PDF20 Spec 11 Transparency

Chapter 11: Transparency

Part of: PDF20-Spec-Index

Navigation: PDF20-Spec-10-Rendering | PDF20-Spec-Index | PDF20-Spec-12-Interactive

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, but a processor need not implement these exactly provided the results are equivalent. NOTE

Transparency was added to PDF in version 1.4.

The following 6 clauses are organised 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 — realised 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. In the transparent imaging model, all of the objects on a page may potentially contribute to the result. Objects at a given point form a transparency stack (or stack for short). The objects are 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 PDF processor 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.

387

ISO 32000-2:2020(E)

Annex Q, "Method for determining transparency on a page" defines a standardised method for determining if transparency is present on a page. This method is not required by this document, however other PDF-related standards may wish to mandate the use of this algorithm to ensure consistent behaviour. 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 11.4, "Transparency groups"), a different backdrop may be chosen. 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 could need to maintain a separate shape parameter to do antialiasing 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 the group backdrop. An additional blend mode, blending colour space, shape, and opacity may also be associated with the group as a whole and used when compositing the objects inside of the group as well as the group itself with the group backdrop. Groups may be nested within other groups, forming a tree-structured hierarchy.

388

ISO 32000-2:2020(E)

Figure 71 — Transparency groups EXAMPLE

"Figure 71 — Transparency groups" 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 8.5.4, "Clipping path operators").

11.3 Basic compositing computations 11.3.1

General

This subclause 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; © ISO 2020 – All rights reserved 389

ISO 32000-2:2020(E)

for instance, 𝐶𝑠 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 𝑞𝑠 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 although 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. In addition, the convention that 0 ÷ 0 = 0 shall 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 subclause 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

𝛼

𝑟

𝐶𝑟 = (1 − 𝛼𝑠 ) × 𝐶𝑏 + 𝛼𝑠 × ((1 − 𝛼𝑏 ) × 𝐶𝑠 + 𝛼𝑏 × 𝐵(𝐶𝑏 , 𝐶𝑠 )) where the variables have the meanings shown in "Table 133 — Variables used in the basic compositing formula". NOTE

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, extended to include a blend mode in the region of overlapping coverage.

Table 133 — Variables used in the basic compositing formula Variable

390

Meaning 𝐶𝑏

Backdrop colour

𝐶𝑠

Source colour

𝐶𝑟

Result colour

𝛼𝑏

Backdrop alpha

𝛼𝑠

Source alpha

𝛼𝑟

ISO 32000-2:2020(E)

Variable 𝐵(𝐶𝑏 , 𝐶𝑠 )

Meaning Blend function

The following subclauses 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 used in the compositing process. The ith component of the result colour 𝐶𝑟 shall be obtained by applying the compositing formula to the ith components of the constituent colours 𝐶𝑏 , Cs , and 𝐵(𝐶𝑏 , 𝐶𝑠 ). 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. The backdrop and source colours are normally converted to the blending colour space before the compositing computation. Of the PDF colour spaces described in 8.6, "Colour spaces", the following shall be supported as blending colour spaces: •

DeviceGray

•

DeviceRGB

•

DeviceCMYK

•

CalGray

•

CalRGB

•

ICCBased bi-directional ‘GRAY’, ‘RGB ’, and ‘CMYK’ colour spaces

The Lab space and ICCBased spaces that represent lightness and chromaticity separately (such as Lab*, Luv*, 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 bi-directional; that is, the ICC profile shall be capable of both device to PCS and PCS to device transformations. When performing blending, process colours (see 10.2, "Raster output device native colour") shall be converted to the blending colour space. 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 8.6.6.4, "Separation colour spaces" and 8.6.6.5, "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 subtractive colour spaces (DeviceCMYK, ICCBased ‘CMYK’, 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. © ISO 2020 – All rights reserved

391

ISO 32000-2:2020(E)

11.3.5

Blend mode

11.3.5.1

General

In principle, any function of the backdrop and source colours that yields another colour, 𝐶𝑟 , for the result may be used as a blend function 𝐵(𝐶𝑏 , 𝐶𝑠 ), in the compositing formula to customise the blending operation. PDF defines a standard set of named blend functions, or blend modes, listed in "Table 134 — Standard separable blend modes" and "Table 135 — Standard non-separable blend modes". "Figure 72 — RGB blend modes" and "Figure 73 — CMYK blend modes" illustrate the resulting visual effects for RGB and CMYK colours, respectively.

Figure 72 — RGB blend modes 392

ISO 32000-2:2020(E)

Figure 73 — CMYK blend modes

11.3.5.2

Separable blend modes

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: 𝑐𝑟 = 𝐵(𝑐𝑏 , 𝑐𝑠 ) where the lowercase variables 𝑐𝑟 , 𝑐𝑏 , and 𝑐𝑠 denote corresponding components of the colours 𝐶𝑟 , 𝐶𝑏 , and 𝐶𝑠 , expressed in additive form. A separable blend mode may be used with any colour space, since it © ISO 2020 – All rights reserved

393

ISO 32000-2:2020(E)

applies independently to any number of components. Only white-preserving separable blend modes shall be used for blending spot colours as discussed in 11.7.3, "Spot colours and transparency". NOTE

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 134 — Standard separable blend modes" lists the standard separable blend modes available in PDF and the algorithms/formulas that shall be used in the calculation of blended colours. Table 134 — Standard separable blend modes Name

Result

Normal

𝐵(𝑐𝑏 , 𝑐𝑠 ) = 𝑐𝑠 NOTE 1 Selects the source colour, ignoring the backdrop.

Compatible

(Deprecated in PDF 2.0) Same as Normal. This mode was introduced in an earlier PDF version and shall not be used by PDF writers.

Multiply

𝐵(𝑐𝑏 , 𝑐𝑠 ) = 𝑐𝑏 × 𝑐𝑠 NOTE 2 Multiplies the backdrop and source colour values. NOTE 3 The result colour is always at least as dark as either of the two constituent colours. When working with additive colours, multiplying any colour with black produces black while multiplying with white leaves the original colour unchanged. For subtractive colours, the maximum tint value used for all colourants of the colour space acts as black does for additive spaces. Painting successive overlapping objects with a colour other than black or white produces progressively darker colours.

Screen

𝐵(𝑐𝑏 , 𝑐𝑠 ) = 1 − ((1 − 𝑐𝑏 ) × (1 − 𝑐𝑠 )) = 𝑐𝑏 + 𝑐𝑠 − (𝑐𝑏 × 𝑐𝑠 ) NOTE 4 Multiplies the complements of the backdrop and source colour values, then complements the result. NOTE 5 The result colour is always at least as light as either of the two constituent colours. When working with additive colours, screening any colour with white produces white while screening with black leaves the original colour unchanged. For subtractive colours, the maximum tint value of all colourants of the color space acts as black does for additive spaces. The effect is similar to projecting multiple photographic slides simultaneously onto a single screen.

Darken

𝐵(𝑐𝑏 , 𝑐𝑠 ) = 𝑚𝑖𝑛(𝑐𝑏 , 𝑐𝑠 ) 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(𝑐𝑏 , 𝑐𝑠 ) = 𝑚𝑎𝑥(𝑐𝑏 , 𝑐𝑠 ) 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.

394

ISO 32000-2:2020(E)

Name

Result

ColorDodge

0 if 𝑐𝑏 = 0 if 𝑐𝑏 ≥ 1 − 𝑐𝑠 𝐵(𝑐𝑏 , 𝑐𝑠 ) = {1 𝑐𝑏 /(1 − 𝑐𝑠 ) otherwise NOTE 10 Brightens the backdrop colour to reflect the source colour. Painting with black produces no change. NOTE 11 This function is formulated in a different way here than it is in ISO 32000-1:2008. However, it produces the same results except in one special edge case. For ColorDodge, the special case is cb = 0 and cs = 1, where the result is now 0 instead of 1. The rationale for the change is that for any given cb, the result should be a continuous function of cs.

ColorBurn

1 if 𝑐𝑏 = 1 0 if 1 − 𝑐𝑏 ≥ 𝑐𝑠 ) 𝐵(𝑐𝑏 , 𝑐𝑠 = { 1 − ((1 − 𝑐𝑏 )/𝑐𝑠 ) otherwise NOTE 12 Darkens the backdrop colour to reflect the source colour. Painting with white produces no change. NOTE 13 This function is formulated in a different way here than it is in ISO 32000-1:2008. However, it produces the same results except in one special edge case. For ColorBurn, the special case is cb = 1 and cs = 0, where the result is now 1 instead of 0. The rationale for the change is that for any given cb, the result should be a continuous function of cs.

HardLight

Multiply(𝑐𝑏 , 2 × 𝑐𝑠 ) if 𝑐𝑠 ≤ 0.5 𝐵(𝑐𝑏 , 𝑐𝑠 ) = { Screen(𝑐𝑏 , 2 × 𝑐𝑠 − 1) if 𝑐𝑠 > 0.5 NOTE 14 Multiplies or screens the colours, depending on the source colour value. The effect is similar to shining a harsh spotlight on the backdrop.

SoftLight

𝑐𝑏 − (1 − 2 × 𝑐𝑠 ) × 𝑐𝑏 × (1 − 𝑐𝑏 ) if 𝑐𝑠 ≤ 0.5 𝐵(𝑐𝑏 , 𝑐𝑠 ) = {

𝑐𝑏 + (2 × 𝑐𝑠 − 1) × (𝐷(𝑐𝑏 ) − 𝑐𝑏 ) if 𝑐𝑠 > 0.5

((16 × 𝑥 − 12) × 𝑥 + 4) × 𝑥 if 𝑥 ≤ 0.25 𝐷(𝑥) = { if 𝑥 > 0.25 √𝑥 NOTE 15 Darkens or lightens the colours, depending on the source colour value. The effect is similar to shining a diffused spotlight on the backdrop.

Overlay

𝐵(𝑐𝑏 , 𝑐𝑠 ) = HardLight(𝑐𝑠 , 𝑐𝑏 ) NOTE 16 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.

Difference

𝐵(𝑐𝑏 , 𝑐𝑠 ) = |𝑐𝑏 − 𝑐𝑠 | NOTE 17 Subtracts the darker of the two constituent colours from the lighter colour: Painting with white inverts the backdrop colour; painting with black produces no change. For subtractive colours, the maximum tint value for all colourants of the colour space acts as black does for additive spaces. NOTE 18

This blend mode is not white-preserving.

395

ISO 32000-2:2020(E)

Name

Result

Exclusion

𝐵(𝑐𝑏 , 𝑐𝑠 ) = 𝑐𝑏 + 𝑐𝑠 − 2 × 𝑐𝑏 × 𝑐𝑠 NOTE 19 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. For subtractive colours, the maximum tint value for all colourants of the colour space acts as black does for additive spaces. NOTE 20

11.3.5.3

This blend mode is not white-preserving.

Non-separable blend modes

"Table 135 — Standard non-separable blend modes" lists the standard non-separable blend modes. Since the non-separable 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 colour spaces that are allowed as blending colour spaces (see 11.3.4, "Blending colour space"). All of the non-separable blend modes conceptually entail the following steps: •

Convert the backdrop and source colours from the blending colour space to an intermediate HSL (hue-saturation-luminosity) representation.

•

Create a new colour from some combination of hue, saturation, and luminosity components selected from the backdrop and source colours.

•

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

However, the following formulas 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 non-separable 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 in gray colour spaces (DeviceGray, CalGray and ICCBased gray) shall be done by conversion to RGB, blending in RGB, and then converting back to gray. Blending of CMYK colour spaces requires special treatment, and is described later in this subclause. The following formulas apply to RGB spaces (including DeviceRGB, CalRGB and ICCBased 'RGB '): These functions shall have the following definitions:

Lum(C) = 0.3 × Cred + 0.59 × Cgreen + 0.11 × Cblue

SetLum(C, 𝑙 ) let 𝑑 = 𝑙 − Lum(𝐶 ) 𝐶red = 𝐶red + 𝑑 𝐶green = 𝐶green + 𝑑 𝐶blue = 𝐶blue + 𝑑 396

ISO 32000-2:2020(E)

return ClipColor(𝐶)

ClipColor(𝐶 ) let 𝑙 = Lum(𝐶 ) let 𝑛 = 𝑚𝑖𝑛(𝐶red , 𝐶green , 𝐶blue ) let 𝑥 = 𝑚𝑎𝑥(𝐶red, 𝐶green , 𝐶blue ) if 𝑛 < 0.0 𝐶red = 𝑙 + (((𝐶red − 𝑙) × 𝑙)/(𝑙 − 𝑛)) 𝐶green = 𝑙 + (((𝐶green − 𝑙) × 𝑙) /(𝑙 − 𝑛)) 𝐶blue = 𝑙 + (((𝐶blue − 𝑙) × 𝑙)/(𝑙 − 𝑛))

endif if 𝑥 > 1.0 𝐶red = 𝑙 + (((𝐶red − 𝑙) × (1 − 𝑙))/(𝑥 − 𝑙)) 𝐶green = 𝑙 + (((𝐶green − 𝑙) × (1 − 𝑙)) /(𝑥 − 𝑙)) 𝐶blue = 𝑙 + (((𝐶blue − 𝑙) × (1 − 𝑙))/(𝑥 − 𝑙))

endif return 𝐶

Sat(𝐶 ) = 𝑚𝑎𝑥 (𝐶red , 𝐶green , 𝐶blue ) − 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 𝐶max > 𝐶min 𝐶mid = (((𝐶mid − 𝐶min ) × 𝑠)/(𝐶max − 𝐶min )) 𝐶max = 𝑠

else 𝐶mid = 𝐶max = 0.0

endif 𝐶min = 0.0

397

ISO 32000-2:2020(E)

NOTE

The SetSat algorithm has a distinct discontinuity between neutral and near neutral colours which makes it very sensitive to variations between implementations with respect to colour management and quantisation of colour values. Therefore the visual appearance of elements can be very different between different PDF processors used for viewing or printing pages containing elements that use the Hue and Saturation blend modes that use the SetSat algorithm.

Table 135 — Standard non-separable blend modes Name

Result

Hue

𝐵(𝐶𝑏 , 𝐶𝑠 ) = SetLum (SetSat(𝐶𝑠 ,Sat(𝐶𝑏 )),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(𝐶𝑏 , 𝐶𝑠 ) = SetLum (SetSat(𝐶𝑏 ,Sat(𝐶𝑠 )),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.

Color

𝐵(𝐶𝑏 , 𝐶𝑠 ) = SetLum(𝐶𝑠 , Lum(𝐶𝑏 )) 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(𝐶𝑏 , 𝐶𝑠 ) = SetLum(𝐶𝑏 , Lum(𝐶𝑠 )) 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 subclause apply to RGB spaces (including DeviceRGB, CalRGB and ICCBased RGB). Blending in CMYK spaces (including both DeviceCMYK and ICCBased 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 by subtracting each from 1.0. The formulae in this subclause shall be applied to the RGB colour values. The results shall be complemented back to C, M and Y in the same way.

•

For the K component, the result shall be the K component of Cb for the Hue, Saturation, and Color blend modes; it shall be the K component of Cs for the Luminosity blend mode.

11.3.6

Interpretation of alpha

The colour compositing formula 𝐶𝑟 = (1 −

𝛼𝑠 𝛼𝑠 ) × 𝐶𝑏 + × ((1 − 𝛼𝑏 ) × 𝐶𝑠 + 𝛼𝑏 × 𝐵(𝐶𝑏 , 𝐶𝑠 )) 𝛼𝑟 𝛼𝑟

produces a result colour that is a weighted average of the backdrop colour, the source colour, and the blended 𝐵(𝐶𝑏 , 𝐶𝑠 ) term, with the weighting determined by the backdrop and source alphas 𝛼𝑏 and 𝛼𝑠 . NOTE 1

398

This formula represents a simplification of the following formula, which presents the relative contributions of backdrop, source, and blended colours in a more straightforward way: © ISO 2020 – All rights reserved

ISO 32000-2:2020(E)

𝛼𝑟 × 𝐶𝑟 = ((1 − 𝛼𝑠 ) × 𝛼𝑏 × 𝐶𝑏 ) + (((1 − 𝛼𝑏 ) × 𝛼𝑠 × 𝐶𝑠 ) + (𝛼𝑏 × 𝛼𝑠 × 𝐵(𝐶𝑏 , 𝐶𝑠 ))) For the simplest blend mode, Normal, defined by 𝐵(𝐶𝑏 , 𝐶𝑠 ) = 𝐶𝑠 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 realised or is toned down by mixing the result with the backdrop and source colours. The result alpha, αr , actually represents a computed result, described in 11.3.7, "Shape and opacity computations". The result colour shall be normalised 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 2

If 𝛼𝑟 is zero, the result colour is undefined.

The simplification requires a substitution based on the alpha compositing formula, which is presented in 11.3.7.3, "Result shape and opacity". 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 αs = 0.0 or αb = 0.0 results in no blend mode effect; setting αs = 1.0 and αb = 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: 𝛼𝑏 = 𝑓𝑏 × 𝑞𝑏 𝛼𝑟 = 𝑓𝑟 × 𝑞𝑟 𝛼𝑠 = 𝑓𝑠 × 𝑞𝑠 This subclause 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 11.6.4, "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 8.9.6.3, "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 (as defined in 11.3.7.3, "Result shape and opacity") 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 © ISO 2020 – All rights reserved 399

ISO 32000-2:2020(E)

the boundaries can 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.

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. 𝑓𝑠 = 𝑓𝑗 × 𝑓𝑚 × 𝑓𝑘 The three opacity inputs shall be multiplied together, producing an intermediate value called the source opacity. 𝑞𝑠 = 𝑞𝑗 × 𝑞𝑚 × 𝑞𝑘 Where the variables have the meanings shown in "Table 136 — Variables used in the source shape and opacity formulas". Table 136 — Variables used in the source shape and opacity formulas Variable

400

Meaning 𝒇𝒔

Source shape

𝒇𝒋

Object shape

𝒇𝒎

Mask shape

𝒇𝒌

Constant shape

𝒒𝒔

Source opacity

𝒒𝒋

ISO 32000-2:2020(E)

Variable

NOTE 5

Meaning 𝒒𝒎

Mask opacity

𝒒𝒌

Constant opacity

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 11.6.7, "Patterns and transparency").

11.3.7.3

Result shape and opacity

In addition to a result colour, the painting operation shall also 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 𝑓𝑟 = Union(𝑓𝑏 , 𝑓𝑠 ) 𝑞𝑟 =

Union(𝑓𝑏 × 𝑞𝑏 , 𝑓𝑠 × 𝑞𝑠 ) 𝑓𝑟

where the variables have the meanings shown in "Table 137 — Variables used in the result shape and opacity formulas". Table 137 — Variables used in the result shape and opacity formulas Variable

Meaning

𝑓𝒓

Result shape

𝑓𝑏

Backdrop shape

𝑓𝑠

Source shape

𝑞𝑟

Result opacity

𝑞𝑏

Backdrop opacity

𝑞𝑠

Source opacity

401

ISO 32000-2:2020(E)

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 (normalised by) the result shape.

NOTE 2

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

𝛼𝑟 = Union(𝛼𝑏 , 𝛼𝑠 ) This formula can be used whenever the independent shape and opacity are not needed.

11.3.8

Summary of basic compositing computations

This subclause is a summary of all the computations presented in subclause 11.3.1 through subclause 11.3.7. 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 "Table 133 — Variables used in the basic compositing formula", "Table 136 — Variables used in the source shape and opacity formulas", and "Table 137 — Variables used in the result shape and opacity formulas" for the meanings of the variables used in these formulas. Union(𝑏, 𝑠) = 1 − ((1 − 𝑏) × (1 − 𝑠)) = 𝑏 + 𝑠 − (𝑏 × 𝑠) 𝑓𝑠 = 𝑓𝑗 × 𝑓𝑚 × 𝑓𝑘 𝑞𝑠 = 𝑞𝑗 × 𝑞𝑚 × 𝑞𝑘 𝑓𝑟 = Union(𝑓𝑏 , 𝑓𝑠 )

𝛼𝑏 = 𝑓𝑏 × 𝑞𝑏 𝛼𝑠 = 𝑓𝑠 × 𝑞𝑠 𝛼𝑟 = Union(𝛼𝑏 , 𝛼𝑠 ) 𝑞𝑟 =

𝛼𝑟 𝑓𝑟

𝐶𝑟 = (1 −

𝛼𝑠 𝛼𝑠 ) × 𝐶𝑏 + × ((1 − 𝛼𝑏 ) × 𝐶𝑠 + 𝛼𝑏 × 𝐵(𝐶𝑏 , 𝐶𝑠 )) 𝛼𝑟 𝛼𝑟

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

402

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. © ISO 2020 – All rights reserved

ISO 32000-2:2020(E)

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

•

The group may be knockout or non-knockout, which shall determine whether the objects within the group stack are composited with one another or only with 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 11.5, "Soft masks").

11.4.2

Notation for group compositing computations

This subclause introduces some notation for dealing with group compositing. Subsequent subclauses describe the group compositing formulas for a non-isolated, non-knockout group and the special properties of isolated and knockout groups. Since multiple objects are being dealt with 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. 𝐶𝑠𝑖 stands for the source colour of the ith object in the stack. The subscript 0 represents the initial backdrop; 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 Cb , fb , qb , αb , Cr , fr , qr , and α𝑟 ; 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 Ci (formerly Cr ). 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 Cb). The revised formulas for a simple n-element stack (not including any groups) shall be, for i = 1, …, n: 𝑓𝑠𝑖 = 𝑓𝑗𝑖 × 𝑓𝑚𝑖 × 𝑓𝑘𝑖 𝑞𝑠𝑖 = 𝑞𝑗𝑖 × 𝑞𝑚𝑖 × 𝑞𝑘𝑖 𝛼𝑠𝑖 = 𝑓𝑠𝑖 × 𝑞𝑠𝑖 𝛼𝑖 = Union(𝛼𝑖−1 , 𝛼𝑠𝑖 ) © ISO 2020 – All rights reserved

403

ISO 32000-2:2020(E)

𝑓𝑖 = Union(𝑓𝑖−1 , 𝑓𝑠𝑖 ) 𝛼𝑖 𝑞𝑖 = 𝑓𝑖 𝐶𝑖 = (1 −

𝛼𝑠𝑖 𝛼𝑠 ) × 𝐶𝑖−1 + 𝑖 × ((1 − 𝛼𝑖−1 ) × 𝐶𝑠𝑖 + 𝛼𝑖−1 × 𝐵𝑖 (𝐶𝑖−1 , 𝐶𝑠𝑖 )) 𝛼𝑖 𝛼𝑖

where the variables have the meanings shown in "Table 138 — Revised variables for the basic compositing formulas". NOTE

Compare these formulas with those shown in 11.3.8, "Summary of basic compositing computations".

Table 138 — Revised variables for the basic compositing formulas

404

Variable

Meaning

𝑓𝑠𝑖

Source shape for object i

𝑓𝑗𝑖

Object shape for object i

𝑓𝑚𝑖

Mask shape for object i

𝑓𝑘𝑖

Constant shape for object i

𝑓𝑖

Result shape after compositing object i

𝑞𝑠𝑖

Source opacity for object i

𝑞𝑗𝑖

Object opacity for object i

𝑞𝑚𝑖

Mask opacity for object i

𝑞𝑘𝑖

Constant opacity for object i

𝑞𝑖

Result opacity after compositing object i

𝛼𝑠𝑖

Source alpha for object i

𝛼𝑖

Result alpha after compositing object i

𝑐𝑠𝑖

Source colour for object i

𝐶𝑖

Result colour after compositing object i

Bi (Ci−1 , Csi )

Blend function for object i

ISO 32000-2:2020(E)

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 backdrop chosen for compositing the elements of the group was the group backdrop or a transparent backdrop. A PDF processor 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 , 𝐺) where the variables have the meanings shown in "Table 139 — Arguments and results of the group compositing function". Table 139 — Arguments and results of the group compositing function Variable

Meaning

𝐺

The transparency group: a compound object consisting of all elements E1,…, En of the group — the n constituent objects’ colours, shapes, opacities, and blend modes

405

ISO 32000-2:2020(E)

NOTE 1

Variable

Meaning

𝐶0

Colour of the group’s backdrop

𝐶

Computed colour of the group, which shall be used as the source colour when the group is treated as an object

𝑓

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

𝛼

Computed alpha of the group, which shall be used as the object alpha when the group is treated as an object

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 subclause. 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 𝐶𝑠 , the object shape 𝑓j , and the object alpha αj . The group compositing formulas for a non-isolated, non-knockout group are defined as follows: •

Initialization: 𝑓𝑔0 = α𝑔0 = 0.0

•

For each group element 𝐸𝑖 ∈ 𝐺 (𝑖 = 1, … , 𝑛): Composite(𝐶𝑖−1 , 𝛼𝑖−1 , 𝐸𝑖 ) if 𝐸𝑖 is a group ⟨𝐶𝑠𝑖 , 𝑓𝑗𝑖 , 𝛼𝑗𝑖 ⟩ = { intrinsic color, shape, and (shape × opacity) of 𝐸𝑖 otherwise 𝑓𝑠𝑖 = 𝑓𝑗𝑖 × 𝑓𝑚𝑖 × 𝑓𝑘𝑖 𝛼𝑠𝑖 = 𝛼𝑗𝑖 × (𝑓𝑚𝑖 × 𝑞𝑚𝑖 ) × (𝑓𝑘𝑖 × 𝑞𝑘𝑖 ) 𝑓𝑔𝑖 = Union(𝑓𝑔𝑖−1 , 𝑓𝑠𝑖 ) 𝛼𝑔𝑖 = Union(𝛼𝑔𝑖−1 , 𝛼𝑠𝑖 ) 𝛼𝑖 = Union(α0 , 𝛼𝑔𝑖 ) Ci = (1 −

•

αsi αs ) × Ci−1 + i × ((1 − αi−1 ) × Csi + αi−1 × Bi (Ci−1 , Csi )) αi αi

Result: 𝐶 = 𝐶𝑛 + (𝐶𝑛 − 𝐶0 ) × (

𝛼0 − 𝛼0 ) 𝛼𝑔𝑛

𝑓 = 𝑓𝑔𝑛 𝛼 = 𝛼𝑔𝑛 406

ISO 32000-2:2020(E)

where the variables have the meanings shown in "Table 140 — Variables used in the group compositing formulas" (in addition to those in "Table 139 — Arguments and results of the group compositing function"). For an element Ei that is an elementary object, the colour, shape, and alpha values Csi, 𝑓𝑗 , and αji are intrinsic 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 its 𝐶𝑆 i, 𝑓𝑗 i, and 𝛼𝑗 i in the calculations for the parent group. Table 140 — Variables used in the group compositing formulas

NOTE 2

Variable

Meaning

𝐸𝑖

Element i of the group: a compound variable representing the element’s colour, shape, opacity, and blend mode

𝑓𝑠𝑖

Source shape for element Ei

𝑓𝑗𝑖

Object shape for element Ei

𝑓𝑚𝑖

Mask shape for element Ei

𝑓𝑘𝑖

Constant shape for element Ei

𝑓𝑔𝑖

Group shape: the accumulated source shapes of group elements E1 to Ei, excluding the initial backdrop

𝑞𝑚𝑖

Mask opacity for element Ei

𝑞𝑘𝑖

Constant opacity for element Ei

𝛼𝑠𝑖

Source alpha for element Ei

𝛼𝑗𝑖

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

𝛼𝑔𝑖

Group alpha: the accumulated source alphas of group elements E1 to Ei, excluding the initial backdrop

𝛼𝑖

Accumulated alpha after compositing element Ei, including the initial backdrop

𝑐𝑠𝑖

Source colour for element Ei

𝑐𝑖

Accumulated colour after compositing element Ei, including the initial backdrop

Bi (ci−1 , csi )

Blend function for element Ei

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

407

ISO 32000-2:2020(E)

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 subclause. NOTE 3

Special attention is 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: ϕb =

𝐶=

(1 − αgn ) × α0 Union(α0 , αgn )

𝐶𝑛 − 𝜙𝑏 × 𝐶0 1 − 𝜙𝑏

where 𝜙𝑏 is the backdrop fraction, the relative contribution of the backdrop colour to the overall colour. NOTE 4

For shape and alpha, backdrop removal can be accomplished by maintaining two sets of variables to hold the accumulated values. There is never any need to compute the corresponding complete shape, fi, that includes the backdrop contribution.

The group shape and alpha, 𝑓g i and αg i, 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, 𝛼𝑖 , 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 11.4.6, “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.

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 the group backdrop. 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

408

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

ISO 32000-2:2020(E)

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

Figure 74 — Isolated and knockout groups "Figure 74 — Isolated and knockout groups" (see 11.4.5, "Isolated groups" and 11.4.6, "Knockout groups") 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 nonisolated and composites with the backdrop. The figure also illustrates the difference between knockout and non-knockout groups (see 11.4.6, "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.

For an isolated group, the group compositing formulas shall be altered by adding one statement to the initialization: 𝑎0 = 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 = 𝐶𝑛 , since there is no backdrop contribution to be factored out.

When compositing the group’s results with the group backdrop, any required colour conversion from the blending space to the colour space in effect for the back drop shall use the rendering intent and black point compensation values specified in the current graphics state (see 8.4, "Graphics state") at the time the group was invoked.

11.4.6

Knockout groups

409

ISO 32000-2:2020(E)

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

NOTE 1

"Figure 74 — Isolated and knockout 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.

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. 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 unnormalised temporary alpha and colour results, αt and Ct. 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.

𝛼𝑡 = Union(𝛼𝑔𝑏 , 𝑞𝑠𝑖 ) 𝐶𝑡 = (1 − 𝑞𝑠𝑖 ) × 𝛼𝑏 × 𝐶𝑏 + 𝑞𝑠𝑖 × ((1 − 𝛼𝑏 ) × 𝐶𝑠𝑖 + 𝛼𝑏 × B𝑖 (𝐶𝑏 , 𝐶𝑠𝑖 )) b) Compute a weighted average of this result with the object’s immediate backdrop, using the source shape as the weighting factor. Then normalise the result colour by the result alpha: 𝛼𝑔𝑖 = (1 − 𝑓𝑠𝑖 ) × 𝛼𝑔𝑖−1 + 𝑓𝑠𝑖 × 𝛼𝑡 𝛼𝑖 = Union(𝛼0 , 𝛼𝑔𝑖 ) Ci =

(1 − 𝑓si ) × αi−1 × Ci−1 + 𝑓si × Ct αi

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

Ct in Group Compositing Computations is slightly different from the preceding Ct: it is

410

premultiplied by 𝑓si.

ISO 32000-2:2020(E)

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

11.4.7

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.

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 (in a colour space chosen by the PDF processor), although varying according to the actual properties of the medium. However, some interactive PDF processors 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, for example, when used as a reference XObject (see 8.10.4, "Reference XObjects"). In this situation the PDF “page” shall not be composited with the media colour; instead it shall be treated as a transparency group using the page Group attributes dictionary and is composited with its backdrop in the usual way according to the page Group attributes dictionary settings.

The remainder of this subclause 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: ⟨𝐶𝑔 , 𝑓𝑔 , 𝛼𝑔 ⟩ = Composite(𝑈, 0, 𝑃) 𝐶 = (1 − 𝛼𝑔 ) × 𝑊 + 𝛼𝑔 × 𝐶𝑔 where the variables have the meanings shown in "Table 141 — Variables used in the page group compositing formulas". 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). © ISO 2020 – All rights reserved

411

ISO 32000-2:2020(E)

Table 141 — Variables used in the page group compositing formulas Variable

Meaning

𝑃

The page group, consisting of all elements E1,…, En in the page’s top-level stack

𝐶𝑔

Computed colour of the page group

𝑓𝑔

Computed shape of the page group

𝛼𝑔

Computed alpha of the page group

𝐶

Computed colour of the page

𝑊

Initial colour of the page (nominally white but may vary depending on the properties of the medium or the needs of the application)

𝑈

An undefined colour (which is not used, since the α0 argument of Composite is 0)

The page group’s initial blending colour space is inherited from the native colour space of the actual, assumed or simulated output device. NOTE 1

A PDF processor can choose to simulate an output device other than the actual one being used, for example when doing soft proofing.

NOTE 2

A PDF processor rendering for a device with a native colour space that cannot be represented as a PDF colour space can choose to require that the output be treated as a simulation of a print characterization that can be represented as a PDF colour space.

That initial colour space shall serve as the default blending colour space for each page, unless the page explicitly specifies an alternative default by means of its page dictionary containing a Group key that contains a CS key whose value represents a different colour space from the initial blending colour space. If a PDF processor chooses to simulate an output device other than the actual one being used, for example when doing “Soft Proofing”, then the native colour space of that simulated output device should be used as the default blending colour space for each page of the document. A PDF writer should provide a CIE-based colour space, either by the page group’s CS entry or some other means, to ensure more predictable results of the compositing computations within the page group. NOTE 3

PDF/X-4 (ISO 15930-7) establishes the destination profile in the PDF/X OutputIntent as the implied default page blending colour space, which allows the page group’s CS entry to be a device colour but still provide a CIE-based colour space.

All page-level compositing shall be done in the default blending colour space of the page, and the entire result shall then, if the colour spaces are not equivalent, be converted to the native colour space of the output device before being composited with the context-dependent backdrop. If the page group needs to be converted to the colour space of the output device, the colour conversion shall use a rendering intent of RelativeColorimetric unless the processor has an implementationdependent way of specifying it otherwise. Additionally, the use of black point compensation in this colour conversion process is implementation-dependent. 412 © ISO 2020 – All rights reserved

ISO 32000-2:2020(E)

11.4.8

Summary of group compositing computations

This subclause is a restatement of the group compositing formulas that also takes isolated groups and knockout groups into account. See "Table 139 — Arguments and results of the group compositing function" and "Table 140 — Variables used in the group compositing formulas" in 11.4.4, "Group compositing computations" for the meanings of the variables. ⟨𝐶, 𝑓, 𝛼⟩ = Composite(𝐶0 , 𝛼0 , 𝐺) Initialization: 𝑓𝑔0 = 𝑎𝑔0 = 0 if the group is isolated

𝑎0 = 0

For each group element 𝐸𝑖 ∈ 𝐺 (𝑖 = 1, … , 𝑛): 0 𝑏={ 𝑖−1

if the group is a knockout otherwise

Composite(Cb ,αb ,Ei ) ⟨Csi ,𝑓𝑗𝑖 ,αji ⟩= { intrinsic color, shape, and (shape×opacity) of Ei

if Ei is a group otherwise

𝑓𝑠𝑖 = 𝑓𝑗𝑖 × 𝑓𝑚𝑖 × 𝑓𝑘𝑖 𝛼𝑠𝑖 = 𝛼𝑗𝑖 × (𝑓𝑚𝑖 × 𝑞𝑚𝑖 ) × (𝑓𝑘𝑖 × 𝑞𝑘𝑖 ) 𝑓𝑔𝑖 = Union(𝑓𝑔𝑖−1 , 𝑓𝑠𝑖 ) 𝛼𝑔𝑖 = (1 − 𝑓𝑠𝑖 ) × 𝛼𝑔𝑖−1 + (𝑓𝑠𝑖 − 𝛼𝑠𝑖 ) × 𝛼𝑔𝑏 + 𝛼𝑠𝑖 𝛼𝑖 = Union(𝛼0 , 𝛼𝑔𝑖 ) 𝐶𝑡 = (𝑓𝑠𝑖 − 𝛼𝑠𝑖 ) × 𝛼𝑏 × 𝐶𝑏 + 𝛼𝑠𝑖 × ((1 − 𝛼𝑏 ) × 𝐶𝑠𝑖 + 𝛼𝑏 × 𝐵𝑖 (𝐶𝑏 , 𝐶𝑠𝑖 )) 𝐶𝑖 =

(1 − 𝑓𝑠𝑖 ) × 𝛼𝑖−1 × 𝐶𝑖−1 + 𝐶𝑡 𝛼𝑖

Result: 𝐶 = 𝐶𝑛 + (𝐶𝑛 − 𝐶0 ) × (

𝛼0 − 𝛼0 ) 𝛼𝑔𝑛

𝑓 = 𝑓𝑔𝑛 𝛼 = 𝛼𝑔𝑛 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 can use the simplified derived formulas.

413

ISO 32000-2:2020(E)

11.5 Soft masks 11.5.1

General

As stated in earlier subclauses, the shape and opacity values used in compositing an object may include components called the mask shape (fm) and mask opacity (qm), 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 8.5.4, "Clipping path operators"). 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 can 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 can then be used to derive the mask in either of two ways, as described in the following subclauses.

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 , 𝐺) 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 customised. NOTE 1

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

NOTE 2

The shape and alpha of an empty group is 0.0.

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 414

ISO 32000-2:2020(E)

⟨𝐶𝑔 , 𝑓𝑔 , 𝛼𝑔 ⟩ = Composite(𝐶0 , 1, 𝐺) 𝐶 = (1 − 𝛼𝑔 ) × 𝐶0 + 𝛼𝑔 × 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 colorimetrically correct luminosity.

EXAMPLE 1

In the case of a PDF CalRGB space, the formula is 𝑌 = 𝑌𝐴 × 𝐴𝐺𝑅 + 𝑌𝐵 × 𝐵𝐺𝐺 + 𝑌𝐶 × 𝐶 𝐺𝐵 using components of the Gamma and Matrix entries of the colour space dictionary (see "Table 63 — Entries in a CalRGB colour space dictionary" in 8.6.5, "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.

EXAMPLE 2

This method makes no pretence of colorimetric 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 = 1 − min(1, 0.3 × 𝐶 + 0.59 × 𝑀 + 0.11 × 𝑌 + 𝐾)

Following this conversion, the result shall be passed through a separately specified transfer function, allowing the masking effect to be customised. NOTE 2

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.

11.6 Specifying transparency in PDF 11.6.1

General

Subclauses 11.1 through 11.5 inclusive have presented the transparent imaging model at an abstract level, with little mention of its representation in PDF. This subclause describes the facilities available for specifying transparency in PDF.

11.6.2

Specifying source and backdrop colours

Single graphics objects, as defined in 8.2, "Graphics objects", shall be treated as elementary objects for transparency compositing purposes (subject to special treatment for text objects, as described in 9.3.8, "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 © ISO 2020 – All rights reserved

415

ISO 32000-2:2020(E)

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 Cs , 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 Cb 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 blend mode 𝐵(𝐶𝑏 , 𝐶𝑠 ) shall be determined by the current blend mode parameter in the graphics state (see 8.4, "Graphics state"), which is specified by the BM entry in a graphics state parameter dictionary (8.4.5, "Graphics state parameter dictionaries"). Its value shall be either a name object, designating one of the standard blend modes listed in "Table 134 — Standard separable blend modes" and "Table 135 — Standard non-separable blend modes" in 11.3.5, "Blend mode" or its value shall be an array of such names. However, a value which is an array of names is deprecated in PDF 2.0, and should not be used. If encountered, a PDF processor shall use the first blend mode in the array that it recognizes (or Normal if it recognizes none of them).

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 (fj) and opacity (qj) of the object being composited

•

A separate shape (fm) or opacity (qm) mask independent of the object itself

•

A scalar shape (fk) or opacity (qk) constant to be added at every point

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

11.6.4.2

Object shape and opacity

The shape value fj 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 (8.5.3, "Path-painting operators", and 9.4.3, "Text-showing operators"), the shape shall always be 1.0 inside and 0.0 outside the path.

•

For images (8.9, "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 (8.9.6.3, "Explicit masking" and 8.9.6.4, "Colour key masking").

•

For image masks (8.9.6.2, "Stencil masking"), the shape shall be 1.0 for painted areas and 0.0 for masked areas.

•

For objects painted with a tiling pattern (8.7.3, "Tiling patterns") or a shading pattern (8.7.4, "Shading patterns"), the shape shall be further constrained by the objects that define the pattern (see 11.6.7, "Patterns and transparency").

416

ISO 32000-2:2020(E)

•

For objects painted with the sh operator (8.7.4.2, "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 8.7.4.3, "Shading dictionaries").

All elementary objects shall have an intrinsic opacity qj 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 “11.6.4.3, “Mask shape and opacity” and 11.6.4.4, “Constant shape and opacity”.

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 (fm) or opacity (qm) values, depending on the setting of the alpha source parameter in the graphics state (see 8.4, "Graphics state"). NOTE 1

This is a boolean flag, set with the AIS ("alpha is shape") entry in a graphics state parameter dictionary (8.4.5, "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 11.6.5.1, "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. It shall also mean that any existing mask shall be removed from the current graphics state. In this case, the mask shape or opacity shall be implicitly 1.0 everywhere.

NOTE 2

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 11.6.4.4, “Constant shape and opacity”).

•

An image XObject may contain its own soft-mask image in the form of a subsidiary image XObject referenced as the value of the SMask entry of the parent image dictionary (see 8.9.5, "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, for this image object only, the current soft mask in the graphics state.

•

An image XObject that has an announced JPXDecode filter may specify an SMaskInData entry, indicating that the soft mask is embedded in the data stream as an opacity channel (see 7.4.9, "JPXDecode filter"). If SMaskInData is present with a value other than 0, the embedded soft-mask shall override any explicit or colour key mask specified by the image dictionary’s Mask entry, and it shall override, for this image object only, the current soft mask in the graphics state.

11.6.4.4

Constant shape and opacity

The current alpha constant parameter in the graphics state (see 8.4, "Graphics state") shall be two scalar values — one for strokes and one for all other painting operations — to be used for the constant shape (fk) or constant opacity (qk) component in the colour compositing formulas. NOTE

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

417

ISO 32000-2:2020(E)

The stroking and nonstroking alpha constants shall be set, respectively, by the CA and ca entries in a graphics state parameter dictionary (see 8.4.5, "Graphics state parameter dictionaries"). As described previously for the soft mask, the AIS (“alpha is shape”) entry in a graphics state parameter dictionary shall determine whether the alpha constants are interpreted as shape values (true) or opacity values (false).

11.6.5

Specifying soft masks

11.6.5.1

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 8.4, "Graphics state"). "Table 142 — Entries in a soft-mask dictionary" 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 11.6.6, "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 may be omitted. The value of the TR key in the SoftMask dictionary, which is a transfer function, 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 value of the TR key in the SoftMask dictionary, which is a transfer function, 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.

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 8.10.2, "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 8.6.6.4, "Separation colour spaces" and 8.6.6.5, "DeviceN colour spaces"). NOTE

418

The special colourant names All and None do not specify spot colour components and are therefore not subject to this requirement.

ISO 32000-2:2020(E)

Table 142 — 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.

S

name

(Required) A subtype specifying the method that shall 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 11.5.2, "Deriving a soft mask from group alpha").

Luminosity The group’s computed colour shall be converted to a singlecomponent luminosity value (see 11.5.3, "Deriving a soft mask from group luminosity"). G

stream

(Required) A transparency group XObject (see 11.6.6, "Transparency group XObjects") that shall 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.

BC

array

(Optional) An array of component values specifying the colour that shall 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 11.6.6, "Transparency group XObjects"). Default value: the colour space’s initial value, representing black.

TR

function or name

(Optional) A function object (see 7.10, "Functions") specifying the transfer function that shall 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.

11.6.5.2

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 8.9.5, "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 87 — Additional entries specific to an image dictionary" in 8.9.5, "Image dictionaries"), subject to the restrictions listed in "Table 143 — Restrictions on the entries in a soft-mask image dictionary". 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 pre-blended 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.) © ISO 2020 – All rights reserved 419

ISO 32000-2:2020(E)

If the image data are pre-blended, the matte colour shall be specified by a Matte entry in the soft-mask image dictionary (see "Table 143 — Restrictions on the entries in a soft-mask image dictionary"). The pre-blending computation, performed independently for each component, shall be 𝑐 ′ = 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 143 — Restrictions on the entries in a soft-mask image dictionary

420

Key

Restriction

Type

If present, shall be XObject.

Subtype

Required, shall be Image.

Width

If a Matte entry (see "Table 144 — Additional entry in a soft-mask image dictionary") 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

Optional; default value: [0 1].

Interpolate

Optional.

Alternates

Ignored.

Name

ISO 32000-2:2020(E)

Key

Restriction

StructParent

Ignored.

ID

Ignored.

OPI

Ignored.

Table 144 — 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 pre-blended. The array shall consist of n numbers, where n is the number of components in the colour space specified by the ColorSpace entry (or the base entry of the colour space, if the colour space is Indexed) 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 pre-blended.

When pre-blended image data are 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 PDF processor 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. NOTE

When deriving c from c’ and α is 0.0, the inverted formula will result in a divide by zero. In this special case an arbitrary value for c can be chosen within the range of colour component values for the image colour space. Because α is 0.0, the arbitrary value of c does not affect output as described in 11.3.2 "Basic notation for compositing computations".

The pre-blending 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 pre-blending shall precede the colour conversion. If the image colour space is an Indexed space (see 8.6.6.3, "Indexed colour spaces"), the colour values in the colour table (not the index values themselves) shall be pre-blended.

11.6.6

Transparency group XObjects

A transparency group is represented in PDF as a special type of group XObject (see 8.10.3, "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 8.10.2, "Form dictionaries"). The value of this entry is a group attributes dictionary defining the properties of the group. The format and meaning of the dictionary’s contents is 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 145 — Additional entries specific to a transparency group attributes dictionary". A page object (see 7.7.3.3, "Page objects") may also have a Group entry, whose value is a group attributes dictionary specifying the attributes of the page group (see 11.4.7, "Page group"). Some of the © ISO 2020 – All rights reserved

421

ISO 32000-2:2020(E)

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 145 — Additional entries specific to a transparency group attributes dictionary Key

Type

Value

S

name

(Required) The group subtype, which identifies the type of group whose attributes this dictionary describes; shall be Transparency for a transparency group.

CS

name or array

(Sometimes required for Luminosity groups, otherwise optional) 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 11.3.4, "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 8.6.5.6, "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 11.6.5.1, "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. 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 12.5.5, "Appearance streams"), the default colour space shall be inherited from the page on which the annotation appears. I

boolean

(Optional) A flag specifying whether the transparency group is isolated (see 11.4.5, "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.

K

boolean

(Optional) A flag specifying whether the transparency group is a knockout group (see 11.4.6, "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.

422

ISO 32000-2:2020(E)

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 8.10, "Form XObjects"): •

Initial backdrop: If the transparency group is non-isolated, 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 immediate 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.

•

Initial blend mode: Before execution of the transparency group XObject’s content stream, the current blend mode in the graphics state shall be initialised 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.

•

Compositing: 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.

•

Group colour space:

•

o

For isolated groups, if a group colour space (CS) is specified in the group attributes dictionary, all painting operators shall convert source colours in a colour space (that are not equivalent to the group colour space) to the group colour space before compositing objects into the group. The resulting colour at each point shall be interpreted in the group colour space. Rules for handling Separation and DeviceN colour spaces are described in 11.7.3, "Spot colours and transparency".

o

For non-isolated groups, or if no group colour space is specified, the group colour space shall be inherited from the parent group or page. If not otherwise specified, the page group’s colour space shall be defined as described in 11.4.7, "Page group". All painting operators shall convert source colours in a colour space that is not equivalent to the inherited colour space, to that inherited colour space before compositing objects onto the backdrop.

Final compositing: 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 colour conversion needs to take place in order to composite the group into its parent, the rendering intent and black point compensation from the graphics state at the point of invocation of the Do operator shall be used for the conversion.

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. © ISO 2020 – All rights reserved

423

ISO 32000-2:2020(E)

NOTE 2

Applications that perform caching of rendered form XObjects need to 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 contains a group attributes subdictionary whose group subtype (S) is Transparency. An ordinary form XObject — one having no Group entry — or having a Group entry with a subtype other than Transparency — shall not be subject to any grouping behaviour for transparency purposes.

11.6.7

Patterns and transparency

In the transparent imaging model, the graphics objects making up the pattern cell of a tiling pattern (see 8.7.3, "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 (8.7.4, "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 initialised as follows: •

As always for transparency groups, those parameters related to transparency (blend mode, soft mask, and alpha constant) shall be initialised to their standard default values.

•

Any parameters that are not so specified shall be inherited from the graphics state that was in effect at the beginning of the content stream in which the shading pattern is set to be the current colour in the graphics state or in which the sh operator is used.

•

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 8.7.4, "Shading patterns"). Only those parameters that affect the sh operator, such as the current transformation matrix, black point compensation 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 (𝐶𝑠 ), object shape (fj), and object opacity (qi) 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

424

Unlike the opaque imaging model, in which the pattern cell of a tiling pattern can 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 re-executed 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 optimised 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. © ISO 2020 – All rights reserved

ISO 32000-2:2020(E)

NOTE 2

In a raster-based implementation of tiling, it is advisable to treat all tiles 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.

11.7 Colour space and rendering issues 11.7.1

General

The following subclauses describe the interactions between transparency and other aspects of colour specification and rendering in the PDF imaging model.

11.7.2

Colour spaces for transparency groups

As discussed in 11.6.6, "Transparency group XObjects", an isolated transparency group shall either have an explicitly declared colour space or inherit that of its parent group. If the colour space of the transparency group is a device colour space, and some ancestor of the group has a CIE-based colour space with the same number of colourants, then the colour space of this group shall be the CIE-based space of the nearest such ancestor. If an isolated transparency group or page has an ICCBased ‘CMYK’ colour space, DeviceCMYK shall be redefined within the transparency group to be the same as the blending colour space and references to the process colourants Cyan, Magenta, Yellow and Black are defined to be references to the corresponding colourants in the blending colour space, even where the actual or simulated output device is not CMYK. Non-isolated groups shall inherit their colour space from the nearest ancestor isolated parent group (subject to special treatment for the page group, as described in 11.4.7, "Page group"). NOTE 1

This is because the use of an explicit colour space in a non-isolated group would require converting colours from the backdrop’s colour space to that of the group in order to perform the compositing computations. Such conversion is not always feasible (since some colour conversions can be performed only in one direction), and even if feasible, it would entail an excessive number of colour conversions.

If the colour space of a graphics object within the group is not equivalent to the group’s blending colour space, then it shall be converted to the group’s colour space, and all blending and compositing computations shall be done in that space (see 11.3.4, "Blending colour space"). The resulting colours shall then be interpreted in the group’s colour space when the group is subsequently composited with its backdrop. When converting colours, if the colour space of any graphics object is a device colour space, and the current group or an ancestor of the current group is defined with a CIE-based colour space with the same number of colourants, then, for compositing purposes only, the colour space of the graphics object shall be the CIE-based space of the nearest such ancestor. Nevertheless for graphics objects that © ISO 2020 – All rights reserved

425

ISO 32000-2:2020(E)

are specified in DeviceCMYK, the full semantics of DeviceCMYK shall still apply, including overprinting. The choice of a group colour space has significant effects on the results that are produced because the result of compositing in a device colour space is device-dependent. For the compositing computations to work in a device-independent way, the group’s colour space should be CIE-based. NOTE 2

A consequence of choosing a CIE-based group colour space is that only CIE-based spaces can be used to predictably specify the colours of objects within the group. This is because conversion from device to CIE-based colours is implementation-dependent. See further discussion subsequently.

NOTE 3

The compositing computations and blend functions generally compute linear combinations of colour component values, on the assumption that the component values themselves are linear. For this reason, it is usually best to choose a group colour space that has a linear gamma function. If a nonlinear colour space is chosen, the results are still well-defined, but the appearance might not match the user’s expectations.

NOTE 4

The CIE-based sRGB colour space (see 8.6.5, "CIE-Based colour spaces") is nonlinear and hence can be unsuitable for use as a group colour space.

NOTE 5

To minimise the accumulation of round off errors and avoid additional errors arising from the use of linear group colour spaces, more precision is needed for intermediate results than is typically used to represent either the original source data or the final rasterized results.

If a group’s colour space — whether specified explicitly or inherited from the parent group — is CIEbased, any use for painting objects of device colour spaces with a different number of colourants than the group’s colour space shall be subject to special treatment. These device colours cannot be painted directly into such a group, since there is no generally defined method for converting them to the CIEbased colour space. This problem arises in the following cases: •

DeviceGray, DeviceRGB, and DeviceCMYK colour spaces, unless remapped to default CIE-based colour spaces (see 8.6.5.6, "Default colour spaces")

•

Operators (such as rg) that specify a device colour space implicitly, unless that space is remapped

•

Special colour spaces whose base or underlying space is a device colour space, unless that space is remapped

The default colour space remapping mechanism should always be employed when defining a transparency group whose colour space is CIE-based. If a device colour is specified and is not remapped, it shall be converted or mapped to a CIE-based colour space in an implementationdependent fashion. The restrictions concerning device colourants do not apply if the group’s colour space is implicitly converted to DeviceCMYK, as discussed in 8.6.5.7, "Implicit conversion of CIE-Based colour spaces". NOTE 6

11.7.3

See Annex P, "An algorithm to determine the actual blending colour space of a transparency group" for a diagram that illustrates an algorithm to determine the actual blending colour space for a transparency group.

Spot colours and transparency

The foregoing discussion of colour spaces has been concerned with process colours — those produced by combinations of an output device’s process colourants. Process colours may be specified directly in the device’s native colour space (such as DeviceCMYK), or they may be produced by conversion from some other colour space, such as a CIE-based (CalRGB or ICCBased) space. Whatever means is used to 426

ISO 32000-2:2020(E)

specify them, process colours may be subject to conversion to and from the group’s colour space. A spot colour is an additional colour component, independent of those used to produce process colours. It may represent either an additional separation to be produced or an additional colourant to be applied to the composite page (see 8.6.6.4, "Separation colour spaces" and 8.6.6.5, "DeviceN colour spaces"). The colour component value, or tint, for a spot colour specifies the concentration of the corresponding spot colourant. Tints are conventionally represented as subtractive, rather than additive, values. Spot colours are inherently device-dependent and are not always available. In the opaque imaging model, each use of a spot colour component in a Separation or DeviceN colour space is accompanied by an alternate colour space and a tint transformation function for mapping tint values into that space. This enables the colour to be approximated with process colourants when the corresponding spot colourant is not available on the device. Spot colours can be accommodated straightforwardly in the transparent imaging model (except for issues relating to overprinting, discussed in 11.7.4, "Overprinting and transparency"). When an object is painted transparently with a spot colour component that is available in the output device, that colour shall be composited with the corresponding spot colour component of the backdrop, independently of the compositing that is performed for process colours. A spot colour retains its own identity; it shall not be subject to conversion to or from the colour space of the enclosing transparency group or page. If the object is an element of a transparency group, one of two things should happen: •

The group shall maintain a separate colour value for each spot colour component, independently of the group’s colour space. In effect, the spot colour passes directly through the group hierarchy to the device, with no colour conversions performed. However, it shall still be subject to blending and compositing with other objects that use the same spot colour.

•

The spot colour shall be converted to its alternate colour space. The resulting colour shall then be subject to the usual compositing rules for process colours. In particular, spot colours shall not be available in a transparency group XObject that is used to define a soft mask; the alternate colour space shall always be substituted in that case.

Only a single shape value and opacity value shall be maintained at each point in the computed group results; they shall apply to both process and spot colour components. In effect, every object paints every existing colour component, both process and spot. Where no value has been explicitly specified for a given component in a given object, an additive value of 1.0 (or a subtractive tint value of 0.0) shall be assumed. For instance, when painting an object with a colour specified in a DeviceCMYK or ICCBased colour space, the process colour components shall be painted as specified and the spot colour components shall be painted with an additive value of 1.0. Likewise, when painting an object with a colour specified in a Separation colour space, the named spot colour shall be painted as specified and all other components (both process colours and other spot colours) shall be painted with an additive value of 1.0. The consequences of this are discussed in 11.7.4, "Overprinting and transparency". Under the opaque imaging model, a Separation or DeviceN colour space may specify the individual process colour components of the output device, as if they were spot colours. However, within a transparency group, this should be done only if the group inherits the native colour space of the output device (or is implicitly converted to DeviceCMYK, as discussed in 8.6.5.7, "Implicit conversion of CIE-

427

ISO 32000-2:2020(E)

Based colour spaces"). If any other colour space has been specified for the group, the Separation or DeviceN colour space shall be converted to its alternate colour space. NOTE 1

In general, within a transparency group containing an explicitly specified colour space, the group's process colour components are different from the device's process colour components. Conversion to the device's process colour components occurs only after all colour compositing computations for the group have been completed. Consequently, the device's process colour components are not accessible within the group. For instance, outside of any transparency group, a device whose native colour space is DeviceCMYK has a Cyan component that can be specified in a Separation or DeviceN colour space. On the other hand, within a transparency group whose colour space is ICCBased, the group has no Cyan component available to be painted.

NOTE 2

The special colourant All is defined as applying tint values to all available colourants at once (see 8.6.6.4, “Separation colour spaces”). When All is used inside a transparency group, "all available colourants" is no longer the same as "all colourants available on the output device." Painting All inside a transparency group can only apply tint values to the process colourants that are defined by the group blending colour space and to the spot colourants available on the output device (as the spot colours are maintained separate from the group blending colour space). Indeed, inside a transparency group, the process colourants of the output device are irrelevant and unknown, only the colourants of the group blending colour space (and the spot colours of the output device) are available. Once a tint of Separation All has been applied to all colourants available in the transparency group, this result is then subject to the usual colour conversion rules when the group as a whole is composited on its own backdrop. The practical implication of this is that applying All inside a transparency group does not necessarily result in an equal tint percentage for all process colour components on that location on the page.

11.7.4

Overprinting and transparency

11.7.4.1

General

In the opaque imaging model, overprinting is controlled by two parameters of the graphics state: the overprint parameter and the overprint mode (see 8.6.7, "Overprint control"). Painting an object causes some specific set of device colourants to be marked, as determined by the current colour space and current colour in the graphics state. The remaining colourants shall be either erased or left unchanged, depending on whether the overprint parameter is false or true. When the current colour space is DeviceCMYK, the overprint mode parameter additionally enables this selective marking of colourants to be applied to individual colour components according to whether the component value is zero or nonzero. NOTE 1

Because this model of overprinting deals directly with the painting of device colourants, independently of the colour space in which source colours have been specified, it is highly device-dependent and primarily addresses production needs rather than design intent. Overprinting is usually reserved for opaque colourants or for very dark colours, such as black. It is also invoked during late-stage production operations such as trapping (see 14.11.6, "Trapping support"), when the actual set of device colourants has already been determined.

NOTE 2

Consequently, it is best to think of transparency as taking place in appearance space, but overprinting of device colourants in device space. This means that colourant overprint decisions are made at output time, based on the actual resultant colourants of any transparency compositing operation. On the other hand, effects similar to overprinting can be achieved in a device-independent manner by taking advantage of blend modes, as described in 11.7.4.2, “Blend modes and overprinting”.

428

ISO 32000-2:2020(E)

11.7.4.2

Blend modes and overprinting

As stated in 11.7.3, "Spot colours and transparency", each graphics object that is painted shall affect all existing colour components: all process colourants in the transparency group’s colour space as well as any available spot colourants. For colour components whose value has not been specified, a source colour value of 1.0 shall be assumed; when objects are fully opaque and the Normal blend mode is used, this shall have the effect of erasing those components. This treatment is consistent with the behaviour of the opaque imaging model with the overprint parameter set to false. The transparent imaging model defines some blend modes, such as Darken, that may be used to achieve effects similar to overprinting. The blend function for Darken is: B(cb , cs ) = min(cb , cs ) In this blend mode, the result of compositing shall always be the same as the backdrop colour when the source colour is 1.0, as it is for all unspecified colour components. When the backdrop is fully opaque, this shall leave the result colour unchanged from that of the backdrop. This is consistent with the behaviour of the opaque imaging model with the overprint parameter set to true. If the object or backdrop is not fully opaque, the actions described previously are altered accordingly. That is, the erasing effect shall be reduced, and overprinting an object with a colour value of 1.0 may affect the result colour. While these results may or may not be useful, they lie outside the realm of the overprinting and erasing behaviour defined in the opaque imaging model. When process colours are overprinted or erased (because a spot colour is being painted), the blending computations described previously shall be done independently for each component in the group’s colour space. If the group colour space is different from the native colour space of the output device, its components are not the device’s actual process colourants; the blending computations shall affect the process colourants only after the group’s results have been converted to the device colour space. Thus the effect is different from that of overprinting or erasing the device’s process colourants directly. On the other hand, this is a fully general operation that works uniformly, regardless of the type of object or of the computations that produced the source colour. NOTE 1

The discussion so far has focused on those colour components whose values are not specified and that are to be either erased or left unchanged. However, the Normal or Darken blend modes used for these purposes are not always suitable for use on those components whose colour values are specified. In particular, using the Darken blend mode for such components would preclude overprinting a dark colour with a lighter one. Moreover, some other blend mode could be specifically desired for those components.

The PDF graphics state specifies only one current blend mode parameter, which shall always apply to process colourants and sometimes to spot colourants as well. Specifically, only separable, whitepreserving blend modes shall be used for spot colours. If the specified blend mode is not separable or not white-preserving, it shall apply only to process colour components, and the Normal blend mode shall be substituted for spot colours. A blend mode is white-preserving if its blend function B has the property that 𝐵(1.0,1.0) = 1.0. NOTE 2

Of the standard separable blend modes listed in "Table 134 — Standard separable blend modes" in 11.3.5, "Blend mode" all except Difference and Exclusion are white-preserving. This ensures that when objects accumulate in an isolated transparency group, the accumulated values for

429

ISO 32000-2:2020(E)

unspecified components remain 1.0 as long as only white-preserving blend modes are used. The group’s results can then be overprinted using Darken (or other useful modes) while avoiding unwanted interactions with components whose values were never specified within the group.

11.7.4.3

Compatibility with opaque overprinting

For compatibility with the methods of overprint control used in the opaque imaging model, a PDF processor may consider implementing a special blend mode that consults the overprint-related graphics state parameters to compute its result. This mode shall apply only when painting elementary graphics objects (fills, strokes, text, images, and shadings). It shall not be invoked explicitly; rather, it may be implicitly invoked whenever an elementary graphics object is painted while overprinting is enabled (that is, when the overprint parameter in the graphics state is true). NOTE 1

Earlier designs of the transparent imaging model included an additional blend mode named Compatible, which explicitly invoked the blend mode described here. Because this mode can be invoked implicitly whenever appropriate, it is never necessary to specify the Compatible blend mode for use in compositing.

The value of the blend function 𝐵(𝐶𝑏 , 𝐶𝑠 ) in the this mode shall be either 𝐶𝑏 or 𝐶𝑠 , depending on the setting of the overprint mode parameter, the current and group colour spaces, and the source colour value 𝐶𝑠 : •

If the overprint mode is 1 (nonzero overprint mode) and the current colour space and group colour space are both DeviceCMYK, then process colour components with nonzero values shall replace the corresponding component values of the backdrop; components with zero values leave the existing backdrop value unchanged. That is, the value of the blend function 𝐵(𝐶𝑏 , 𝐶𝑠 ) shall be the source component Cs for any process (DeviceCMYK) colour component whose (subtractive) colour value is nonzero; otherwise it shall be the backdrop component 𝐶𝑏 . For spot colour components, the value shall always be 𝐶𝑏 .

•

In all other cases, the value of 𝐵(𝐶𝑏 , 𝐶𝑠 ) shall be 𝐶𝑠 for all colour components specified in the current colour space, otherwise 𝐶𝑏 .

EXAMPLE 1

NOTE 2

If the current colour space is DeviceCMYK or equivalent, the value of the blend function is 𝐶𝑠 for process colour components and 𝐶𝑏 for spot components. On the other hand, if the current colour space is a Separation space representing a spot colour component, the value is 𝐶𝑠 for that spot component and 𝐶𝑏 for all process components and all other spot components.

In the previous descriptions, the term current colour space refers to the colour space used for a painting operation. This can be specified by the current colour space parameter in the graphics state (see 8.6.2, "Colour values"), implicitly by colour operators such as rg (8.6.8, "Colour operators"), or by the ColorSpace entry of an image XObject (8.9.5, "Image dictionaries"). In the case of an Indexed space, it refers to the base colour space (see 8.6.6.3, "Indexed colour spaces"); likewise for Separation and DeviceN spaces that revert to their alternate colour space, as described under 8.6.6.4, "Separation colour spaces" and 8.6.6.5, "DeviceN colour spaces".

If the current blend mode is any mode other than Normal when invoking this special overprinting blend mode, the object being painted shall be implicitly treated as if it were defined in a non-isolated, non-knockout transparency group, and painted using the this special blend mode. The group’s results shall then be painted using the current blend mode in the graphics state. NOTE 3

430

It is not necessary to create such an implicit transparency group if the current blend mode is Normal; simply substituting the special blend mode while painting the object produces equivalent results. There are some additional cases in which the implicit transparency group can be optimised out.

ISO 32000-2:2020(E)

Figure 75 — Blending and overprinting EXAMPLE 2

"Figure 75 — Blending and overprinting" shows the effects of all four possible combinations of blending and overprinting, using the Screen blend mode in the DeviceCMYK colour space. The label “overprint enabled” means that the overprint parameter in the graphics state is true and the overprint mode is 1. In the upper half of the figure, a light green oval is painted opaquely (opacity = 1.0) over a backdrop shading from pure yellow to pure magenta. In the lower half, the same object is painted with transparency (opacity = 0.5).

11.7.4.4

Special path-painting considerations

The overprinting considerations discussed in 11.7.4.3, "Compatibility with opaque overprinting" also affect those path-painting operations that combine filling and stroking a path in a single operation. These include the B, B*, b, and b* operators (see 8.5.3, "Path-painting operators") and the painting of glyphs with text rendering mode 2 or 6 (9.3.6, "Text rendering mode"). For transparency compositing purposes, the combined fill and stroke shall be treated as a single graphics object, as if they were enclosed in a transparency group. This implicit group is established and used as follows: © ISO 2020 – All rights reserved

431

ISO 32000-2:2020(E)

•

If overprinting is enabled (the overprint parameters for both stroking and non-stroking operations in the graphics state are true) and the current stroking and nonstroking alpha constants are equal, a non-isolated, non-knockout transparency group shall be established. Within the group, the fill and stroke shall be performed with an alpha value of 1.0 but with the special overprinting blend mode described in 11.7.4.3, “Compatibility with opaque overprinting”. The group results shall then be composited with the backdrop, using the originally specified alpha and blend mode.

•

In all other cases, a non-isolated knockout group shall be established. Within the group, the fill and stroke shall be performed with their respective prevailing alpha constants and the prevailing blend mode. The group results shall then be composited with the backdrop, using an alpha value of 1.0 and the Normal blend mode.

NOTE 1

In the case of showing text with the combined filling and stroking text rendering modes, this behaviour is independent of the text knockout parameter in the graphics state (see 9.3.8, "Text knockout").

NOTE 2

The purpose of these rules is to avoid having a non-opaque stroke composite with the result of the fill in the region of overlap, which would produce a double border effect that is usually undesirable. The special case that applies when the overprint parameter is true is for backward compatibility with the overprinting behaviour of the opaque imaging model. If a desired effect cannot be achieved with a combined filling and stroking operator or text rendering mode, it can be achieved by specifying the fill and stroke with separate path objects and an explicit transparency group.

NOTE 3

Overprinting of the stroke over the fill does not work in the second case described previously (although either the fill or the stroke can still overprint the backdrop). Furthermore, if the overprint graphics state parameter is true, the results are discontinuous at the transition between equal and unequal values of the stroking and nonstroking alpha constants. For this reason, it is best not to use overprinting for combined filling and stroking operations if the stroking and nonstroking alpha constants are being varied independently.

11.7.4.5

Summary of overprinting behavior

“Table 146 — Overprinting behaviour in the transparent imaging model” shows overprinting behavior in the transparent imaging model. Table 146 — Overprinting behaviour in the transparent imaging model Source colour space

Affected colour Value of blend function 𝑩(𝑪𝒃 , 𝑪𝒔 ) expressed as tint component of group OP false OP true, OP true, space OPM 0 OPM 1

DeviceCMYK, specified directly, not in a sampled image

C, M, Y, or K

𝐶𝑠

𝐶𝑠 𝑖𝑓 𝐶𝑠 ≠ 0.0 𝐶𝑏 𝑖𝑓 𝐶𝑠 = 0.0

Process colour component other than CMYK

𝐶𝑠

Spot colourant

𝐶𝑠 (= 0.0)

𝐶𝑏

Process colour component

𝐶𝑠

Spot colourant

𝐶𝑠 (= 0.0)

𝐶𝑏

Any process colour space (including other cases of DeviceCMYK)

432

ISO 32000-2:2020(E)

Source colour space

Affected colour Value of blend function 𝑩(𝑪𝒃 , 𝑪𝒔 ) expressed as tint component of group OP false OP true, OP true, space OPM 0 OPM 1

Separation or DeviceN

Process colour component

𝐶𝑠 (= 0.0)

𝐶𝑏

Spot colourant named in source space

𝐶𝑠

Spot colourant not named in source space

𝐶𝑠 (= 0.0)

𝐶𝑏

𝐶𝑠

A group (not an elementary object)

All colour components

Colour component values are represented in these tables as subtractive tint values because overprinting is typically applied to subtractive colourants such as inks rather than to additive ones such as phosphors on a display screen. The special overprinting blend mode is therefore described as if it took subtractive arguments and returned subtractive results. In reality, however, the special overprinting blend mode (like all blend modes) shall treat colour components as additive values; subtractive components shall be complemented before and after application of the special blend function. NOTE 1

The process colour components are those of the group’s colour space, which is not necessarily the same as that of the output device (and can even be something like CalRGB or ICCBased). For this reason, the process colour components of the group colour space cannot be treated as if they were spot colours in a Separation or DeviceN colour space (see 11.7.3, "Spot colours and transparency"). This difference between opaque and transparent overprinting and erasing rules arises only within a transparency group (including the page group, if its colour space is different from the native colour space of the output device). There is no difference in the treatment of spot colour components.

NOTE 2

"Table 146 — Overprinting behaviour in the transparent imaging model" has one additional row at the bottom. It applies when painting an object that is a transparency group rather than an elementary object (fill, stroke, text, image, or shading). As stated in 11.7.3, "Spot colours and transparency", a group is considered to paint all colour components, both process and spot. Colour components that were not explicitly painted by any object in the group have an additive colour value of 1.0 (subtractive tint 0.0). Since no information is retained about which components were actually painted within the group, compatible overprinting is unavailable in this case; the special overprinting blend mode reverts to Normal, with no consideration of the overprint and overprint mode parameters. A transparency-aware PDF writer can choose a more suitable blend mode, such as Darken, to produce an effect similar to overprinting.

11.7.5

Rendering parameters and transparency

11.7.5.1

General

The opaque imaging model has several graphics state parameters dealing with the rendering of colour: the current halftone (see 10.6.5, "Halftone dictionaries"), transfer functions (10.5, "Transfer functions"), rendering intent (8.6.5.8, "Rendering intents"), black point compensation (8.6.5.9, "Use of black point compensation", and black-generation and undercolour-removal functions (10.4.2.3, © ISO 2020 – All rights reserved

433

ISO 32000-2:2020(E)

"Conversion between DeviceGray and DeviceCMYK"). All of these rendering parameters may be specified on a per-object basis; they control how a particular object is rendered. When all objects are opaque, it is easy to define what this means. But when they are transparent, more than one object may contribute to the colour at a given point; it is unclear which rendering parameters to apply in an area where transparent objects overlap. At the same time, the transparent imaging model should be consistent with the opaque model when only opaque objects are painted. There are two categories of rendering parameters that are treated somewhat differently in the presence of transparency. In the first category are halftone and transfer functions, which are applied only when the final colour at a given point on the page is known. In the second category are rendering intent, black generation, and undercolour removal, which are applied whenever colours are converted from one colour space to another.

11.7.5.2

Halftone and transfer function

When objects are transparent, rendering of an object may not occur when the object is specified but at some later time. Hence, the implementation shall keep track of the halftone and transfer function parameters at each point on the page from the time they are specified until the time rendering actually occurs. This means that these rendering parameters may be associated with regions of the page rather than with individual objects. The halftone and transfer function to be used at any given point on the page shall be those in effect at the time of painting the last (topmost) elementary graphics object enclosing that point, but only if the object is fully opaque. Only elementary objects shall be relevant; the rendering parameters associated with a group object are ignored. The topmost object at any point shall be defined to be the topmost elementary object in the entire page stack that has a nonzero object shape value (fj) at that point (that is, for which the point is inside the object). An object is fully opaque if all of the following conditions hold at the time the object is painted: •

The current alpha constant in the graphics state (stroking or nonstroking, depending on the painting operation) is 1.0.

•

The current blend mode in the graphics state is Normal.

•

The current soft mask in the graphics state is None.

•

If the object is an image XObject and there is not an SMask entry in its image dictionary.

•

The foregoing four conditions were also true at the time the Do operator was invoked for the group containing the object, as well as for any direct ancestor groups.

•

If the current colour is a tiling pattern, all objects in the definition of its pattern cell also satisfy the foregoing conditions.

Together, these conditions ensure that only the object itself shall contribute to the colour at the given point, completely obscuring the backdrop. For portions of the page whose topmost object is not fully opaque or that are never painted at all, the default halftone and transfer function for the page shall be used (see "Table 52 — Device-dependent graphics state parameters"). If a graphics object is painted with overprinting enabled—that is, if the applicable (stroking or nonstroking) overprint parameter in the graphics state is true—the halftone and transfer function to use at a given point shall be determined independently for each colour component. An object is opaque 434

ISO 32000-2:2020(E)

for a given component only if overprinting yields the source colour (not the backdrop colour) for that component. See 11.7.4, "Overprinting and transparency".

11.7.5.3

Rendering intent, black point compensation and colour conversions

The rendering intent, black-generation, undercolour-removal and black point compensation parameters control certain colour conversions. In the presence of transparency, they may need to be applied earlier than the actual rendering of colour onto the page. The rendering intent influences the conversion from a CIE-based colour space to a target colour space, taking into account the target space’s colour gamut (the range of colours it can reproduce). Whereas in the opaque imaging model the target space shall always be the native colour space of the output device, in the transparent model it may instead be the group colour space of a transparency group into which an object is being painted. The rendering intent is needed at the moment such a conversion is performed — that is, when painting an elementary or group object specified in a CIE-based colour space into a parent group having a different colour space. NOTE

This differs from the current halftone and transfer function, whose values are used only when all colour compositing has been completed and rasterization is being performed.

In all cases, the rendering intent to use for converting an object’s colour (whether that of an elementary object or of a transparency group) is determined by the rendering intent parameter associated with the object. In particular: •

When painting an elementary object with a CIE-based colour into a transparency group having a different colour space, the rendering intent used shall be the current rendering intent in effect in the graphics state at the time of the painting operation.

•

When painting a transparency group whose colour space is CIE-based into a parent group having a different colour space, the rendering intent used shall be the current rendering intent in effect at the time the Do operator is applied to the group.

Black point compensation is needed during colour conversions in cases where the detail in dark regions or shadow section of an image can otherwise be lost. Black point compensation addresses this conversion problem by adjusting for differences between the darkest level of black achievable in one colour space and the darkest level of black achievable on another. The graphics state parameter UseBlackPtComp ("Table 57 — Entries in a graphics state parameter dictionary) enables or disables the use of black point compensation when doing colour conversions. A similar approach works for the black-generation and undercolour-removal functions, which shall be applied only during conversion from DeviceRGB to DeviceCMYK colour spaces: •

When painting an elementary object with a DeviceRGB colour directly into a transparency group whose colour space is DeviceCMYK, the functions used shall be the current black-generation and undercolour-removal functions in effect in the graphics state at the time of the painting operation.

•

When painting a transparency group whose colour space is DeviceRGB into a parent group whose colour space is DeviceCMYK, the functions used shall be the ones in effect at the time the Do operator is applied to the group.

435

ISO 32000-2:2020(E)

•

436

When the colour space of the page group is DeviceRGB and the native colour space of the output device is DeviceCMYK, the functions used to convert colours to the device’s colour space shall be the default functions for the page.

ISO 32000-2:2020(E)

12

Navigation: PDF20-Spec-10-Rendering | PDF20-Spec-Index | PDF20-Spec-12-Interactive

PDF20 Spec 11 Transparency

Chapter 11: Transparency

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!