Simplification of alpha compositing in the presence of transfer functions

A method determines a color at a plurality of locations in a region of overlap of a first graphic element and a second graphic element, with each graphic element having a color value and a partial opacity value defined at each location. The method includes the steps of determining a transfer color as a combination of the color value of the first graphic element and the color value of the second graphic element, with the transfer color being independent of the opacity values of each element, and determining a first color value of a set of possible color values. At least one color value in the set of possible color values is derived from the transfer color, and another color value in the set of possible color values is derived from the color value of at least one of the first graphical element and the second graphical element. Additional steps include selecting the first color value from the set of possible color values to determine the color at a first selected location in the region of overlap, and determining a second color value from the set of possible color values, and selecting the second color value for a second selected location in the region of overlap. The selection of the first and second color values is at least dependent upon the partial opacity value of the first or second graphical elements.

FIELD OF THE INVENTION

The present invention relates generally to image processing and, in particular, to a method and apparatus for combining a first graphic element and a second graphic element. The present invention also relates to a computer readable medium having recorded thereon a computer program for combining a first graphic element and a second graphic element.

BACKGROUND

Two raster graphic elements, both of which have color and opacity (also known as “alpha” and “transparency”) defined at each point of the elements may be combined. These two elements may be combined through a method of compositing for example as described by Porter and Duff in the publication entitled “Compositing Digital Images”;Computer Graphics, Vol. 18 No. 3 (1984) pp. 253-259 (hereafter Porter and Duff). In particular, in this method, an upper (or source) graphic element (s) and a lower (or destination) graphic element (d) may be composited together with an over operator (one of several operators defined in the publication). The composition of the graphic elements produces a resultant graphic clement (r) in accordance with the following Equations (1) and (2) applied at each point (e.g., a pixel):
ro=do*(1−so)+so(1)
rc=(dc*do*(1−so)+sc*so)/ro(2)
where:ro represents a result opacity (a value ranging from 0 . . . 1 representing the degree of opacity, with 0 being completely transparent and 1 being completely opaque);do represents opacity of the lower graphic element;so represents opacity of the upper graphic element;rc represents a result color. There may be several color channels in a graphic element, such as red, green, and blue for a color image. The rc calculation is used for each such channel;dc represents the color of a lower graphic element; andsc represents the color of an upper graphic element.

To simplify the compositing equations (and operations) for simple compositing it is sometimes convenient to use pre-multiplied color values. A pre-multiplied color value is the color value multiplied by the corresponding opacity value. For example, in pre-multiplied form, the Porter and Duff over operation becomes:
ro=do*(1−so)+so(3)
rco=dco*(1−so)+sco(4)
where:rco represents rc*ro;dco represents dc*do; andsco represents sc*so.

However, pre-multiplied forms of the Porter and Duff compositing operations are only usefull to a sub-set of compositing operations. In the remainder of this description, operations will be described in terms of un-premultiplied values unless otherwise stated.

A second known method of combining two graphic elements is based upon combining the colors of pairs of opaque graphic elements. Examples of such color combining operations include bit-wise logical raster operations (“raster ops”) as exercised by Microsoft Windows Graphical Device Interface (GDI) Application Programming Interface (API) with operations such as R2_MERGEPEN (bitwise OR), and R2_MASKPEN (bitwise AND). Such color combining operations also include “transfer modes” as exercised by Adobe Photoshop with functions such as LIGHTEN, and DARKEN. The above operations, which are just examples of a large class of functions, are defined in Table 1 as follows:

Many such operations are possible and exercised by various graphic systems. However, the above definitions assume both s and d are completely opaque elements. A generalization of color combining operations where a graphic element with non-unity opacity (referred to herein as a semi-transparent element) is being combined with a transfer function onto (i.e., over) an opaque background element is exercised in Adobe PhotoShop and described in U.S. Pat. No. 6,421,460 (Hamburg). Hamburg discloses the following compositing equation:
ro=1  (5)
rc=T(sc, dc)*so+dc*(1−so)  (6)
where T is the transfer function (such as LIGHTEN or DARKEN) producing a transfer color.

Note however that in the above case the lower graphic element (d) is assumed to be fully opaque.

U.S. Pat. No. 6,483,519 by Long et. al. (also U.S. patent application Ser. No. 10/176,644 filed Nov. 24, 2002, by Long et. al.) describes a method of combining two graphical objects (an upper graphic element and a lower graphic element) with a transfer function, both objects having a non-unity opacity value. U.S. Pat. No. 6,421,460 by Hamburg, describes a less generic method for combining an upper graphic element and a lower graphic element. The method of combining two graphic elements described above uses the equations:
ro=do*(1−so)+so*do+so*(1−do)  (7)
rc=(dc*do*(1−so)+T(sc, dc)*so*do+sc*so*(1−do))/ro(8)
These equations can be derived by extending the ideas of Porter and Duff. They allow the combination of semi-transparent graphic elements with raster operations such as R2_MERGEPEN or transfer functions such as LIGHTEN. Such color combining operations had previously been considered incompatible with partial opacity of the lower graphic element.

Whilst Long et. al. (U.S. Pat. No. 6,483,519) describes a graphics accelerator capable of efficiently performing the above generalized technique, for systems without such an accelerator there are a number of practical difficulties in using the above technique. Firstly, the compositing equations are computationally expensive and must be performed on every pixel pair of the two operands of an operation. Such computation is a heavy burden when carried out in a software system. Compounding this problem is the common use of graphics acceleration based on application specific integrated circuits. Graphics accelerators are now commonly used in desktop computers and printers to achieve an acceptable level of graphics performance. However, such accelerators have only a limited repertoire of primitive operations. These primitive operations may include both Porter and Duff compositing, and/or raster operations (or transfer functions), however they do not usually allow the general case of Porter and Duff compositing in the presence of raster operations (or transfer functions) where both operands can have transparency, as described above. This can present considerable difficulties since there are large time penalties for stopping the pipeline of a graphics accelerator in order to substitute software calculations for aspects that the graphics accelerator is unable to compute. When combined with the very expensive calculations described above, the performance penalty is large.

Thus, a need clearly exists for a more efficient method of combining a first graphic element and a second graphic element, where this combining may be performed by accelerators that have a limited repertoire of primitive operations as described above.

SUMMARY

According to one aspect of the present invention there is provided a method of determining a color at a location in a region of overlap of a first graphic element and a second graphic element, each said graphic element having a color value and an opacity value defined at a plurality of locations, the method comprising the steps of:

a) determining a transfer color as a combination of the color value of the first graphic element and the color value of the second graphic element, said transfer color being independent of the opacity values of each said element;

b) determining at least one color value of possible color values with said at least one color value being derived from the transfer color; and

c) selecting, for at least one location in said overlap region, said at least one color value from the possible color values, said selection being dependent upon at least one of the opacity value of the first or second graphical element.

According to another aspect of the present invention there is provided a method of combining an upper graphic element and a lower graphic element, each with color and opacity defined at a plurality of locations, and a background graphic element with color defined at a plurality of locations, to produce an updated background graphic element, said method being characterized in that:a) a transfer color is the result of a function combining an upper element color with a lower element color without regard to either the upper element opacity or the lower element opacity;b) the color of a location in the updated background element is one of a palette of colors defined for that location, which one being dependent on either the upper element opacity, the lower element opacity, or both; andc) one of the colors of the palette is dependent on the transfer color.

According to still another aspect of the present invention there is provided a method of combining an upper graphic element and a lower graphic element, each with color and opacity defined at a plurality of locations, said method comprising the steps of:a) combining the color of said upper graphic element with the color of said lower graphic element using a transfer function, without regard to the opacity of said lower graphic element, to determine a combination graphic element;b) determining at least one mask using the opacity of said lower graphic element, or the opacity of said upper graphic element, or both; andc) combining said combination graphic element with either the upper graphic element, or the lower graphic element, or both, subject to masking by said at least one mask.

According to still another aspect of the present invention there is provided an apparatus for determining a color at a location in a region of overlap of a first graphic element and a second graphic element, each said graphic element having a color value and an opacity value defined at a plurality of locations, said apparatus comprising:

transfer color determining means for determining a transfer color as a combination of the color value of the first graphic element and the color value of the second graphic element, said transfer color being independent of the opacity values of each said element;

color value determining means for determining at least one color value of possible color values with said at least one color value being derived from the transfer color;

selection means for selecting, for at least one location in said overlap region, said at least one color value from the possible color values, said selection being dependent upon at least one of the opacity value of the first or second graphical element.

According to still another aspect of the present invention there is provided an apparatus for combining an upper graphic element, and a lower graphic element, each with color and opacity defined at a plurality of locations, and a background graphic element with color defined at a plurality of locations, to produce an updated background graphic element, said apparatus being characterized in that:a) a transfer color is the result of a function combining an upper element color with a lower element color without regard to either the upper element opacity or the lower element opacity;b) the color of a location in the updated background element is one of a palette of colors defined for that location, which one being dependent on either the upper element opacity, the lower element opacity, or both; andc) one of the colors of the palette is dependent on the transfer color.

According to still another aspect of the present invention there is provided an apparatus for combining an upper graphic element and a lower graphic element, each with color and opacity defined at a plurality of locations, said apparatus comprising:

first combining means for combining the said upper graphic element with the color of said lower graphic element using a transfer function, without regard to the opacity of said lower graphic element, to determine a combination graphic element;

mask determining means for determining at least one mask using the opacity of said lower graphic element, or the opacity of said upper graphic element, or both; and

second combining means for combining said combination graphic element with either the upper graphic element, or the lower graphic element, or both, subject to masking by said at least one mask.

According to still another aspect of the present invention there is provided a computer program product having a computer readable medium having a computer program recorded therein for determining a color at a location in a region of overlap of a first graphic element and a second graphic element, each said graphic element having a color value and an opacity value defined at a plurality of locations, the computer program comprising:

code for determining a transfer color as a combination of the color value of the first graphic element and the color value of the second graphic element, said transfer color being independent of the opacity values of each said element;

code for determining at least one color value of possible color values with said at least one color value being derived from the transfer color; and

code for selecting, for at least one location in said overlap region, said at least one color value from the possible color values, said selection being dependent upon at least one of the opacity value of the first or second graphical element.

According to still another aspect of the present invention there is provided a computer program product having a computer readable medium having a computer program recorded therein for combining an upper graphic element, and a lower graphic element, each with color and opacity defined at a plurality of locations, and a background graphic element with color defined at a plurality of locations, to produce an updated background graphic element, said computer program product being characterized in that:a) a transfer color is the result of a function combining an upper element color with a lower element color without regard to either the upper element opacity or the lower element opacity;b) the color of a location in the updated background element is one of a palette of colors defined for that location, which one being dependent on either the upper element opacity, the lower element opacity, or both; andc) one of the colors of the palette is dependent on the transfer color.

According to still another aspect of the present invention there is provided a computer program product having a computer readable medium having a computer program recorded therein for combining an upper graphic element and a lower graphic element, each with color and opacity defined at a plurality of locations, said computer program product comprising:

computer program code means for combining the said upper graphic element with the color of said lower graphic element using a transfer function, without regard to the opacity of said lower graphic element, to determine a combination graphic element;

computer program code means for determining at least one mask using the opacity of said lower graphic element, or the opacity of said upper graphic element, or both; and

computer program code means for combining said combination graphic element with either the upper graphic element, or the lower graphic element, or both, subject to masking by said at least one mask.

According to still another aspect of the present invention there is provided a method of combining an upper graphic element and a lower graphic element to produce a result graphic element, said upper graphic element and said lower graphic element comprising color and opacity, said method comprising the steps of:

combining the color of said upper graphic element with the color of said lower graphic element using a transfer function, without regard to either opacity of said upper graphic element or opacity of said lower graphic element, to determine a combination graphic element;

determining a mask using the opacity of said lower graphic element and a halftone dither matrix; and

combining said combination graphic element with said upper graphic element according to said mask to produce said result graphic element, wherein color of a location in said result graphic element is one of a palette of colors defined for said location, said one color being dependent on one of either the opacity of said upper graphic element or the opacity of said lower graphic element.

Other aspects of the invention are also disclosed.

DETAILED DESCRIPTION INCLUDING BEST MODE

A method300(seeFIG. 3) of combining an upper (or first) graphic element and a lower (or second) graphic element, according to one embodiment of the present invention, will now be described below with reference toFIGS. 1 to 4. The method300achieves a substantially similar visual result to generalized Porter and Duff compositing in the presence of a transfer function, while only using a series of simpler graphical operations. These simpler graphical operations may be performed by a graphics accelerator that does not support generalized Porter and Duff compositing in the presence of a transfer function. One or both of the graphic elements are treated as purely opaque elements and are combined by a transfer function using available simple (preferably accelerated) operations.

Using a series of masked and/or un-masked painting operations (preferably accelerated), the upper graphic element, the lower graphic element, or the combination of the two graphic elements are painted to the result in patterns. These patterns achieve a visually similar result to generalized Porter and Duff compositing in the presence of a transfer function described in Long et. al. (U.S. Pat. No. 6,483,519). The result, although different in detailed pixel values from the true color generated by generalized Porter and Duff compositing in the presence of a transfer function, has a similar overall visual appearance. This similar visual appearance is produced through a set of simple operations that may be accelerated by many graphics accelerators which do not support generalized Porter and Duff compositing in the presence of transfer functions.

The method300is preferably practiced using a general-purpose computer system400, such as that shown inFIG. 4wherein the processes ofFIGS. 1 to 3may be implemented as software, such as an application program executing within the computer system400. Preferably the software uses a graphics accelerator430to accelerate certain primitive operations. In particular, the steps of the method300are effected by instructions in the software that are carried out by the computer. The instructions may be formed as one or more code modules, each for performing one or more particular tasks. The software may also be divided into two separate parts, in which a first part performs the method300and a second part manages a user interface between the first part and the user. The software may be stored in a computer readable medium, including the storage devices described below, for example. The software is loaded into the computer from the computer readable medium, and then executed by the computer. A computer readable medium having such software or computer program recorded on it is a computer program product. The use of the computer program product in the computer preferably effects an advantageous apparatus for implementing the method300.

The computer system400is formed by a computer module401, input devices such as a keyboard402and mouse403, output devices including a printer415, a display device414and loudspeakers417. A Modulator-Demodulator (Modem) transceiver device416is used by the computer module401for communicating to and from a communications network420, for example connectable via a telephone line421or other functional medium. The modem416can be used to obtain access to the Internet, and other network systems, such as a Local Area Network (LAN) or a Wide Area Network (WAN), and may be incorporated into the computer module401in some implementations.

The computer module401typically includes at least one processor unit405, and a memory unit406, for example formed from semiconductor random access memory (RAM) and read only memory (ROM). The module401also includes an number of input/output (I/O) interfaces including an audio-video interface407that couples to the video display414and loudspeakers417, an I/O interface413for the keyboard402and mouse403and optionally a joystick (not illustrated), and an interface408for the modem416and printer415. In some implementations, the modem416may be incorporated within the computer module401, for example within the interface408. A storage device409is provided and typically includes a hard disk drive410and a floppy disk drive411. A magnetic tape drive (not illustrated) may also be used. A CD-ROM drive412is typically provided as a non-volatile source of data. The components405to413of the computer module401, typically communicate via an interconnected bus404and in a manner which results in a conventional mode of operation of the computer system400known to those in the relevant art. Examples of computers on which the described arrangements can be practised include IBM-PC's and compatibles, Sun Sparcstations or alike computer systems evolved therefrom.

Typically, the application program is resident on the hard disk drive410and read and controlled in its execution by the processor405. Intermediate storage of the program and any data fetched from the network420may be accomplished using the semiconductor memory406, possibly in concert with the hard disk drive410. In some instances, the application program may be supplied to the user encoded on a CD-ROM or floppy disk and read via the corresponding drive412or411, or alternatively may be read by the user from the network420via the modem device416. Still further, the software can also be loaded into the computer system400from other computer readable media. The term “computer readable medium” as used herein refers to any storage or transmission medium that participates in providing instructions and/or data to the computer system400for execution and/or processing. Examples of storage media include floppy disks, magnetic tape, CD-ROM, hard disk drive, ROM or integrated circuit, magneto-optical disk, or computer readable card, and the like, whether or not such devices are internal or external of the computer module401.

The method300may alternatively be implemented in dedicated hardware such as one or more integrated circuits performing the functions or sub functions of the described method. Such dedicated hardware may include graphic processors, digital signal processors, or one or more microprocessors and associated memories.

In the alpha compositing method disclosed by Porter and Duff, the opacity value of a pixel is the proportion of a background (or background graphic element) that the pixel covers. That is, a pixel is conceptually regarded as an area of opaque color with a hole through which the color of the background graphic element is visible. In this conceptual model the transparency of a pixel is represented by the size of the hole. Of course, this model of a pixel regards a digital image as being tessellated into an array of pixels, each of which covers an area. Other models, such as that used by sampling theory are different, but will not be considered here.

FIG. 1shows a conceptual representation of a first pixel100(first graphic element, upper graphic element or source graphic element), which has color sc (i.e., first element color, upper element color or source color) and opacity so (i.e., first element opacity, upper element opacity or source opacity). The opaque color of the pixel100has been arranged at a location on the left of a unit square and the transparent hole on the right.FIG. 1shows conceptual representation of a second pixel101(second graphic element, lower graphic element or destination graphic element), which has color dc (i.e., second element color, lower element color or destination color) and opacity do (second element opacity, lower element opacity or destination opacity). In the second pixel101the color has been arranged at a top location and the transparent hole at a bottom location of the pixel101, as seenFIG. 1. The different arrangements (or subdivisions) between the first pixel and the second pixel represents, conceptually, the independent aspect of the color and transparency of the first pixel100and the second pixel101before the pixels are combined. The first pixel100and the second pixel101may be combined using a transfer function, T(sc, dc) to produce the resultant pixel102(or result graphic element). The resultant pixel102is the basis of Porter and Duff compositing and its generalisation to handle transfer functions. The color of the resultant pixel (with result color rc and result opacity ro) is the weighted average of the colors of areas103,104and105; the weights being proportional to the areas of103,104, and105respectively. The opacity of the resultant pixel102is the sum of the areas of103,104, and105(or in alternate expression, the resultant transparency is the area of106). In particular, the result opacity ro and result color rc of the pixel102may be determined in accordance with Equations (7) and (8) as described above.

In the absence of primitive operations to support the determination of the result opacity and color in accordance Equations (7) and (8), the method300uses a series of available primitive operations. The exact sequence of primitive operations depends on the available primitive operations of the graphics accelerator430being used by the computer system400. Examples of primitive capabilities of graphics accelerators include the following:A. The capability to perform a transfer function possibly limited to a raster operation) to combine the color of two opaque operands. This capability is available in accelerators commonly used in personal computers, for instance those running Microsoft Windows and can be accessed through the GDI API;B. As above for A., plus the capability to composite a semi-transparent operand over an opaque background graphic element. This capability is available in Microsoft Windows GDI+ API;C. As above for B., plus the capability to composite a semi-transparent operand over a second semi-transparent operand. This capability is commonly available in three dimensional (3D) accelerators used in personal computers and may be accessed through the OpenGL API. Often the full range of Porter and Duff operators is available as well, however only over will be considered herein;D. As above for C., plus the capability to composite a semi-transparent operand over an opaque operand subject to a transfer function;E. As above for D., plus the capability to composite a semi-transparent operand over a second semi-transparent operand subject to a transfer function;F. As above for E., plus the capability to composite a semi-transparent operand with a second semi-transparent operand using any Porter and Duff compositing operator subject to a transfer function.

The methods of the preferred embodiment concern the efficient achievement of capability E in environments with capabilities limited to one of the capabilities A. through D. The methods of the preferred embodiment are based on recognition that certain of the color and opacity values contributing to the true pixel color (hereafter “contributing values”) may be generated with lower capability graphics accelerator operations. In particular, the opaque transfer color T(sc, dc) alone, of region103, may be achieved with capability A., as may the opaque color sc of region104and the opaque color dc of the region105. Opaque color values may be obtained from partially opaque color values simply by ignoring (i.e., without having regard to) associated opacity. Purely transparent pixels may also be achieved. Further, certain pair-wise blends of the colors may also be achieved with capability D., specifically the weighted average between the opaque transfer color T(sc, dc) of area103and the opaque destination color dc of area105.

The methods of the preferred embodiment achieve a similar visual result by selecting one contributing value at each pixel, where the probability of selecting any one contributing value is weighted in the same manner as a weighted average which would be used to achieve the true color. Thus, for example, if a palette of contributing values representing colors consists of each of the opaque colors T(sc, dc), sc, and dc, the relative probability of a result pixel being each of those colors will be, by construction, the area of regions103,104, and105respectively. There is a remaining probability that the result pixel will be none of these colors, representing the transparent hole106. In this case, the result pixel is fully transparent.

There are a number of different palettes from which contributing values may be selected. The ones of interest to the described methods are listed in the Table 2, below, where dotted lines delimit alternative palettes.

There are other palette combinations possible, such as those based on regions103&106and104&105, however the complexity of their color and opacity equations means they are not of interest to the methods described herein.

The palette of contributing values of interest to the preferred embodiment of the present invention comprises s and dtc. As can be seen from Table 2 , the formula for dtc is:
ro=1
rc=T(sc, dc)*so+dc*(1−so)
which is identical to the formula for a graphic element with non-unity opacity combined (using a transfer function) onto an opaque background graphic element (see Equations 5 and 6). Further, the relative frequency of use of each of these values is simply the opacity component of the lower element, and its complement.

There are a number of methods of determining the probability based selection required. In the methods described herein, the techniques of color halftoning are adapted.

In halftoning, a “true color” image, in which each color component of each true color pixel has a large number of possible values, is reduced to a “halftoned” image in which each color component of each halftoned pixel has just one of a small set of discrete color values. The probability of each discrete value is related to the true color value. There are many halftoning methods, however two of the most commonly used methods are error diffusion and dither matrices, both of which are well known in the art.

In the described methods a dither matrix is adapted for use. However an analogous adaptation of any halftoning method, such as error diffusion, is possible. A dither matrix such as the dither matrix208ofFIG. 2Fmay be used. The dither matrix is conceptually tiled over the surface of a lower graphic element and used to derive a mask image with one bit of information per pixel. This is achieved by addressing the dither matrix with modulus arithmetic. At each location (i.e. pixel), the opacity channel is compared to the corresponding value in the dither matrix. If the opacity value is greater than the value of the dither matrix, the mask has a one (1) value at that location, else the mask has a value of zero (0).

To achieve the appropriate probability, or relative frequency, of each of the contributing colors, while still taking maximum advantage of graphics acceleration, one or more such single-bit per pixel image masks are generated by halftoning the relative contribution that is required for each contributing color. These image masks are used to mask painting operations of objects consisting of the contributing values—which in some cases are the original operands.

In the preferred embodiment, the final result is achieved using a graphics accelerator (e.g., the graphics accelerator430), having capability D, by the following numbered steps of the method300described with reference toFIG. 3.1. In301the lower graphic element is copied to a temporary area configured within memory406without the opacity of the lower graphic element.2. In302the upper graphic element is composited over the temporary area using the transfer function. This results in contributing value dtc which is opaque.3. In303, the upper graphic element is copied to a result buffer configured within memory406. This forms the initial value of the result. This is contributing value s and may be semi-transparent.4. In304the opacity component of the lower graphic element is used, via a halftone dither matrix, to determine a mask.5. In305the temporary area is copied onto the result subject to the mask. That is, values of the temporary area where the mask is one (1) are copied to the result buffer; other values are not used. After this the temporary area configured within the memory406may be discarded.

In the common case that the result of step305is to be further composited over an opaque background, the above method300may be simplified. In particular, the method300may be simplified by, at step303, compositing the upper graphic element s directly over the background instead of copying to the result buffer result, then at step305copying the temporary buffer temp where the mask mask is one (1) to the background instead of the result buffer result. This eliminates the need for an intermediate result buffer.

The preferred embodiment relies on the observation that the dtc contribution is completely opaque, so may be copied over the previously painted s contribution thus overriding the value of s. Alternatively, either dtc or s may be generated at each pixel depending on the mask value.

An example of the method300will now be described with reference toFIGS. 2A to 21.FIG. 2Ashows a 5×5 pixel upper graphic element201which has a color and opacity at each pixel (or location). In this example, the opacity of each pixel of the upper graphic element201is 0.5. The 50% opacity is represented diagrammatically by the half shading of each pixel. Similarly,FIG. 2Bshows a lower graphic element202, which is a triangle. The lower graphic element202also has a color and opacity at each pixel (or location), and the opacity is similarly 0.5 at each pixel. The color and opacity may be different from object to object and pixel to pixel, however for simplicity in this example, the color and opacity will be assumed to have only one value.

The upper graphic element201is to be composited over the lower graphic clement202at a location indicated by the dotted outline203, as seen inFIG. 213. The example will now be explained in the same numbered steps used to describeFIG. 3above:1. A temporary buffet204is created in memory406large enough to cover a bounding box of the lower graphic element202. As at301, the lower graphic element202is copied to the temporary buffer204by the processor405without the opacity of the lower graphic element, resulting in shaded pixels205, as seen inFIG. 2C. In practice the temporary buffer may be the size of the bounding box of the intersection of the bounds of the upper graphic element201and the lower graphic element202. However, the example uses the bounding box of the lower graphic element202for clarity. The temporary buffer need not, and in the preferred embodiment does not, support an opacity channel. The lower graphic element202is implicitly opaque. The “don't care” pixels outside the bounds of the lower graphic element202are marked with crosses212, as seen inFIG. 2C2. As at302, the upper graphic element201is composited over the temporary buffer204by the processor405in concert with graphics accelerator430using the transfer function resulting in a combination graphic element in the temporary buffer204comprising new pixel values206, as seen inFIG. 2D. Pixels of the combination graphic element (e.g.,200) are shown as two shaded areas to represent the weighted average of two contributing colors, those being the transfer color T(sc, dc) and the color dc of the lower graphic element. In this example, since the upper graphic element201is 0.5 opaque, a 0.5 and 0.5 weight is used for each color. The over operator and the transfer function have been used to achieve this, which has resulted in composited opaque pixels, such as212, outside the bounds of the dc pixels previously generated. However the composited opaque pixels, such as212, outside the bounds will be ignored, so their generation is not important.3. As at303, the upper graphic element201is copied by the processor405to the result buffer207, as seen inFIG. 2E. This forms the initial value of the result graphical element210. The initial value is contributing value s and includes an opacity channel.4.

As at304, the opacity component of the lower graphic element202is used, via the halftone dither matrix208to determine a mask209, as seen inFIG. 2G. The dither matrix208is a 4×4 dither matrix for the simplicity of the example. In practice a larger dither matrix may be used. When a threshold value of 0.5 is applied to the dither matrix208, a checkerboard pattern results, which is reflected in the checkerboard pattern of the mask209. Values outside the bounds of the lower graphic element result in zero (blank) values in the mask209.5. As at305, the temporary buffer206is copied onto the result buffer207by the processor405according to the mask209to produce a result graphic element210ofFIG. 2H. That is, values of the temporary buffer206, including the implicit opacity of the temporary buffer206, where the mask209is 1 (black) are copied to the result buffer207to produce the result graphic element210. Other values are not used.

The result graphic element210as seen inFIG. 2H, although different from a true result graphic element211in detail (seeFIG. 2I), has similar visual appearance for large collections of pixels, especially in high resolution prints.

The method300requires accelerator capability D., for step302of the method300. Where capabilities are more limited, each of the contributing color values sc, dc, and tc may be copied to the result graphic element in the same manner using the relative probabilities for those values listed in the first palette of Table 1 above. This approach only requires accelerator capability A., above, which is common to almost all graphic accelerators. However, the result graphic element has a higher granularity than the method300.

Thus, by using a series of masked and/or un-masked painting operations (preferably accelerated), an upper graphic element, a lower graphic element, or a combination of the two, may be painted to a result graphic element in patterns. These patterns achieve a visually similar result graphic element to generalized Porter and Duff compositing in the presence of a transfer function, although different in detailed pixel values from the true color.

The aforementioned preferred method(s) comprise a particular control flow. There are many other variants of the preferred method(s) which use different control flows without departing the spirit or scope of the invention. Furthermore one or more of the steps of the preferred method(s) may be performed in parallel rather sequentially.

INDUSTRIAL APPLICABILITY

It is apparent from the above that the arrangements described are applicable to the computer and data processing industries.

In the context of this specification, the word “comprising” means “including principally but not necessarily solely” or “having” or “including”, and not “consisting only of”. Variations of the word “comprising”, such as “comprise” and “comprises” have correspondingly varied meanings.