ISO 32000-1 Document management — Portable document format

Like a type 6 halftone, a type 10 halftone shall be represented as a stream containing the threshold values, with

the parameters defining the halftone specified by entries in the stream dictionary. This dictionary may contain

the entries shown in Table 132 in addition to the usual entries common to all streams (see Table 5). The

Xsquare and Ysquare entries replace the type 6 halftone’s Width and Height entries.

Table 132 - Additional entries specific to a type 10 halftone dictionary

Key

Type

Value

Type

name

(Optional) The type of PDF object that this dictionary describes; if

present, shall be Halftone for a halftone dictionary.

HalftoneType

integer

(Required) A code identifying the halftone type that this dictionary

describes; shall be 10 for this type of halftone.

HalftoneName

byte string

(Optional) The name of the halftone dictionary.

Xsquare

integer

(Required) The side of square X, in device pixels; see below.

Ysquare

integer

(Required) The side of square Y, in device pixels; see below.

TransferFunction

function or

(Optional) A transfer function, which shall override the current

name

transfer function in the graphics state for the same component.

This entry shall be present if the dictionary is a component of a type

5 halftone (see “Type 5 Halftones” in 10.5.5.6) and represents

either a nonprimary or nonstandard primary colour component (see

10.4, "Transfer Functions"). The name Identity may be used to

specify the identity function.

The Xsquare and Ysquare entries shall specify the dimensions of the two squares in device pixels. The stream

shall contain Xsquare 2 + Ysquare 2 bytes, each representing a single threshold value. The contents of square

X shall be specified first, followed by those of square Y. Threshold values within each square shall be defined in

device space in the same order as image samples in image space (see Figure 34), with the first value at device

coordinates (0, 0) and horizontal coordinates changing faster than vertical coordinates.

10.5.5.5

Type 16 Halftones

Like type 10, a type 16 halftone (PDF 1.3) defines a halftone screen with a threshold array and allows nonzero

screen angles. In type 16, however, each element of the threshold array shall be 16 bits wide instead of 8. This

allows the threshold array to distinguish 65,536 levels of colour rather than only 256 levels. The threshold array

may consist of either one rectangle or two rectangles. If two rectangles are specified, they shall tile the device

space as shown in Figure 53. The last row in the first rectangle shall be immediately adjacent to the first row in

the second and shall start in the same column.

Width

Height

Width ´ Height

Height2

Width2 ´

Height2

Width2

Figure 53 - Tiling of device space in a type 16 halftone

A type 16 halftone, like type 6 and type 10, shall be represented as a stream containing the threshold values,

with the parameters defining the halftone specified by entries in the stream dictionary. This dictionary may

contain the entries shown in Table 133 in addition to the usual entries common to all streams (see Table 5). The

313

dictionary’s Width and Height entries define the dimensions of the first (or only) rectangle. The dimensions of

the second, optional rectangle are defined by the optional entries Width2 and Height2. Each threshold value

shall be represented as 2 bytes, with the high-order byte first. The stream shall contain 2 × Width × Height

bytes if there is only one rectangle or

2 × (Width × Height + Width2 × Height2) bytes if there are two

rectangles. The contents of the first rectangle are specified first, followed by those of the second rectangle.

Threshold values within each rectangle shall be defined in device space in the same order as image samples in

image space (see Figure 34), with the first value at device coordinates (0, 0) and horizontal coordinates

changing faster than vertical coordinates.

Table 133 - Additional entries specific to a type 16 halftone dictionary

Key

Type

Value

Type

name

(Optional) The type of PDF object that this dictionary describes;

if present, shall be Halftone for a halftone dictionary.

HalftoneType

integer

(Required) A code identifying the halftone type that this

dictionary describes; shall be 16 for this type of halftone.

HalftoneName

byte string

(Optional) The name of the halftone dictionary.

Width

integer

(Required) The width of the first

(or only) rectangle in the

threshold array, in device pixels.

Height

integer

(Required) The height of the first (or only) rectangle in the

threshold array, in device pixels.

Width2

integer

(Optional) The width of the optional second rectangle in the

threshold array, in device pixels. If this entry is present, the

Height2 entry shall be present as well. If this entry is absent, the

Height2 entry shall also be absent, and the threshold array has

only one rectangle.

Height2

integer

(Optional) The height of the optional second rectangle in the

threshold array, in device pixels.

TransferFunction

function or name

(Optional) A transfer function, which shall override the current

transfer function in the graphics state for the same component.

This entry shall be present if the dictionary is a component of a

type

5 halftone

(see

10.5.5.6, "Type

5 Halftones") and

represents either a nonprimary or nonstandard primary colour

component (see 10.4, "Transfer Functions"). The name Identity

may be used to specify the identity function.

10.5.5.6

Type 5 Halftones

Some devices, particularly colour printers, require separate halftones for each individual colorant. Also, devices

that can produce named separations may require individual halftones for each separation. Halftone dictionaries

of type 5 allow individual halftones to be specified for an arbitrary number of colorants or colour components.

A type 5 halftone dictionary (Table 134) is a composite dictionary containing independent halftone definitions

for multiple colorants. Its keys shall be name objects representing the names of individual colorants or colour

components. The values associated with these keys shall be other halftone dictionaries, each defining the

halftone screen and transfer function for a single colorant or colour component. The component halftone

dictionaries shall not be of halftone type 5.

314

Table 134 - Entries in a type 5 halftone dictionary

Key

Type

Value

Type

name

(Optional) The type of PDF object that this dictionary describes; if

present, shall be Halftone for a halftone dictionary.

HalftoneType

number

(Required) A code identifying the halftone type that this dictionary

describes; shall be 5 for this type of halftone.

HalftoneName

byte string

(Optional) The name of the halftone dictionary.

any colorant

dictionary

(Required, one per colorant) The halftone corresponding to the

name

or stream

colorant or colour component named by the key. The halftone may be

of any type other than 5.

Default

dictionary

(Required) A halftone to be used for any colorant or colour component

or stream

that does not have an entry of its own. The value shall not be 5. If there

are any nonprimary colorants, the default halftone shall have a transfer

function.

The colorants or colour components represented in a type 5 halftone dictionary (aside from the Default entry)

fall into two categories:

•

Primary colour components for the standard native device colour spaces (Gray for DeviceGray; Red,

Green, and Blue for DeviceRGB; Cyan, Magenta, Yellow, and Black for DeviceCMYK;).

•

Nonstandard colour components for use as spot colorants in Separation and DeviceN colour spaces.

Some of these may also be used as process colorants if the native colour space is nonstandard.

When a halftone dictionary of some other type appears as the value of an entry in a type 5 halftone dictionary,

it shall apply only to the single colorant or colour component named by that entry’s key. This is in contrast to

such a dictionary’s being used as the current halftone parameter in the graphics state, which shall apply to all

colour components. If nonprimary colorants are requested when the current halftone is defined by any means

other than a type 5 halftone dictionary, the gray halftone screen and transfer function shall be used for all such

colorants.

EXAMPLE

In this example, the halftone dictionaries for the colour components and for the default all use the same

spot function. In this example, the halftone dictionaries for the colour components and for the default all

use the same spot function.

27 0 obj

<< /Type /Halftone

/HalftoneType 5

/Cyan 31 0 R

/Magenta 32 0 R

/Yellow 33 0 R

/Black 34 0 R

/Default

35 0 R

endobj

31 0 obj

<< /Type /Halftone

/HalftoneType 1

/Frequency 89.827

/Angle 15

/SpotFunction /Round

/AccurateScreens true

endobj

32 0 obj

315

<< /Type /Halftone

/HalftoneType 1

/Frequency 89.827

/Angle 75

/SpotFunction /Round

/AccurateScreens true

endobj

33 0 obj

<< /Type /Halftone

/HalftoneType 1

/Frequency 90.714

/Angle 0

/SpotFunction /Round

/AccurateScreens true

endobj

34 0 obj

<< /Type /Halftone

/HalftoneType 1

/Frequency 89.803

/Angle 45

/SpotFunction /Round

/AccurateScreens true

endobj

35 0 obj

<< /Type /Halftone

/HalftoneType 1

/Frequency 90.000

/Angle 45

/SpotFunction /Round

/AccurateScreens true

endobj

10.6

Scan Conversion Details

10.6.1

General

The final step of rendering shall be scan conversion. The conforming reader executes a scan conversion

algorithm to paint graphics, text, and images in the raster memory of the output device.

NOTE

The specifics of the scan conversion algorithm are not defined as part of PDF. Different implementations may

perform scan conversion in different ways; techniques that are appropriate for one device may be

inappropriate for another. Still, it is useful to have a general understanding of how scan conversion works,

particularly when creating PDF files intended for viewing on a display. At the low resolutions typical of displays,

variations of even one pixel’s width can have a noticeable effect on the appearance of painted shapes.

Most scan conversion details are not under program control, but a few are; the parameters for controlling them

are described here.

10.6.2

Flatness Tolerance

The flatness tolerance controls the maximum permitted distance in device pixels between the mathematically

correct path and an approximation constructed from straight line segments, as shown in Figure 54. Flatness

may be specified as the operand of the i operator (see Table 57) or as the value of the FL entry in a graphics

state parameter dictionary (see Table 58). It shall be a positive number.

316

NOTE 1

Smaller values yield greater precision at the cost of more computation.

NOTE 2

Although the figure exaggerates the difference between the curved and flattened paths for the sake of clarity,

the purpose of the flatness tolerance is to control the precision of curve rendering, not to draw inscribed

polygons. If the parameter’s value is large enough to cause visible straight line segments to appear, the result

is unpredictable.

Flatness error

tolerance

Figure 54 - Flatness tolerance

10.6.3

Smoothness Tolerance

The smoothness tolerance (PDF 1.3) controls the quality of smooth shading (type 2 patterns and the sh

operator) and thus indirectly controls the rendering performance. Smoothness is the allowable colour error

between a shading approximated by piecewise linear interpolation and the true value of a (possibly nonlinear)

shading function. The error shall be measured for each colour component, and the maximum independent error

shall be used. The allowable error (or tolerance) shall be expressed as a fraction of the range of the colour

component, from 0.0 to 1.0. Thus, a smoothness tolerance of 0.1 represents a tolerance of 10 percent in each

colour component. Smoothness may be specified as the value of the SM entry in a graphics state parameter

dictionary (see Table 58).

EXAMPLE

Each output device may have internal limits on the maximum and minimum tolerances attainable. setting

smoothness to 1.0 may result in an internal smoothness of 0.5 on a high-quality colour device, while

setting it to 0.0 on the same device may result in an internal smoothness of 0.01 if an error of that

magnitude is imperceptible on the device.

NOTE 1

The smoothness tolerance may also interact with the accuracy of colour conversion. In the case of a colour

conversion defined by a sampled function, the conversion function is unknown. Thus the error may be sampled

at too low a frequency, in which case the accuracy defined by the smoothness tolerance cannot be

guaranteed. In most cases, however, where the conversion function is smooth and continuous, the accuracy

should be within the specified tolerance.

NOTE 2

The effect of the smoothness tolerance is similar to that of the flatness tolerance. However, that flatness is

measured in device-dependent units of pixel width, whereas smoothness is measured as a fraction of colour

component range.

10.6.4

Scan Conversion Rules

The following rules determine which device pixels a painting operation affects. All references to coordinates

and pixels are in device space. A shape is a path to be painted with the current colour or with an image. Its

coordinates are mapped into device space but not rounded to device pixel boundaries. At this level, curves

have been flattened to sequences of straight lines, and all “insideness” computations have been performed.

Pixel boundaries always fall on integer coordinates in device space. A pixel is a square region identified by the

location of its corner with minimum horizontal and vertical coordinates. The region is half-open, meaning that it

includes its lower but not its upper boundaries. More precisely, for any point whose real-number coordinates

317

are (x, y), let i = floor (x) and j = floor (y). The pixel that contains this point is the one identified as (i, j). The

region belonging to that pixel is defined to be the set of points (x ′, y ′) such that i ≤ x ′ < i + 1 and j ≤ y′ < j + 1.

Like pixels, shapes to be painted by filling and stroking operations are also treated as half-open regions that

include the boundaries along their “floor” sides, but not along their “ceiling” sides.

A shape shall be scan-converted by painting any pixel whose square region intersects the shape, no matter

how small the intersection is. This ensures that no shape ever disappears as a result of unfavourable

placement relative to the device pixel grid, as might happen with other possible scan conversion rules. The

area covered by painted pixels shall always be at least as large as the area of the original shape. This rule

applies both to fill operations and to strokes with nonzero width. Zero-width strokes may be done in an

implementation-defined manner that may include fewer pixels than the rule implies.

NOTE 1

Normally, the intersection of two regions is defined as the intersection of their interiors. However, for purposes

of scan conversion, a filling region is considered to intersect every pixel through which its boundary passes,

even if the interior of the filling region is empty.

EXAMPLE

A zero-width or zero-height rectangle paints a line 1 pixel wide.

The region of device space to be painted by a sampled image is determined similarly to that of a filled shape,

though not identically. The conforming reader transforms the image’s source rectangle into device space and

defines a half-open region, just as for fill operations. However, only those pixels whose centres lie within the

region shall be painted. The position of the centre of such a pixel—in other words, the point whose coordinate

values have fractional parts of one-half—shall be mapped back into source space to determine how to colour

the pixel. There shall not be averaging over the pixel area;

NOTE 2

If the resolution of the source image is higher than that of device space, some source samples may not be

used.

For clipping, the clipping region consists of the set of pixels that would be included by a fill operation.

Subsequent painting operations shall affect a region that is the intersection of the set of pixels defined by the

clipping region with the set of pixels for the region to be painted.

Scan conversion of character glyphs may be performed by a different algorithm from the preceding one.

NOTE 3

That font rendering algorithm uses hints in the glyph descriptions and techniques that are specialized to glyph

rasterization.

10.6.5

Automatic Stroke Adjustment

When a stroke is drawn along a path, the scan conversion algorithm may produce lines of nonuniform

thickness because of rasterization effects. In general, the line width and the coordinates of the endpoints,

transformed into device space, are arbitrary real numbers not quantized to device pixels. A line of a given width

can intersect with different numbers of device pixels, depending on where it is positioned. Figure 55 illustrates

this effect.

For best results, it is important to compensate for the rasterization effects to produce strokes of uniform

thickness. This is especially important in low-resolution display applications. To meet this need, PDF 1.2

provides an optional automatic stroke adjustment feature. When stroke adjustment is enabled, the line width

and the coordinates of a stroke shall automatically be adjusted as necessary to produce lines of uniform

thickness. The thickness shall be as near as possible to the requested line width—no more than half a pixel

different.

318

Transparency

11.1

General

The PDF imaging model includes the notion of transparency. Transparent objects do not necessarily obey a

strict opaque painting model but may blend (composite) in interesting ways with other overlapping objects. This

clause describes the general transparency model but does not cover how it is implemented. At various points it

uses implementation-like descriptions to describe how things work, for the purpose of elucidating the behaviour

of the model. The actual implementation will almost certainly be different from what these descriptions might

imply.

NOTE

Transparency was added to PDF in version 1.4

The clause is organized as follows:

•

11.2, "Overview of Transparency," introduces the basic concepts of the transparency model and its

associated terminology.

•

11.3, "Basic Compositing Computations," describes the mathematics involved in compositing a single

object with its backdrop.

•

11.4, "Transparency Groups," introduces the concept of transparency groups and describes their

properties and behaviour.

•

11.5, "Soft Masks," covers the creation and use of masks to specify position-dependent shape and opacity.

•

11.6, "Specifying Transparency in PDF," describes how transparency properties are represented in a PDF

document.

•

11.7, "Colour Space and Rendering Issues," deals with some specific interactions between transparency

and other aspects of colour specification and rendering.

11.2

Overview of Transparency

The original PDF imaging model paints objects (fills, strokes, text, and images), possibly clipped by a path,

opaquely onto a page. The colour of the page at any point shall be that of the topmost enclosing object,

disregarding any previous objects it may overlap. This effect may be—and often is—realized simply by

rendering objects directly to the page in the order in which they are specified, with each object completely

overwriting any others that it overlaps.

Under the transparent imaging model, all of the objects on a page may potentially contribute to the result.

Objects at a given point may be thought of as forming a transparency stack (or stack for short). The objects

shall be arranged from bottom to top in the order in which they are specified. The colour of the page at each

point shall be determined by combining the colours of all enclosing objects in the stack according to

compositing rules defined by the transparency model.

NOTE 1

The order in which objects are specified determines the stacking order but not necessarily the order in which

the objects are actually painted onto the page. In particular, the transparency model does not require a

conforming reader to rasterize objects immediately or to commit to a raster representation at any time before

rendering the entire stack onto the page. This is important, since rasterization often causes significant loss of

information and precision that is best avoided during intermediate stages of the transparency computation.

A given object shall be composited with a backdrop. Ordinarily, the backdrop consists of the stack of all objects

that have been specified previously. The result of compositing shall then be treated as the backdrop for the

next object. However, within certain kinds of transparency groups (see “Transparency Groups”), a different

backdrop may be chosen.

320

During the compositing of an object with its backdrop, the colour at each point shall be computed using a

specified blend mode, which is a function of both the object’s colour and the backdrop colour. The blend mode

shall determine how colours interact; different blend modes may be used to achieve a variety of useful effects.

A single blend mode shall be in effect for compositing all of a given object, but different blend modes may be

applied to different objects.

Two scalar quantities called shape and opacity mediate compositing of an object with its backdrop.

Conceptually, for each object, these quantities shall be defined at every point in the plane, just as if they were

additional colour components. (In actual practice, they may be obtained from auxiliary sources rather than

being intrinsic to the object.)

Both shape and opacity vary from 0.0 (no contribution) to 1.0 (maximum contribution). At any point where either

the shape or the opacity of an object is equal to 0.0, its colour shall be undefined. At points where the shape is

equal to 0.0, the opacity shall also be undefined. The shape and opacity shall be subject to compositing rules;

therefore, the stack as a whole also has a shape and opacity at each point.

An object’s opacity, in combination with the backdrop’s opacity, shall determine the relative contributions of the

backdrop colour, the object’s colour, and the blended colour to the resulting composite colour. The object’s

shape shall then determine the degree to which the composite colour replaces the backdrop colour. Shape

values of 0.0 and 1.0 identify points that lie outside and inside a conventional sharp-edged object; intermediate

values are useful in defining soft-edged objects.

Shape and opacity are conceptually very similar. In fact, they can usually be combined into a single value,

called alpha, which controls both the colour compositing computation and the fading between an object and its

backdrop. However, there are a few situations in which they shall be treated separately; see 11.4.6, "Knockout

Groups."

NOTE 2

Raster-based implementations may need to maintain a separate shape parameter to do anti-aliasing properly;

it is therefore convenient to have shape as an explicit part of the model.

One or more consecutive objects in a stack may be collected together into a transparency group (often referred

to hereafter simply as a group). The group as a whole may have various properties that modify the compositing

behaviour of objects within the group and their interactions with its backdrop. An additional blend mode, shape,

and opacity may also be associated with the group as a whole and used when compositing it with its backdrop.

Groups may be nested within other groups, forming a tree-structured hierarchy.

EXAMPLE

Figure L.16 in Annex L illustrates the effects of transparency grouping. In the upper two figures, three

coloured circles are painted as independent objects with no grouping. At the upper left, the three objects

are painted opaquely (opacity = 1.0); each object completely replaces its backdrop (including previously

painted objects) with its own colour. At the upper right, the same three independent objects are painted

with an opacity of 0.5, causing them to composite with each other and with the gray and white backdrop.

In the lower two figures, the three objects are combined as a transparency group. At the lower left, the

individual objects have an opacity of 1.0 within the group, but the group as a whole is painted in the

Normal blend mode with an opacity of 0.5. The objects thus completely overwrite each other within the

group, but the resulting group then composites transparently with the gray and white backdrop. At the

lower right, the objects have an opacity of 0.5 within the group and thus composite with each other. The

group as a whole is painted against the backdrop with an opacity of 1.0 but in a different blend mode

(HardLight), producing a different visual effect.

The colour result of compositing a group may be converted to a single-component luminosity value and treated

as a soft mask. Such a mask may then be used as an additional source of shape or opacity values for

subsequent compositing operations. When the mask is used as a shape, this technique is known as soft

clipping; it is a generalization of the current clipping path in the opaque imaging model (see “Clipping Path

Operators”).

The notion of current page is generalized to refer to a transparency group consisting of the entire stack of

objects placed on the page, composited with a backdrop that is pure white and fully opaque. Logically, this

entire stack shall then be rasterized to determine the actual pixel values to be transmitted to the output device.

321

NOTE 3

In contexts where a PDF page is treated as a piece of artwork to be placed on some other page it is treated not

as a page but as a group, whose backdrop may be defined differently from that of a page.

11.3

Basic Compositing Computations

11.3.1

General

This sub-clause describes the basic computations for compositing a single object with its backdrop. These

computations are extended in 11.4, "Transparency Groups," to cover groups consisting of multiple objects.

11.3.2

Basic Notation for Compositing Computations

In general, variable names in this clause consisting of a lowercase letter denote a scalar quantity, such as an

opacity. Uppercase letters denote a value with multiple scalar components, such as a colour. In the descriptions

of the basic colour compositing computations, colour values are generally denoted by the letter C, with a

mnemonic subscript indicating which of several colour values is being referred to; for instance, C_s stands for

“source colour.” Shape and opacity values are denoted respectively by the letters f (for “form factor”) and q (for

“opaqueness”)—again with a mnemonic subscript, such as q_s for “source opacity.” The symbol α (alpha) stands

for a product of shape and opacity values.

In certain computations, one or more variables may have undefined values; for instance, when opacity is equal

to zero, the corresponding colour is undefined. A quantity can also be undefined if it results from division by

zero. In any formula that uses such an undefined quantity, the quantity has no effect on the ultimate result

because it is subsequently multiplied by zero or otherwise cancelled out. It is significant that while any arbitrary

value may be chosen for such an undefined quantity, the computation shall not malfunction because of

exceptions caused by overflow or division by zero. The further convention that 0 ÷ 0 = 0 should also be

adopted.

11.3.3

Basic Compositing Formula

The primary change in the imaging model to accommodate transparency is in how colours are painted. In the

transparent model, the result of painting (the result colour) is a function of both the colour being painted (the

source colour) and the colour it is painted over (the backdrop colour). Both of these colours may vary as a

function of position on the page; however, this sub-clause focuses on some fixed point on the page and

assumes a fixed backdrop and source colour.

This computation uses two other parameters: alpha, which controls the relative contributions of the backdrop

and source colours, and the blend function, which specifies how they shall be combined in the painting

operation. The resulting basic colour compositing formula (or just basic compositing formula for short) shall

determine the result colour produced by the painting operation:

⎛

α_s⎞

α_s

C_r

⎜1

- -----⎟

C_b

-----

×[

(

α_b

)× C_s + α_b× B(C_b, _Cs

)]

α_r

⎝

⎠

where the variables have the meanings shown in Table 135.

Table 135 - Variables used in the basic compositing formula

Variable

Meaning

C_b

Backdrop colour

Source colour

C_s

C_r

Result colour

322

Table 135 - Variables used in the basic compositing formula (continued)

Variable

Meaning

α_b

Backdrop alpha

α_s

Source alpha

α_r

Result alpha

B(C_b,C_s)

Blend function

This formula represents a simplified form of the compositing formula in which the shape and opacity values are

combined and represented as a single alpha value; the more general form is presented later. This function is

based on the over operation defined in the article “Compositing Digital Images,” by Porter and Duff (see

the Bibliography), extended to include a blend mode in the region of overlapping coverage. The following sub-

clauses elaborate on the meaning and implications of this formula.

11.3.4

Blending Colour Space

The compositing formula shown in 11.3.3, "Basic Compositing Formula," represents a vector function: the

colours it operates on are represented in the form of n-element vectors, where n denotes the number of

components required by the colour space in used in the compositing process. The ith component of the result

colour C_r shall be obtained by applying the compositing formula to the ith components of the constituent

colours C_b , C_s , and B (C_b, C_s ). The result of the computation thus depends on the colour space in which the

colours are represented. For this reason, the colour space used for compositing, called the blending colour

space, is explicitly made part of the transparent imaging model. When necessary, backdrop and source colours

shall be converted to the blending colour space before the compositing computation.

Of the PDF colour spaces described in Section 8.6, the following shall be supported as blending colour spaces:

•

DeviceGray

•

DeviceRGB

•

DeviceCMYK

•

CalGray

•

CalRGB

•

ICCBased colour spaces equivalent to the preceding (including calibrated CMYK)

The Lab space and ICCBased spaces that represent lightness and chromaticity separately (such as L*a*b*,

L*u*v*, and HSV) shall not be used as blending colour spaces because the compositing computations in such

spaces do not give meaningful results when applied separately to each component. In addition, an ICCBased

space used as a blending colour space shall be bidirectional; that is, the ICC profile shall contain both AToB

and BToA transformations.

The blending colour space shall be consulted only for process colours. Although blending may also be done on

individual spot colours specified in a Separation or DeviceN colour space, such colours shall not be converted

to a blending colour space (except in the case where they first revert to their alternate colour space, as

described under Section 8.6.6.4 and “DeviceN Colour Spaces”). Instead, the specified colour components shall

be blended individually with the corresponding components of the backdrop.

The blend functions for the various blend modes are defined such that the range for each colour component

shall be 0.0 to 1.0 and that the colour space shall be additive. When performing blending operations in

323

subtractive colour spaces (DeviceCMYK, Separation, and DeviceN), the colour component values shall be

complemented (subtracted from 1.0) before the blend function is applied and the results of the function shall

then be complemented back before being used.

NOTE

This adjustment makes the effects of the various blend modes numerically consistent across all colour spaces.

However, the actual visual effect produced by a given blend mode still depends on the colour space. Blending

in a device colour space produces device-dependent results, whereas in a CIE-based space it produces

results that are consistent across all devices. See 11.7, "Colour Space and Rendering Issues," for additional

details concerning colour spaces.

11.3.5

Blend Mode

In principle, any function of the backdrop and source colours that yields another colour, C_r, for the result may be

used as a blend function B (C_b , C_s), in the compositing formula to customize the blending operation. PDF

defines a standard set of named blend functions, or blend modes, listed in Tables 136 and 137. Figures L.18

and L.19 in Annex L illustrate the resulting visual effects for RGB and CMYK colours, respectively.

A blend mode is termed separable if each component of the result colour is completely determined by the

corresponding components of the constituent backdrop and source colours—that is, if the blend mode function

B is applied separately to each set of corresponding components:

c_r

B(c_b, _cs

)

where the lowercase variables c_r, c

, and c

, and C_s ,

s denote corresponding components of the colours Cr, Cb

expressed in additive form. A separable blend mode may be used with any colour space, since it applies

independently to any number of components. Only separable blend modes shall be used for blending spot

colours.

NOTE 1

Theoretically, a blend mode could have a different function for each colour component and still be separable;

however, none of the standard PDF blend modes have this property.

Table 136 lists the standard separable blend modes available in PDF and the algorithms/formulas that shall be

used in the calculation of blended colours.

Table 136 - Standard separable blend modes

Name

Result

Normal

B(c_b,c_s) = c_s

NOTE

Selects the source colour, ignoring the backdrop.

Compatible

Same as Normal. This mode exists only for compatibility and should not be used.

Multiply

B(c_b,c_s) = c_b× c_s

NOTE 1

Multiplies the backdrop and source colour values.

NOTE 2

The result colour is always at least as dark as either of the two

constituent colours. Multiplying any colour with black produces black;

multiplying with white leaves the original colour unchanged. Painting

successive overlapping objects with a colour other than black or white

produces progressively darker colours.

324

Table 136 - Standard separable blend modes (continued)

Name

Result

Screen

B(c_b,c_s)

– [

(

c_b

)

(

–

c_s

)]

c_b + c_s

(

c_b × c_s

)

NOTE 3

Multiplies the complements of the backdrop and source colour values,

then complements the result.

NOTE 4

The result colour is always at least as light as either of the two

constituent colours. Screening any colour with white produces white;

screening with black leaves the original colour unchanged. The effect

is similar to projecting multiple photographic slides simultaneously

onto a single screen.

Overlay

(

)

HardLight(c_s, c_b)

NOTE 5

Multiplies or screens the colours, depending on the backdrop colour

value. Source colours overlay the backdrop while preserving its

highlights and shadows. The backdrop colour is not replaced but is

mixed with the source colour to reflect the lightness or darkness of the

backdrop.

Darken

B(c_b,c_s)

min(c_b, c_s

)

NOTE 6

Selects the darker of the backdrop and source colours.

NOTE 7

The backdrop is replaced with the source where the source is darker;

otherwise, it is left unchanged.

Lighten

B(c_b,c_s)

max(c_b, c_s

)

NOTE 8

Selects the lighter of the backdrop and source colours.

NOTE 9

The backdrop is replaced with the source where the source is lighter;

otherwise, it is left unchanged.

ColorDodge

min(1, _cb

⁄

(

–

c_s

))

if c_s

⎧

B(c_b,c_s)

⎨

if c

⎩

NOTE 10

Brightens the backdrop colour to reflect the source colour. Painting

with black produces no changes.

ColorBurn

–

min(1,

(

c_b

)⁄ _cs)

if c_s

⎧

B(c_b,c_s)

⎨

⎩0

if c

NOTE 11

Darkens the backdrop colour to reflect the source colour. Painting

with white produces no change.

HardLight

Multiply(c_b, 2

c_s)

if c_s ≤ 0.5

⎧

B(c_b,c_s)

⎨

Screen(c

c_s

if c_s > 0.5

⎩

b, 2

NOTE 12

Multiplies or screens the colours, depending on the source colour

value. The effect is similar to shining a harsh spotlight on the

backdrop.

325

Table 136 - Standard separable blend modes (continued)

Name

Result

SoftLight

c_b

–

(

–

c_s

)× c_b

(

–

c_b

)

if c_s ≤ 0.5

⎧

(

)

⎨

⎩c

(

c_s

)

(

) c_b

)

if c_s > 0.5

where

⎧((16 × x - 12) × x + 4) × x

if x ≤ 0.25

D(x)

⎨

⎩

if x > 0.25

NOTE 13

Darkens or lightens the colours, depending on the source colour

value. The effect is similar to shining a diffused spotlight on the

backdrop.

Difference

B(c_b,c_s)

c_b – c_s

NOTE 14

Subtracts the darker of the two constituent colours from the lighter

colour:

NOTE 15

Painting with white inverts the backdrop colour; painting with black

produces no change.

Exclusion

(

)

c_b + c_s

–

c_b

NOTE 16

Produces an effect similar to that of the Difference mode but lower in

contrast. Painting with white inverts the backdrop colour; painting with

black produces no change.

Table 137 lists the standard nonseparable blend modes. Since the nonseparable blend modes consider all

colour components in combination, their computation depends on the blending colour space in which the

components are interpreted. They may be applied to all multiple-component colour spaces that are allowed as

blending colour spaces (see “Blending Colour Space”).

NOTE 2

All of these blend modes conceptually entail the following steps:

a) Convert the backdrop and source colours from the blending colour space to an intermediate HSL (hue-

saturation-luminosity) representation.

b) Create a new colour from some combination of hue, saturation, and luminosity components selected from

the backdrop and source colours.

c) Convert the result back to the original (blending) colour space.

However, the following formulas given do not actually perform these conversions. Instead, they start with

whichever colour (backdrop or source) is providing the hue for the result; then they adjust this colour to have

the proper saturation and luminosity.

The nonseparable blend mode formulas make use of several auxiliary functions. These functions operate on

colours that are assumed to have red, green, and blue components. Blending of CMYK colour spaces requires

special treatment, as described in this sub-clause.

These functions shall have the following definitions:

Lum(C)

0.3

C_red

0.59

C_green

0.11

C_blue

326

SetLum(C, l)

let d

Lum(C)

C_red

C_red + d

C_green

C_green + d

C_blue

C_blue + d

returnClipColor(C)

ClipColor(C)

let l

Lum(C)

let n

min(C_red, C_green, C_blue)

let x

max(C_red, C_green, C_blue)

if n

0.0

C_red

(((

C_red

)×l)⁄(l-n))

C_green

(((

C_green

)×l)⁄(l-n))

C_blue

(((

C_blue

)×l)⁄(l-n))

if x

1.0

C_red

(((

C_red

)×(1-l))⁄(x-l))

C_green

(((

C_green

)×(1-l))⁄(x-l))

C_blue

(((

C_blue

)×(1-l))⁄(x-l))

return C

Sat(C)

max(C_red, C_green, C_blue) min(Cred, Cgreen, Cblue)

The subscripts min, mid, and max (in the next function) refer to the colour components having the minimum,

middle, and maximum values upon entry to the function.

SetSat(C, s)

if C_max > Cmin

C_mid

(

C_mid C_min

)×s)⁄(Cmax – Cmin

))

C_max

else

C_mid = Cmax

0.0

C_min

0.0

return C

Table 137 - Standard nonseparable blend modes

Name

Result

Hue

B(C_b,C_s) = SetLum(SetSa

(

)), Lum(Cb))

NOTE 1

Creates a colour with the hue of the source colour and the saturation

and luminosity of the backdrop colour.

Saturation

B(C_b,C_s) = SetLum(SetSa

(

)), Lum(Cb))

NOTE 2

Creates a colour with the saturation of the source colour and the hue

and luminosity of the backdrop colour. Painting with this mode in an

area of the backdrop that is a pure gray (no saturation) produces no

change.

327

Table 137 - Standard nonseparable blend modes (continued)

Name

Result

Color

B(C_b,C_s) = SetLum(C_s,Lum(C_b))

NOTE 3

Creates a colour with the hue and saturation of the source colour and

the luminosity of the backdrop colour. This preserves the gray levels

of the backdrop and is useful for colouring monochrome images or

tinting colour images.

Luminosity

B(C_b,C_s) = SetLum(C_b,Lu

(

))

NOTE 4

Creates a colour with the luminosity of the source colour and the hue

and saturation of the backdrop colour. This produces an inverse effect

to that of the Color mode.

The formulas in this sub-clause apply to RGB spaces. Blending in CMYK spaces (including both DeviceCMYK

and ICCBased calibrated CMYK spaces) shall be handled in the following way:

•

The C, M, and Y components shall be converted to their complementary R, G, and B components in the

usual way. The preceding formulas shall be applied to the RGB colour values. The results shall be

converted back to C, M, and Y.

•

For the K component, the result shall be the K component of C_b for the Hue, Saturation, and Color blend

modes; it shall be the K component of C_s for the Luminosity blend mode.

11.3.6

Interpretation of Alpha

The colour compositing formula

⎛

α_s⎞

α_s

C_r

⎜1

- -----⎟

C_b

-----

×[

(

α_b

)× C_s + α_b× B(C_b, _Cs

)]

α_r

⎝

⎠

produces a result colour that is a weighted average of the backdrop colour, the source colour, and the blended

B (C_b , C_s ) term, with the weighting determined by the backdrop and source alphas α_β and α_s . For the simplest

blend mode, Normal, defined by

B(c_b,

c_s

)

c_s

the compositing formula collapses to a simple weighted average of the backdrop and source colours, controlled

by the backdrop and source alpha values. For more interesting blend functions, the backdrop and source

alphas control whether the effect of the blend mode is fully realized or is toned down by mixing the result with

the backdrop and source colours.

The result alpha, α_ρ , actually represents a computed result, described in 11.3.7, "Shape and Opacity

Computations." The result colour shall be normalized by the result alpha, ensuring that when this colour and

alpha are subsequently used together in another compositing operation, the colour’s contribution is correctly

represented.

NOTE 1

If α_ρ is zero, the result colour is undefined.

NOTE 2

The preceding formula represents a simplification of the following formula, which presents the relative

contributions of backdrop, source, and blended colours in a more straightforward way:

α_r × C_r

[

(

α_s

)× α_b× C_b

]

[

(

α_b

)× α_s× C_s

]

α_b

α_s

(

C_b

C_s

)

328

(The simplification requires a substitution based on the alpha compositing formula, which is presented in the

next sub-clause.) Thus, mathematically, the backdrop and source alphas control the influence of the backdrop

and source colours, respectively, while their product controls the influence of the blend function. An alpha

value of α_s = 0.0 or α_β = 0.0 results in no blend mode effect; setting α_s = 1.0 and α_β = 1.0 results in maximum

blend mode effect.

11.3.7

Shape and Opacity Computations

11.3.7.1

General

As stated earlier, the alpha values that control the compositing process shall be defined as the product of

shape and opacity:

α_b = f_b × q_b

α_r = f_r × q_r

α_s = f_s × q_s

This sub-clause examines the various shape and opacity values individually. Once again, keep in mind that

conceptually these values are computed for every point on the page.

11.3.7.2

Source Shape and Opacity

Shape and opacity values may come from several sources. The transparency model provides for three

independent sources for each. However, the PDF representation imposes some limitations on the ability to

specify all of these sources independently (see “Specifying Shape and Opacity”).

•

Object shape. Elementary objects such as strokes, fills, and text have an intrinsic shape, whose value shall

be 1.0 for points inside the object and 0.0 outside. Similarly, an image with an explicit mask (see “Explicit

Masking”) has a shape that shall be 1.0 in the unmasked portions and 0.0 in the masked portions. The

shape of a group object shall be the union of the shapes of the objects it contains.

NOTE 1

Mathematically, elementary objects have “hard” edges, with a shape value of either 0.0 or 1.0 at every point.

However, when such objects are rasterized to device pixels, the shape values along the boundaries may be

anti-aliased, taking on fractional values representing fractional coverage of those pixels. When such anti-

aliasing is performed, it is important to treat the fractional coverage as shape rather than opacity.

•

Mask shape. Shape values for compositing an object may be taken from an additional source, or soft

mask, independent of the object itself, as described in 11.5, "Soft Masks."

NOTE 2

The use of a soft mask to modify the shape of an object or group, called soft clipping, can produce effects such

as a gradual transition between an object and its backdrop, as in a vignette.

•

Constant shape. The source shape may be modified at every point by a scalar shape constant.

NOTE 3

This is merely a convenience, since the same effect could be achieved with a shape mask whose value is the

same everywhere.

•

Object opacity. Elementary objects have an opacity of 1.0 everywhere. The opacity of a group object shall

be the result of the opacity computations for all of the objects it contains.

•

Mask opacity. Opacity values, like shape values, may be provided by a soft mask independent of the object

being composited.

•

Constant opacity. The source opacity may be modified at every point by a scalar opacity constant.

NOTE 4

It is useful to think of this value as the “current opacity,” analogous to the current colour used when painting

elementary objects.

329

All of the shape and opacity inputs shall have values in the range 0.0 to 1.0 (inclusive), with a default value of

1.0.

The three shape inputs shall be multiplied together, producing an intermediate value called the source shape.

f_s

f_j

f_m × f_k

The three opacity inputs shall be multiplied together, producing an intermediate value called the source opacity.

q_s

q_j × q_m × q_k

Where the variables have the meanings shown in Table 138.

Table 138 - Variables used in the source shape and opacity formulas

Variable

Meaning

f_s

Source shape

f_j

Object shape

f_m

Mask shape

f_k

Constant shape

q_s

Source opacity

q_j

Object opacity

q_m

Mask opacity

q_k

Constant opacity

NOTE 5

The effect of each of these inputs is that the painting operation becomes more transparent as the input values

decreases.

When an object is painted with a tiling pattern, the object shape and object opacity for points in the object’s

interior are determined by those of corresponding points in the pattern, rather than being 1.0 everywhere (see

“Patterns and Transparency”).

11.3.7.3

Result Shape and Opacity

In addition to a result colour, the painting operation also shall compute an associated result shape and result

opacity. These computations shall be based on the union function

Union ( b, s ) = 1 - [(1 - b) × (1 - s)]

= b + s - (b×s)

where b and s shall be the backdrop and source values to be composited.

NOTE 1

This is a generalization of the conventional concept of union for opaque shapes, and it can be thought of as an

“inverted multiplication”—a multiplication with the inputs and outputs complemented. The result tends toward

1.0: if either input is 1.0, the result is 1.0.

The result shape and opacity shall be given by

330

f_r

Union(f_b, f_s

)

Union(f_b × q_b, f_s × q_s )

q_r

= ---------------------------------------------------------

where the variables have the meanings shown in Table 139.

Table 139 - Variables used in the result shape and opacity formulas

Variable

Meaning

f_r

Result shape

f_b

Backdrop shape

f_s

Source shape

q_r

Result opacity

Backdrop opacity

q_b

q_s

Source opacity

These formulas shall be interpreted as follows:

•

The result shape shall be the union of the backdrop and source shapes.

•

The result opacity shall be the union of the backdrop and source opacities, weighted by their respective

shapes. The result shall then be divided by (normalized by) the result shape.

NOTE 2

Since alpha is just the product of shape and opacity, it can easily be shown that

α_r

Union(αb,

α_s)

This formula can be used whenever the independent shape and opacity are not needed.

11.3.8

Summary of Basic Compositing Computations

This sub-clause is a summary of all the computations presented in this sub-clause. They are given in an order

such that no variable is used before it is computed; also, some of the formulas have been rearranged to

simplify them. See Tables 135, 138, and 139 for the meanings of the variables used in these formulas.

Union ( b, s ) = 1 - [(1 - b) × (1 - s)]

= b + s - (b×s)

f_s

f_j

f_m × f_k

q_s

q_j

q_m ×qk

f_r

Union(f_b,

f_s

)

331

α_b = f_b × q_b

α_s

f_s

q_s

α_r = Union(α_b, α_s )

α_r

= -----

⎛

α_s⎞

α_s

C_r

⎜1

- -----⎟

C_b

-----

×[

(

α_b

)× C_s + α_b× B(C_b, _Cs

)]

α_r

⎝

⎠

11.4

Transparency Groups

11.4.1

General

A transparency group is a sequence of consecutive objects in a transparency stack that shall be collected

together and composited to produce a single colour, shape, and opacity at each point. The result shall then be

treated as if it were a single object for subsequent compositing operations. Groups may be nested within other

groups to form a tree-structured group hierarchy.

NOTE

This facilitates creating independent pieces of artwork, each composed of multiple objects, and then combining

them, possibly with additional transparency effects applied during the combination.

The objects contained within a group shall be treated as a separate transparency stack called the group stack.

The objects in the stack shall be composited against an initial backdrop (discussed later), producing a

composite colour, shape, and opacity for the group as a whole. The result is an object whose shape is the

union of the shapes of its constituent objects and whose colour and opacity are the result of the compositing

operations. This object shall then be composited with the group’s backdrop in the usual way.

In addition to its computed colour, shape, and opacity, the group as a whole may have several further attributes:

•

All of the input variables that affect the compositing computation for individual objects may also be applied

when compositing the group with its backdrop. These variables include mask and constant shape, mask

and constant opacity, and blend mode.

•

The group may be isolated or non-isolated, which shall determine the initial backdrop against which its

stack is composited.

•

The group may be knockout or non-knockout, which shall determine whether the objects within its stack

are composited with one another or only with the group’s backdrop.

•

An isolated group may specify its own blending colour space, independent of that of the group’s backdrop.

•

Instead of being composited onto the current page, a group’s results may be used as a source of shape or

opacity values for creating a soft mask (see “Soft Masks”).

11.4.2

Notation for Group Compositing Computations

This sub-clause introduces some notation for dealing with group compositing. Subsequent sub-clauses

describe the group compositing formulas for a non-isolated, non-knockout group and the special properties of

isolated and knockout groups.

332

Since we are now dealing with multiple objects at a time, it is useful to have some notation for distinguishing

among them. Accordingly, the variables introduced earlier are altered to include a second-level subscript

denoting an object’s position in the transparency stack.

stands for the source colour of the ith object in the stack. The subscript 0 represents the initial backdrop;

C_s

subscripts 1 to n denote the bottommost to topmost objects in an n-element stack. In addition, the subscripts b

and r are dropped from the variables C_b , f_β , q_β , α_β , C_r, f_ρ, q_ρ, and α_ρ ; other variables retain their mnemonic

subscripts.

These conventions permit the compositing formulas to be restated as recurrence relations among the elements

of a stack. For instance, the result of the colour compositing computation for object i is denoted by C_i (formerly

C_r ). This computation takes as one of its inputs the immediate backdrop colour, which is the result of the colour

compositing computation for object i − 1; this is denoted by Ci − 1 (formerly C_b ).

The revised formulas for a simple n-element stack (not including any groups) shall be, for i = 1, … , n:

f_s

f_j

f_m

f_k

q_s

q_j

q_m

q_k

α_s

f_s

q_s

α_i

Union(αi-1,

α_s

)

f_i

Union(fi-1,

f_s

)

α_i

q_i

= -----

α_s

⎛

⎞

C_i

⎜1

- ------

⎟

C_i-1

×[(

α_i-1

)× C_s

α_i-1

B_i (Ci-1

)]

s_i

α_i

⎝

⎠

where the variables have the meanings shown in Table 140.

NOTE

Compare these formulas with those shown in 11.3.8, "Summary of Basic Compositing Computations."

Table 140 - Revised variables for the basic compositing formulas

Variable

Meaning

f_s

Source shape for object i

f_j

Object shape for object i

Mask shape for object i

f_m

f_k

Constant shape for object i

f_i

Result shape after compositing object i

333

Table 140 - Revised variables for the basic compositing formulas (continued)

Variable

Meaning

q_s

Source opacity for object i

q_j

Object opacity for object i

q_m

Mask opacity for object i

Constant opacity for object i

q_k

q_i

Result opacity after compositing object i

α_s

Source alpha for object i

α_i

Result alpha after compositing object i

C_s

Source colour for object i

C_i

Result colour after compositing object i

B_i(Ci-1, _Cs

)

Blend function for object i

11.4.3

Group Structure and Nomenclature

As stated earlier, the elements of a group shall be treated as a separate transparency stack, referred to as the

group stack. These objects shall be composited against a selected initial backdrop and the resulting colour,

shape, and opacity shall then be treated as if they belonged to a single object. The resulting object is in turn

composited with the group’s backdrop in the usual way.

NOTE

This computation entails interpreting the stack as a tree. For an n-element group that begins at position i in the

stack, it treats the next n objects as an n-element substack, whose elements are given an independent

numbering of 1 to n. These objects are then removed from the object numbering in the parent (containing)

stack and replaced by the group object, numbered i, followed by the remaining objects to be painted on top of

the group, renumbered starting at i + 1. This operation applies recursively to any nested subgroups.

The term element (denoted Ei ) refers to a member of some group; it can be either an individual object or a

contained subgroup.

From the perspective of a particular element in a nested group, there are three different backdrops of interest:

•

The group backdrop is the result of compositing all elements up to but not including the first element in the

group. (This definition is altered if the parent group is a knockout group; see 11.4.6, "Knockout Groups")

•

The initial backdrop is a backdrop that is selected for compositing the group’s first element. This is either

the same as the group backdrop (for a non-isolated group) or a fully transparent backdrop (for an isolated

group).

•

The immediate backdrop is the result of compositing all elements in the group up to but not including the

current element.

When all elements in a group have been composited, the result shall be treated as if the group were a single

object, which shall then be composited with the group backdrop. This operation shall occur whether the initial

334

backdrop chosen for compositing the elements of the group was the group backdrop or a transparent backdrop.

A conforming reader shall ensure that the backdrop’s contribution to the overall result is applied only once.

11.4.4

Group Compositing Computations

The colour and opacity of a group shall be defined by the group compositing function:

〈 C, f, α 〉

Composite(C₀, α₀,

)

where the variables have the meanings shown in Table 141.

Table 141 - Arguments and results of the group compositing function

Variable

Meaning

The transparency group: a compound object consisting of all

elements E₁, … , E_n of the group—the n constituent objects’

colours, shapes, opacities, and blend modes

C₀

Colour of the group’s backdrop

Computed colour of the group, which shall be used as the

source colour when the group is treated as an object

Computed shape of the group, which shall be used as the

object shape when the group is treated as an object

α₀

Alpha of the group’s backdrop

Computed alpha of the group, which shall be used as the

object alpha when the group is treated as an object

NOTE 1

The opacity is not given explicitly as an argument or result of this function. Almost all of the computations use

the product of shape and opacity (alpha) rather than opacity alone; therefore, it is usually convenient to work

directly with shape and alpha rather than shape and opacity. When needed, the opacity can be computed by

dividing the alpha by the associated shape.

The result of applying the group compositing function shall then be treated as if it were a single object, which in

turn is composited with the group’s backdrop according to the formulas defined in this sub-clause. In those

formulas, the colour, shape, and alpha (C, f, and α) calculated by the group compositing function shall be used,

respectively, as the source colour C_s , the object shape f_j , and the object alpha α_j.

The group compositing formulas for a non-isolated, non-knockout group are defined as follows:

•

Initialization:

f_g

= 0.0

g₀

•

For each group element E_i ∈ G (i = 1, … , n):

⎧

Composite(Ci-1,

α_i-1,

E_i)

if E_i is a group

〈

〉

⎨

Cs_i, fj_i, αj_i

⎩

intrinsic color, shape, and (shape × opacity) of E_i

otherwise

f_s

f_j

f_m

k_i

α_s

α_j

( fm

q_m

)

( fk

)

k_i

335

f_g

Union(fg

f_s

)

i-1

α_g

Union(α_g

α_s

)

i-1

α_i

Union(α₀,αg

)

α_s

⎛

⎞

C_i

⎜1

- ------

⎟

C_i-1

×((

α_i-1

)× C_s

α_i-1

B_i (Ci-1

))

s_i

α_i

⎝

⎠

•

Result:

⎛

α₀

⎞

C = C_n + (Cn –C0₎

⎜

-------- –α₀⎟

⎝

g_n

⎠

f_g

α = α_g

where the variables have the meanings shown in Table 142 (in addition to those in Table 141).

For an element E

C_s

f_j

, and

α_j

are intrinsic

i that is an elementary object, the colour, shape, and alpha values

attributes of the object. For an element that is a group, the group compositing function shall be applied

recursively to the subgroup and the resulting C, f, and α values shall be used for itsCs,

f_j

, and

α_j

in the

calculations for the parent group.

Table 142 - Variables used in the group compositing formulas

Variable

Meaning

E_i

Element i of the group: a compound variable representing the

element’s colour, shape, opacity, and blend mode

f_s

Source shape for element E_i

f_j

Object shape for element E_i

f_m

Mask shape for element E_i

f_k

Constant shape for element E_i

f_g

Group shape: the accumulated source shapes of group

elements E₁ to Ei , excluding the initial backdrop

q_m

Mask opacity for element E_i

Constant opacity for element E_i

q_k

α_s

Source alpha for element E_i

α_j

Object alpha for element Ei : the product of its object shape

and object opacity

336

Table 142 - Variables used in the group compositing formulas (continued)

Variable

Meaning

α_g

Group alpha: the accumulated source alphas of group

elements E₁ to E_i, excluding the initial backdrop

α_i

Accumulated alpha after compositing element E_i , including

the initial backdrop

C_s

Source colour for element E_i

C_i

Accumulated colour after compositing element E_i , including

the initial backdrop

B_i(Ci-1, _Cs

)

Blend function for element E_i

NOTE 2

The elements of a group are composited onto a backdrop that includes the group’s initial backdrop. This is

done to achieve the correct effects of the blend modes, most of which are dependent on both the backdrop and

source colours being blended. This feature is what distinguishes non-isolated groups from isolated groups,

discussed in the next sub-clause.

NOTE 3

Special attention should be directed to the formulas at the end that compute the final results C, f, and α, of the

group compositing function. Essentially, these formulas remove the contribution of the group backdrop from

the computed results. This ensures that when the group is subsequently composited with that backdrop

(possibly with additional shape or opacity inputs or a different blend mode), the backdrop’s contribution is

included only once.

For colour, the backdrop removal is accomplished by an explicit calculation, whose effect is essentially the

reverse of compositing with the Normal blend mode. The formula is a simplification of the following formulas,

which present this operation more intuitively:

α_g

)× α₀

φ_b

= --------------------------------------

Union(α

)

C_n – φ_b × C₀

= -------------------------------

where

φ_b

is the backdrop fraction, the relative contribution of the backdrop colour to the overall colour.

NOTE 4

For shape and alpha, backdrop removal is accomplished by maintaining two sets of variables to hold the

accumulated values. There is never any need to compute the corresponding complete shape, f_i , that includes

the backdrop contribution.

The group shape and alpha,

f_g

and

α_g

, shall accumulate only the shape and alpha of the group elements,

excluding the group backdrop. Their final values shall become the group results returned by the group

compositing function. The complete alpha, α_i , includes the backdrop contribution as well; its value is used in

the colour compositing computations.

NOTE 5

As a result of these corrections, the effect of compositing objects as a group is the same as that of compositing

them separately (without grouping) if the following conditions hold:

The group is non-isolated and has the same knockout attribute as its parent group (see 11.4.5, "Isolated

Groups," and “Knockout Groups”).

When compositing the group’s results with the group backdrop, the Normal blend mode is used, and the

shape and opacity inputs are always 1.0.

337

11.4.5

Isolated Groups

An isolated group is one whose elements shall be composited onto a fully transparent initial backdrop rather

than onto the group’s backdrop. The resulting source colour, object shape, and object alpha for the group shall

be therefore independent of the group backdrop. The only interaction with the group backdrop shall occur when

the group’s computed colour, shape, and alpha are composited with it.

In particular, the special effects produced by the blend modes of objects within the group take into account only

the intrinsic colours and opacities of those objects; they shall not be influenced by the group’s backdrop.

EXAMPLE

Applying the Multiply blend mode to an object in the group produces a darkening effect on other objects

lower in the group’s stack but not on the group’s backdrop.

Figure L.17 in Annex L illustrates this effect for a group consisting of four overlapping circles in a light gray

colour (C = M = Y = 0.0; K = 0.15). The circles are painted within the group with opacity 1.0 in the

Multiply blend mode; the group itself is painted against its backdrop in Normal blend mode. In the top

row, the group is isolated and thus does not interact with the rainbow backdrop. In the bottom row, the

group is non-isolated and composites with the backdrop. The figure also illustrates the difference between

knockout and non-knockout groups (see “Knockout Groups”).

NOTE 1

Conceptually, the effect of an isolated group could be represented by a simple object that directly specifies a

colour, shape, and opacity at each point. This flattening of an isolated group is sometimes useful for importing

and exporting fully composited artwork in applications. Furthermore, a group that specifies an explicit blending

colour space shall be an isolated group.

For an isolated group, the group compositing formulas shall be altered by adding one statement to the

initialization:

α₀ = 0.0

if the group is isolated

That is, the initial backdrop on which the elements of the group are composited shall be transparent rather than

inherited from the group’s backdrop.

NOTE 2

This substitution also makes C₀ undefined, but the normal compositing formulas take care of that. Also, the

result computation for C automatically simplifies to C = C_n, since there is no backdrop contribution to be

factored out.

11.4.6

Knockout Groups

In a knockout group, each individual element shall be composited with the group’s initial backdrop rather than

with the stack of preceding elements in the group. When objects have binary shapes (1.0 for inside, 0.0 for

outside), each object shall overwrite (knocks out) the effects of any earlier elements it overlaps within the same

group. At any given point, only the topmost object enclosing the point shall contribute to the result colour and

opacity of the group as a whole.

EXAMPLE

Figure L.17 in Annex L about 11.4.5, "Isolated Groups," illustrates the difference between knockout and

non-knockout groups. In the left column, the four overlapping circles are defined as a knockout group and

therefore do not composite with each other within the group. In the right column, the circles form a non-

knockout group and thus do composite with each other. In each column, the upper and lower figures

depict an isolated and a non-isolated group, respectively.

NOTE 1

This model is similar to the opaque imaging model, except that the “topmost object wins” rule applies to both

the colour and the opacity. Knockout groups are useful in composing a piece of artwork from a collection of

overlapping objects, where the topmost object in any overlap completely obscures those beneath. At the same

time, the topmost object interacts with the group’s initial backdrop in the usual way, with its opacity and blend

mode applied as appropriate.

The concept of knockout is generalized to accommodate fractional shape values. In that case, the immediate

backdrop shall be only partially knocked out and shall be replaced by only a fraction of the result of compositing

the object with the initial backdrop.

338

The restated group compositing formulas deal with knockout groups by introducing a new variable, b, which is

a subscript that specifies which previous result to use as the backdrop in the compositing computations: 0 in a

knockout group or i − 1 in a non-knockout group. When b = i − 1, the formulas simplify to the ones given in

11.4.4, "Group Compositing Computations."

In the general case, the computation shall proceed in two stages:

a) Composite the source object with the group’s initial backdrop, disregarding the object’s shape and using a

source shape value of 1.0 everywhere. This produces unnormalized temporary alpha and colour results, α_t

and C_t .

NOTE 2

For colour, this computation is essentially the same as the unsimplified colour compositing formula given in

11.3.6, "Interpretation of Alpha," but using a source shape of 1.0.

α_t

Union(α_g

q_s

)

C_t

q_s

)× α_b× C_b

q_s

×((

α_b

)× C_s

α_b ×Bi (Cb_,Cs

))

b) Compute a weighted average of this result with the object’s immediate backdrop, using the source shape

as the weighting factor. Then normalize the result colour by the result alpha:

α_g

f_s

)× α_g

f_s

α_t

i-1

α_i

Union(α₀,αg

)

f_s

)× αi-1

C_i-1

f_s

C_t

C_i

= -----------------

This averaging computation shall be performed for both colour and alpha.

NOTE 3

The preceding formulas show this averaging directly. The formulas in 11.4.8, "Summary of Group Compositing

Computations," are slightly altered to use source shape and alpha rather than source shape and opacity,

avoiding the need to compute a source opacity value explicitly.

NOTE 4

C_t in Group Compositing Computations is slightly different from the preceding C_t: it is premultiplied by

f_s

NOTE 5

The extreme values of the source shape produce the straightforward knockout effect. That is, a shape value of

1.0 (inside) yields the colour and opacity that result from compositing the object with the initial backdrop. A

shape value of 0.0 (outside) leaves the previous group results unchanged.

The existence of the knockout feature is the main reason for maintaining a separate shape value rather than

only a single alpha that combines shape and opacity. The separate shape value shall be computed in any

group that is subsequently used as an element of a knockout group.

A knockout group may be isolated or non-isolated; that is, isolated and knockout are independent attributes. A

non-isolated knockout group composites its topmost enclosing element with the group’s backdrop. An isolated

knockout group composites the element with a transparent backdrop.

NOTE 6

When a non-isolated group is nested within a knockout group, the initial backdrop of the inner group is the

same as that of the outer group; it is not the immediate backdrop of the inner group. This behaviour, although

perhaps unexpected, is a consequence of the group compositing formulas when b = 0.

339

11.4.7

Page Group

All of the elements painted directly onto a page—both top-level groups and top-level objects that are not part of

any group—shall be treated as if they were contained in a transparency group P, which in turn is composited

with a context-dependent backdrop. This group is called the page group.

The page group shall be treated in one of two distinctly different ways:

•

Ordinarily, the page shall be imposed directly on an output medium, such as paper or a display screen. The

page group shall be treated as an isolated group, whose results shall then be composited with a backdrop

colour appropriate for the medium. The backdrop is nominally white, although varying according to the

actual properties of the medium. However, some conforming readers may choose to provide a different

backdrop, such as a checker board or grid to aid in visualizing the effects of transparency in the artwork.

•

A “page” of a PDF file may be treated as a graphics object to be used as an element of a page of some

other document.

EXAMPLE

This case arises, for example, when placing a PDF file containing a piece of artwork produced by a

drawing program into a page layout produced by a layout program. In this situation, the PDF “page” is not

composited with the media colour; instead, it is treated as an ordinary transparency group, which can be

either isolated or non-isolated and is composited with its backdrop in the normal way.

The remainder of this sub-clause pertains only to the first use of the page group, where it is to be imposed

directly on the medium.

The colour C of the page at a given point shall be defined by a simplification of the general group compositing

formula:

〈

C_g,fg,αg

〉

Composite(U, 0, P)

(

α_g

)×W + α_g×Cg

where the variables have the meanings shown in Table 143. The first formula computes the colour and alpha

for the group given a transparent backdrop—in effect, treating P as an isolated group. The second formula

composites the results with the context-dependent backdrop (using the equivalent of the Normal blend mode).

Table 143 - Variables used in the page group compositing formulas

Variable

Meaning

The page group, consisting of all elements E₁, … , E_n in the

page’s top-level stack

C_g

Computed colour of the page group

f_g

Computed shape of the page group

α_g

Computed alpha of the page group

Computed colour of the page

Initial colour of the page

(nominally white but may vary

depending on the properties of the medium or the needs of

the application)

An undefined colour

(which is not used, since the α₀

argument of Composite is 0)

340

If not otherwise specified, the page group’s colour space shall be inherited from the native colour space of the

output device—that is, a device colour space, such as DeviceRGB or DeviceCMYK. An explicit colour space

should be specified, particularly a CIE-based space, to ensure more predictable results of the compositing

computations within the page group. In this case, all page-level compositing shall be done in the specified

colour space, and the entire result shall then be converted to the native colour space of the output device

before being composited with the context-dependent backdrop.

NOTE

This case also arises when the page is not actually being rendered but is converted to a flattened

representation in an opaque imaging model, such as PostScript.

11.4.8

Summary of Group Compositing Computations

This sub-clause is a restatement of the group compositing formulas that also takes isolated groups and

knockout groups into account. See Tables 141 and 142 in 11.4.4, "Group Compositing Computations," for the

meanings of the variables.

〈 C, f, α 〉

Composite(C₀, α₀,

)

Initialization:

f_g

α_g

α₀ = 0

if the group is isolated

For each group element E_i ∈ G (i = 1, … , n):

⎧

if the group is knockout

⎨

⎩i-1

otherwise

⎧

Composite(C_b, α_b, E_i )

if E_i is a group

〈

〉

⎨

Cs_i, fj_i, αj_i

⎩

intrinsic color, shape, and (shape × opacity) of E_i

otherwise

f_s

f_j

f_m

f_k

α_s

α_j

( fm

q_m

)

( fk

)

k_i

f_g

Union(fg

f_s

)

i-1

α_g

f_s

)× α_g

( fs

α_s

)× α_g

α_s

i-1

α_i

Union(α₀,αg

)

C_t

(fs

α_s

)× α_b× C_b + αs

×((

α_b

)× C_s

α_b ×Bi (Cb_,C

)

s_i

f_s

)× αi-1

C_i-1

C_t

C_i = -------------------------------------------------------------------------

α_i

341

Result:

⎛

α₀

⎞

C = C_n + (Cn –C0₎

⎜

-------- –α₀⎟

⎝α

⎠

g_n

f_g

α = α_g

NOTE

Once again, keep in mind that these formulas are in their most general form. They can be significantly

simplified when some sources of shape and opacity are not present or when shape and opacity need not be

maintained separately. Furthermore, in each specific type of group (isolated or not, knockout or not), some

terms of these formulas cancel or drop out. An efficient implementation should use the simplified derived

formulas.

11.5

Soft Masks

11.5.1

General

As stated in earlier sub-clauses, the shape and opacity values used in compositing an object may include

components called the mask shape (f_m) and mask opacity (q_m), which may be supplied in a PDF file from a

source independent of the object. Such an independent source, called a soft mask, defines values that may

vary across different points on the page.

NOTE 1

The word soft emphasizes that the mask value at a given point is not limited to just 0.0 or 1.0 but can take on

intermediate fractional values as well. Such a mask is typically the only means of providing position-dependent

opacity values, since elementary objects do not have intrinsic opacity of their own.

NOTE 2

A mask used as a source of shape values is also called a soft clip, by analogy with the “hard” clipping path of

the opaque imaging model (see Section 8.5.4). The soft clip is a generalization of the hard clip: a hard clip can

be represented as a soft clip having shape values of 1.0 inside and 0.0 outside the clipping path. Everywhere

inside a hard clipping path, the source object’s colour replaces the backdrop; everywhere outside, the

backdrop shows through unchanged. With a soft clip, by contrast, a gradual transition can be created between

an object and its backdrop, as in a vignette.

A mask may be defined by creating a transparency group and painting objects into it, thereby defining colour,

shape, and opacity in the usual way. The resulting group may then be used to derive the mask in either of two

ways, as described in the following sub-clauses.

11.5.2

Deriving a Soft Mask from Group Alpha

In the first method of defining a soft mask, the colour, shape, and opacity of a transparency group G shall be

first computed by the usual formula

〈 C, f, α 〉

Composite(C₀,α0

)

where C₀ and α₀ represent an arbitrary backdrop whose value does not contribute to the eventual result. The

C, f, and α results shall be the group’s colour, shape, and alpha, respectively, with the backdrop factored out.

The mask value at each point shall then be derived from the alpha of the group. The alpha value shall be

passed through a separately specified transfer function, allowing the masking effect to be customized.

NOTE

Since the group’s colour is not used in this case, there is no need to compute it.

342

11.5.3

Deriving a Soft Mask from Group Luminosity

The second method of deriving a soft mask from a transparency group shall begin by compositing the group

with a fully opaque backdrop of a specified colour. The mask value at any given point shall then be defined to

be the luminosity of the resulting colour.

NOTE 1

This allows the mask to be derived from the shape and colour of an arbitrary piece of artwork drawn with

ordinary painting operators.

The colour C used to create the mask from a group G shall be defined by

〈

C_g,fg,αg

〉

Composite(C₀, 1, G )

(

α_g

)× C₀

α_g ×Cg

where C₀ is the selected backdrop colour.

G may be any kind of group—isolated or not, knockout or not—producing various effects on the C result in

each case. The colour C shall then be converted to luminosity in one of the following ways, depending on the

group’s colour space:

•

For CIE-based spaces, convert to the CIE 1931 XYZ space and use the Y component as the luminosity.

This produces a colourimetrically correct luminosity.

NOTE 2

In the case of a PDF CalRGB space, the formula is

G_R

G_G

Y = Y_A ×A

Y_B × B

Y_C × C

using components of the Gamma and Matrix entries of the colour space dictionary (see Table 64 in “CIE-

Based Colour Spaces”). An analogous computation applies to other CIE-based colour spaces.

•

For device colour spaces, convert the colour to DeviceGray by implementation-defined means and use

the resulting gray value as the luminosity, with no compensation for gamma or other colour calibration.

NOTE 3

This method makes no pretence of colourimetric correctness; it merely provides a numerically simple means to

produce continuous-tone mask values. The following are formulas for converting from DeviceRGB and

DeviceCMYK, respectively:

Y = 0.30 × R + 0.59 × G + 0.11 × B

Y = 0.30 × (1 - C) × (1 - K)

+ 0.59 × (1 - M) × (1 - K)

+ 0.11 × (1 - Y) × (1 - K)

Following this conversion, the result shall be passed through a separately specified transfer function, allowing

the masking effect to be customized.

NOTE 4

The backdrop colour most likely to be useful is black, which causes any areas outside the group’s shape to

have zero luminosity values in the resulting mask. If the contents of the group are viewed as a positive mask,

this produces the results that would be expected with respect to points outside the shape.

343

11.6

Specifying Transparency in PDF

11.6.1

General

The preceding sub-clauses have presented the transparent imaging model at an abstract level, with little

mention of its representation in PDF. This sub-clause describes the facilities available for specifying

transparency in PDF.

11.6.2

Specifying Source and Backdrop Colours

Single graphics objects, as defined in

“Graphics Objects”, shall be treated as elementary objects for

transparency compositing purposes (subject to special treatment for text objects, as described in “Text

Knockout”). That is, all of a given object shall be considered to be one element of a transparency stack.

Portions of an object shall not be composited with one another, even if they are described in a way that would

seem to cause overlaps (such as a self-intersecting path, combined fill and stroke of a path, or a shading

pattern containing an overlap or fold-over). An object’s source colour C_s , used in the colour compositing

formula, shall be specified in the same way as in the opaque imaging model: by means of the current colour in

the graphics state or the source samples in an image. The backdrop colour C_b shall be the result of previous

painting operations.

11.6.3

Specifying Blending Colour Space and Blend Mode

The blending colour space shall be an attribute of the transparency group within which an object is painted; its

specification is described in 11.6.6, "Transparency Group XObjects." The page as a whole shall also be treated

as a group, the page group (see “Page Group”), with a colour space attribute of its own. If not otherwise

specified, the page group’s colour space shall be inherited from the native colour space of the output device.

The blend mode B (C_b , C_s ) shall be determined by the current blend mode parameter in the graphics state (see

“Graphics State”), which is specified by the BM entry in a graphics state parameter dictionary (“Graphics State

Parameter Dictionaries”). Its value shall be either a name object, designating one of the standard blend modes

listed in Tables 136 and 137 in 11.3.5, "Blend Mode," or an array of such names. In the latter case, the

application shall use the first blend mode in the array that it recognizes (or Normal if it recognizes none of

them).

NOTE

New blend modes may be introduced in the future, and conforming readers that do not recognize them should

have reasonable fallback behavior.

The current blend mode shall always apply to process colour components; but only sometimes may apply to spot colorants,

see 11.7.4.2, "Blend Modes and Overprinting," for details.

11.6.4

Specifying Shape and Opacity

11.6.4.1

General

As discussed under 11.3.7.2, "Source Shape and Opacity," the shape (f) and opacity (q) values used in the

compositing computation shall come from one or more of the following sources:

•

The intrinsic shape (f_j ) and opacity (q_j ) of the object being composited

•

A separate shape (f_m ) or opacity (q_m ) mask independent of the object itself

•

A scalar shape (f_k ) or opacity (q_k ) constant to be added at every point

The following sub-clauses describe how each of these shape and opacity sources shall be specified in PDF.

344

11.6.4.2

Object Shape and Opacity

The shape value f_j of an object painted with PDF painting operators shall be defined as follows:

•

For objects defined by a path or a glyph and painted in a uniform colour with a path-painting or text-

showing operator (“Path-Painting Operators”, and “Text-Showing Operators”), the shape shall always be

1.0 inside and 0.0 outside the path.

•

For images (“Images”), the shape shall be 1.0 inside the image rectangle and 0.0 outside it. This may be

further modified by an explicit or colour key mask (“Explicit Masking” and “Colour Key Masking”).

•

For image masks (“Stencil Masking”), the shape shall be 1.0 for painted areas and 0.0 for masked areas.

•

For objects painted with a tiling pattern (“Tiling Patterns”) or a shading pattern (“Shading Patterns”), the

shape shall be further constrained by the objects that define the pattern

(see

“Patterns and

Transparency”).

•

For objects painted with the sh operator (“Shading Operator”), the shape shall be 1.0 inside and 0.0

outside the bounds of the shading’s painting geometry, disregarding the Background entry in the shading

dictionary (see “Shading Dictionaries”).

All elementary objects shall have an intrinsic opacity q_j of 1.0 everywhere. Any desired opacity less than 1.0

shall be applied by means of an opacity mask or constant, as described in the following sub-clauses.

11.6.4.3

Mask Shape and Opacity

At most one mask input—called a soft mask, or alpha mask—shall be provided to any PDF compositing

operation. The mask may serve as a source of either shape (f_m ) or opacity (q_m ) values, depending on the

setting of the alpha source parameter in the graphics state (see “Graphics State”). This is a boolean flag, set

with the AIS (“alpha is shape”) entry in a graphics state parameter dictionary (“Graphics State Parameter

Dictionaries”): true if the soft mask contains shape values, false for opacity.

The soft mask shall be specified in one of the following ways:

•

The current soft mask parameter in the graphics state, set with the SMask entry in a graphics state

parameter dictionary, contains a soft-mask dictionary (see “Soft-Mask Dictionaries”) defining the contents

of the mask. The name None may be specified in place of a soft-mask dictionary, denoting the absence of

a soft mask. In this case, the mask shape or opacity shall be implicitly 1.0 everywhere.

•

An image XObject may contain its own soft-mask image in the form of a subsidiary image XObject in the

SMask entry of the image dictionary (see “Image Dictionaries”). This mask, if present, shall override any

explicit or colour key mask specified by the image dictionary’s Mask entry. Either form of mask in the

image dictionary shall override the current soft mask in the graphics state.

•

An image XObject that has a JPXDecode filter as its data source may specify an SMaskInData entry,

indicating that the soft mask is embedded in the data stream (see “JPXDecode Filter”).

NOTE

The current soft mask in the graphics state is intended to be used to clip only a single object at a time (either

an elementary object or a transparency group). If a soft mask is applied when painting two or more overlapping

objects, the effect of the mask multiplies with itself in the area of overlap (except in a knockout group),

producing a result shape or opacity that is probably not what is intended. To apply a soft mask to multiple

objects, it is usually best to define the objects as a transparency group and apply the mask to the group as a

whole. These considerations also apply to the current alpha constant (see the next sub-clause).

345

11.6.4.4

Constant Shape and Opacity

The current alpha constant parameter in the graphics state (see “Graphics State”) shall be two scalar

values—one for strokes and one for all other painting operations—to be used for the constant shape (f_k) or

constant opacity (q_k) component in the colour compositing formulas.

NOTE 1

This parameter is analogous to the current colour used when painting elementary objects.

The nonstroking alpha constant shall also be applied when painting a transparency group’s results onto its

backdrop.

The stroking and nonstroking alpha constants shall be set, respectively, by the CA and ca entries in a graphics

state parameter dictionary (see “Graphics State Parameter Dictionaries”). As described previously for the soft

mask, the alpha source flag in the graphics state shall determine whether the alpha constants are interpreted

as shape values (true) or opacity values (false).

NOTE 2

The note at the end of 11.6.4.3, "Mask Shape and Opacity," applies to the current alpha constant parameter as

well as the current soft mask.

11.6.5

Specifying Soft Masks

11.6.5.1

General

As noted under 11.6.4.3, "Mask Shape and Opacity," soft masks for use in compositing computations may be

specified in one of the following ways:

•

As a soft-mask dictionary in the current soft mask parameter of the graphics state; see 11.6.5.2, "Soft-

Mask Dictionaries," for more details.

•

As a soft-mask image associated with a sampled image; see 11.6.5.3, "Soft-Mask Images," for more

details.

•

(PDF 1.5) as a mask channel embedded in JPEG2000 encoded data; see “JPXDecode Filter”, and the

SMaskInData entry of Table 89 for more details.

11.6.5.2

Soft-Mask Dictionaries

The most common way of defining a soft mask is with a soft-mask dictionary specified as the current soft mask

in the graphics state (see “Graphics State”). Table 144 shows the contents of this type of dictionary.

The mask values shall be derived from those of a transparency group, using one of the two methods described

in 11.5.2, "Deriving a Soft Mask from Group Alpha," and 11.5.3, "Deriving a Soft Mask from Group Luminosity."

The group shall be defined by a transparency group XObject (see “Transparency Group XObjects”) designated

by the G entry in the soft-mask dictionary. The S (subtype) entry shall specify which of the two derivation

methods to use:

•

If the subtype is Alpha, the transparency group XObject G shall be evaluated to compute a group alpha

only. The colours of the constituent objects shall be ignored and the colour compositing computations shall

not be performed. The transfer function TR shall then be applied to the computed group alpha to produce

the mask values. Outside the bounding box of the transparency group, the mask value shall be the result of

applying the transfer function to the input value 0.0.

•

If the subtype is Luminosity, the transparency group XObject G shall be composited with a fully opaque

backdrop whose colour is everywhere defined by the soft-mask dictionary’s BC entry. The computed result

colour shall then be converted to a single-component luminosity value, and the transfer function TR shall

be applied to this luminosity to produce the mask values. Outside the transparency group’s bounding box,

the mask value shall be derived by transforming the BC colour to luminosity and applying the transfer

function to the result.

346

The mask’s coordinate system shall be defined by concatenating the transformation matrix specified by the

Matrix entry in the transparency group’s form dictionary

(see

“Form Dictionaries”) with the current

transformation matrix at the moment the soft mask is established in the graphics state with the gs operator.

In a transparency group XObject that defines a soft mask, spot colour components shall never be available,

even if they are available in the group or page on which the soft mask is used. If the group XObject’s content

stream specifies a Separation or DeviceN colour space that uses spot colour components, the alternate colour

space shall be substituted (see “Separation Colour Spaces” and “DeviceN Colour Spaces”).

Table 144 - Entries in a soft-mask dictionary

Key

Type

Value

Type

name

(Optional) The type of PDF object that this dictionary describes; if

present, shall be Mask for a soft-mask dictionary.

name

(Required) A subtype specifying the method to be used in deriving the

mask values from the transparency group specified by the G entry:

Alpha

The group’s computed alpha shall be used,

disregarding its colour (see “Deriving a Soft Mask from

Group Alpha”).

Luminosity The group’s computed colour shall be converted to a

single-component luminosity value

(see

“Deriving a

Soft Mask from Group Luminosity”).

stream

(Required) A transparency group XObject (see “Transparency Group

XObjects”) to be used as the source of alpha or colour values for

deriving the mask. If the subtype S is Luminosity, the group attributes

dictionary shall contain a CS entry defining the colour space in which

the compositing computation is to be performed.

array

(Optional) An array of component values specifying the colour to be

used as the backdrop against which to composite the transparency

group XObject G. This entry shall be consulted only if the subtype S is

Luminosity. The array shall consist of n numbers, where n is the

number of components in the colour space specified by the CS entry in

the group attributes dictionary (see “Transparency Group XObjects”).

Default value: the colour space’s initial value, representing black.

function or name

(Optional) A function object (see “Functions”) specifying the transfer

function to be used in deriving the mask values. The function shall

accept one input, the computed group alpha or luminosity (depending

on the value of the subtype S), and shall return one output, the

resulting mask value. The input shall be in the range 0.0 to 1.0. The

computed output shall be in the range 0.0 to 1.0; if it falls outside this

range, it shall be forced to the nearest valid value. The name Identity

may be specified in place of a function object to designate the identity

function. Default value: Identity.

11.6.5.3

Soft-Mask Images

The second way to define a soft mask is by associating a soft-mask image with an image XObject. This is a

subsidiary image XObject specified in the SMask entry of the parent XObject’s image dictionary (see “Image

Dictionaries”). Entries in the subsidiary image dictionary for such a soft-mask image shall have the same format

and meaning as in that of an ordinary image XObject (as described in Table 89 in “Image Dictionaries”), subject

to the restrictions listed in Table 145. This type of image dictionary may contain an additional entry, Matte.

When an image is accompanied by a soft-mask image, it is sometimes advantageous for the image data to be

preblended with some background colour, called the matte colour. Each image sample represents a weighted

average of the original source colour and the matte colour, using the corresponding mask sample as the

weighting factor. (This is a generalization of a technique commonly called premultiplied alpha.)

347

If the image data is preblended, the matte colour shall be specified by a Matte entry in the soft-mask image

dictionary (see Table 145). The preblending computation, performed independently for each component, shall

= m + α×(c-m)

where

c′ is the value to be provided in the image source data

c is the original image component value

m is the matte colour component value

α is the corresponding mask sample

This computation shall use actual colour component values, with the effects of the Filter and Decode

transformations already performed. The computation shall be the same whether the colour space is additive or

subtractive.

Table 145 - Restrictions on the entries in a soft-mask image dictionary

Key

Restriction

Type

If present, shall be XObject.

Subtype

Shall be Image.

Width

If a Matte entry (see Table 146) is present, shall be the

same as the Width value of the parent image; otherwise

independent of it. Both images shall be mapped to the

unit square in user space (as are all images), regardless

of whether the samples coincide individually.

Height

Same considerations as for Width.

ColorSpace

Required; shall be DeviceGray.

BitsPerComponent

Required.

Intent

Ignored.

ImageMask

Shall be false or absent.

Mask

Shall be absent.

SMask

Shall be absent.

Decode

Default value: [ 0 1 ].

Interpolate

Optional.

Alternates

Ignored.

Name

Ignored.

StructParent

Ignored.

OPI

Ignored.

348

Table 146 - Additional entry in a soft-mask image dictionary

Key

Type

Value

Matte

array

(Optional; PDF 1.4) An array of component values specifying the matte colour

with which the image data in the parent image shall have been preblended. The

array shall consist of n numbers, where n is the number of components in the

colour space specified by the ColorSpace entry in the parent image’s image

dictionary; the numbers shall be valid colour components in that colour space. If

this entry is absent, the image data shall not be preblended.

When preblended image data is used in transparency blending and compositing computations, the results shall

be the same as if the original, unblended image data were used and no matte colour were specified. In

particular, the inputs to the blend function shall be the original colour values. To derive c from c′, the conforming

reader may sometimes need to invert the formula shown previously. The resulting c value shall lie within the

range of colour component values for the image colour space.

The preblending computation shall be done in the colour space specified by the parent image’s ColorSpace

entry. This is independent of the group colour space into which the image may be painted. If a colour

conversion is required, inversion of the preblending shall precede the colour conversion. If the image colour

space is an Indexed space (see “Indexed Colour Spaces”), the colour values in the colour table (not the index

values themselves) shall be preblended.

11.6.6

Transparency Group XObjects

A transparency group is represented in PDF as a special type of group XObject (see “Group XObjects”) called

a transparency group XObject. A group XObject is in turn a type of form XObject, distinguished by the presence

of a Group entry in its form dictionary (see “Form Dictionaries”). The value of this entry is a subsidiary group

attributes dictionary defining the properties of the group. The format and meaning of the dictionary’s contents

shall be determined by its group subtype, which is specified by the dictionary’s S entry. The entries for a

transparency group (subtype Transparency) are shown in Table 147.

A page object (see “Page Objects”) may also have a Group entry, whose value is a group attributes dictionary

specifying the attributes of the page group (see “Page Group”). Some of the dictionary entries are interpreted

slightly differently for a page group than for a transparency group XObject; see their descriptions in the table for

details.

Table 147 - Additional entries specific to a transparency group attributes dictionary

Key

Type

Value

name

(Required) The group subtype, which identifies the type of group whose

attributes this dictionary describes; shall be Transparency for a

transparency group.

349

Table 147 - Additional entries specific to a transparency group attributes dictionary (continued)

Key

Type

Value

name or array

(Sometimes required) The group colour space, which is used for the

following purposes:

•

As the colour space into which colours shall be converted when

painted into the group

•

As the blending colour space in which objects shall be composited

within the group (see “Blending Colour Space”)

•

As the colour space of the group as a whole when it in turn is painted

as an object onto its backdrop

The group colour space shall be any device or CIE-based colour space

that treats its components as independent additive or subtractive values

in the range 0.0 to 1.0, subject to the restrictions described in 11.3.4,

"Blending Colour Space." These restrictions exclude Lab and lightness-

chromaticity ICCBased colour spaces, as well as the special colour

spaces Pattern, Indexed, Separation, and DeviceN. Device colour

spaces shall be subject to remapping according to the DefaultGray,

DefaultRGB, and DefaultCMYK entries in the ColorSpace subdictionary

of the current resource dictionary (see “Default Colour Spaces”).

Ordinarily, the CS entry may be present only for isolated transparency

groups (those for which I is true), and even then it is optional. However,

this entry shall be present in the group attributes dictionary for any

transparency group XObject that has no parent group or page from which

to inherit—in particular, one that is the value of the G entry in a soft-mask

dictionary of subtype Luminosity (see “Soft-Mask Dictionaries”).

Additionally, the CS entry may be present in the group attributes

dictionary associated with a page object, even if I is false or absent. In

the normal case in which the page is imposed directly on the output

medium, the page group is effectively isolated regardless of the I value,

and the specified CS value shall therefore be honoured. But if the page is

in turn used as an element of some other page and if the group is non-

isolated, CS shall be ignored and the colour space shall be inherited from

the actual backdrop with which the page is composited (see “Page

Group”).

Default value: the colour space of the parent group or page into which this

transparency group is painted. (The parent’s colour space in turn may be

either explicitly specified or inherited.)

For a transparency group XObject used as an annotation appearance

(see “Appearance Streams”), the default colour space shall be inherited

from the page on which the annotation appears.

boolean

(Optional) A flag specifying whether the transparency group is isolated

(see “Isolated Groups”). If this flag is true, objects within the group shall

be composited against a fully transparent initial backdrop; if false, they

shall be composited against the group’s backdrop. Default value: false.

In the group attributes dictionary for a page, the interpretation of this entry

shall be slightly altered. In the normal case in which the page is imposed

directly on the output medium, the page group is effectively isolated and

the specified I value shall be ignored. But if the page is in turn used as an

element of some other page, it shall be treated as if it were a

transparency group XObject; the I value shall be interpreted in the normal

way to determine whether the page group is isolated.

350

Table 147 - Additional entries specific to a transparency group attributes dictionary (continued)

Key

Type

Value

boolean

(Optional) A flag specifying whether the transparency group is a knockout

group (see “Knockout Groups”). If this flag is false, later objects within the

group shall be composited with earlier ones with which they overlap; if

true, they shall be composited with the group’s initial backdrop and shall

overwrite (“knock out”) any earlier overlapping objects. Default value:

false.

The transparency group XObject’s content stream shall define the graphics objects belonging to the group.

When applied to a transparency group XObject, the Do operator shall execute its content stream and shall

composite the resulting group colour, shape, and opacity into the group’s parent group or page as if they had

come from an elementary graphics object. Do shall perform the following actions in addition to the normal ones

for a form XObject (as described in “Form XObjects”):

•

If the transparency group is non-isolated (the value of the I entry in its group attributes dictionary is false),

its initial backdrop, within the bounding box specified by the XObject’s BBox entry, shall be defined to be

the accumulated colour and alpha of the parent group or page—that is, the result of everything that has

been painted in the parent up to that point. However, if the parent is a knockout group, the initial backdrop

shall be the same as that of the parent. If the group is isolated (I is true), its initial backdrop shall be

defined to be transparent.

•

Before execution of the transparency group XObject’s content stream, the current blend mode in the

graphics state shall be initialized to Normal, the current stroking and nonstroking alpha constants to 1.0,

and the current soft mask to None.

NOTE 1

The purpose of initializing these graphics state parameters at the beginning of execution is to ensure that they

are not applied twice: once when member objects are painted into the group and again when the group is

painted into the parent group or page.

•

Objects painted by operators in the transparency group XObject’s content stream shall be composited into

the group according to the rules described in 11.3.3, "Basic Compositing Formula." The knockout flag (K)

in the group attributes dictionary and the transparency-related parameters of the graphics state shall be

honoured during this computation.

•

If a group colour space (CS) is specified in the group attributes dictionary, all painting operators shall

convert source colours to that colour space before compositing objects into the group, and the resulting

colour at each point shall be interpreted in that colour space. If no group colour space is specified, the

prevailing colour space shall be dynamically inherited from the parent group or page. (If not otherwise

specified, the page group’s colour space shall be inherited from the native colour space of the output

device.)

•

After execution of the transparency group XObject’s content stream, the graphics state shall revert to its

former state before the invocation of the Do operator (as it does for any form XObject). The group’s

shape—the union of all objects painted into the group, clipped by the group XObject’s bounding box—

shall then be painted into the parent group or page, using the group’s accumulated colour and opacity at

each point.

If the Do operator is invoked more than once for a given transparency group XObject, each invocation shall be

treated as a separate transparency group. That is, the result shall be as if the group were independently

composited with the backdrop on each invocation.

NOTE 2

Applications that perform caching of rendered form XObjects shall take this requirement into account.

The actions described previously shall occur only for a transparency group XObject—a form XObject having a

Group entry that designates a group attributes subdictionary whose group subtype (S) is Transparency. An

ordinary form XObject—one having no Group entry—shall not be subject to any grouping behaviour for

351

transparency purposes. That is, the graphics objects it contains shall be composited individually, just as if they

were painted directly into the parent group or page.

11.6.7

Patterns and Transparency

In the transparent imaging model, the graphics objects making up the pattern cell of a tiling pattern (see “Tiling

Patterns”) may include transparent objects and transparency groups. Transparent compositing may occur both

within the pattern cell and between it and the backdrop wherever the pattern is painted. Similarly, a shading

pattern (“Shading Patterns”) composites with its backdrop as if the shading dictionary were applied with the sh

operator.

In both cases, the pattern definition shall be treated as if it were implicitly enclosed in a non-isolated

transparency group: a non-knockout group for tiling patterns, a knockout group for shading patterns. The

definition shall not inherit the current values of the graphics state parameters at the time it is evaluated; those

parameters shall take effect only when the resulting pattern is later used to paint an object. Instead, the

graphics state parameters shall be initialized as follows:

•

As always for transparency groups, those parameters related to transparency (blend mode, soft mask, and

alpha constant) shall be initialized to their standard default values.

•

All other parameters shall be initialized to their values at the beginning of the content stream (such as a

page or a form XObject) in which the pattern shall be defined as a resource. (This is the normal behaviour

for all patterns, in both the opaque and transparent imaging models.)

•

In the case of a shading pattern, the parameter values may be augmented by the contents of the

ExtGState entry in the pattern dictionary (see “Shading Patterns”). Only those parameters that affect the

sh operator, such as the current transformation matrix and rendering intent, shall be used. Parameters that

affect path-painting operators shall not be used, since the execution of sh does not entail painting a path.

•

If the shading dictionary has a Background entry, the pattern’s implicit transparency group shall be filled

with the specified background colour before the sh operator is invoked.

When the pattern is later used to paint a graphics object, the colour, shape, and opacity values resulting from

the evaluation of the pattern definition shall be used as the object’s source colour (C_s ), object shape (f_j ), and

object opacity (q_j) in the transparency compositing formulas. This painting operation is subject to the values of

the graphics state parameters in effect at the time, just as in painting an object with a constant colour.

NOTE 1

Unlike the opaque imaging model, in which the pattern cell of a tiling pattern may be evaluated once and then

replicated indefinitely to fill the painted area, the effect in the general transparent case is as if the pattern

definition were reexecuted independently for each tile, taking into account the colour of the backdrop at each

point. However, in the common case in which the pattern consists entirely of objects painted with the Normal

blend mode, this behaviour can be optimized by treating the pattern cell as if it were an isolated group. Since in

this case the results depend only on the colour, shape, and opacity of the pattern cell and not on those of the

backdrop, the pattern cell can be evaluated once and then replicated, just as in opaque painting.

NOTE 2

In a raster-based implementation of tiling, all tiles should be treated as a single transparency group. This

avoids artifacts due to multiple marking of pixels along the boundaries between adjacent tiles.

The foregoing discussion applies to both coloured (PaintType 1) and uncoloured (PaintType 2) tiling patterns.

In the latter case, the restriction that an uncoloured pattern’s definition shall not specify colours extends as well

to any transparency group that the definition may include. There are no corresponding restrictions, however, on

specifying transparency-related parameters in the graphics state.

352

ISO 32000-1 Document management — Portable document format — Part 1: PDF 1.7 - page 9