PDF Reference sixth edition, Adobe Portable Document Format Version 1.7 (book 1) — page 8

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Patterns come in two varieties:

• Tiling patterns consist of a small graphical figure (called a pattern cell) that is

replicated at fixed horizontal and vertical intervals to fill the area to be painted.

The graphics objects to use for tiling are described by a content stream.

• Shading patterns define a gradient fill that produces a smooth transition

between colors across the area. The color to use is specified as a function of

position using any of a variety of methods.

Note: The ability to paint with patterns is a feature of PDF 1.2 (tiling patterns) and

PDF 1.3 (shading patterns). With some effort, it is possible to achieve a limited form

of tiling patterns in PDF 1.1 by defining them as character glyphs in a special font

and painting them repeatedly with the Tj operator. Another technique, defining

patterns as halftone screens, is not recommended because the effects produced are

device-dependent.

Patterns are specified in a special family of color spaces named Pattern. These

spaces use pattern objects as the equivalent of color values instead of the numeric

component values used with other spaces. A pattern object may be a dictionary

or a stream, depending on the type of pattern; the term pattern dictionary is used

generically throughout this section to refer to either a dictionary object or the

dictionary portion of a stream object. (Those pattern objects that are streams are

specifically identified as such in the descriptions of particular pattern types; un-

less otherwise stated, they are understood to be simple dictionaries instead.) This

section describes Pattern color spaces and the specification of color values within

them. See Section 4.5, “Color Spaces,” for information about color spaces and col-

or values in general and Section 7.5.6, “Patterns and Transparency,” for further

discussion of the treatment of patterns in the transparent imaging model.

4.6.1

General Properties of Patterns

A pattern dictionary contains descriptive information defining the appearance

and properties of a pattern. All pattern dictionaries contain an entry named

PatternType, whose value identifies the kind of pattern the dictionary describes:

type 1 for a tiling pattern or type 2 for a shading pattern. The remaining contents

of the dictionary depend on the pattern type and are detailed below in the sec-

tions on individual pattern types.

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SECTION 4.6

Patterns

All patterns are treated as colors; a Pattern color space is established with the CS

or cs operator just like other color spaces, and a particular pattern is installed as

the current color with the SCN or scn operator (see Table 4.24 on page 287).

A pattern’s appearance is described with respect to its own internal coordinate

system. Every pattern has a pattern matrix, a transformation matrix that maps the

pattern’s internal coordinate system to the default coordinate system of the pat-

tern’s parent content stream (the content stream in which the pattern is defined as

a resource). The concatenation of the pattern matrix with that of the parent con-

tent stream establishes the pattern coordinate space, within which all graphics ob-

jects in the pattern are interpreted.

For example, if a pattern is used on a page, the pattern appears in the Pattern sub-

dictionary of that page’s resource dictionary, and the pattern matrix maps pattern

space to the default (initial) coordinate space of the page. Changes to the page’s

transformation matrix that occur within the page’s content stream, such as rota-

tion and scaling, have no effect on the pattern; it maintains its original relation-

ship to the page no matter where on the page it is used. Similarly, if a pattern is

used within a form XObject (see Section 4.9, “Form XObjects”), the pattern ma-

trix maps pattern space to the form’s default user space (that is, the form co-

ordinate space at the time the form is painted with the Do operator). A pattern

may be used within another pattern; the inner pattern’s matrix defines its

relationship to the pattern space of the outer pattern.

Note: PostScript allows a pattern to be defined in one context but used in another.

For example, a pattern might be defined on a page (that is, its pattern matrix maps

the pattern coordinate space to the user space of the page) but be used in a form on

that page, so that its relationship to the page is independent of each individual

placement of the form. PDF does not support this feature; in PDF, all patterns are

local to the context in which they are defined.

4.6.2

Tiling Patterns

A tiling pattern consists of a small graphical figure called a pattern cell. Painting

with the pattern replicates the cell at fixed horizontal and vertical intervals to fill

an area. The effect is as if the figure were painted on the surface of a clear glass

tile, identical copies of which were then laid down in an array covering the area

and trimmed to its boundaries. This process is called tiling the area.

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The pattern cell can include graphical elements such as filled areas, text, and sam-

pled images. Its shape need not be rectangular, and the spacing of tiles can differ

from the dimensions of the cell itself. When performing painting operations such

as S (stroke) or f (fill), the application paints the cell on the current page as many

times as necessary to fill an area. The order in which individual tiles (instances of

the cell) are painted is unspecified and unpredictable; it is inadvisable for the fig-

ures on adjacent tiles to overlap.

The appearance of the pattern cell is defined by a content stream containing the

painting operators needed to paint one instance of the cell. Besides the usual en-

tries common to all streams (see Table 3.4 on page 62), this stream’s dictionary

has the additional entries listed in Table 4.25.

TABLE 4.25 Additional entries specific to a type 1 pattern dictionary

KEY

TYPE

VALUE

Type

name

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

must be Pattern for a pattern dictionary.

PatternType

integer

(Required) A code identifying the type of pattern that this dictionary de-

scribes; must be 1 for a tiling pattern.

PaintType

integer

(Required) A code that determines how the color of the pattern cell is to be

specified:

Colored tiling pattern. The pattern’s content stream specifies the col-

ors used to paint the pattern cell. When the content stream begins ex-

ecution, the current color is the one that was initially in effect in the

pattern’s parent content stream. (This is similar to the definition of

the pattern matrix; see Section 4.6.1, “General Properties of Pat-

terns.”)

Uncolored tiling pattern. The pattern’s content stream does not specify

any color information. Instead, the entire pattern cell is painted with

a separately specified color each time the pattern is used. Essentially,

the content stream describes a stencil through which the current col-

or is to be poured. The content stream must not invoke operators that

specify colors or other color-related parameters in the graphics state;

otherwise, an error occurs (see Section 4.5.7, “Color Operators”).

The content stream may paint an image mask, however, since it does

not specify any color information (see “Stencil Masking” on page

350).

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SECTION 4.6

Patterns

KEY

TYPE

VALUE

TilingType

integer

(Required) A code that controls adjustments to the spacing of tiles relative to

the device pixel grid:

Constant spacing. Pattern cells are spaced consistently—that is, by a

multiple of a device pixel. To achieve this, the application may need

to distort the pattern cell slightly by making small adjustments to

XStep, YStep, and the transformation matrix. The amount of distor-

tion does not exceed 1 device pixel.

No distortion. The pattern cell is not distorted, but the spacing

between pattern cells may vary by as much as 1 device pixel, both

horizontally and vertically, when the pattern is painted. This achieves

the spacing requested by XStep and YStep on average but not neces-

sarily for each individual pattern cell.

Constant spacing and faster tiling. Pattern cells are spaced consistently

as in tiling type 1 but with additional distortion permitted to enable a

more efficient implementation.

BBox

rectangle

(Required) An array of four numbers in the pattern coordinate system giving

the coordinates of the left, bottom, right, and top edges, respectively, of the

pattern cell’s bounding box. These boundaries are used to clip the pattern

cell.

XStep

number

(Required) The desired horizontal spacing between pattern cells, measured in

the pattern coordinate system.

YStep

number

(Required) The desired vertical spacing between pattern cells, measured in

the pattern coordinate system. Note that XStep and YStep may differ from the

dimensions of the pattern cell implied by the BBox entry. This allows tiling

with irregularly shaped figures. XStep and YStep may be either positive or

negative but not zero.

Resources

dictionary

(Required) A resource dictionary containing all of the named resources

required by the pattern’s content stream (see Section 3.7.2, “Resource Dic-

tionaries”).

Matrix

array

(Optional) An array of six numbers specifying the pattern matrix (see Section

4.6.1, “General Properties of Patterns”). Default value: the identity matrix

[ 1

0 0 1 0 0 ].

The pattern dictionary’s BBox, XStep, and YStep values are interpreted in the pat-

tern coordinate system, and the graphics objects in the pattern’s content stream

are defined with respect to that coordinate system. The placement of pattern cells

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in the tiling is based on the location of one key pattern cell, which is then dis-

placed by multiples of XStep and YStep to replicate the pattern. The origin of the

key pattern cell coincides with the origin of the pattern coordinate system. The

phase of the tiling can be controlled by the translation components of the Matrix

entry in the pattern dictionary.

The first step in painting with a tiling pattern is to establish the pattern as the cur-

rent color in the graphics state. Subsequent painting operations tile the painted

areas with the pattern cell described by the pattern’s content stream. To obtain the

pattern cell, the application performs these steps:

1. Saves the current graphics state (as if by invoking the q operator)

2. Installs the graphics state that was in effect at the beginning of the pattern’s

parent content stream, with the current transformation matrix altered by the

pattern matrix as described in Section 4.6.1, “General Properties of Patterns”

3. Paints the graphics objects specified in the pattern’s content stream

4. Restores the saved graphics state (as if by invoking the Q operator)

Note: The pattern’s content stream should not set any of the device-dependent

parameters in the graphics state (see Table 4.3 on page 212) because it may result in

incorrect output.

Colored Tiling Patterns

A colored tiling pattern is a pattern whose color is self-contained. In the course of

painting the pattern cell, the pattern’s content stream explicitly sets the color of

each graphical element it paints. A single pattern cell can contain elements that

are painted different colors; it can also contain sampled grayscale or color images.

This type of pattern is identified by a pattern type of 1 and a paint type of 1 in the

pattern dictionary.

When the current color space is a Pattern space, a colored tiling pattern can be

selected as the current color by supplying its name as the single operand to the

SCN or scn operator. This name must be the key of an entry in the Pattern subdic-

tionary of the current resource dictionary (see Section 3.7.2, “Resource Diction-

aries”), whose value is the stream object representing the pattern. Since the

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Patterns

pattern defines its own color information, no additional operands representing

color components are specified to SCN or scn. For example, if P1 is the name of a

pattern resource in the current resource dictionary, the following code establishes

it as the current nonstroking color:

/Pattern cs

/P1 scn

Subsequent executions of nonstroking painting operators, such as f (fill), Tj (show

text), or Do (paint external object) with an image mask, use the designated pat-

tern to tile the areas to be painted.

Example 4.23 defines a page (object 5) that paints three circles and a triangle

using a colored tiling pattern (object 15) over a yellow background. The pattern

consists of the symbols for the four suits of playing cards (spades, hearts, dia-

monds, and clubs), which are character glyphs taken from the ZapfDingbats font

(see Section D.5, “ZapfDingbats Set and Encoding”); the pattern’s content stream

specifies the color of each glyph. Plate 8 shows the results.

Example 4.23

5 0 obj

% Page object

<< /Type /Page

/Parent 2 0 R

/Resources 10 0 R

/Contents 30 0 R

/CropBox [ 0 0 225 225 ]

endobj

10 0 obj

% Resource dictionary for page

<< /Pattern << /P1 15 0 R >>

endobj

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15 0 obj

% Pattern definition

<< /Type /Pattern

/PatternType 1

% Tiling pattern

/PaintType 1

% Colored

/TilingType 2

/BBox [ 0 0 100 100 ]

/XStep 100

/YStep 100

/Resources 16 0 R

/Matrix [ 0.4

0.0

0.4

0.0

0.0 ]

/Length 183

stream

% Begin text object

/F1 1 Tf

% Set text font and size

64 0 0 64 7.1771 2.4414

% Set text matrix

0 Tc

% Set character spacing

0 Tw

% Set word spacing

1.0

0.0

0.0 rg

% Set nonstroking color to red

( \001 ) Tj

% Show spade glyph

0.7478 −0.007 TD

% Move text position

0.0

1.0

0.0 rg

% Set nonstroking color to green

( \002 ) Tj

% Show heart glyph

−0.7323 0.7813 TD

% Move text position

0.0

1.0 rg

% Set nonstroking color to blue

( \003 ) Tj

% Show diamond glyph

0.6913 0.007 TD

% Move text position

0.0

0.0 rg

% Set nonstroking color to black

( \004 ) Tj

% Show club glyph

% End text object

endstream

endobj

16 0 obj

% Resource dictionary for pattern

<< /Font << /F1 20 0 R >>

endobj

20 0 obj

% Font for pattern

<< /Type /Font

/Subtype /Type1

/Encoding 21 0 R

/BaseFont /ZapfDingbats

endobj

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21 0 obj

% Font encoding

<< /Type /Encoding

/Differences [ 1 /a109 /a110 /a111 /a112 ]

endobj

30 0 obj

% Contents of page

<< /Length 1252 >>

stream

0.0 G

% Set stroking color to black

1.0

0.0 rg

% Set nonstroking color to yellow

25 175 175 −150 re

% Construct rectangular path

% Fill path

/Pattern cs

% Set pattern color space

/P1 scn

% Set pattern as nonstroking color

99.92 49.92 m

% Start new path

99.92 77.52 77.52 99.92 49.92 99.92 c

% Construct lower-left circle

22.32 99.92 −0.08 77.52 −0.08 49.92 c

−0.08 22.32 22.32 −0.08 49.92 −0.08 c

77.52 −0.08 99.92 22.32 99.92 49.92 c

% Fill and stroke path

224.96 49.92 m

% Start new path

224.96 77.52 202.56 99.92 174.96 99.92 c

% Construct lower-right circle

147.36 99.92 124.96 77.52 124.96 49.92 c

124.96 22.32 147.36 -0.08 174.96 −0.08 c

202.56 −0.08 224.96 22.32 224.96 49.92 c

% Fill and stroke path

87.56 201.70 m

% Start new path

63.66 187.90 55.46 157.32 69.26 133.40 c

% Construct upper circle

83.06 109.50 113.66 101.30 137.56 115.10 c

161.46 128.90 169.66 159.50 155.86 183.40 c

142.06 207.30 111.46 215.50 87.56 201.70 c

% Fill and stroke path

50 50 m

% Start new path

175 50 l

% Construct triangular path

112.5 158.253 l

% Close, fill, and stroke path

endstream

endobj

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Several features of Example 4.23 are noteworthy:

• The three circles and the triangle are painted with the same pattern. The pat-

tern cells align, even though the circles and triangle are not aligned with re-

spect to the pattern cell. For example, the position of the blue diamonds varies

relative to the three circles.

• The pattern cell does not completely cover the tile: it leaves the spaces between

the glyphs unpainted. When the tiling pattern is used as a color, the existing

background (the yellow rectangle) shows through these unpainted areas.

Uncolored Tiling Patterns

An uncolored tiling pattern is a pattern that has no inherent color: the color must

be specified separately whenever the pattern is used. It provides a way to tile dif-

ferent regions of the page with pattern cells having the same shape but different

colors. This type of pattern is identified by a pattern type of 1 and a paint type of

2 in the pattern dictionary. The pattern’s content stream does not explicitly speci-

fy any colors; it can paint an image mask (see “Stencil Masking” on page 350) but

no other kind of image.

A Pattern color space representing an uncolored tiling pattern requires a parame-

ter: an object identifying the underlying color space in which the actual color of

the pattern is to be specified. The underlying color space is given as the second

element of the array that defines the Pattern color space. For example, the array

[ /Pattern

/DeviceRGB ]

defines a Pattern color space with DeviceRGB as its underlying color space.

Note: The underlying color space cannot be another Pattern color space.

Operands supplied to the SCN or scn operator in such a color space must include

a color value in the underlying color space, specified by one or more numeric

color components, as well as the name of a pattern object representing an un-

colored tiling pattern. For example, if the current resource dictionary (see Section

3.7.2, “Resource Dictionaries”) defines Cs3 as the name of a ColorSpace resource

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SECTION 4.6

Patterns

whose value is the Pattern color space shown above and P2 as a Pattern resource

denoting an uncolored tiling pattern, the code

/Cs3 cs

0.30 0.75 0.21 /P2 scn

establishes Cs3 as the current nonstroking color space and P2 as the current non-

stroking color, to be painted in the color represented by the specified components

in the DeviceRGB color space. Subsequent executions of nonstroking painting op-

erators, such as f (fill), Tj (show text), and Do (paint external object) with an im-

age mask, use the designated pattern and color to tile the areas to be painted. The

same pattern can be used repeatedly with a different color each time.

Example 4.24 is similar to Example 4.23 on page 295, except that it uses an uncol-

ored tiling pattern to paint the three circles and the triangle, each in a different

color (see Plate 9). To do so, it supplies four operands each time it invokes the scn

operator: three numbers denoting the color components in the underlying

DeviceRGB color space, along with the name of the pattern.

Example 4.24

5 0 obj

% Page object

<< /Type /Page

/Parent 2 0 R

/Resources 10 0 R

/Contents 30 0 R

/CropBox [ 0 0 225 225 ]

endobj

10 0 obj

% Resource dictionary for page

<< /ColorSpace << /Cs12 12 0 R >>

/Pattern << /P1 15 0 R >>

endobj

12 0 obj

% Color space

[ /Pattern

/DeviceRGB ]

endobj

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15 0 obj

% Pattern definition

<< /Type /Pattern

/PatternType 1

% Tiling pattern

/PaintType 2

% Uncolored

/TilingType 2

/BBox [ 0 0 100 100 ]

/XStep 100

/YStep 100

/Resources 16 0 R

/Matrix [ 0.4

0.0

0.4

0.0

0.0 ]

/Length 127

stream

% Begin text object

/F1 1 Tf

% Set text font and size

64 0 0 64 7.1771 2.4414

% Set text matrix

0 Tc

% Set character spacing

0 Tw

% Set word spacing

( \001 ) Tj

% Show spade glyph

0.7478 −0.007 TD

% Move text position

( \002 ) Tj

% Show heart glyph

−0.7323 0.7813 TD

% Move text position

( \003 ) Tj

% Show diamond glyph

0.6913 0.007 TD

% Move text position

( \004 ) Tj

% Show club glyph

% End text object

endstream

endobj

16 0 obj

% Resource dictionary for pattern

<< /Font << /F1 20 0 R >>

endobj

20 0 obj

% Font for pattern

<< /Type /Font

/Subtype /Type1

/Encoding 21 0 R

/BaseFont /ZapfDingbats

endobj

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SECTION 4.6

Patterns

21 0 obj

% Font encoding

<< /Type /Encoding

/Differences [ 1 /a109 /a110 /a111 /a112 ]

endobj

30 0 obj

% Contents of page

<< /Length 1316 >>

stream

0.0 G

% Set stroking color to black

1.0

0.0 rg

% Set nonstroking color to yellow

25 175 175 −150 re

% Construct rectangular path

% Fill path

/Cs12 cs

% Set pattern color space

0.77 0.20 0.00 /P1 scn

% Set nonstroking color and pattern

99.92 49.92 m

% Start new path

99.92 77.52 77.52 99.92 49.92 99.92 c

% Construct lower-left circle

22.32 99.92 −0.08 77.52 −0.08 49.92 c

−0.08 22.32 22.32 −0.08 49.92 −0.08 c

77.52 −0.08 99.92 22.32 99.92 49.92 c

% Fill and stroke path

0.2

0.8

0.4

/P1 scn

% Change nonstroking color

224.96 49.92 m

% Start new path

224.96 77.52 202.56 99.92 174.96 99.92 c

% Construct lower-right circle

147.36 99.92 124.96 77.52 124.96 49.92 c

124.96 22.32 147.36 -0.08 174.96 −0.08 c

202.56 −0.08 224.96 22.32 224.96 49.92 c

% Fill and stroke path

0.3

0.7

1.0

/P1 scn

% Change nonstroking color

87.56 201.70 m

% Start new path

63.66 187.90 55.46 157.30 69.26 133.40 c

% Construct upper circle

83.06 109.50 113.66 101.30 137.56 115.10 c

161.46 128.90 169.66 159.50 155.86 183.40 c

142.06 207.30 111.46 215.50 87.56 201.70 c

% Fill and stroke path

0.5

0.2

1.0

/P1 scn

% Change nonstroking color

50 50 m

% Start new path

175 50 l

% Construct triangular path

112.5 158.253 l

% Close, fill, and stroke path

endstream

endobj

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4.6.3

Shading Patterns

Shading patterns (PDF 1.3) provide a smooth transition between colors across an

area to be painted, independent of the resolution of any particular output device

and without specifying the number of steps in the color transition. Patterns of

this type are described by pattern dictionaries with a pattern type of 2. Table 4.26

shows the contents of this type of dictionary.

TABLE 4.26 Entries in a type 2 pattern dictionary

KEY

TYPE

VALUE

Type

name

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

must be Pattern for a pattern dictionary.

PatternType

integer

(Required) A code identifying the type of pattern that this dictionary de-

scribes; must be 2 for a shading pattern.

Shading

dictionary

(Required) A shading object (see below) defining the shading pattern’s gradi-

or stream

ent fill. The contents of the dictionary consist of the entries in Table 4.28 and

those in one of Tables 4.29 to 4.34.

Matrix

array

(Optional) An array of six numbers specifying the pattern matrix (see Section

4.6.1, “General Properties of Patterns”). Default value: the identity matrix

[ 1

0 0 1 0 0 ].

ExtGState

dictionary

(Optional) A graphics state parameter dictionary (see Section 4.3.4, “Graph-

ics State Parameter Dictionaries”) containing graphics state parameters to be

put into effect temporarily while the shading pattern is painted. Any parame-

ters that are not so specified are inherited from the graphics state that was in

effect at the beginning of the content stream in which the pattern is defined

as a resource.

The most significant entry is Shading, whose value is a shading object defining

the properties of the shading pattern’s gradient fill. This is a complex “paint” that

determines the type of color transition the shading pattern produces when paint-

ed across an area. A shading object may be a dictionary or a stream, depending

on the type of shading; the term shading dictionary is used generically throughout

this section to refer to either a dictionary object or the dictionary portion of a

stream object. (Those shading objects that are streams are specifically identified

as such in the descriptions of particular shading types; unless otherwise stated,

they are understood to be simple dictionaries instead.)

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SECTION 4.6

Patterns

By setting a shading pattern as the current color in the graphics state, a PDF con-

tent stream can use it with painting operators such as f (fill), S (stroke), Tj (show

text), or Do (paint external object) with an image mask to paint a path, character

glyph, or mask with a smooth color transition. When a shading is used in this

way, the geometry of the gradient fill is independent of that of the object being

painted.

Shading Operator

When the area to be painted is a relatively simple shape whose geometry is the

same as that of the gradient fill itself, the sh operator can be used instead of the

usual painting operators. sh accepts a shading dictionary as an operand and

applies the corresponding gradient fill directly to current user space. This opera-

tor does not require the creation of a pattern dictionary or a path and works with-

out reference to the current color in the graphics state. Table 4.27 describes the sh

operator.

Note: Patterns defined by type 2 pattern dictionaries do not tile. To create a tiling

pattern containing a gradient fill, invoke the sh operator from within the content

stream of a type 1 (tiling) pattern.

TABLE 4.27 Shading operator

OPERANDS OPERATOR DESCRIPTION

name

(PDF 1.3) Paint the shape and color shading described by a shading dictionary, sub-

ject to the current clipping path. The current color in the graphics state is neither

used nor altered. The effect is different from that of painting a path using a shading

pattern as the current color.

name is the name of a shading dictionary resource in the Shading subdictionary of

the current resource dictionary (see Section 3.7.2, “Resource Dictionaries”). All co-

ordinates in the shading dictionary are interpreted relative to the current user

space. (By contrast, when a shading dictionary is used in a type 2 pattern, the

coordinates are expressed in pattern space.) All colors are interpreted in the color

space identified by the shading dictionary’s ColorSpace entry (see Table 4.28). The

Background entry, if present, is ignored.

This operator should be applied only to bounded or geometrically defined shad-

ings. If applied to an unbounded shading, it paints the shading’s gradient fill across

the entire clipping region, which may be time-consuming.

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Shading Dictionaries

A shading dictionary specifies details of a particular gradient fill, including the

type of shading to be used, the geometry of the area to be shaded, and the geome-

try of the gradient fill. Various shading types are available, depending on the val-

ue of the dictionary’s ShadingType entry:

• Function-based shadings (type 1) define the color of every point in the domain

using a mathematical function (not necessarily smooth or continuous).

• Axial shadings (type 2) define a color blend along a line between two points,

optionally extended beyond the boundary points by continuing the boundary

colors.

• Radial shadings (type 3) define a blend between two circles, optionally ex-

tended beyond the boundary circles by continuing the boundary colors. This

type of shading is commonly used to represent three-dimensional spheres and

cones.

• Free-form Gouraud-shaded triangle meshes (type 4) define a common construct

used by many three-dimensional applications to represent complex colored

and shaded shapes. Vertices are specified in free-form geometry.

• Lattice-form Gouraud-shaded triangle meshes (type 5) are based on the same

geometrical construct as type 4 but with vertices specified as a pseudo-

rectangular lattice.

• Coons patch meshes (type 6) construct a shading from one or more color

patches, each bounded by four cubic Bézier curves.

• Tensor-product patch meshes (type 7) are similar to type 6 but with additional

control points in each patch, affording greater control over color mapping.

Table 4.28 shows the entries that all shading dictionaries share in common;

entries specific to particular shading types are described in the relevant sections

below.

Note: The term target coordinate space, used in many of the following descriptions,

refers to the coordinate space into which a shading is painted. For shadings used

with a type 2 pattern dictionary, this is the pattern coordinate space, discussed in

Section 4.6.1, “General Properties of Patterns.” For shadings used directly with the

sh operator, it is the current user space.

305

SECTION 4.6

Patterns

TABLE 4.28 Entries common to all shading dictionaries

KEY

TYPE

VALUE

ShadingType

integer

(Required) The shading type:

Function-based shading

Axial shading

Radial shading

Free-form Gouraud-shaded triangle mesh

Lattice-form Gouraud-shaded triangle mesh

Coons patch mesh

Tensor-product patch mesh

ColorSpace

name or

(Required) The color space in which color values are expressed. This may be

array

any device, CIE-based, or special color space except a Pattern space. See

“Color Space: Special Considerations” on page 306 for further information.

Background

array

(Optional) An array of color components appropriate to the color space,

specifying a single background color value. If present, this color is used, be-

fore any painting operation involving the shading, to fill those portions of the

area to be painted that lie outside the bounds of the shading object. In the

opaque imaging model, the effect is as if the painting operation were

performed twice: first with the background color and then with the shading.

Note: The background color is applied only when the shading is used as part of

a shading pattern, not when it is painted directly with the sh operator.

BBox

rectangle

(Optional) An array of four numbers giving the left, bottom, right, and top

coordinates, respectively, of the shading’s bounding box. The coordinates are

interpreted in the shading’s target coordinate space. If present, this bounding

box is applied as a temporary clipping boundary when the shading is painted,

in addition to the current clipping path and any other clipping boundaries in

effect at that time.

AntiAlias

boolean

(Optional) A flag indicating whether to filter the shading function to prevent

aliasing artifacts. The shading operators sample shading functions at a rate

determined by the resolution of the output device. Aliasing can occur if the

function is not smooth—that is, if it has a high spatial frequency relative to

the sampling rate. Anti-aliasing can be computationally expensive and is usu-

ally unnecessary, since most shading functions are smooth enough or are

sampled at a high enough frequency to avoid aliasing effects. Anti-aliasing

may not be implemented on some output devices, in which case this flag is

ignored. Default value: false.

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Shading types 4 to 7 are defined by a stream containing descriptive data charac-

terizing the shading’s gradient fill. In these cases, the shading dictionary is also a

stream dictionary and can contain any of the standard entries common to all

streams (see Table 3.4 on page 62). In particular, it always includes a Length en-

try, which is required for all streams.

In addition, some shading dictionaries also include a Function entry whose value

is a function object (dictionary or stream) defining how colors vary across the

area to be shaded. In such cases, the shading dictionary usually defines the geom-

etry of the shading, and the function defines the color transitions across that

geometry. The function is required for some types of shading and optional for

others. Functions are described in detail in Section 3.9, “Functions.”

Note: Discontinuous color transitions, or those with high spatial frequency, may ex-

hibit aliasing effects when painted at low effective resolutions.

Color Space: Special Considerations

Conceptually, a shading determines a color value for each individual point within

the area to be painted. In practice, however, the shading may actually be used to

compute color values only for some subset of the points in the target area, with

the colors of the intervening points determined by interpolation between the

ones computed. Consumer applications are free to use this strategy as long as the

interpolated color values approximate those defined by the shading to within the

smoothness tolerance specified in the graphics state (see Section 6.5.2, “Smooth-

ness Tolerance”). The ColorSpace entry common to all shading dictionaries not

only defines the color space in which the shading specifies its color values but

also determines the color space in which color interpolation is performed.

Note: Some shading types (4 to 7) perform interpolation on a parametric value sup-

plied as input to the shading’s color function, as described in the relevant sections

below. This form of interpolation is conceptually distinct from the interpolation

described here, which operates on the output color values produced by the color

function and takes place within the shading’s target color space.

Gradient fills between colors defined by most shadings are implemented using a

variety of interpolation algorithms, and these algorithms are sensitive to the char-

acteristics of the color space. Linear interpolation, for example, may have observ-

ably different results when applied in a DeviceCMYK color space than in a Lab

color space, even if the starting and ending colors are perceptually identical. The

307

SECTION 4.6

Patterns

difference arises because the two color spaces are not linear relative to each other.

Shadings are rendered according to the following rules:

• If ColorSpace is a device color space different from the native color space of the

output device, color values in the shading are converted to the native color

space using the standard conversion formulas described in Section 6.2, “Con-

versions among Device Color Spaces.” To optimize performance, these conver-

sions may take place at any time (before or after any interpolation on the color

values in the shading). Thus, shadings defined with device color spaces may

have color gradient fills that are less accurate and somewhat device-dependent.

(This does not apply to axial and radial shadings—shading types 2 and 3—be-

cause those shading types perform gradient fill calculations on a single variable

and then convert to parametric colors.)

• If ColorSpace is a CIE-based color space, all gradient fill calculations are per-

formed in that space. Conversion to device colors occurs only after all interpo-

lation calculations have been performed. Thus, the color gradients are device-

independent for the colors generated at each point.

• If ColorSpace is a Separation or DeviceN color space and the specified colo-

rants are supported, no color conversion calculations are needed. If the speci-

fied colorants are not supported (so that the space’s alternate color space must

be used), gradient fill calculations are performed in the designated Separation

or DeviceN color space before conversion to the alternate space. Thus, non-

linear tint transformation functions are accommodated for the best possible

representation of the shading.

• If ColorSpace is an Indexed color space, all color values specified in the shading

are immediately converted to the base color space. Depending on whether the

base color space is a device or CIE-based space, gradient fill calculations are

performed as stated above. Interpolation never occurs in an Indexed color

space, which is quantized and therefore inappropriate for calculations that as-

sume a continuous range of colors. For similar reasons, an Indexed color space

is not allowed in any shading whose color values are generated by a function;

this rule applies to any shading dictionary that contains a Function entry.

Shading Types

In addition to the entries listed in Table 4.28, all shading dictionaries have entries

specific to the type of shading they represent, as indicated by the value of their

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ShadingType entry. The following sections describe the available shading types

and the dictionary entries specific to each.

Type 1 (Function-Based) Shadings

In type 1 (function-based) shadings, the color at every point in the domain is

defined by a specified mathematical function. The function need not be smooth

or continuous. This type is the most general of the available shading types and is

useful for shadings that cannot be adequately described with any of the other

types. Table 4.29 shows the shading dictionary entries specific to this type of

shading, in addition to those common to all shading dictionaries (Table 4.28).

Note: This type of shading cannot be used with an Indexed color space.

TABLE 4.29 Additional entries specific to a type 1 shading dictionary

KEY

TYPE

VALUE

Domain

array

(Optional) An array of four numbers [ x_min x_max y_min y_max ] specifying the

rectangular domain of coordinates over which the color function(s) are defined.

Default value: [ 0.0 1.0

0.0 1.0 ].

Matrix

array

(Optional) An array of six numbers specifying a transformation matrix mapping

the coordinate space specified by the Domain entry into the shading’s target co-

ordinate space. For example, to map the domain rectangle [ 0.0 1.0

0.0 1.0 ] to a

1-inch square with lower-left corner at coordinates (100, 100) in default user

space, the Matrix value would be [ 72 0 0 72 100 100 ]. Default value: the iden-

tity matrix [ 1 0 0 1 0 0 ].

Function

function

(Required) A 2-in, n-out function or an array of n 2-in, 1-out functions (where n

is the number of color components in the shading dictionary’s color space). Each

function’s domain must be a superset of that of the shading dictionary. If the val-

ue returned by the function for a given color component is out of range, it is ad-

justed to the nearest valid value.

The domain rectangle (Domain) establishes an internal coordinate space for the

shading that is independent of the target coordinate space in which it is to be

painted. The color function(s) (Function) specify the color of the shading at each

point within this domain rectangle. The transformation matrix (Matrix) then

maps the domain rectangle into a corresponding rectangle or parallelogram in

the target coordinate space. Points within the shading’s bounding box (BBox) that

fall outside this transformed domain rectangle are painted with the shading’s

309

SECTION 4.6

Patterns

background color (Background); if the shading dictionary has no Background

entry, such points are left unpainted. If the function is undefined at any point

within the declared domain rectangle, an error may occur, even if the corre-

sponding transformed point falls outside the shading’s bounding box.

Type 2 (Axial) Shadings

Type 2 (axial) shadings define a color blend that varies along a linear axis be-

tween two endpoints and extends indefinitely perpendicular to that axis. The

shading may optionally be extended beyond either or both endpoints by continu-

ing the boundary colors indefinitely. Table 4.30 shows the shading dictionary en-

tries specific to this type of shading, in addition to those common to all shading

dictionaries (Table 4.28).

Note: This type of shading cannot be used with an Indexed color space.

TABLE 4.30 Additional entries specific to a type 2 shading dictionary

KEY

TYPE

VALUE

Coords

array

(Required) An array of four numbers [ x₀ y₀ x₁ y₁ ] specifying the starting and

ending coordinates of the axis, expressed in the shading’s target coordinate

space.

Domain

array

(Optional) An array of two numbers [ t₀ t₁ ] specifying the limiting values of a

parametric variable t. The variable is considered to vary linearly between these

two values as the color gradient varies between the starting and ending points of

the axis. The variable t becomes the input argument to the color function(s). De-

fault value: [ 0.0

1.0 ].

Function

function

(Required) A 1-in, n-out function or an array of n 1-in, 1-out functions (where n

is the number of color components in the shading dictionary’s color space). The

function(s) are called with values of the parametric variable t in the domain de-

fined by the Domain entry. Each function’s domain must be a superset of that of

the shading dictionary. If the value returned by the function for a given color

component is out of range, it is adjusted to the nearest valid value.

Extend

array

(Optional) An array of two boolean values specifying whether to extend the

shading beyond the starting and ending points of the axis, respectively. Default

value: [ false false ].

The color blend is accomplished by linearly mapping each point (x, y) along the

axis between the endpoints (x₀ , y₀ ) and (x₁ , y₁ ) to a corresponding point in the

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domain specified by the shading dictionary’s Domain entry. The points (0, 0) and

(1, 0) in the domain correspond respectively to (x₀ , y₀ ) and (x₁ , y₁ ) on the axis.

Since all points along a line in domain space perpendicular to the line from (0, 0)

to (1, 0) have the same color, only the new value of x needs to be computed:

(

x₁

x₀

)

(

x x₀

)

(

y₁

y₀

)

(

y y₀

)

x′

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

x₀

)²

(

y₁

y₀

)²

The value of the parametric variable t is then determined from x ′ as follows:

• For 0 ≤ x ′ ≤ 1, t = t₀ + (t₁ − t₀ ) × x ′.

• For x ′ < 0, if the first element of the Extend array is true, then t = t₀ ; otherwise,

t is undefined and the point is left unpainted.

• For x ′ > 1, if the second element of the Extend array is true, then t = t₁ ; other-

wise, t is undefined and the point is left unpainted.

The resulting value of t is passed as input to the function(s) defined by the shad-

ing dictionary’s Function entry, yielding the component values of the color with

which to paint the point (x, y).

Plate 10 shows three examples of the use of an axial shading to fill a rectangle and

display text. The area to be filled extends beyond the shading’s bounding box.

The shading is the same in all three cases, except for the values of the Background

and Extend entries in the shading dictionary. In the first example, the shading is

not extended at either end and no background color is specified; therefore, the

shading is clipped to its bounding box at both ends. The second example still has

no background color specified, but the shading is extended at both ends; the re-

sult is to fill the remaining portions of the filled area with the colors defined at the

ends of the shading. In the third example, the shading is extended at both ends

and a background color is specified; therefore, the background color is used for

the portions of the filled area beyond the ends of the shading.

Type 3 (Radial) Shadings

Type 3 (radial) shadings define a color blend that varies between two circles.

Shadings of this type are commonly used to depict three-dimensional spheres

and cones. Shading dictionaries for this type of shading contain the entries shown

in Table 4.31, as well as those common to all shading dictionaries (Table 4.28).

311

SECTION 4.6

Patterns

Note: This type of shading cannot be used with an Indexed color space.

TABLE 4.31 Additional entries specific to a type 3 shading dictionary

KEY

TYPE

VALUE

Coords

array

(Required) An array of six numbers [ x₀ y₀ r₀ x₁ y₁ r₁ ] specifying the centers and

radii of the starting and ending circles, expressed in the shading’s target coor-

dinate space. The radii r₀ and r₁ must both be greater than or equal to 0. If one

radius is 0, the corresponding circle is treated as a point; if both are 0, nothing is

painted.

Domain

array

(Optional) An array of two numbers [ t₀ t₁ ] specifying the limiting values of a

parametric variable t. The variable is considered to vary linearly between these

two values as the color gradient varies between the starting and ending circles.

The variable t becomes the input argument to the color function(s). Default

value: [ 0.0

1.0 ].

Function

function

(Required) A 1-in, n-out function or an array of n 1-in, 1-out functions (where n

is the number of color components in the shading dictionary’s color space). The

function(s) are called with values of the parametric variable t in the domain de-

fined by the shading dictionary’s Domain entry. Each function’s domain must be

a superset of that of the shading dictionary. If the value returned by the function

for a given color component is out of range, it is adjusted to the nearest valid val-

ue.

Extend

array

(Optional) An array of two boolean values specifying whether to extend the

shading beyond the starting and ending circles, respectively. Default value:

[ false false ].

The color blend is based on a family of blend circles interpolated between the

starting and ending circles that are defined by the shading dictionary’s Coords

entry. The blend circles are defined in terms of a subsidiary parametric variable

t₀

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

t₁

t₀

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which varies linearly between 0.0 and 1.0 as t varies across the domain from t₀ to

t₁ , as specified by the dictionary’s Domain entry. The center and radius of each

blend circle are given by the following parametric equations:

x_c(s)

x₀

(

x₁

–

x₀

)

y_c(s)

y₀

(

y₁

–

y₀

)

r(s)

r₀

(

r₁

–

r₀

)

Each value of s between 0.0 and 1.0 determines a corresponding value of t, which

is passed as the input argument to the function(s) defined by the shading dictio-

nary’s Function entry. This yields the component values of the color with which

to fill the corresponding blend circle. For values of s not lying between 0.0 and

1.0, the boolean elements of the shading dictionary’s Extend array determine

whether and how the shading is extended. If the first of the two elements is true,

the shading is extended beyond the defined starting circle to values of s less than

0.0; if the second element is true, the shading is extended beyond the defined

ending circle to s values greater than 1.0.

Note that either of the starting and ending circles may be larger than the other. If

the shading is extended at the smaller end, the family of blend circles continues as

far as that value of s for which the radius of the blend circle r (s) = 0. If the shading

is extended at the larger end, the blend circles continue as far as that s value for

which r (s) is large enough to encompass the shading’s entire bounding box

(BBox). Extending the shading can thus cause painting to extend beyond the

areas defined by the two circles themselves. The two examples in the rightmost

column of Plate 11 depict the results of extending the shading at the smaller and

larger ends, respectively.

Conceptually, all of the blend circles are painted in order of increasing values of s,

from smallest to largest. Blend circles extending beyond the starting circle are

painted in the same color defined by the shading dictionary’s Function entry for

the starting circle (t = t₀ , s = 0.0). Blend circles extending beyond the ending cir-

cle are painted in the color defined for the ending circle (t = t₁ , s = 1.0). The

painting is opaque, with the color of each circle completely overlaying those pre-

ceding it. Therefore, if a point lies within more than one blend circle, its final col-

or is that of the last of the enclosing circles to be painted, corresponding to the

greatest value of s.

313

SECTION 4.6

Patterns

Note the following points:

• If one of the starting and ending circles entirely contains the other, the shading

depicts a sphere, as in Plates 12 and 13. In Plate 12, the inner circle has zero ra-

dius; it is the starting circle in the figure on the left and the ending circle in the

figure on the right. Neither shading is extended at either the smaller or larger

end. In Plate 13, the inner circle in both figures has a nonzero radius and the

shading is extended at the larger end. In each plate, a background color is spec-

ified for the figure on the right but not for the figure on the left.

• If neither circle contains the other, the shading depicts a cone. If the starting

circle is larger, the cone appears to point out of the page. If the ending circle is

larger, the cone appears to point into the page (see Plate 11).

Example 4.25 paints the leaf-covered branch shown in Plate 14. Each leaf is filled

with the same radial shading (object number 5). The color function (object 10) is

a stitching function (described in Section 3.9.3, “Type 3 (Stitching) Functions”)

whose two subfunctions (objects 11 and 12) are both exponential interpolation

functions (see Section 3.9.2, “Type 2 (Exponential Interpolation) Functions”).

Each leaf is drawn as a path and then filled with the shading, using code such as

that shown in Example 4.26 (where the name Sh1 is associated with object 5 by

the Shading subdictionary of the current resource dictionary; see Section 3.7.2,

“Resource Dictionaries”).

Example 4.25

5 0 obj

% Shading dictionary

<< /ShadingType 3

/ColorSpace /DeviceCMYK

/Coords [ 0.0 0.0 0.096 0.0 0.0 1.0 00]

% Concentric circles

/Function 10 0 R

/Extend [ true true ]

endobj

10 0 obj

% Color function

<< /FunctionType 3

/Domain [ 0.0 1.0 ]

/Functions [ 11 0 R 12 0 R ]

/Bounds [ 0.708 ]

/Encode [ 1.0 0.0 0.0 1.0 ]

endobj

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Graphics

11 0 obj

% First subfunction

<< /FunctionType 2

/Domain [ 0.0 1.0 ]

/C0 [ 0.929 0.357 1.000 0.298 ]

/C1 [ 0.631 0.278 1.000 0.027 ]

/N 1.048

endobj

12 0 obj

% Second subfunction

<< /FunctionType 2

/Domain [ 0.0 1.0 ]

/C0 [ 0.929 0.357 1.000 0.298 ]

/C1 [ 0.941 0.400 1.000 0.102 ]

/N 1.374

endobj

Example 4.26

316.789 140.311 m

% Move to start of leaf

303.222 146.388 282.966 136.518 279.122

121.983

% Curved segment

277.322 120.182 l

% Straight line

285.125 122.688 291.441 121.716 298.156

119.386

% Curved segment

336.448 119.386 l

% Straight line

331.072 128.643 323.346 137.376 316.789

140.311

% Curved segment

W n

% Set clipping path

% Save graphics state

27.7843 0.0000 0.0000 −27.7843 310.2461 121.1521

% Set matrix

/Sh1 sh

% Paint shading

% Restore graphics state

Type 4 Shadings (Free-Form Gouraud-Shaded Triangle Meshes)

Type 4 shadings (free-form Gouraud-shaded triangle meshes) are commonly

used to represent complex colored and shaded three-dimensional shapes. The

area to be shaded is defined by a path composed entirely of triangles. The color at

each vertex of the triangles is specified, and a technique known as Gouraud

interpolation is used to color the interiors. The interpolation functions defining

the shading may be linear or nonlinear. Table 4.32 shows the entries specific to

this type of shading dictionary, in addition to those common to all shading dic-

tionaries (Table 4.28) and stream dictionaries (Table 3.4 on page 62).

315

SECTION 4.6

Patterns

TABLE 4.32 Additional entries specific to a type 4 shading dictionary

KEY

TYPE

VALUE

BitsPerCoordinate

integer

(Required) The number of bits used to represent each vertex coordinate.

Valid values are 1, 2, 4, 8, 12, 16, 24, and 32.

BitsPerComponent

integer

(Required) The number of bits used to represent each color component.

Valid values are 1, 2, 4, 8, 12, and 16.

BitsPerFlag

integer

(Required) The number of bits used to represent the edge flag for each ver-

tex (see below). Valid values of BitsPerFlag are 2, 4, and 8, but only the

least significant 2 bits in each flag value are used. Valid values for the edge

flag are 0, 1, and 2.

Decode

array

(Required) An array of numbers specifying how to map vertex coordinates

and color components into the appropriate ranges of values. The decoding

method is similar to that used in image dictionaries (see “Decode Arrays”

on page 344). The ranges are specified as follows:

[ x_min x_max y_min y_max c_1,min c_1,max … cn,min cn,max ]

Note that only one pair of c values should be specified if a Function entry

is present.

Function

function

(Optional) A 1-in, n-out function or an array of n 1-in, 1-out functions

(where n is the number of color components in the shading dictionary’s

color space). If this entry is present, the color data for each vertex must be

specified by a single parametric variable rather than by n separate color

components. The designated function(s) are called with each interpolated

value of the parametric variable to determine the actual color at each

point. Each input value is forced into the range interval specified for the

corresponding color component in the shading dictionary’s Decode array.

Each function’s domain must be a superset of that interval. If the value re-

turned by the function for a given color component is out of range, it is

adjusted to the nearest valid value.

This entry may not be used with an Indexed color space.

Unlike shading types 1 to 3, types 4 to 7 are represented as streams. Each stream

contains a sequence of vertex coordinates and color data that defines the triangle

mesh. In a type 4 shading, each vertex is specified by the following values, in the

order shown:

f x y c₁… c_n

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Graphics

where

f is the vertex’s edge flag (discussed below)

x and y are its horizontal and vertical coordinates

c₁… c_n are its color components

All vertex coordinates are expressed in the shading’s target coordinate space. If

the shading dictionary includes a Function entry, only a single parametric value,

t, is permitted for each vertex in place of the color components c₁… c_n .

The edge flag associated with each vertex determines the way it connects to the

other vertices of the triangle mesh. A vertex v_a with an edge flag value f_a = 0

begins a new triangle, unconnected to any other. At least two more vertices (v_b

and v_c ) must be provided, but their edge flags are ignored. These three vertices

define a triangle (v_a , v_b , v_c ), as shown in Figure 4.16.

f_a=0

(Start new triangle)

Previous

triangle

v_b

v_c

FIGURE 4.16 Starting a new triangle in a free-form Gouraud-shaded triangle mesh

Subsequent triangles are defined by a single new vertex combined with two verti-

ces of the preceding triangle. Given triangle (v_a , v_b , v_c ), where vertex v_a precedes

vertex v_b in the data stream and v_b precedes v_c , a new vertex v_d can form a new

triangle on side v_bc or side v_ac , as shown in Figure 4.17. (Side v_ab is assumed to be

shared with a preceding triangle and therefore is not available for continuing the

mesh.) If the edge flag is f_d = 1 (side v_bc ), the next vertex forms the triangle

(v_b , v_c , v_d ); if the edge flag is f_d = 2 (side v_ac ), the next vertex forms the triangle

(v_a , v_c , v_d ). An edge flag of f_d = 0 would start a new triangle, as described above.

317

SECTION 4.6

Patterns

f_d =0

f_d =1

f_d =2

v_a

v_d

One new

vertex

v_b

v_c

v_b

v_c

v_b

v_c

v_d

One new

Three new

vertex

v_d

vertices

v_e

v_f

FIGURE 4.17 Connecting triangles in a free-form Gouraud-shaded triangle mesh

Complex shapes can be created by using the edge flags to control the edge on

which subsequent triangles are formed. Figure 4.18 shows two simple examples.

Mesh 1 begins with triangle 1 and uses the following edge flags to draw each suc-

ceeding triangle:

(

f_a

f_b

f_c

)

(

f_i

)

(

f_d

)

(

f_j

)

(

f_e

)

(

f_k

)

(

f_f

)

(

f_l

)

(

f_g

)

(

f_m

)

(

f_h

)

Mesh 2 again begins with triangle 1 and uses the following edge flags:

(

f_a

f_b

f_c

)

(

f_f

)

(

f_d

)

(

f_g

)

(

f_e

)

(

f_h

)

The stream must provide vertex data for a whole number of triangles with appro-

priate edge flags; otherwise, an error occurs.

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Graphics

v_a

v_c

v_e

v_g

v_a

v_c

v_h

v_h = v_a

v_d

v_f

v_b

v_h

v_g

v_d

v_m

v_k

v_m = v_b

v_l

v_j

v_i

v_f

v_e

v_k = v_d

Mesh 1

Mesh 2

FIGURE 4.18 Varying the value of the edge flag to create different shapes

The data for each vertex consists of the following items, reading in sequence from

higher-order to lower-order bit positions:

• An edge flag, expressed in BitsPerFlag bits

• A pair of horizontal and vertical coordinates, expressed in BitsPerCoordinate

bits each

• A set of n color components (where n is the number of components in the

shading’s color space), expressed in BitsPerComponent bits each, in the order

expected by the sc operator

Each set of vertex data must occupy a whole number of bytes. If the total number

of bits required is not divisible by 8, the last data byte for each vertex is padded at

the end with extra bits, which are ignored. The coordinates and color values are

decoded according to the Decode array in the same way as in an image dictionary

(see “Decode Arrays” on page 344).

If the shading dictionary contains a Function entry, the color data for each vertex

must be specified by a single parametric value t rather than by n separate color

components. All linear interpolation within the triangle mesh is done using the t

values. After interpolation, the results are passed to the function(s) specified in

the Function entry to determine the color at each point.

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Patterns

Type 5 Shadings (Lattice-Form Gouraud-Shaded Triangle Meshes)

Type 5 shadings (lattice-form Gouraud-shaded triangle meshes) are similar to

type 4, but instead of using free-form geometry, their vertices are arranged in a

pseudorectangular lattice, which is topologically equivalent to a rectangular grid.

The vertices are organized into rows, which need not be geometrically linear (see

Figure 4.19).

(i, j)

(i, j+1)

(i+1, j)

(i+1, j+1)

Ideal lattice

Pseudorectangular lattice

FIGURE 4.19 Lattice-form triangle meshes

Table 4.33 shows the shading dictionary entries specific to this type of shading, in

addition to those common to all shading dictionaries (Table 4.28) and stream dic-

tionaries (Table 3.4 on page 62).

The data stream for a type 5 shading has the same format as for type 4, except that

type 5 does not use edge flags to define the geometry of the triangle mesh. The

data for each vertex thus consists of the following values, in the order shown:

x y c₁… c_n

where

x and y are the vertex’s horizontal and vertical coordinates

c₁… c_n are its color components

320

CHAPTER 4

Graphics

TABLE 4.33 Additional entries specific to a type 5 shading dictionary

KEY

TYPE

VALUE

BitsPerCoordinate

integer

(Required) The number of bits used to represent each vertex coordinate.

Valid values are 1, 2, 4, 8, 12, 16, 24, and 32.

BitsPerComponent

integer

(Required) The number of bits used to represent each color component.

Valid values are 1, 2, 4, 8, 12, and 16.

VerticesPerRow

integer

(Required) The number of vertices in each row of the lattice; the value

must be greater than or equal to 2. The number of rows need not be

specified.