Abstract:
A method for rendering hair particles includes determining a grid with vertices and voxels bounding the hair particles, determining hair densities for the vertices, smoothing the hair densities, solving a distance function to form a distance field in response to the smooth hair densities, wherein a distance function returns zero at a pre-determined hair particle density, determining a surface normal direction for a hair particle in response to the distance field values, determining a hair illumination value in response to a first illumination source, and determining a shading value for the hair particle using the hair illumination value and the surface normal direction for the hair particle.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
     The present invention is related to and incorporates by reference for all purposes the following co-pending patent application, Application No.10/428,321 titled: Shot Rendering Method and Apparatus, filed Apr. 30, 2003 and Application No. 10/428,322 titled: Method and Apparatus for Rendering of Translucent Objects Using Volumetric Grids, filed Apr. 30, 2003. 
     BACKGROUND OF THE INVENTION 
     The present invention relates to computer animation. More particularly, the present invention relates to techniques and apparatus for efficient rendering of hair on objects. 
     Throughout the years, movie makers have often tried to tell stories involving make-believe creatures, far away places, and fantastic things. To do so, they have often relied on animation techniques to bring the make-believe to “life.” Two of the major paths in animation have traditionally included, drawing-based animation techniques and physical animation techniques. 
     Drawing-based animation techniques were refined in the twentieth century, by movie makers such as Walt Disney and used in movies such as “Snow White and the Seven Dwarfs” (1937) and “Fantasia” (1940). This animation technique typically required artists to hand-draw (or paint) animated images onto a transparent media or cels. After painting, each cel would then be captured or recorded onto film as one or more frames in a movie. 
     Physical-based animation techniques typically required the construction of miniature sets, props, and characters. The filmmakers would construct the sets, add props, and position the miniature characters in a pose. After the animator was happy with how everything was arranged, one or more frames of film would be taken of that specific arrangement. Physical animation techniques were developed by movie makers such as Willis O&#39;Brien for movies such as “King Kong” (1933). Subsequently, these techniques were refined by animators such as Ray Harryhausen for movies including “The Mighty Joe Young” (1948) and Clash Of The Titans (1981). 
     With the wide-spread availability of computers in the later part of the twentieth century, animators began to rely upon computers to assist in the animation process. This included using computers to facilitate drawing-based animation, for example, by painting images, by generating in-between images (“tweening”), and the like. This also included using computers to augment physical animation techniques. For example, physical models could be represented by virtual models in computer memory, and manipulated. 
     One of the pioneering companies in the computer aided animation (CA) industry was Pixar. Pixar developed both computing platforms specially designed for, computer animation and animation software now known as RenderMan®. RenderMan® was particularly well received in the animation industry and recognized with two Academy Awards®. 
     RenderMan® software is used to convert graphical specifications of objects and convert them into one or more images. This technique is known in the industry as rendering. One specific portion of the rendering process is known as surface shading. In the surface shading process, the surface shader software determines how much light is directed towards the viewer from the surface of objects in an image in response to the applied light sources. Two specific parameters that are used for shading calculations includes a surface normal and a surface illumination. 
     The surface shading process is quite effective for coherent surfaces where there are smoothly varying surface properties. However, this process is not effective for shading hair, because hair is typically a large collection of infinitely thin curves (one-dimensional) that have little physical relation to neighboring hairs. Further, this process is not effective because unlike standard surfaces, hair does not have a well-defined surface normal. 
     Hair illumination processes have been proposed to solve the problem of illuminating a one dimensional hair in a three dimensional world. One such process has included the use of tangent-based lighting response to determine hair illumination, and the use of deep shadows for self-shadowing. 
     Drawbacks to tangent-based illumination solutions include that this method often leads to visually distracting artifacts. That is, viewers typically expect hair to have smooth illumination across neighboring hairs, but with this method, there is no hair to hair lighting coherency, thus hair will “sparkle” or “pop” to a viewer. Another drawback is that unrelated hairs that are spatially far apart may erroneously have the same lighting response. For example, in the case of back-lit head, if a hair on the front of a head and a hair on back of the head have the same tangent, they will have the same illumination. As a result, even though the head is supposed to be silhouetted, hairs on the front the head will be still be illuminated. 
     Drawbacks to the use of deep shadows for hair self-shadowing include that they are computationally intensive, and they are inflexible. As is known, deep shadows maps are computed separately for each illumination source, and for a specific illumination position. If an animator decides to change the position of the camera, the entire deep shadow map for that illumination source will need to be recomputed. Yet another drawback is that because hair is computationally expensive to shade, a hair model having fewer hairs may used. However, if the hair is back-lit, the thinness of the hair model will be apparent to a viewer. 
     In light of the above, what is needed are improved techniques to render hair without the visual problems described above. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention relates to the field of computer animation. More particularly, the present invention relates to improved techniques and apparatus for rendering hair. 
     According to an aspect of the present invention, a method for rendering a plurality of hair objects is described. The method may include determining a bounding object including a plurality of voxels and a plurality of vertices, wherein the plurality of voxels bound the plurality of hair objects, determining hair density values associated with each of the plurality of vertices, and spatially smoothing the hair density values associated with each of the plurality of vertices to form smoothed density values associated with each of the plurality of vertices. Techniques may also include identifying a group of vertices from the plurality of vertices having associated smoothed density values approximately equal to a desired surface density value, the group of vertices defining a hair shell surface, and determining a distance field value for each of the plurality of vertices with respect to the hair shell surface. The method may also include determining a set of surface normal directions associated with a set of vertices associated with a voxel, in response to at least a portion of the distance field values for the plurality of vertices, and determining a surface normal direction for a hair particle within the voxel in response to the set of surface normal directions associate with the set of vertices. A first hair particle illumination value in response to a first illumination source can be determined, and the hair particle may be shaded using the hair particle illumination value and the surface normal direction for the hair particle. 
     According to another aspect of the invention, a computer program product for rendering a plurality of hair objects on computer system including a processor is described. The computer program product is on a tangible media that includes code that directs the processor to determine a grid including a plurality of voxels and a plurality of vertices, wherein at least a subset of the voxels bound at least a subset of the hair objects, code that directs the processor to determine a hair density value associated with each of at least a first set of vertices, and code that directs the processor to filter the hair density value associated with each vertex from at least the first set of vertices with a filter to form filtered density values. Additionally, the tangible media includes code that directs the processor to identify a group of vertices having associated filtered density values no greater than a desired surface density value, wherein some of the group of vertices are used to define a hair shell surface, code that directs the processor to calculate a distance field value for a second set of vertices with respect to the hair shell surface, and code that directs the processor to determine a set of surface normal directions associated with vertices associated with a voxel, in response to a set of distance field values for the second set of vertices. The media may include code that directs the processor to determine a surface normal direction for a hair particle within the voxel in response to the set of surface normal directions, and code that directs the processor to determine a first hair particle illumination value in response to a first illumination source. The tangible media may be a hard disk drive, volatile memory, an optical memory, or the like. A shader subsequently receives the first hair particle illumination value and the surface normal direction for the hair particle to determine the surface shading of the hair particle. 
     According to yet another aspect of the invention, a computer system for rendering a plurality of hair objects is described to include a memory and a processor. In various configurations, the processor is configured to determine a grid having a plurality of voxels and a plurality of vertices, wherein hair objects comprise a plurality of hair particles, and wherein the plurality of hair particles are located within a group of voxels, the processor is configured to determine hair particle density values associated with vertices associated with the group of voxels, and the processor is configured to spatially smooth the hair particle density values across the vertices associated with the group of voxels. In various embodiments, the processor is also configured to solve a distance function for a first set of vertices to form a distance field in response to the hair particle density values, wherein a distance function returns zero at a pre-determined hair particle density, and configured to determine a surface normal direction for a hair particle within a voxel in response to the distance field. The processor may also be configured to determine a first hair particle illumination value in response to a first illumination source, and the processor may be configured to determine a shading value for the hair particle using the hair particle illumination value and the surface normal direction for the hair particle. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In order to more fully understand the present invention, reference is made to the accompanying drawings. Understanding that these drawings are not to be considered limitations in the scope of the invention, the presently described embodiments and the presently understood best mode of the invention are described with additional detail through use of the accompanying drawings in which: 
         FIG. 1  illustrates a block diagram of a rendering system according to one embodiment of the present invention; 
         FIGS. 2A-C  illustrate a block diagram of a flow process according to an embodiment of the present invention; 
         FIG. 3  illustrate an example of an embodiment of the present invention; 
         FIG. 4  illustrate an example of an embodiment of the present invention; 
         FIG. 5  illustrate an example of an embodiment of the present invention; 
         FIG. 6  illustrate an example of an embodiment of the present invention; 
         FIG. 7  illustrate an example of an embodiment of the present invention; 
         FIG. 8  illustrate an example of an embodiment of the present invention; 
         FIG. 9  illustrate an example of an embodiment of the present invention; and 
         FIG. 10  illustrates another example of an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       FIG. 1  is a block diagram of typical computer rendering system  100  according to an embodiment of the present invention. 
     In the present embodiment, computer system  100  typically includes a monitor  110 , computer  120 , a keyboard  130 , a user input device  140 , a network interface  150 , and the like. 
     In the present embodiment, user input device  140  is typically embodied as a computer mouse, a trackball, a track pad, wireless remote, and the like. User input device  140  typically allows a user to select objects, icons, text and the like that appear on the monitor  110 . 
     Embodiments of network interface  150  typically include an Ethernet card, a modem (telephone, satellite, cable, ISDN), (asynchronous) digital subscriber line (DSL) unit, and the like. Network interface  150  are typically coupled to a computer network as shown. In other embodiments, network interface  150  may be physically integrated on the motherboard of computer  120 , may be a software program, such as soft DSL, or the like. 
     Computer  120  typically includes familiar computer components such as a processor  160 , and memory storage devices, such as a random access memory (RAM)  170 , disk drives  180 , and system bus  190  interconnecting the above components. 
     In one embodiment, computer  120  is a PC compatible computer having multiple microprocessors such as Xeon™ microprocessor from Intel Corporation. Further, in the present embodiment, computer  120  typically includes a UNIX-based operating system. 
     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 description of hair, hair generation algorithms, object data files, shader descriptors, a rendering engine, output image files, texture maps, displacement maps, scattering lengths and absorption data of object materials, and the like. Other types of tangible media include floppy disks, removable hard disks, optical storage media such as CD-ROMS and bar codes, semiconductor memories such as flash memories, read-only-memories (ROMS), battery-backed volatile memories, networked storage devices, and the like. 
     In the present embodiment, computer system  100  may also include software that enables communications over a network such as the HTTP, TCP/IP, RTP/RTSP protocols, and the like. In alternative embodiments of the present invention, other communications software and transfer protocols may also be used, for example IPX, UDP or the like. 
       FIG. 1  is representative of computer rendering systems capable of embodying the present invention. It will be readily apparent to one of ordinary skill in the art that many other hardware and software configurations are suitable for use with the present invention. For example, the use of other micro processors are contemplated, such as Pentium™ or Itanium™ microprocessors; Opteron™ or AthlonXP™ microprocessors from Advanced Micro Devices, Inc; PowerPC G3™, G4™ microprocessors from Motorola, Inc.; and the like. Further, other types of operating systems are contemplated, such as Windows® operating system such as WindowsXP®, WindowsNT®, or the like from Microsoft Corporation, Solaris from Sun Microsystems, LINUX, UNIX, MAC OS from Apple Computer Corporation, and the like. 
       FIGS. 2A-C  illustrates a block diagram of a flow process according to an embodiment of the present invention. More particularly, the block diagram discloses a process in which hair is efficiently rendered. 
     In one embodiment of the present invention, the process begins with the specification of hair to be rendered, step  200 . In one embodiment, the geometric representation of each strand of hair may be retrieved from memory, and in another embodiment, geometric representations of strands of hair may be dynamically generated based upon hair-generation algorithms or methods. 
     In the present embodiment, each strand of hair is composed of a string of hair “particles.” For example, a geometric description of a typical hair may include the coordinates of ten to twenty hair particles. In other embodiments, a greater or lesser number of hair particles may represent a strand of hair. 
     Next, an outer bounding box is constructed that bounds all of the hair particles, step  210 . In this example, this step is performed by constructing a grid including voxels and vertices. In the present embodiment, the grid may include from 200 to 500 vertices per side, depending upon the shape of the hair being rendered. In other embodiments, the number of vertices may vary. 
     In the present embodiment, the hair particle density in each voxel is distributed to the respective vertices, step  220 . An example of this process uses linear interpolation to distribute a hair particle to the vertices, although many other methods for interpolation or distribution can also be used in other embodiments. 
       FIG. 3  illustrates an embodiment of the present invention. In particular,  FIG. 3  illustrates a process of determining a hair density value for vertices in a voxel. In  FIG. 3 , a voxel  400  is illustrated having respective vertices  410 - 480 , and a hair particle  490 . 
     In this embodiment, the presence of hair particle  490  is distributed to vertices  410 - 480  based upon the location of hair particle  490  within voxel  400 . In this example, hair particle  490  is located three-quarters in the z-direction of voxel  400 , accordingly, vertices  410 - 440  are assigned 0.75 the presence of hair particle  490  and vertices  450 - 480  are assigned 0.25 the presence. Further, in this example, hair particle  490  located half-way in the x-direction and y-direction of voxel  400 , thus vertices  410 - 440  evenly split the 0.75 value, and vertices  450 - 480  evenly split the 0.25 value. The distributed results can be seen in FIG.  3 . 
     In the present embodiment, the distribution of the presence of a hair particle is typically repeated for all hair particles in a voxel. Mathematically, the density equation is:
 
Density( t )=(1−( Px - x ))*(1−( Py - y ))*(1−( Pz - z ))
 
Where (Px,Py,Pz) are the hair particle coordinates in world space, and (x,y,z) are the cell coordinates in world space.
 
     Returning to  FIGS. 2A-C , in the present embodiment, the hair density values of vertices of adjacent voxels are then added together, step  230 . As a result, each vertex is then associated with a hair density value with contributions of up to eight adjacent voxels. An example of this is illustrated in FIG.  4 . 
       FIG. 4  illustrates an embodiment of the present invention. In particular,  FIG. 4  illustrates a process of determining a hair density value for a vertex from adjacent voxels. In  FIG. 4 , voxels  500 - 570  are illustrated having vertex  580  in common. As can be seen, when the hair density values are placed within the grid, the hair density value for vertex  580  is the combination of the contributions from voxels  500 - 570 . In other embodiments, fewer than eight voxels may contribute to the hair density value, for example, for voxels on an outer surface or boundary of the grid. 
     In  FIGS. 2A-C , the next step is to perform a smoothing operation of the hair density values on the vertices, step  240 . In one embodiment, a tri-linear filter is used, as illustrated in FIG.  5 . In other embodiments, other types of smoothing operations may also be used, for example, a cubic filter, a tri-linear filter with different weights, a polynomial filter, and the like. As a result of this step, the hair density values for the vertices is greatly smoothed, reducing high frequencies. This reduction in high frequency reduces the potential for hair “sparkling” during shading. 
     In present embodiment of the present invention, the hair density value is determined within a specific time period, typically a frame. In one embodiment, hair density values for respective vertices are then averaged between frames, step  245 . More specifically, a particle velocity V is introduced into the density equation. In one example, the equation becomes:
 
Density( t )=α*[(1−( Px - x ))*(1−( Py - y ))*(1−( Pz - z ))]+(1-α)*[(1−( Px - x ))*(1−( Py - y ))*(1−( Pz - z ))]
 
     In other embodiments, the hair density values are averaged with a previous frame, and a next frame (e.g. 25% previous, 50% current, 25% next). As a result of this step, a more coherent topology for the hair density values is provided between adjacent frames. This process virtually eliminates the “sparkling” or “popping” appearance of hair between different images. 
     In the present embodiment, a desired surface density is then determined, step  250 . In one embodiment of the present invention, the desired surface density may be determined by an animator ahead of time or during the animation process. In other embodiments, the desired surface density may be automatically determined based upon a variety of factors including the hair density value distribution (e.g. desired surface density encompass 90% of the hair particles), or the like. In some embodiments of the present invention, the desired surface density may be within a range of values. 
     In this embodiment, the desired surface density is used to determine a hair shell surface, step  260 . The hair shell surface is used in embodiments below to help determine normal directions. In embodiments of the present invention, hair shell surface is determined by comparing the hair density values of the vertices closest to the edge of the bounding box to the desired surface density. If the hair density values do not exceed the desired surface density, the hair density values of the next inward vertices and examined, and so on, until vertices having the desired surface density are identified. These identified vertices then form the hair shell surface. 
     In other embodiments, steps  250  and  260  may not be performed, and the outer bounding box is used for the hair shell surface. 
       FIG. 6  illustrates an embodiment of the present invention. In this two-dimensional example, a number of vertices  600  are illustrated, each having a respective hair density value  610 . As can be seen, hair density values  610  typically vary, with higher hair density values towards the surface of the object. In this example, the desired surface density is set by an animator to “2.” Thus as shown, a two-dimensional hair shell surface  620  is formed. Hair shell surface  620  may be automatically or manually adjusted to account for unexpected low hair density values below hair shell surface  620 . In the present embodiment, the hair shell surface is typically a three-dimensional surface. 
     In the embodiment illustrated in  FIGS. 2A-C , the next step is determining a distance field with respect to the hair shell surface, step  270 . Mathematically, the present embodiment relies upon a signed distance field having the following relationships: 
     |∇ SignedDistance|=1 
     SignedDistance=0 at the desired surface density. 
     When particle velocity V is included, the following additional relationship applies: 
     d(SignedDistance)/dt=V 
     In this embodiment, a new grid is formed, and the vertices of the grid are assigned a scalar value representing the shortest distance to the hair shell surface. In this example, the new grid is typically of the same spacing as the grid used for the hair density values, above, although in other embodiments, the grid may have a different spacing. In yet another embodiment, only one grid is allocated, and the hair density values and the scalar values are associated with each vertex in a grid. 
       FIG. 7  illustrates an embodiment of the present invention.  FIG. 7  includes a hair shell surface  700 , a number of vertices  710 , and scalar distance values  720  for vertices  710 . 
     In this two-dimensional example, hair shell surface  700  may be formed according to the process described above. For example, referring to  FIG. 6 , hair shell surface  700  is set to be the location where the hair surface density was at least equal to two, in FIG.  6 . As discussed above, hair shell surface  700  may be set to be at any other desired surface density. 
     In this example, scalar distance values  720  represent the smallest distance between a vertex location and hair shell surface  700 . This distance may be signed in various embodiments, with positive values inside the hair shell and negative values outside the hair shell. Embodiments may be applied to two-dimensional or three-dimensional hair shell surfaces. 
     In the present embodiment, the next step in  FIGS. 2A-C  is the determination of a surface normal for each vertex, step  280 . In this embodiment, the surface normal is defined as the direction of the shortest distance to the hair shell surface. The surface normal for each vertex can easily be determined by comparing the scalar distance values of adjacent vertices. Mathematically, the equation is as follows:
 
Surface Normal=( d (SignedDistance)/ d ( x ),  d (SignedDistance)/ d ( y ),  d (SignedDistance)/ d ( z ))
 
       FIG. 8  illustrates an embodiment of the present invention. Continuing the two-dimensional example of  FIG. 7 , vertices  800  are illustrated in detail and the scalar distance values  810  of vertices  800 . 
     In this example, in the x-direction, the change in scalar distance values for vertex  820  towards-the surface is 0.2 (3−2.8=0.2). Further, in the y-direction, the change in scalar distance values towards the surface is 1 (3−2=1). Accordingly, the surface normal  830  has a x component of 0.2 and a y component of 1. Using simple trigonometry, this corresponds to a surface normal of approximately 78 degrees, as shown. 
     Next, in  FIGS. 2A-C , a surface normal for each hair particle is determined, step  290 . In the present embodiment, the location of each hair particle in a voxel is interpolated using the surface normals of the vertices in the voxel. The surface normals for each hair particle is then used in the shading process, described later below. 
       FIG. 9  illustrates an embodiment of the present invention. In particular,  FIG. 9  illustrates a two-dimensional example including hair particles  900 ,  910  and  920  within a voxel  930 . Additionally, the surface normals  940 - 960  are illustrated. 
     In this example, surface normals of hair particles are dependent upon the position of hair particles  900 - 920  within voxel  930 . In this example, hair particle  910  is in the middle of voxel  930 . Accordingly, a surface normal  950  is simply the average of the surface normals, as shown. Further, the surface normals  940  and  960  are the respective weighted averages of the surface normals, as shown. 
     As a result of this process, neighboring hair particles have smoothly varying surface normals that results in coherent hair to hair illumination. 
     In the example in  FIGS. 2A-C , the attenuated light intensity at each hair particle is determined with respect to each light source, step  300 . One embodiment of the present invention relies upon a simple light attenuation relationship as follows: 
     hair particle attenuated light intensity=bounding box surface light intensity/(1+length (Pe−P)) 
     In this equation, P is the hair particle point of interest, and Pe is the point of entry of illumination from an illumination source towards P. Length(Pe, P) is a function that determines the distance between Pe and P. An example of this is illustrated in FIG.  10 . In the present embodiment, an attenuated light intensity is determined for each separate illumination source and for each hair particle. 
     In this embodiment, the attenuation of the light intensity is assumed to be approximately uniform. However, in other embodiments of the present invention, more complex attenuation relationships may be implemented. For example, extinction values described in the co-pending U.S. patent application referred to above, may be calculated for the present grid vertices. Based upon the extinction values and the surface light intensity, a more accurate determination of the hair particle surface illumination can be determined. For example, such an embodiment would illustrate that hair that is less dense admits more light to a particular hair particle than hair that is more dense. In other embodiments of the present invention, this process is performed separately for each of the primary color components (red, green, and blue.) Such cases are useful when the hair has different extinction and/or attenuation and scattering properties for the component colors. 
     In the present embodiment illustrated in  FIGS. 2A-C , for each hair particle, the surface normal, and attenuated light intensity values from each illumination source are entered into a surface shader. The shader result is a surface shading value of the hair particle in response to the different illumination sources in the direction of the viewer, step  310 . In embodiments of the present invention, it is envisioned that a great number of shaders currently compatible with RenderMan® could be used to implement the above techniques. If the hair particle is not occluded by another object, the surface shading value of the hair particle is typically recorded within an image. The image is then stored to memory, step  320   
     In the foregoing specification, the invention has been described with reference to specific exemplary embodiments thereof. Many changes or modifications are readily envisioned. For example, the hair particle surface illumination from each light source may be attenuated in a variety of methods including, assuming a uniformly attenuating media, and compensating for non-uniformly attenuating media, and the like. 
     In embodiments of the present invention, the inventors have determined that advantages of the present schema may be applied to the shot rendering techniques described in the above-referenced U.S. patent applications. In particular, the present embodiments can provide great time savings to an animator when “bracketing” using shot rendering techniques, as described in that application. As an example of bracketing is where all rendering parameters and illumination parameters remain constant, but the shot is rendered from different camera angles or positions. In such an example, the majority of the steps described in  FIGS. 2A-C  need not be repeated, and only portions of the final shading step need to be repeated to account for the different camera position. This provides a tremendous time savings in the rendering process. In contrast, using the deep shadow maps described above, when the camera position moves, the deep shadow map must be entirely recomputed for each light source. 
     Embodiments of the present invention may be applied to any number of rendering platforms and for a variety of purposes. For example, embodiments may be use on engineering workstations for development purposes, on visualization systems for artists and animators, in a rendering farm machine for final production, and the like. Accordingly, the concepts disclosed above are extremely valuable in a variety of applications. 
     It is believed that images that include hair rendered according to the above-described techniques appear more naturally than any previous hair rendering technique while at the same time providing hair to hair coherency. Additionally, a sequence of images rendered according to these techniques do not have the hair “pop” or “sparkle” associated with previous techniques of rendering hair. This is due, in part to the compensation for hair particle velocity, described above. Further, the images rendered herein provide a great degree of hair to hair coherency, without resorting to a static “hair cap” as was also previously used. In light of the above, hair rendered according to the above technique are visually superior to hair rendered using existing hair rendering techniques. 
     Further embodiments can be envisioned to one of ordinary skill in the art. 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.