The graphics state includes the following key parameters:

<strong>Current Transformation Matrix (CTM)</strong> — A 3×3 matrix (represented as 6 values [a b c d e f]) that maps from user space coordinates (as written in the content stream) to device space coordinates. The CTM controls scaling, rotation, shearing, and translation. The <code>cm</code> operator concatenates (multiplies) a new matrix onto the current CTM. The initial CTM for a page is determined by the page's /MediaBox and optional /UserUnit.

<strong>Colour spaces and colours</strong> — The graphics state maintains separate colour specifications for stroke operations (painting paths) and fill operations (filling areas): current stroke colour space and colour value; current fill colour space and colour value. Set with <code>CS</code>/<code>cs</code> (colour space) and <code>SC</code>/<code>sc</code>/<code>SCN</code>/<code>scn</code> (colour values), or with the shorthand operators <code>RG</code>/<code>rg</code> (DeviceRGB), <code>K</code>/<code>k</code> (DeviceCMYK), <code>G</code>/<code>g</code> (DeviceGray).

<strong>Line parameters</strong> — Line width (<code>w</code> operator, default 1.0 user space units); line cap style (<code>J</code>: butt=0, round=1, projecting square=2); line join style (<code>j</code>: miter=0, round=1, bevel=2); miter limit (<code>M</code>, default 10.0); dash pattern (<code>d</code>: array of on/off lengths, phase).

<strong>Text state</strong> — Several graphics state parameters relate specifically to text: current font and size (<code>Tf</code>); character spacing (<code>Tc</code>); word spacing (<code>Tw</code>); horizontal scaling (<code>Tz</code>); text leading (<code>TL</code>); text rendering mode (<code>Tr</code>: fill, stroke, fill+stroke, invisible, clip); text rise (<code>Ts</code> for superscript/subscript).

<strong>Current clipping path</strong> — The clipping path defines the region within which painting is allowed. Painting outside the clipping path has no visible effect. Set with the <code>W</code> or <code>W*</code> operators after a path construction sequence. The initial clipping path covers the entire page.

<strong>Alpha constants and blend mode</strong> — For transparency: constant alpha for stroke (ca) and fill (CA); blend mode (BM); soft mask (SMask). Set via the <code>gs</code> operator using an ExtGState dictionary in the page resources.

The most important mechanism in the graphics state is the <code>q</code>/<code>Q</code> save/restore stack. Its usage is ubiquitous in PDF content streams:

<code>q % save current state</code> <code> 1 0 0 1 100 200 cm % translate to (100,200)</code> <code> 0.5 w % set line width to 0.5</code> <code> 0 0 1 RG % set stroke colour to blue</code> <code> 0 0 200 100 re S % draw blue 200×100 rectangle</code> <code>Q % restore: CTM, line width, colour all back to pre-q values</code>

This pattern means that any graphics state changes made between <code>q</code> and <code>Q</code> are automatically reverted when <code>Q</code> is executed. Well-formed PDF content streams balance every <code>q</code> with a corresponding <code>Q</code>. Unbalanced <code>q</code>/<code>Q</code> pairs can cause state pollution — subsequent drawing operations inherit unintended graphics state from within an unclosed <code>q</code> block.

The PDF specification permits a maximum nesting depth of 28 for the graphics state stack. Exceeding this limit is a conformance error. In practice, most PDFs stay well within this limit, but pathological cases (deeply nested form XObjects each using q/Q) can approach it.

<strong>Extended graphics state (ExtGState)</strong> — Some graphics state parameters are not directly settable with individual operators. They are grouped into an ExtGState dictionary referenced by name from the page's /ExtGState resource dictionary. The <code>gs</code> operator applies an entire ExtGState dictionary to the current graphics state at once. ExtGState parameters include: alpha constants (ca/CA), blend mode (BM), soft mask (SMask), overprint mode (OPM), smoothness tolerance, and others. This dictionary-based mechanism allows setting multiple related parameters atomically and allows the specification to add new parameters without requiring new operators.

The CTM is a 2D affine transformation represented as a 3×3 matrix in homogeneous coordinates, but expressed as 6 values [a b c d e f]:

<code>[ a b 0 ]</code> <code>[ c d 0 ]</code> <code>[ e f 1 ]</code>

The CTM maps user space point (x, y) to device space point (x', y'): - x' = a*x + c*y + e - y' = b*x + d*y + f

Common transformations: - <strong>Identity</strong>: [1 0 0 1 0 0] (no transformation) - <strong>Translate by (tx, ty)</strong>: [1 0 0 1 tx ty] - <strong>Scale by (sx, sy)</strong>: [sx 0 0 sy 0 0] - <strong>Rotate by θ</strong>: [cos(θ) sin(θ) −sin(θ) cos(θ) 0 0]

The <code>cm</code> operator concatenates the specified matrix onto the current CTM by matrix multiplication. Since matrix multiplication is not commutative, order matters: translate-then-scale produces different results than scale-then-translate.

In a web-based PDF editor, converting between CSS pixel coordinates and PDF user space requires the inverse of the CTM composition. If the page is rendered at scale=1.5 and the CTM maps page coordinates to PDF coordinates, the full conversion from screen click to PDF annotation position requires accounting for: (1) CSS display scale, (2) device pixel ratio, (3) page origin, and (4) the bottom-left vs top-left origin convention.