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Checkpoint 12Low Priority1 failure condition

Checkpoint 12: Stretchable Characters

Stretched mathematical or technical characters must be represented with appropriate Unicode characters or glyph variants to ensure proper screen reader pronunciation.

Related WCAG:1.3.1

Checkpoint 12: Stretchable Characters

When characters are stretched vertically or horizontally to span mathematical expressions (such as large brackets, braces, or integral signs), they must be represented using appropriate Unicode characters or glyph mechanisms that assistive technology can interpret correctly.

What This Means

In mathematical and technical documents, certain characters need to be stretched to accommodate the content they contain or describe:

  • Brackets and parentheses: ( ) [ ] { } that span multiple lines of expressions
  • Integral signs: The elongated integral symbol spanning the height of an expression
  • Summation and product signs: Large sigma and pi symbols
  • Square roots: The radical sign extending over complex expressions
  • Fraction bars: Horizontal lines spanning the width of fractions
  • Matrix delimiters: Brackets that encompass multi-row matrices

When these characters are stretched, the PDF must represent them in a way that:

  1. Preserves semantic meaning: Screen readers should announce the character correctly
  2. Maintains logical structure: The relationship between the stretchy character and its content should be clear
  3. Uses appropriate glyphs: The visual representation should use proper font mechanisms, not distorted standard characters

The problem arises when standard characters are simply scaled (stretched) visually without proper semantic representation. A visually stretched left parenthesis might still be encoded as a single standard parenthesis character, but the stretching could break the character mapping or create accessibility issues.

Why It Matters

Stretchable characters are fundamental to mathematical notation, and their proper representation affects accessibility in several ways:

  • Screen reader pronunciation: A stretched bracket that is improperly encoded might be read as a series of disconnected characters or not read at all
  • Navigation: Users navigating mathematical expressions need to understand the grouping that brackets provide
  • Content extraction: Copy/paste operations should preserve the semantic meaning
  • Braille output: Refreshable braille displays need correct character information to produce proper mathematical braille notation
  • Semantic understanding: The stretchy character often indicates the scope of an operation (what's being integrated, summed, or grouped)

For example, consider the integral:

    b
    ∫ f(x) dx
    a

The integral sign must stretch to show it spans from a to b. If improperly represented, a screen reader might:

  • Announce nothing (if the stretched glyph loses its mapping)
  • Announce "vertical line" instead of "integral"
  • Fail to convey the relationship between the integral and its bounds

Common Violations

The Matterhorn Protocol defines one failure condition for stretchable characters, which requires human testing.

12-001: Stretched Characters Not Represented Appropriately (Human Testing)

What's Wrong: Characters that have been stretched to accommodate content are not represented using appropriate Unicode values or font mechanisms. The visual appearance may be correct, but the underlying character data is incorrect or missing.

How to Identify:

This violation requires manual inspection:

  1. Visual identification: Look for any stretched characters in the document

    • Large brackets, braces, or parentheses
    • Extended integral or summation signs
    • Radical signs spanning expressions
    • Fraction bars of various lengths

  2. Text extraction test: Select and copy the mathematical expression

    • Paste into a plain text editor
    • Check if the stretched character appears correctly
    • If missing, garbled, or replaced with incorrect characters, this indicates a problem

  3. Screen reader test: Use a screen reader to navigate the expression

    • Listen for proper announcement of the character
    • Check if the stretchy element is announced in context
    • Verify the pronunciation makes mathematical sense

  4. Character inspection: In Acrobat, use the Content panel to examine the actual character content

    • Right-click the stretched element
    • Check Properties to see the actual characters/glyphs used
    • Verify appropriate Unicode values are present

Common Problem Scenarios:

  • Mathematical expressions created from images rather than text
  • PDF generators that draw brackets as vector graphics without text equivalents
  • Font substitution that breaks character mappings
  • Legacy equation editors that embed equations as graphics
  • Stretched characters created by graphical scaling rather than font mechanisms

How to Fix in Adobe Acrobat

Fixing stretchable character issues in Acrobat is limited because the problem usually originates in the source document or equation creation method.

Identifying Problematic Content

  1. Open the PDF in Adobe Acrobat Pro
  2. Go to View > Show/Hide > Navigation Panes > Content
  3. Expand the page content tree
  4. Look for mathematical expressions
  5. Click on stretchy characters to see their properties
  6. Check the "ActualText" and character content

Adding Actual Text Alternatives

If stretched characters are implemented as graphics:

  1. Locate the graphic element in the Content panel
  2. Right-click and select Properties
  3. In the Tag tab, add Actual Text that represents the character
  4. For a stretched left bracket, enter the Unicode left bracket: "["
  5. For integrals, use the Unicode integral sign: "∫" (U+222B)

Using the Tags Panel

  1. Open the Tags panel (View > Show/Hide > Navigation Panes > Tags)
  2. Navigate to the mathematical expression
  3. Find elements representing stretched characters
  4. Right-click and select Properties
  5. Add or correct the Actual Text field
  6. Ensure the tag type is appropriate (often within a Formula tag)

Content Replacement (Advanced)

For severe issues where characters are entirely graphical:

  1. Consider recreating the mathematical content using proper equation tools
  2. Replace problematic sections with new, accessible content
  3. Use Edit PDF tool to modify text if possible
  4. Re-tag the corrected content appropriately

How to Fix in Microsoft Word

The best approach is to ensure mathematical content is created correctly in the source document.

Using Word's Equation Editor

Word's built-in equation editor creates accessible mathematical content:

  1. Go to Insert > Equation (or press Alt + =)
  2. Use the equation tools to build your expression
  3. Stretched characters (brackets, integrals, etc.) are handled automatically
  4. The equation editor uses Unicode math characters with proper semantics

Proper Equation Editor Techniques

For brackets that need to stretch:

  1. In the Equation Editor, go to the Bracket dropdown
  2. Select bracket styles that auto-size to content
  3. Insert your expression between the brackets
  4. The brackets will stretch automatically with correct encoding

For integrals:

  1. Use the Integral dropdown in the Equation Editor
  2. Select the appropriate integral type (definite, indefinite, contour)
  3. Fill in the bounds and integrand
  4. The integral sign will stretch appropriately

Avoiding MathType Issues

If using MathType or similar add-ins:

  1. Configure MathType to output accessible equations
  2. In MathType preferences, enable "Use Unicode for Greek and Symbol"
  3. Choose output formats that preserve text, not just graphics
  4. Test the exported PDF for proper character mapping

Do Not Use Images for Equations

Avoid inserting mathematical expressions as images:

  1. Do not screenshot equations from other sources
  2. Do not paste equations as pictures
  3. Do not use legacy equation formats that embed as graphics
  4. If you must use an image, add comprehensive alt text

Export Settings

When saving as PDF:

  1. Go to File > Save As and choose PDF
  2. Click Options
  3. Ensure "Document structure tags for accessibility" is checked
  4. This preserves the equation structure in the PDF

How to Fix in Other Applications

LaTeX

LaTeX produces mathematical content with proper structure:

  1. Use standard LaTeX math commands
  2. Compile to PDF using pdflatex, xelatex, or lualatex
  3. Consider using the accessibility or tagpdf packages for better tagging
  4. Test the output PDF for proper character mapping

Example of proper LaTeX for an integral:

\int_a^b f(x) \, dx

Adobe InDesign

  1. Use InDesign's built-in equation features if available
  2. For complex math, consider MathML-based solutions
  3. After export, verify equations in the PDF
  4. Add Actual Text to graphical equations if needed

LibreOffice Math

LibreOffice includes an equation editor:

  1. Go to Insert > Object > Formula
  2. Build your equation using the formula syntax
  3. LibreOffice Math uses Unicode characters appropriately
  4. Export to PDF and verify the result

MathML-Based Solutions

For web-first workflows:

  1. Author equations in MathML
  2. Use tools that convert MathML to accessible PDF
  3. MathML provides strong semantic structure
  4. The conversion should preserve character semantics

Testing Your Fix

Manual Character Testing

  1. Selection test:

    • Try to select the stretched character in the PDF
    • If it cannot be selected, it may be a graphic
    • If selected, check what text is copied

  2. Copy/paste test:

    • Select the mathematical expression
    • Paste into a text editor
    • Verify stretchy characters appear as appropriate Unicode

  3. Font inspection:

    • Check what font is used for the stretched character
    • Ensure it's a font with proper math character support
    • Common math fonts: Cambria Math, STIX, Latin Modern Math

Screen Reader Testing

Using NVDA, JAWS, or VoiceOver:

  1. Navigate to the mathematical expression

  2. Listen for proper character announcements:

    • "left bracket" or "left parenthesis" for (
    • "integral" for ∫
    • "summation" or "sigma" for Σ
    • "square root" for √

  3. Check if the relationship between stretchy characters and content is clear

  4. Verify the expression can be navigated element by element

Accessibility Checker Testing

PAC (PDF Accessibility Checker):

  1. Open the PDF in PAC
  2. Run the PDF/UA check
  3. Note: PAC cannot fully validate this checkpoint automatically
  4. Use PAC's screen reader preview to hear how content is read

Adobe Acrobat:

  1. Go to Tools > Accessibility > Accessibility Check
  2. Run the full check
  3. Look for warnings about characters or formulas
  4. Use the Reading Order panel to verify structure

Validation Checklist

  • Mathematical expressions use proper equation editor (not images)
  • Stretched brackets/braces can be selected as text
  • Copy/paste of expressions yields correct Unicode characters
  • Screen reader announces stretchy characters appropriately
  • Character mappings are intact (not broken by stretching)
  • Formula tags are used where appropriate
  • Actual Text is provided for any graphical math elements

Best Practices for Mathematical Content

Creation Guidelines

  1. Always use equation editors: Never create math using regular text formatting
  2. Use Unicode-aware tools: Modern equation editors output proper Unicode
  3. Test early: Check accessibility before finalizing documents
  4. Consider MathML: For complex documents, MathML provides the best structure
  5. Document consistently: Use the same equation creation method throughout

Font Considerations

  1. Use math fonts: Cambria Math, STIX, Latin Modern Math have proper stretchy glyphs
  2. Avoid font substitution: Embed fonts to prevent mapping issues
  3. Test with different viewers: Ensure fonts display correctly across platforms

Tagging Mathematical Content

  1. Use Formula tags: Mathematical expressions should be tagged as formulas
  2. Provide Actual Text: For complex expressions, add human-readable alternatives
  3. Structure properly: Nest mathematical elements correctly in the tag tree
  4. Consider reading order: Ensure math is read in logical sequence

Additional Resources

Official Standards and Guidelines

Mathematical Accessibility

Tools and Resources

LaTeX and PDF Accessibility

This documentation is based on the Matterhorn Protocol 1.02, the definitive reference for PDF/UA validation. The stretchable characters checkpoint requires human testing as automated tools cannot fully verify proper character representation. For the most current information, consult the PDF Association and W3C WCAG guidelines.

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