Patent Document

CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a continuation of U.S. patent application Ser. No. 10/869,554, filed Jun. 15, 2004, now U.S. Pat. No. 6,970,170, which is a continuation of U.S. patent application Ser. No. 09/944,937, filed Aug. 30, 2001, issued Jul. 20, 2004 as U.S. Pat. No. 6,765,578 B2. 
    
    
     TECHNICAL FIELD 
     The present invention is related generally to the field of computer graphics, and more particularly, a system and method for resampling graphics data of a source image to produce graphics data for a destination image. 
     BACKGROUND OF THE INVENTION 
     As display devices of various sizes and increased resolution have been developed and the demand for them have increased, the ability for a graphics processing system to resize and resample source images and create destination images to take advantage of the various sized and higher resolution displays is a desirable operation. In an electronic display system, color at each pixel is represented by a set of color components, and each color component is represented by a sample value. Color components such as red, green, blue (RGB) or other representations such as YC b C r  are well known in the art. Whichever representation is chosen, each color component can be interpreted as a two dimensional array of samples, so three such arrays can represent images on display systems. Conceptually, resampling can be viewed as a spatial process, working on discrete input samples, represented by pixels of the source image arranged in a two-dimensional bitmap. The output samples of the destination image are spatially located at fractional sample positions within the input sample grid. Various interpolation and modeling methods are used to construct transition models between samples of the source image from which additional graphics data is produced during the resampling operation. 
     The additional graphics data is then used to produce larger or higher resolution destination graphics images. However, the resulting destination image must retain an acceptable image quality with respect to the source image. That is, the destination image should appear to retain at least a similar visual qualities of the source image, such as having nearly the same color balance, contrast, and brightness as the original source image. Otherwise, rather than accurately reproducing a larger or higher resolution graphics image of the source image, the resampling operation will compromise image quality by introducing image distortion. To this end, various resampling algorithms have been developed in order to create high quality destination graphics images. 
     With many conventional resampling algorithms, a transition model between input samples along each axis is constructed to provide output sample values. Generally good results can be obtained with separable processing along each axis for graphics images because image feature cross-sections have the same characteristics when viewed at any angle within the image plane, only at different effective sample rates. That is, the resampling operation is first performed on the pixels along a first axis of the source image followed by resampling of the pixels along the other axis. The output sample values of the resampling operation along the first axis is then used in generating the transition models from which output samples are calculated. The transition models between the input samples are constructed such that the output samples interpolated from the transition model create a destination image that closely resembles the original or source image. The transition models are typically continuous so that an output sample can be generated at any position between the input samples. 
     A typical axis separable resampling circuit performs the resampling operation for the source image along one axis in its entirety before beginning the resampling operation along the second axis. In operation, input samples of a source image are scanned in using a row-by-row access and provided to a resampling circuit. The output sample values calculated by the resampling circuit are written to a memory from which the output sample values are accessed when performing the resampling operation along the other axis. The resulting output samples are then written to a display memory from which the data for a destination image are read for rendering. Although conceptually the simplest, it is not a very efficient manner in which to perform resampling. One reason is related to the manner in which a memory device is accessed. The x- and y-axes of the source image correspond to the row and columns of a memory device. Accessing the data for y-axis resampling is ordinarily not efficient because new row and column addresses must be provided for reading or writing of data. In contrast, accessing input samples along a row of the source image, and consequently a row of memory, can take advantage of page or burst access features of the memory device. These features typically require providing the column address for access along a row, or in some instances, simply strobing a single command signal is all that is necessary to increment the column address once a row address is provided. 
     In another resampling circuit, resampling is again performed along the x-axis first, and subsequently followed by resampling along the y-axis. However, rather than accessing the graphics data in the inefficient manner previously described, the resampling circuit includes a plurality of series connected delay buffers having equal lengths that are sufficient to accommodate an entire row of input samples of the source image. The number of delay buffers depends on the number of samples used to interpolate a new sample along the y-axis. Rows of the stored graphics data from the x-axis resampling operation are read into and shifted through the delay buffers, thus allowing for a page or burst mode to be used. Circuitry for performing the interpolation along the y-axis is coupled to the series of delay buffers such that there is a tap at the input of the first delay buffer, and taps at the output of each delay buffer to provide synchronized access to the data used in the y-resampling operation. As the data continues to shift through the delay buffers, the synchronization is maintained. As a result, the graphics data used to obtain the sample history needed for model generation along the y-axis is available to the interpolation circuitry without the access latency present in the previously described conventional resampling process. 
     In cases where the source image is scaled by {Rx, Ry} to increase image size along the x- and y- axes, respectively, the quantity of intermediate data generated by the resampling circuit along the x-axis is approximately equal to (Rx×source_width), where source_width is the width of the source image. Thus, if generating and evaluating interpolation models along the y-axis requires a history of Ny samples, then a total of (Ny−1) delays, each delay having a length of (Rx_max×source_width_max), where Rx_max is the maximum scaling ratio accommodated by the resampling circuit and source_width_max is the maximum width of a source image resampled by the resampling circuit. As one could imagine, the space occupied by the delays necessary for resampling along the y-axis is considerable. Moreover, the scaling ratio and size of the source image are limited by the widths of the delays in the conventional resampling circuit. 
     Therefore, there is a need for a flexible graphics resampling system and method that can accommodate a variety of different sized source images and various scaling ratios. 
     SUMMARY OF THE INVENTION 
     One aspect of the invention provides a resampling stage for calculating destination data corresponding to pixels of a destination image from source data corresponding to pixels of a source image. The resampling stage includes a resampling circuit operable to calculate the destination data for the destination image from the source data in a plurality of groups of pixels of the source image. For each group of pixels, the resampling circuit samples along a first axis the source data for the group of pixels and calculates therefrom intermediate data corresponding to pixels for a respective portion of the destination image. The resampling circuit further samples intermediate data along a second axis perpendicular to the first axis and calculates therefrom destination data corresponding to pixels scaled along the first and second axes for the respective portion of the destination image. A memory is coupled to the resampling circuit and stores at least a portion of the destination data calculated for a group of pixels of the source image. 
     Another aspect of the invention provides a scaling circuit for scaling a source image to a destination image, the source image having a plurality of pixels arranged in rows and columns along a first axis and a second axis, respectively. The scaling circuit includes first and second scaling stages. The first scaling stage scales along the first axis the pixels for a first portion of pixels of the source image and then for a second portion of pixels of the source image. The first and second portions of pixels of the source image are arranged in spans and columns of pixels, the span of pixels less than the length of one row of pixels of the source image. The second scaling stage is coupled to the first scaling stage and scales along the second axis the scaled pixels of the first portion of pixels and then the second portion of pixels. The scaled pixels of the first and second portions of pixels included in the destination image. 
     Another aspect of the invention provides a processing stage for a graphics processing engine for scaling a source image. The processing stage includes a scaling circuit that divides pixels of the source image into a plurality of groups of pixels. The groups of pixels are arranged in spans and columns of pixels and the span of pixels are less than the length of a row of pixels of the source image. For each group of pixels, the scaling circuit scales the pixels along a first axis and scales the scaled pixels along a second axis. The scaled pixels of each of the plurality of groups of pixels are combined to form a destination image that is a scaled version of the source image. 
     Another aspect of the invention provides a resampling circuit having row and column resampling circuits. The row resampling circuit receives input sample values of samples along a row of a source image for a portion of the source image and provides row output values for the portion of the source image. The column resampling circuit is coupled to the row resampling circuit and has a buffer that buffers the row output values for the portion of the source image. The column resampling circuit calculates column output sample values from the row output values for the portion of the source image. The column output sample values are included in a destination image formed from the column output sample values for a plurality of portions of the source image. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of a computer system in which embodiments of the present invention are implemented. 
         FIG. 2  is a block diagram of a graphics processing system in the computer system of  FIG. 1 . 
         FIG. 3  is a block diagram of a resampling system in the graphics processing system of  FIG. 2  according to an embodiment of the present invention. 
         FIG. 4  is a block diagram of a resampling circuit according to an embodiment of the present invention that may be used in the resampling system of  FIG. 3 . 
         FIG. 5  is a block diagram of a resampling circuit according to another embodiment of the present invention that may be used in the resampling system of  FIG. 3 . 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the present invention are directed to a system and method for resampling graphics data of a source image and for providing graphics data generated therefrom for rendering a scaled destination image. Certain details are set forth below to provide a sufficient understanding of the invention. However, it will be clear to one skilled in the art that the invention may be practiced without these particular details. In other instances, well-known circuits, control signals, timing protocols, and software operations have not been shown in detail in order to avoid unnecessarily obscuring the invention. 
       FIG. 1  illustrates a computer system  100  in which embodiments of the present invention are implemented. The computer system  100  includes a processor  104  coupled to a host memory  108  through a memory/bus interface  112 . The memory/bus interface  112  is coupled to an expansion bus  116 , such as an industry standard architecture (ISA) bus or a peripheral component interconnect (PCI) bus. The computer system  100  also includes one or more input devices  120 , such as a keypad or a mouse, coupled to the processor  104  through the expansion bus  116  and the memory/bus interface  112 . The input devices  120  allow an operator or an electronic device to input data to the computer system  100 . One or more output devices  120  are coupled to the processor  104  to provide output data generated by the processor  104 . The output devices  124  are coupled to the processor  104  through the expansion bus  116  and memory/bus interface  112 . Examples of output devices  124  include printers and a sound card driving audio speakers. One or more data storage devices  128  are coupled to the processor  104  through the memory/bus interface  112  and the expansion bus  116  to store data in, or retrieve data from, storage media (not shown). Examples of storage devices  128  and storage media include fixed disk drives, floppy disk drives, tape cassettes and compact-disc read-only memory drives. 
     The computer system  100  further includes a graphics processing system  132  coupled to the processor  104  through the expansion bus  116  and memory/bus interface  112 . Optionally, the graphics processing system  132  may be coupled to the processor  104  and the host memory  108  through other types of architectures. For example, the graphics processing system  132  may be coupled through the memory/bus interface  112  and a high speed bus  136 , such as an accelerated graphics port (AGP), to provide the graphics processing system  132  with direct memory access (DMA) to the host memory  108 . That is, the high speed bus  136  and memory bus interface  112  allow the graphics processing system  132  to read and write host memory  108  without the intervention of the processor  104 . Thus, data may be transferred to, and from, the host memory  108  at transfer rates much greater than over the expansion bus  116 . A display  140  is coupled to the graphics processing system  132  to display graphics images. The display  140  may be any type of display, such as those commonly used for desktop computers, portable computers, and workstation or server applications, for example, a cathode ray tube (CRT), a field emission display (FED), a liquid crystal display (LCD), or the like. 
       FIG. 2  illustrates circuitry included within the graphics processing system  132  for performing various three-dimensional (3D) graphics functions. As shown in  FIG. 2 , a bus interface  200  couples the graphics processing system  132  to the expansion bus  116 . In the case where the graphics processing system  132  is coupled to the processor  104  and the host memory  108  through the high speed data bus  136  and the memory/bus interface  112 , the bus interface  200  will include a DMA controller (not shown) to coordinate transfer of data to and from the host memory  108  and the processor  104 . A graphics processor  204  is coupled to the bus interface  200  and is designed to perform various graphics and video processing functions, such as, but not limited to, generating vertex data and performing vertex transformations for polygon graphics primitives that are used to model 3D objects. The graphics processor  204  is coupled to a triangle engine  208  that includes circuitry for performing various graphics functions, such as clipping, attribute transformations, rendering of graphics primitives, and generating texture coordinates for a texture map. 
     A pixel engine  212  is coupled to receive the graphics data generated by the triangle engine  208 . The pixel engine  212  contains circuitry for performing various graphics functions, such as, but not limited to, texture application or mapping, bilinear filtering, fog, blending, and color space conversion. A memory controller  216  coupled to the pixel engine  212  and the graphics processor  204  handles memory requests to and from an local memory  220 . The local memory  220  stores graphics data, such as source pixel color values and destination pixel color values. A display controller  224  is coupled to the memory controller  216  to receive processed destination color values for pixels that are to be rendered. Coupled to the display controller  224  is a resampling circuit  228  that facilitates resizing or resampling graphics images. As will be explained below, embodiments of the resampling circuit  228  perform approximations that simplify the calculation of a model between two sample points for use during resampling. The output color values from the resampling circuit  228  are subsequently provided to a display driver  232  that includes circuitry to provide digital color signals, or convert digital color signals to red, green, and blue analog color signals, to drive the display  140  ( FIG. 1 ). 
     Although the resampling circuit  228  is illustrated as being a separate circuit, it will be appreciated that the resampling circuit  228  may also be included in one of the aforementioned circuit blocks of the graphics processing system  132 . For example, the resampling circuit  228  may be included in the graphics processor  204  or the display controller  224 . In other embodiments, the resampling circuit  228  may be included in the display  140  ( FIG. 1 ). Therefore, the particular location of the resampling circuit  228  is a detail that may be modified without deviating from the subject matter of the invention, and should not be used in limiting the scope of the present invention. 
       FIG. 3  illustrates a resampling circuit  300  that may be substituted for the resampling circuit  228  shown in  FIG. 2 . The resampling circuit  300  includes an x-axis resampling circuit  302  and a y-axis resampling circuit  304  coupled in series to perform axis separable resampling. Connected to the input of the x-axis resampling circuit is a source data memory in which image data to be resampled is stored. Coupled to the output of the y-axis resampling circuit  304  is a destination data memory  306  into which the resampled data is temporarily stored prior to writing the resulting data to a display memory (not shown) or the like. The input and output memory may be the same. As will be discussed in more detail below, the resampling circuit  300  resamples graphics data or sample values of the pixels of a source image and generates graphics data for rendering a destination image. 
     The resampling circuit  300  samples the graphics data by scanning in “columns” of graphics data. That is, graphics data for pixels of the source image are sampled in a first direction, typically along a row, for a span of pixels. When the end of the span is reached, the graphics data for the next row is then sampled from the beginning of the length of the span. As a result, the source image is separated into columns of sampled graphics data having widths equal to the span of pixels. Scanning in this columnar fashion continues until the graphics data of the source image are completely read. As will be discussed in more detail below, the length of a span is related to the length of buffers in the y-axis resampling circuit  304 . 
     While the graphics data are read, the resampling circuit  300  calculates graphics data for a destination image in accordance with a resampling or scaling ratio. The resampled graphics data for the destination image are typically calculated from an interpolation model that is generated from the pixel sample values of the source image. Consequently, graphics data for multiple pixels are used simultaneously for the model generation and sample value interpolation. The amount of graphics data generated by the resampling process depends on the scaling or resizing ratio. For example, if the source image is to be scaled to twice its size, while maintaining its aspect ratio (i.e., 2× along each axis), the resampling circuit  300  will then generate approximately four-times as much graphics data as that used to represent the source image. As previously discussed, because of the quantity of graphics data that must be generated for rescaling a source image, conventional resampling circuits may have limited scaling capabilities. However, as will be discussed in greater detail below, the resampling circuit  300  is capable of resampling at a variety of scaling or resizing ratios. 
     The resampling circuit  300  can also perform resampling operations for large scaling ratios by performing consecutive resampling operations until the graphics data for the scaling ratio is achieved. For example, if a source image is to be scaled by 5:1 ratio, the resampling operation can be performed by first performing a 1.25:1 resampling operation, followed by a 4:1 resampling operation on the graphics data from the initial resampling operation. This flexibility is possible if the source and destination memories are the same physical memory. The memory should be able to service the input/output data bandwidth required for all passes. The resulting graphics data is used for the 5:1 destination image. In performing consecutive resampling operations, the resampling operation for the lower scaling ratio should be performed initially because the amount of graphics data resampled in a subsequent resampling operation is reduced, and consequently, will yield a more efficient overall resampling process. It will be appreciated that multiple consecutive resampling operations can be performed to yield very large scaling ratios. For example, scaling a source image by a 100:1 ratio can be performed by first by a 100:64 resampling operation, followed by three consecutive 4:1 resampling operations. 
     It will be appreciated that the sample values for the samples may consist of several different components. For example, the sample value may represent pixel colors which are the combination of red, green, and blue color components. Another example includes sample values representing pixel colors which are the combination of luma and chroma components. Consequently, because it is well understood in the art, although circuitry to perform graphics operation for each of the components is not expressly shown or described herein, embodiments of the present invention include circuitry, control signals, and the like necessary to perform resampling operations on each component for multi-component sample values. Moreover, it will be appreciated that embodiments of the present invention further include the circuitry, control signals, and the like necessary to perform axis separable resampling operations for graphics data represented in multiple axes. Implementation of axis separable resampling is well understood in the art, and a more detailed description of such has been omitted from herein to avoid unnecessarily obscuring the present invention. 
       FIG. 4  illustrates an x-axis resampling circuit  400  according to an embodiment of the present invention. Graphics data of the pixels of the source image are provided to the x-axis resampling circuit  400  and through a series of x-sample buffers  402 - 408  coupled in series. Each of the x-sample buffers  402 - 408  is of sufficient width to accommodate the graphics data for one pixel. The x-sample buffers  402 - 408  may be implemented using conventional data buffer circuits and techniques, such as using static random access memory (SRAM) devices, conventional shift registers, or the like. 
     An x-interpolation circuit  416  is coupled to the input of the first x-sample buffer  402  and the output of the x-sample buffers  402 - 408 . Graphics data is sampled by the x-interpolation circuit  416  and used to generate a model from which resampled graphics data along the x-axis for the destination image are calculated. Since the x-sample buffers  402 - 408  are all of the same length, the graphics data for five pixels (i.e., x −2 , x −1 , x 0 , x 1 , and x 2 ) along a row of the source image are synchronized for sampling by the x-interpolation circuit  416 . Thus, as the graphics data is shifted through the pipeline of x-sample buffers  402 - 408 , a resampling algorithm can be performed to calculate resampled graphics data along the x-axis for a destination image from the multiple sample values provided at the input of the first x-sample buffer  402  and the output of each of the x-sample buffers  402 - 408 . 
     In operation, the x-interpolation circuit  416  samples the graphics data along a row of pixels for a span of pixels and then returns to the beginning of the span on the next row to begin sampling again. Thus, only a portion of each row of pixels is sampled before sampling from the adjacent row. As will be explained in more detail below, the length of the span, or how many pixels are sampled before sampling begins at the next row, is a function of the scaling ratio and buffer length of the y-axis resampling circuit  304  ( FIG. 3 ). As mentioned previously, the result is that the pixels of the source image are divided into columns of pixels, each column having a width equal to the span of pixels. 
     It will be appreciated that various well known algorithms can be used by the x-interpolation circuit  416  to generate graphics data for a destination image. For example, a cubic model can be used to generate a model between two sample points from which resampled graphics data may be interpolated. One such method is described in greater detail in co-pending U.S. patent application Ser. No. 09/760,173, entitled PIXEL RESAMPLING SYSTEM AND METHOD to Slavin, filed Jan. 12, 2001, which is incorporated herein by reference. In summary, the aforementioned patent application describes using a cubic model from which resampled graphics data can be calculated. The coefficients for the solution of the cubic model between two adjacent sample pixels are calculated by using the color values of the adjacent sample pixels and an estimated gradient value co-sited with the two sample pixels. Although the aforementioned algorithm may be used in embodiments of the present invention, it will be appreciated that other algorithms, now known or later developed, may also be used, and consequently, the scope of the present invention should not be limited by the particular interpolation algorithm applied by the x-interpolation circuit  416 , except to the extent recited in the claims attached hereto. 
     It will be further appreciated that the number of samples used for the calculation of the destination graphics data will depend on several factors, one of which is the particular algorithm used for the interpolation model. Although  FIG. 4  illustrates using five samples from the source image, greater or fewer samples may be used as well. Additionally, the interpolation circuits may use different algorithms for different types of graphics data, for example, a first algorithm for graphics data representing text and a second algorithm for graphics data representing video. Consequently, the particular number of samples provided to an interpolation circuit, or the number actually used can be modified without deviating from the scope of the present invention. 
     Following the resampling operation, the sample values of the source image, as well as the sample values calculated therefrom are provided by the x-interpolation circuit  416  to the y-axis resampling circuit  304  ( FIG. 3 ). As previously discussed, the quantity of graphics data generated by the x-resampling circuit  400  will be dependent on the resampling or scaling ratio. In an axis separable resampling circuit, such as that described herein, the quantity of data is increased or decreased for each axis according to the resampling ratio along the particular axis. Thus, as previously mentioned, if a source image is to be doubled (i.e., the scaling ratio is 2×) along both axes, the x-resampling circuit  400  will provide approximately twice as much graphics data along the x-axis as in the source image. The quantity of graphics data along the y-axis (i.e., the number of lines) is not affected by the x-axis resampling. 
       FIG. 5  illustrates a y-axis resampling circuit  500  according to an embodiment of the present invention. Graphics data for pixels of the source image, as well as graphics data calculated for the destination image are provided from a x-axis resampling circuit  302  to the y-resampling circuit  500 . The data is shifted through a pipeline of y-sample buffers  502 - 508  coupled in series. A y-interpolation circuit  520  is coupled to the output of the of x-axis resampling circuit  302  and to the output of each of the y-sample buffers  502 - 508  to sample the graphics data. 
     Graphics data is sampled by the y-interpolation circuit  520  and used to calculate graphics data for the destination image. Since the y-sample buffers  502 - 508  are all of the same length, the graphics data sampled by the y-interpolation circuit  520  at a given moment are vertically aligned such that interpolation along the y-axis of the source image can be performed in a synchronized manner. Moreover, the vertical alignment of the graphics data is maintained as new graphics data provided by the x-axis resampling circuit  302  is shifted into the first y-sample buffer  502 . Following calculation of the graphics data for the destination image, y-interpolation circuit  520  provides the data to a destination buffer  530  which temporarily stores the graphics data prior to being written to a display memory (not shown). 
     As shown in  FIG. 5 , the length of the y-sample buffers  502 - 508  are 128-bytes wide, however, this value has been selected by way of providing an example, and should not be interpreted as limiting the scope of the present invention. The length of the y-sample buffers generally have a length that is less than the width (x_max) of the source image. However, although data buffers of different lengths may be selected for the y-sample buffers  502 - 508 , choosing a length that will take advantage of the access speed of the display memory to which destination data is written is desired. 
     As mentioned previously, the effect is that the graphics data of the source image is resampled in “columns” of data. The widths of the columns, or the span, of data will be a function of the desired scaling ratio and the width of the y-sample buffers  502 - 508 . A larger scaling ratio along the x-axis will result in relatively narrower columns because the sum of the graphics data that generated from the x-axis resampling operation and the graphics data of the source image for one row of the source image must fit within the length of a y-sample buffer. In this manner, synchronized sampling by the y-interpolation circuit  520  can be maintained. 
     Thus, the span of the columns selected by the x-axis resampling circuit  302  ( FIG. 3 ) is such that the sum of the sample values of the span and the resampled graphics data generated for the length of the span will occupy the length of one of the y-sample buffers of the y-axis resampling circuit  500 . The use of smaller y-sample buffers, and consequently shorter span lengths, also allows large source images to be resampled by breaking the original source image into smaller manageable columns of graphics data. Limitations on scaling ratios or source image size are overcome by this approach since the resampling operation is performed for both the x- and y-directions on subsets of the graphics data of a source image rather than performing a resampling operation on the entire source image along one axis before resampling along the other axis, or performing resampling for the entire length of multiple rows of the source image before resampling along the other axis. 
     In operation, the y-interpolation circuit  520  samples the graphics data for five pixels of the source image. The five samples are taken from the source graphics data and calculated graphics data that are provided to a y-resampling circuit  500  from the x-axis resampling circuit  302 . The graphics data is received into the pipeline of y-sample buffers  502 - 508  of the y-resampling circuit  500 , and shifted through the y-sample buffers  502 - 508  such that the y-interpolation circuit  520  uses the sample values to calculate the graphics data for the destination image. The resulting destination graphics data is then provided to a destination buffer  530  and stored temporarily before being written to a memory (not shown). The graphics data is provided to the destination buffer  530  in a “vertical” orientation and then subsequently rewritten to the memory in a “horizontal” orientation for display. 
     It will be appreciated that in resampling the entire source image, the graphics data for the pixels along the edges of the columns will “overlap” in order for the resampling circuit  300  to have a sufficient number of samples when calculating resampled graphics data at the interface between adjacent columns of graphics data. The amount of overlap will depend on the interpolation model used by the y-interpolation circuit and the number of samples required to create the model. If the number of samples from a source column are too small, the extra work and memory access to load and process data twice (from input data overlaps near the column boundaries) may dominate, so the y-pipeline buffers should not be too short, nor should the x-upsampling ratio be too large. 
     From the foregoing it will be appreciated that, although specific embodiments of the invention have been described herein for purposes of illustration, various modifications may be made without deviating from the spirit and scope of the invention. Accordingly, the invention is not limited except as by the appended claims.

Technology Category: 3