail of a routine for it determining the distance traveled through fog from a reference point to a pixel.  
         [0028]      FIG. 13E  is an illustration of a conversion routine for determining a fog factor based upon distance traveled through fog from a reference point to a pixel.  
         [0029]      FIG. 13F  is an illustration of a routine for rendering a scene including fog and other gaseous phenomena based on a final fog factor.  
     
    
     DETAILED DESCRIPTION  
       [0000]     As used herein:  
         [0030]     “Image” or “scene” means an array of data values. A typical image might have red, green, blue, and/or alpha pixel data, or other types of pixel data information as known to a person skilled in the relevant art.  
         [0031]     “Pixel” means a data structure used to represent a picture element. Any type of pixel format can be used.  
         [0032]     “Real-time” refers to a rate at which successive display images can be redrawn without undue delay upon a user or application. This interactive rate can include, but is not limited to, a rate equal to or less than approximately 120 frames per second. In one implementation, an interactive rate is equal to or less than 60 frames per second. In some examples, real time can be one frame update per second or faster.  
         [0033]     “Depth” and “Distance” are interchangeable terms representing a value which is a function of distance between two points.  
         [0034]     “Fog object” refers to a bounded volumetric gas.  
         [0035]     “Travel distance value” refers to the distance traveled from a reference point to a pixel in a scene.  
         [0036]     The boundaries of fog can be defined by polygonal surfaces to create so called “fog objects.” It is possible to determine the travel distance through the fog objects by adding the “depths” of the fog objects in front of the rendered pixel.  
         [0037]     In this discussion, the term “depth” of a fog object refers to distance information through the fog object. In one example, this distance information is equal to the distance within the fog object along a ray between a reference point and a pixel. If the fog object is closed and the pixel is outside the fog object, its depth can be computed by subtracting the distances to all back faces covering the given pixel from the distances to all front face covering the pixel. This has to be done for all fog objects in front of the pixel. If the pixel is inside a fog object, the distance to the pixel is used instead of the distance to the back face.  
         [0038]     In an exemplary implementation, the fog object distance information is converted to a color component (r,g,b) to take advantage of the blending capabilities of the graphics hardware. For this purpose linear fog (converting distance to color) is used. It is noted that the actual distance from the viewpoint is not being measured, but instead measurements are taken from a plane located in the viewpoint.  
         [0039]      FIG. 1  illustrates a block diagram of an example computer architecture  100 , which may be implemented in many different ways, in many environments, and on many different computers or computer systems. Architecture  100  includes six overlapping layers. Layer  110  represents a high level software application program. Example software application programs include visual simulation applications, computer games or any other application that could take advantage of computer generated graphics. Layer  120  represents a three-dimensional (3D) graphics software tool kit, such as OPENGL PERFORMER, available from SGI, Mountain View, Calif. Layer  125  represents a graphics application program interface (API), which can include but is not limited to OPENGL, available from SGI. Layer  130  represents system support such as operating system and/or windowing system support. Examples of such support systems include UNIX, Windows, and LINUX. Layer  135  represents firmware which can include proprietary computer code. Finally, layer  140  represents hardware, including graphics hardware. Hardware can be any hardware or graphics hardware including, but not limited to, a computer graphics processor (single chip or multiple chip), a specially designed computer, an interactive graphics machine, a gaming platform, a low end game system, a game console, a network architecture, a server, et cetera. Some or all of the layers  110 - 140  of architecture  100  will be available in most commercially available computers.  
         [0040]     In one exemplary implementation, a gaseous phenomena generator module  105  is provided. The gaseous phenomena generator module  105  provides control steps necessary to carry out routine  400  (described in detail below). The gaseous phenomena generator module  105  can be implemented in software, firmware, hardware, or in any combination thereof. As shown in  FIG. 1 , in one example implementation, gaseous phenomena generator module  105  is control logic (e.g., software) that is part of application layer  110  and provides control steps necessary to carry out routine  400 . In alternative implementations, gaseous phenomena generator  105  can be implemented as control logic in any one of the layers  110 - 140  of architecture  100 , or in any combination of layers  110 - 140  of architecture  100 .  
         [0041]      FIG. 2  illustrates an example graphics system  200 . Graphics system  200  comprises a host system  205 , a graphics subsystem  212 , and a display  240 . Host system  205  is equipped with an application program  206 , a hardware interface or graphics API  208 , and a processor  210 . Application program  206  can be any program requiring the rendering of a computer image or scene. The computer code of application program  206  is executed by processor  210 . Application program  206  accesses the features of graphics subsystem  212  and display  240  through hardware interface or graphics API  208 . As shown in  FIG. 2 , in one example implementation, gaseous phenomena generator module  105  is control logic (e.g., software) that is part of application  206 .  
         [0042]     Graphics subsystem  212  comprises a vertex operation module  214 , a pixel operation module  216 , a rasterizer  220 , a texture memory  218 , and a frame buffer  235 . Texture memory  218  can store one or more texture images  219 . Rasterizer  220  comprises a fog unit  225  and a blending unit  230 .  
         [0043]     Fog unit  225  can obtain either linear or non-liner fog color values. Blending unit  230  blends the fog color values and/or pixel values to produce a single pixel. The output of blending unit  230  is stored in frame buffer  235 . Display  240  can be used to display images or scenes stored in frame buffer  235 .  
         [0044]     Referring to  FIG. 3 , an example of a computer system  300  is shown. Computer system  300  can be used to implement a computer program product. Computer system  300  represents any single or multi-processor computer. Single-threaded and multi-threaded computers can be used. Unified or distributed memory systems can be used.  
         [0045]     Computer system  300  includes one or more processors, such as a processor  304 , and one or more graphics subsystems, such as a graphics subsystem  306 . One or more processors  304  and one or more graphics subsystems  306  can execute software and implement all or part of the features described herein. Graphics subsystem  306  can be implemented, for example, on a single chip as a part of processor  304 , or it can be implemented on one or more separate chips located on a graphics board. Each processor  304  is connected to a communication infrastructure  302  (e.g., a communications bus, cross-bar, or network).  
         [0046]     Computer system  300  also includes a main memory  312 , preferably random access memory (RAM), and can also include a secondary memory  314 . Secondary memory  314  can include, for example, a hard disk drive  316  and/or a removable storage drive  318 , representing a floppy disk drive, a magnetic tape drive, an optical disk drive, et cetera. The removable storage drive  318  reads from and/or writes to a removable storage unit  320  in a well-known manner. Removable storage unit  320  represents a floppy disk, magnetic tape, optical disk, etc., which is read by and written to by removable storage drive  318 . As will be appreciated, the removable storage unit  320  includes a computer usable storage medium having stored therein computer software and/or data.  
         [0047]     In alternative exemplary implementations, secondary memory  314  may include other similar means for allowing computer programs or other instructions to be loaded into computer system  300 . Such means can include, for example, a removable storage unit  324  and an interface  322 . Examples can include a program cartridge and cartridge interface (such as that found in video game devices), a removable memory chip (such as an EPROM, or PROM) and associated socket, and other removable storage units  324  and interfaces  322  which allow software and data to be transferred from the removable storage unit  324  to computer system  300 .  
         [0048]     In one exemplary illustration, computer system  300  includes a frame buffer  308  and a display  310 . Frame buffer  308  is in electrical communication with graphics subsystem  306 . Images stored in frame buffer  308  can be viewed using display  310 .  
         [0049]     Computer system  300  can also include a communications interface  330 . Communications interface  330  allows software and data to be transferred between computer system  300  and external devices via a communications path  335 . Examples of communications interface  330  can include a modem, a network interface (such as Ethernet card), a communications port, etc. Software and data transferred via communications interface  330  are in the form of signals which can be electronic, electromagnetic, optical or other signals capable of being received by communications interface  330 , via communications path  335 . Note that communications interface  330  provides a means by which computer system  300  can interface to a network such as the Internet.  
         [0050]     Computer system  300  can include one or more peripheral devices  328 , which are coupled to communications infrastructure  302  by graphical user-interface  326 . Example peripheral devices  328 , which can from a part of computer system  300 , include, for example, a keyboard, a pointing device (e.g., a mouse), a joy stick, a game pad as well as other related peripheral devices  328 .  
         [0051]     System  300  can be implemented using software running (that is, executing) in an environment similar to that described above with respect to  FIG. 3 . As used herein, the term “computer program product” is used to generally refer to removable storage unit  320 , a hard disk installed in hard disk drive  316 , or a carrier wave or other signal carrying software over a communication path  335  (wireless link or cable) to communication interface  330 . A computer useable medium can include magnetic media, optical media, or other recordable media, or media that transmits a carrier wave. These computer program products are means for providing software to computer system  300 .  
         [0052]     Computer programs (also called computer control logic) are stored in main memory  312  and/or secondary memory  314 . Computer programs can also be received via communications interface  330 . Such computer programs, when executed, enable the computer system  300  to perform various features discussed herein. In particular, the computer programs, when executed, enable the processor  304  to perform the features rendering fog and other related gaseous phenomena. Accordingly, such computer programs represent controllers of the computer system  300 .  
         [0053]     In a software implementation, the software may be stored in a computer program product and loaded into computer system  300  using removable storage drive  318 , hard drive  316 , or communications interface  330 . Alternatively, the computer program product may be downloaded to computer system  300  over communications path  335 . The control logic (software), when executed by the one or more processors  304 , causes the processor(s)  304  to perform the functions as described herein.  
         [0054]     Computer system  300  can also be implemented primarily in firmware and/or hardware using, for example, hardware components such as application specific integrated circuits (ASICs) or a hardware state machine so as to perform the functions described herein.  
         [0055]      FIG. 4  is a flowchart of a routine  400  (steps  405 - 415 ) for rendering volumetric fog objects or other gaseous phenomena.  
         [0056]     To begin, in step  405 , the distance traveled through fog (or any gaseous phenomena) from a reference point to an object pixel is determined. If the density of the fog object is constant in the areas where the fog is present, the attenuation factor for a given pixel depends only on the distance a ray coming from a reference point travels through the fog object. For example in one implementation the reference point is determined based upon the eye or viewpoint of a user of application program  110 . Step  405  will now be described in greater detail with reference to  FIGS. 5-9 .  
         [0057]      FIG. 5  describes a routine  500  for determining the distance traveled through a fog object from a reference point to a pixel. In step  505  a fog color value and a pixel color are initialized. A OpenGL linear fog is used. In this case, the fog attenuation factor is linearly increasing from 0 at a user-defined start distance to 1 at an end distance. Thus, if the fog color value is set to (1,1,1) and the pixel color to (0,0,0) the resulting pixel color directly corresponds to the distance from the reference point minus the start distance.  
         [0058]     In step  510 , the distance from the reference point to the pixel is determined according to routine  600  described now with reference to  FIG. 6 .  
         [0059]     In step  605 , a minimum distance value and a maximum distance value are initialized. The minimum distance value and the maximum distance value are set so that all the fog objects are inside the bounds set by these two values.  
         [0060]     In step  610 , the fog color is set to a fog scale value. The fog scale value can be defined by a user or set to a default. In one implementation, the fog scale value and, correspondingly, the fog color is set to 0.5.  
         [0061]     In step  615 , linear fog is enabled. Next, in step  620 , the object color values are initialized. The color selected is black. Finally, in step  625 , the scene is rendered using the linear fog equation shown in  FIG. 7 .  
         [0062]     In applying the linear fog equation, a fog attenuation factor (f) value is determined by subtracting the maximum distance value from the pixel distance value. This result is divided by the maximum distance value minus the minimum distance value. The fog factor modifies the pixel color by multiplying the attenuation factor (f) and the pixel color (absent fog), adding the result of one minus the attenuation factor (f) and multiplying the result by the fog color (Equation 2). The pixel color is set to 0 and fog color is set to fog scale. Equation 2 can then be simplified into equation 3. The scene is then rendered using equation 2 from  FIG. 7 . The color value is obtained by subtracting the pixel distance value minus the minimum distance value, dividing by the maximum distance minus the minimum distance and multiplying the result times the fog scale value. The result of the maximum distance minus the minimum distance is equal to |M1,Z1|. Using this approach, the graphics hardware does the computation automatically, given specific values of minimum and maximum distance, fog color (fog scale), and pixel color (0).  
         [0063]     Upon the completion of routine  600 , the pixel color values stored in the frame buffer represents the distance traveled from a reference point to each pixel in the scene. Since only the pixels inside the fog objects are impacted by the presence of fog objects, these pixels need to be identified and the color of other pixels outside of the fog objects needs to be reset. Thus processing continues with routine  500 , step  515 .  
         [0064]     In step  515 , the pixel color values of those pixels located outside the fog objects are reset. To do so, the fog objects are rendered and the number of front and back faces behind each pixel are counted. In counting the front and back faces, one (1) is added to the stencil buffer for each back face and one (1) is subtracted for each front face that fails the depth test. Where the number of front and back faces are equal, the pixel color value is reset to zero.  FIG. 8  illustrates an OpenGL implementation of step  515 .  
         [0065]     In step  805 , the stencil buffer is initialized to zero (0). In step  810 , writing into the color buffer is disabled. In step  815 , the front faces are culled using the OpenGL cull mechanism. In step  820 , the stencil operation is set to increment on depth test fail. In step  825 , the fog objects are drawn. Because culling is set to front faces, only back faces will be drawn. In step  830 , the stencil operation is set to decrement on depth test fail. In step  835 , the back faces are culled using the OpenGL cull mechanism. In step  840 , the fog objects are again drawn. Due to back face culling, only the front faces are drawn.  
         [0066]     Next, in step  845 , writing into the color buffer is enabled. As a result of the adding and subtracting performed in steps  820  and  830 , stencil will be equal to zero in those cases where the number of back faces is equal to the number of front faces. In step  850 , the stencil function is set to draw where stencil is equal to zero (0). Next, in step  855  color is set to zero (0). Finally, in step  860  a full window black polygon is drawn such that drawing is allowed to the color buffer for only pixels with stencil value equal to 0. This has the effect of resetting the color of those pixels located outside the fog objects. Now the color channels are set to the distance from the eye (minus the start distance), but only for pixels that are inside a volume object. In order to enable use of the cull face mechanism, the fog boundary is specified so that front faces can be easily determined by the order of vertices. Also, fog objects have to be fully closed for routine  800  to work. Further description will be continued with reference again to  FIG. 5 .  
         [0067]     In step  520 , the distance from the reference point to the back faces is determined and added to the color buffer. An OpenGL implementation of this step will now be explained with reference to  FIG. 9 .  
         [0068]     Using the OpenGL cull mechanism, the a method of implementing routine  900  is to set culling to cull out all front faces, render all fog objects, then set culling to remove all back faces and render all fog objects again. If there are several back faces overlapping a pixel, the sum of all distances, converted to a color value, may overflow one (1). In this case the result is clamped to one (1) and the result after subtracting is incorrect.  
         [0069]     To prevent overflows, it is desirable to render each fog object separately, adding only its “depth” to the color buffer. Another option is to reduce the initial color for the linear fog. If the color is set to (r,r,r), where r=any value between zero (0) and one (1), instead of pure white (1,1,1) the resulting distances are scaled by the factor r, also referred to as fog scale. The lower the value the less precision available for the distance, but the likelihood of overflows is reduced. This approach works well for complex fog shapes that cannot be easily divided into separate convex pieces. Routine  900  will now be described in detail. In step  910 , fog color and pixel color are initialized. In step  915 , the OpenGL culling mechanism is used to cull front faces.  
         [0070]     In step  920 , the blend function is set to ADD. In step  925  the fog objects are drawn. Because front face culling is used, only the back faces are drawn. Upon completion of step  925 , the sum of the distances from the reference point to the back faces will be stored in the color buffer. Processing then returns to routine  500 .  
         [0071]     In step  525 , the distances from the reference point to the front faces are determined and subtracted from the color buffer. An OpenGL implementation of this step will now be explained with reference to  FIG. 9 .  
         [0072]     In step  930 , the OpenGL culling mechanism is used to cull back faces. In step  935 , the blend function is set to reverse_subtract. Finally, in step  940 , the fog objects are again drawn. Here, only the front faces will be drawn since back face culling is enabled. Updates to the depth buffer are disabled during steps  905 - 940 .  
         [0073]     Upon completion of routine  900  (steps  905 - 940 ), the color buffer contains values that correspond to the distance a ray coming from the reference point to each pixel traveled through fog objects. Processing then returns to routine  400 .  
         [0074]     In step  410 , the travel distance (z) is converted into an attenuation factor (f) that can be used to blend the color of the fog with the scene color. Assuming the fog density (p) in all fog objects is the same, the attenuation factor f is f=e −p·z . The function 1−e −x  for xε(0, R) where R is a value for which the function is almost 1, can be pre-computed into a pixel map. Next, use pixel copy of the window area onto itself, apply a pixel transfer scale S to scale the distances z into the range (0, R) and apply a pixel map to compute the exponential. The scale S can be computed as S=p·(z e −z s )·z/(R·r), where z s  and z e  is the start and end distance of the linear fog and r is the fog color scale factor. As a result, each travel distance (z) gets converted into a value one minus attenuation factor.  
         [0075]     The pixel map can store an arbitrary function, for example the exp2 function supported by OpenGL (1−f=1−e −p−p·z·z ). Unfortunately, on most systems a full screen pixel copy is so slow that the frame rate can drop well below 10 fps. The solution is to use a smaller window size (e.g., 640×480) or a system with several graphics pipes.  
         [0076]     To avoid the use of pixel maps, linear dependency of the attenuation factor f on the distance, as in the case of linear fog in OpenGL, is necessary. If the travel distance z is multiplied by a value s=(z e −z s )/(D·r), where D is the distance for which the attenuation factor becomes 0, the value 1−f is obtained.  
         [0077]     Multiplication by a constant s=2 n ·d is performed in several passes, n times multiplying by two (2) and once multiplying by d (a value between one (1) and two (2)). If s is below one (1), only one pass is required. The multiplication is done by drawing a fill-window polygon of color 1 (or d/2) and blend factors set to DST_COLOR and SRC_ALPHA.  
         [0078]     Once the attenuation factors for each pixel have been determined, the scene is ready to be rendered according to step  415 .  FIG. 10  provides a detailed description of the step  415  for rendering the scene based on the attenuation factor.  
         [0079]     In order to render the scene with the appropriate visual realism, a final fogged color is determined in step  1005 . Here, the equation shown in  FIG. 11  is applied. The final fogged color equation blends the incoming color C (pixel color absent fog), with the color of the fog Cf (defined as a constant blend color) and uses the attenuation factors (fog factors) stored in the color buffer. Next, in step  1010 , the scene is rendered using the final fogged color. Step  1010  is described in further detail with reference to  FIG. 12 .  
         [0080]     In step  1205 , a blend factor is set. The blend factors used are ONE_MINUS_DST_COLOR, and CONSTANT_COLOR. In step  1210 , a constant blend color is set equal to the color of the fog. If the OpenGL blend-color extension is not available the fog color is white. It is necessary to ensure that only pixels that are visible are drawn. Thus in step  1215 , the depth test is set to EQUAL and in step  1220 , stencil test is used to draw each pixel only once.  
         [0081]     Overall, routine  400  draws the scene twice and the fog objects four times (although each time only half the faces are drawn). In addition, there is one full-window polygon drawn in step  860  and several more or one pixel copy in step  410 . This still allows acceptable frame rates in many applications.  
         [0082]     FIGS.  13 A-F illustrate an OpenGL implementation of steps  405 - 415 .  
         [0083]     In  FIG. 13A  a general rendering of a scene including three fog areas is presented. From the illustration, it is apparent that using the eye of the viewer as the reference point, it is necessary to look through at least one fog object to see pixel two (P 2 ) and two fog objects to see pixel one (P 1 ).  
         [0084]     In  FIG. 13B , the scene is rendered using linear fog. The start distances z 1 , z 2 , and the end distances m 1 , m 2 , are set so that all volume objects are inside their bounds.  
         [0085]     In  FIG. 13C , the volume objects are rendered and the number of front and back faces behind each pixel is counted. Next, those pixels, for which the number of back faces is equal to the number of front faces, are set to (0,0,0). Now the color channels are set to the distance from the eye (minus the start distance), but only for pixels that are inside a volume object.  
         [0086]     In  FIG. 13D , the volume objects are drawn using linear fog by adding the distances for the back faces and subtracting distances for the front faces. Updates in depth buffer are still disabled. After this step the color buffer contains values that correspond to the distance a ray coming from the eye to each pixel traveled through volume objects.  
         [0087]     In  FIG. 13E , the travel distance z is converted into an attenuation factor (f) that is used to blend the color of the gas with the scene color.  
         [0088]     Finally, in  FIG. 13F , the attenuation factors for each pixel are used to render the scene with correct materials and blend the incoming color C, with the color of the gas Cf (defined as a constant blend color), using the attenuation factors stored in the color buffer.  
       CONCLUSION  
       [0089]     Although the invention has been described in language specific to structural features and/or methodological acts, it is to be understood that the invention defined in the appended claims is not necessarily limited to the specific features or acts described. Rather, the specific features and acts are disclosed as exemplary forms of implementing the claimed invention.