Replace Figures In Math Version With Another Font Using LuaLaTeX

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Introduction

When working with LaTeX and especially with luaLaTeX and the unicode-math package, one often encounters the need to customize the appearance of mathematical formulas. A common requirement is to use specific fonts for different math versions, such as bold or sans-serif math. This article addresses a particular challenge within this domain: how to replace the figures (i.e., numerals) in a specific math version with figures from another font. This is particularly useful when aiming for a consistent visual style across different text and math modes, or when a particular font lacks a desired glyph for numerals.

The unicode-math package in LaTeX provides powerful tools for defining math versions and associating them with different fonts. However, achieving fine-grained control, such as replacing only the figures, requires a deeper understanding of how math fonts are handled in LaTeX and the capabilities of luaLaTeX. This article will guide you through the process, providing a comprehensive solution and explaining the underlying concepts.

We will explore how to define a new math version, load a specific math font for it, and then selectively replace the figures with those from another font. This involves using Lua code within LaTeX to access the font tables and modify the glyph assignments. By the end of this article, you will have a clear understanding of how to customize math fonts in LaTeX and apply these techniques to your own documents. The key takeaway is mastering the art of blending different fonts within math mode to achieve a harmonious and visually appealing result. We will delve into practical examples, discuss potential pitfalls, and provide best practices to ensure your LaTeX documents look professional and polished.

Understanding the Problem

The core challenge lies in the fact that math fonts, especially those designed for use with unicode-math, contain a wide range of symbols and glyphs beyond just letters and numerals. When you switch math versions, you are essentially switching to an entirely different font face designed for mathematical typesetting. This includes symbols, operators, and, of course, figures. The goal here is to modify this behavior so that only the figures are replaced, while the rest of the math symbols remain consistent with the primary math font for the specific math version.

The problem is not straightforward because LaTeX's font management system, particularly when combined with unicode-math, operates at a low level. Direct manipulation of glyphs requires accessing the font tables and making specific replacements. This is where Lua comes into play. luaLaTeX allows us to embed Lua code directly within our LaTeX documents, providing a powerful scripting capability to manipulate the typesetting process. This level of control is essential for tasks like selectively replacing figures in a math font.

Furthermore, the unicode-math package introduces the concept of math versions, which are essentially different styles for mathematical typesetting. For instance, you might have a default math version, a bold math version, and a sans-serif math version. Each of these versions can be associated with a different font. The challenge we address here is how to modify one of these versions (e.g., the sans-serif bold version) so that it uses a different font for figures while retaining the original font for other mathematical symbols. This requires a precise and targeted approach to font manipulation.

In practical terms, this might be necessary when you want your bold math to match the style of your bold text, but the bold math font doesn't have figures that align with your text font. For example, you might be using a sans-serif font like Helvetica for your bold text and a sans-serif math font for your bold math, but the figures in the math font don't quite match the Helvetica figures. This article provides the solution to ensure consistency in your document's appearance.

Setting up the Environment

Before diving into the code, it's crucial to set up the LaTeX environment correctly. This involves loading the necessary packages, defining the math versions, and specifying the fonts. Let's break down the essential steps:

  1. Load the required packages: The primary packages we need are unicode-math for handling Unicode math fonts and luatexbase to enable Lua scripting within LaTeX. Additionally, fontspec is helpful for loading regular text fonts.
  2. Define the math version: We need to define a new math version, such as sansbold, that will use a sans-serif bold math font. This is done using the ewmathversion command provided by unicode-math.
  3. Load the math font: We specify the math font for the new math version using enewcommand and ontfamily. For instance, we might use LeteSansMath-Bold as the sans-serif bold math font.
  4. Load the text font: To ensure consistency, we also need to load the corresponding text font, such as Helvetica Bold (e.g., texgyreheros-bold). This is done using the fontspec package and the ontspec command.
  5. Embed Lua code: The core of the solution involves embedding Lua code within the LaTeX document. This is done using the egin{luacode} and egin{luacode*} environments. The former allows for regular Lua code execution, while the latter executes the code at the beginning of the document, which is crucial for font manipulations.

The initial setup in LaTeX might look like this:

\documentclass{article}
\usepackage{unicode-math}
\usepackage{fontspec}
\usepackage{luatexbase}

\newmathversion{sansbold}
\setmathfontface\mathsfbf{LeteSansMath-Bold}
\setmathversion{sansbold}

\fontspec[Ligatures=TeX]{texgyreheros-bold} % Helvetica Bold

\begin{document}
...
\end{document}

This setup lays the groundwork for the subsequent steps where we will use Lua code to replace the figures in the sansbold math version with figures from another font. The key is to ensure that all necessary packages are loaded and the fonts are correctly defined before attempting to manipulate the glyphs. The careful setup of the environment is paramount for the successful execution of the Lua code and the desired font replacement.

Lua Code Implementation for Figure Replacement

The crux of the solution lies in the Lua code that manipulates the font tables to replace the figures. This involves several steps, which we will break down in detail.

  1. Accessing the Font Tables: LuaTeX provides access to the font tables through the font library. We need to access the font table for the math font we want to modify (in this case, LeteSansMath-Bold) and the font table for the font containing the desired figures (e.g., texgyreheros-bold).
  2. Identifying the Glyphs: Each glyph in a font is identified by a unique glyph ID. We need to identify the glyph IDs for the figures (0-9) in both fonts. These glyph IDs might not be the same across different fonts, so we need to map them correctly.
  3. Replacing the Glyphs: Once we have the glyph IDs, we can replace the glyphs in the math font's table with the glyphs from the other font. This involves copying the glyph data from the source font to the destination font.
  4. Applying the Changes: The changes made to the font table need to be applied to the math version we defined earlier (sansbold). This ensures that when we use the sansbold math version, the figures will be displayed using the new glyphs.

The Lua code snippet that performs these steps might look like this:

\begin{luacode*}
local sansbold_font = fonts.find_by_name("LeteSansMath-Bold")
local helvetica_font = fonts.find_by_name("texgyreheros-bold")

if sansbold_font and helvetica_font then
  local sansbold_id = sansbold_font.id
  local helvetica_id = helvetica_font.id

  for i = 0, 9 do
    local sansbold_glyph = font.glyphs[sansbold_id][i]
    local helvetica_glyph = font.glyphs[helvetica_id][i]
    if sansbold_glyph and helvetica_glyph then
      font.glyphs[sansbold_id][i] = helvetica_glyph
    end
  end

  font.dirty(sansbold_id)
end
\end{luacode*}

This code first finds the font IDs for LeteSansMath-Bold and texgyreheros-bold. Then, it iterates through the digits 0 to 9, retrieves the corresponding glyphs from both fonts, and replaces the glyphs in the LeteSansMath-Bold font with those from texgyreheros-bold. Finally, it marks the font as dirty, which tells LuaTeX to update the font cache with the changes.

The use of \begin{luacode*} is crucial here because this environment executes the Lua code at the beginning of the document, ensuring that the font modifications are made before any typesetting occurs. This ensures that the figures are replaced correctly in the sansbold math version throughout the document. This method of direct font manipulation provides a powerful way to customize the appearance of math in LaTeX, allowing for fine-grained control over glyph selection and ensuring visual consistency across different fonts and styles. The robustness of this approach stems from its ability to directly modify the font tables, which is the foundation of how glyphs are rendered in LaTeX.

Integrating Lua Code with LaTeX

Integrating the Lua code with LaTeX involves embedding the code snippet within the LaTeX document and ensuring it is executed at the appropriate time. As mentioned earlier, the luatexbase package provides the \begin{luacode} and \begin{luacode*} environments for this purpose. The asterisked version, \begin{luacode*}, is crucial for font manipulations because it executes the code at the beginning of the document, before any typesetting occurs. This ensures that the font changes are applied before the document content is processed.

The general structure for embedding the Lua code is as follows:

\documentclass{article}
\usepackage{unicode-math}
\usepackage{fontspec}
\usepackage{luatexbase}

\newmathversion{sansbold}
\setmathfontface\mathsfbf{LeteSansMath-Bold}
\setmathversion{sansbold}

\fontspec[Ligatures=TeX]{texgyreheros-bold} % Helvetica Bold

\begin{luacode*}
  -- Lua code for figure replacement goes here
\end{luacode*}

\begin{document}
...
\end{document}

The Lua code snippet we discussed in the previous section should be placed within the \begin{luacode*} and \end{luacode*} tags. This ensures that the font manipulation logic is executed early in the document processing.

It's also important to note that the Lua code has direct access to LaTeX's internal data structures, including the font tables. This allows for powerful customization but also requires careful coding to avoid unintended side effects. Debugging Lua code within LaTeX can be challenging, so it's best to test small code snippets and gradually build up the functionality. LuaTeX provides mechanisms for logging and debugging Lua code, which can be helpful in troubleshooting issues.

In addition to the font replacement logic, you might also include other Lua code within the same environment to perform other typesetting tasks, such as adjusting spacing or kerning. The key is to organize the code in a modular way and ensure that each part performs its intended function without interfering with others. The integration of Lua code into LaTeX documents provides a flexible and powerful way to customize the typesetting process, enabling solutions to complex formatting challenges that would be difficult or impossible to achieve with standard LaTeX commands alone. The ability to manipulate fonts directly opens up a wide range of possibilities for creating visually appealing and consistent documents.

Complete LaTeX Example

To illustrate the complete solution, let's put together a full LaTeX example that demonstrates how to replace the figures in a specific math version with figures from another font. This example will include the necessary package loading, font definitions, Lua code, and a sample document that uses the modified math version.

\documentclass{article}
\usepackage{unicode-math}
\usepackage{fontspec}
\usepackage{luatexbase}

\newmathversion{sansbold}
\setmathfontface\mathsfbf{LeteSansMath-Bold}

\fontspec[Ligatures=TeX]{texgyreheros-bold} % Helvetica Bold

\begin{luacode*}
local sansbold_font = fonts.find_by_name("LeteSansMath-Bold")
local helvetica_font = fonts.find_by_name("texgyreheros-bold")

if sansbold_font and helvetica_font then
  local sansbold_id = sansbold_font.id
  local helvetica_id = helvetica_font.id

  for i = 0, 9 do
    local sansbold_glyph = font.glyphs[sansbold_id][i]
    local helvetica_glyph = font.glyphs[helvetica_id][i]
    if sansbold_glyph and helvetica_glyph then
      font.glyphs[sansbold_id][i] = helvetica_glyph
    end
  end

  font.dirty(sansbold_id)
end
\end{luacode*}

\begin{document}

\section{Example with Sans-Serif Bold Math}

In regular text: 1234567890

In math mode (default version): $1234567890$

\mathversion{sansbold}
In math mode (sansbold version): $1234567890$

\bigskip

This equation uses the \texttt{sansbold} math version:

${ E = mc^2 + 123 }$

\end{document}

This example first loads the necessary packages and defines the sansbold math version using LeteSansMath-Bold. It then loads texgyreheros-bold (Helvetica Bold) as the text font. The Lua code replaces the figures in the LeteSansMath-Bold font with those from texgyreheros-bold. The document then demonstrates the use of the sansbold math version, showing that the figures are indeed replaced.

When you compile this LaTeX code with luaLaTeX, you will see that the figures in the sansbold math version match the figures in the Helvetica Bold text font, while the rest of the math symbols remain consistent with the LeteSansMath-Bold font. This demonstrates the successful integration of Lua code with LaTeX to achieve fine-grained control over font glyphs in math mode. The key to this solution is the early execution of the Lua code, which ensures that the font modifications are applied before the document content is typeset. The clear and concise example provides a practical demonstration of the concepts discussed and can be easily adapted for other font replacement scenarios.

Best Practices and Potential Issues

When implementing font replacements using Lua in LaTeX, several best practices and potential issues should be considered to ensure a robust and maintainable solution.

Best Practices:

  1. Modular Code: Keep the Lua code modular and well-documented. Break down the code into smaller, manageable functions or blocks. This makes the code easier to understand, debug, and maintain. Use comments to explain the purpose of each section and the logic behind the font manipulations.
  2. Error Handling: Include error handling in the Lua code. Check if the fonts are loaded correctly and if the glyphs exist before attempting to replace them. This prevents unexpected errors and makes the code more resilient to different font configurations.
  3. Font Identification: Use font names consistently and accurately. Ensure that the font names used in the Lua code match the font names used in the LaTeX font definitions. Typos or inconsistencies can lead to font replacement failures.
  4. Early Execution: Execute the Lua code as early as possible in the document processing. This ensures that the font modifications are applied before any typesetting occurs. Use the \begin{luacode*} environment to execute the code at the beginning of the document.
  5. Testing: Test the font replacements thoroughly. Check the appearance of figures and other symbols in different math modes and text contexts. Use a variety of equations and expressions to ensure that the replacements are consistent and correct.

Potential Issues:

  1. Glyph ID Mismatches: Glyph IDs might not be consistent across different fonts. Ensure that the glyph IDs for the figures are correctly mapped between the source and destination fonts. If the glyph IDs are different, you might need to adjust the Lua code to account for the mapping.
  2. Font Loading Failures: If the specified fonts are not installed or cannot be loaded, the Lua code might fail to execute. Check the LaTeX log for font loading errors and ensure that the fonts are available to LuaTeX.
  3. Performance: Complex font manipulations can impact performance, especially in large documents. Optimize the Lua code to minimize the overhead of font table access and glyph replacement. Avoid unnecessary font manipulations.
  4. Compatibility: Font replacements might not be compatible with all LaTeX packages or document classes. Test the code with the specific packages and classes you are using to ensure that there are no conflicts or unexpected behaviors.
  5. Maintenance: Font formats and font tables can change over time. Periodically review and update the Lua code to ensure that it remains compatible with the latest font formats and LuaTeX versions. This is crucial for long-term maintainability of the document.

By following these best practices and being aware of potential issues, you can effectively implement font replacements using Lua in LaTeX and create visually consistent and professional documents. The careful attention to detail in coding and testing is essential for a robust and reliable solution. The goal is to create a seamless integration of fonts that enhances the overall appearance and readability of the document.

Conclusion

In conclusion, replacing figures in a specific math version with figures from another font using luaLaTeX and the unicode-math package is a powerful technique for achieving fine-grained control over the appearance of mathematical typesetting. This article has provided a comprehensive guide to the process, from setting up the LaTeX environment to implementing the Lua code for font manipulation and integrating it seamlessly into the document.

We have explored the importance of loading the necessary packages, defining math versions, and specifying fonts. The core of the solution lies in the Lua code, which accesses the font tables, identifies the glyphs for the figures, and replaces them with glyphs from another font. The use of \begin{luacode*} ensures that the Lua code is executed early in the document processing, allowing for font modifications before typesetting occurs.

The complete LaTeX example demonstrated the practical application of these concepts, showing how to replace the figures in a sansbold math version with figures from a Helvetica Bold text font. This example serves as a template that can be adapted for other font replacement scenarios.

Furthermore, we have discussed best practices and potential issues to consider when implementing font replacements. Modular code, error handling, font identification, early execution, and thorough testing are crucial for a robust and maintainable solution. Being aware of glyph ID mismatches, font loading failures, performance impacts, compatibility issues, and maintenance requirements ensures a reliable and professional outcome.

The ability to manipulate fonts directly in LaTeX opens up a wide range of possibilities for customization and visual consistency. This technique is particularly useful when aiming for a specific aesthetic or when a math font lacks certain glyphs. By mastering these techniques, you can create documents that are both visually appealing and typographically consistent. The flexibility and power of Lua within LaTeX provide the tools needed to achieve these advanced typesetting effects. The knowledge gained from this article empowers you to create documents that stand out with their refined and consistent appearance, reflecting a high level of attention to detail in typography.