Table of Contents

• 1. Coordinate Transformations
  • 1.1. Overview
    • 1.1.1. Basic Transformations
    • 1.1.2. Matrix Operations
    • 1.1.3. Coordinate Transformations
  • 1.2. Transformation Matrix
  • 1.3. Current Transformation Matrix (CTM)
  • 1.4. Common Operations
    • 1.4.1. Centering Content
    • 1.4.2. Scaling and Rotation
    • 1.4.3. Saving Transformations
  • 1.5. Status

1. Coordinate Transformations

Commands for coordinate system transformations and matrix operations.

1.1. Overview

The PostScript coordinate transformation system provides powerful tools for manipulating the coordinate space in which graphics are drawn. These commands fall into three main categories:

1.1.1. Basic Transformations

• translate - Move the origin

• scale - Change unit size

• rotate - Rotate axes

• concat - Concatenate matrix with CTM

1.1.2. Matrix Operations

• matrix - Create identity matrix

• identmatrix - Replace matrix with identity

• defaultmatrix - Get device default matrix

• currentmatrix - Get current transformation matrix

• setmatrix - Replace CTM with matrix

• initmatrix - Reset CTM to default

• concatmatrix - Multiply two matrices

• invertmatrix - Invert a matrix

1.1.3. Coordinate Transformations

• transform - Transform user→device coordinates

• itransform - Transform device→user coordinates

• dtransform - Transform distance vector

• idtransform - Inverse transform distance vector

1.2. Transformation Matrix

PostScript uses a 6-element matrix to represent coordinate transformations:

[a b c d tx ty]

This matrix transforms coordinates according to:

x' = a×x + c×y + tx
y' = b×x + d×y + ty

Where:

• a, d - Scaling factors in x and y

• b, c - Rotation/skewing components

• tx, ty - Translation components

The identity matrix is [1 0 0 1 0 0].

1.3. Current Transformation Matrix (CTM)

The CTM maps user space coordinates to device space coordinates. It is part of the graphics state and is affected by:

• gsave and grestore

• Basic transformation commands

• setmatrix

1.4. Common Operations

1.4.1. Centering Content

% Center a 100x100 square on page
306 396 translate  % Move to center of letter page
-50 -50 translate  % Move back by half size

1.4.2. Scaling and Rotation

% Scale by 2 and rotate 45 degrees
2 2 scale
45 rotate

1.4.3. Saving Transformations

gsave
  % Temporary transformations
  100 100 translate
  2 2 scale
  % Draw transformed content
grestore
% Original CTM restored

1.5. Status

Complete documentation for all transformation commands.