mathlive
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Render and edit beautifully typeset math
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JavaScript
/* eslint no-unused-vars:0 */
/**
* This module contains metrics regarding fonts and individual symbols. The sigma
* and xi variables, as well as the metricMap map contain data extracted from
* TeX, TeX font metrics, and the TTF files. These data are then exposed via the
* `metrics` variable and the getCharacterMetrics function.
* @module core/fontMetrics
* @private
*/
import metricMap from './fontMetricsData.js';
// This metricMap contains a mapping from font name and character code to character
// metrics, including height, depth, italic correction, and skew (kern from the
// character to the corresponding \skewchar)
// This map is generated via `make metrics`. It should not be changed manually.
// const hangulRegex = /[\uAC00-\uD7AF]/;
// This regex combines
// - Hiragana: [\u3040-\u309F]
// - Katakana: [\u30A0-\u30FF]
// - CJK ideograms: [\u4E00-\u9FAF]
// - Hangul syllables: [\uAC00-\uD7AF]
// Notably missing are half width Katakana and Romaji glyphs.
const cjkRegex =
/[\u3040-\u309F]|[\u30A0-\u30FF]|[\u4E00-\u9FAF]|[\uAC00-\uD7AF]/;
/*
*
* In TeX, there are actually three sets of dimensions, one for each of
* textstyle, scriptstyle, and scriptscriptstyle. These are provided in the
* the arrays below, in that order.
*
* The font metrics are stored in fonts cmsy10, cmsy7, and cmsy5 respectively.
* This was determined by running the following script:
*``` bash
latex -interaction=nonstopmode \
'\documentclass{article}\usepackage{amsmath}\begin{document}' \
'$a$ \expandafter\show\the\textfont2' \
'\expandafter\show\the\scriptfont2' \
'\expandafter\show\the\scriptscriptfont2' \
'\stop'
```
* The metrics themselves were retrieved using the following commands:
* ``` bash
tftopl cmsy10
tftopl cmsy7
tftopl cmsy5
```
*
* The output of each of these commands is quite lengthy. The only part we
* care about is the FONTDIMEN section. Each value is measured in EMs.
* @memberof module:fontMetrics
*/
export const SIGMAS = {
slant: [0.250, 0.250, 0.250], // sigma1
space: [0.000, 0.000, 0.000], // sigma2
stretch: [0.000, 0.000, 0.000], // sigma3
shrink: [0.000, 0.000, 0.000], // sigma4
xHeight: [0.431, 0.431, 0.431], // sigma5
quad: [1.000, 1.171, 1.472], // sigma6
extraSpace: [0.000, 0.000, 0.000], // sigma7
num1: [0.677, 0.732, 0.925], // sigma8
num2: [0.394, 0.384, 0.387], // sigma9
num3: [0.444, 0.471, 0.504], // sigma10
denom1: [0.686, 0.752, 1.025], // sigma11
denom2: [0.345, 0.344, 0.532], // sigma12
sup1: [0.413, 0.503, 0.504], // sigma13
sup2: [0.363, 0.431, 0.404], // sigma14
sup3: [0.289, 0.286, 0.294], // sigma15
sub1: [0.150, 0.143, 0.200], // sigma16
sub2: [0.247, 0.286, 0.400], // sigma17
supDrop: [0.386, 0.353, 0.494], // sigma18
subDrop: [0.050, 0.071, 0.100], // sigma19
delim1: [2.390, 1.700, 1.980], // sigma20
delim2: [1.010, 1.157, 1.420], // sigma21
axisHeight: [0.250, 0.250, 0.250], // sigma22
};
// These font metrics are extracted from TeX by using
// \font\a=cmex10
// \showthe\fontdimenX\a
// where X is the corresponding variable number. These correspond to the font
// parameters of the extension fonts (family 3). See the TeXbook, page 441.
const xi1 = 0;
const xi2 = 0;
const xi3 = 0;
const xi4 = 0;
const xi5 = 0.431;
const xi6 = 1;
const xi7 = 0;
const xi8 = 0.04;
const xi9 = 0.111;
const xi10 = 0.166;
const xi11 = 0.2;
const xi12 = 0.6;
const xi13 = 0.1;
// This value determines how large a pt is, for metrics which are defined in
// terms of pts.
// This value is also used in katex.less; if you change it make sure the values
// match.
const ptPerEm = 10.0;
// The space between adjacent `|` columns in an array definition. From
// article.cls.txt:455
const doubleRuleSep = 2.0 / ptPerEm;
/*
* This is just a mapping from common names to real metrics
*/
export const METRICS = {
defaultRuleThickness: xi8,
bigOpSpacing1: xi9,
bigOpSpacing2: xi10,
bigOpSpacing3: xi11,
bigOpSpacing4: xi12,
bigOpSpacing5: xi13,
ptPerEm: ptPerEm,
pxPerEm: ptPerEm * 4.0 / 3.0, // A CSS pt is fixed at 1.333px
doubleRuleSep: 2.0 / ptPerEm,
arraycolsep: 5.0 / ptPerEm,
baselineskip: 12.0 / ptPerEm,
arrayrulewidth: 0.4 / ptPerEm,
fboxsep: 3 / ptPerEm, // From letter.dtx:1626
fboxrule: 0.4 / ptPerEm, // From letter.dtx:1627
};
// These are very rough approximations. We default to Times New Roman which
// should have Latin-1 and Cyrillic characters, but may not depending on the
// operating system. The metrics do not account for extra height from the
// accents. In the case of Cyrillic characters which have both ascenders and
// descenders we prefer approximations with ascenders, primarily to prevent
// the fraction bar or root line from intersecting the glyph.
// TODO(kevinb) allow union of multiple glyph metrics for better accuracy.
const extraCharacterMap = {
'\u00a0': '\u0020', // NON-BREAKING SPACE is like space
'\u200b': '\u0020', // ZERO WIDTH SPACE is like space
// Latin-1
'Å': 'A',
'Ç': 'C',
'Ð': 'D',
'Þ': 'o',
'å': 'a',
'ç': 'c',
'ð': 'd',
'þ': 'o',
// Cyrillic
'А': 'A',
'Б': 'B',
'В': 'B',
'Г': 'F',
'Д': 'A',
'Е': 'E',
'Ж': 'K',
'З': '3',
'И': 'N',
'Й': 'N',
'К': 'K',
'Л': 'N',
'М': 'M',
'Н': 'H',
'О': 'O',
'П': 'N',
'Р': 'P',
'С': 'C',
'Т': 'T',
'У': 'y',
'Ф': 'O',
'Х': 'X',
'Ц': 'U',
'Ч': 'h',
'Ш': 'W',
'Щ': 'W',
'Ъ': 'B',
'Ы': 'X',
'Ь': 'B',
'Э': '3',
'Ю': 'X',
'Я': 'R',
'а': 'a',
'б': 'b',
'в': 'a',
'г': 'r',
'д': 'y',
'е': 'e',
'ж': 'm',
'з': 'e',
'и': 'n',
'й': 'n',
'к': 'n',
'л': 'n',
'м': 'm',
'н': 'n',
'о': 'o',
'п': 'n',
'р': 'p',
'с': 'c',
'т': 'o',
'у': 'y',
'ф': 'b',
'х': 'x',
'ц': 'n',
'ч': 'n',
'ш': 'w',
'щ': 'w',
'ъ': 'a',
'ы': 'm',
'ь': 'a',
'э': 'e',
'ю': 'm',
'я': 'r',
};
/**
* This function is a convenience function for looking up information in the
* metricMap table. It takes a character as a string, and a font name.
*
* Note: the `width` property may be undefined if fontMetricsData.js wasn't
* built using `Make extended_metrics`.
* @param {string} character
* @param {string} fontCode
* @memberof module:fontMetrics
* @private
*/
const getCharacterMetrics = function(character, fontCode) {
const fontName = {
'cal': 'Caligraphic-Regular',
'ams': 'AMS-Regular',
'frak': 'Fraktur-Regular',
'bb': 'AMS-Regular',
'scr': 'Script-Regular',
'cmr': 'Main-Regular',
'cmtt': 'Typewriter-Regular',
'cmss': 'SansSerif-Regular'
}[fontCode] || fontCode;
// console.assert(character.length === 1);
// console.assert(metricMap[fontName], 'Unknown font "' + fontName + '"');
let ch = character.charCodeAt(0);
if (character[0] in extraCharacterMap) {
ch = extraCharacterMap[character[0]].charCodeAt(0);
} else if (cjkRegex.test(character[0])) {
ch = 77; // 'M'.charCodeAt(0);
}
const metrics = metricMap[fontName][ch];
if (!metrics) {
// console.warn(
// 'No metrics for ' +
// '"' + character + '" (U+' + ('000000' + ch.toString(16)).substr(-6) + ')' +
// ' in font "' + fontName + '"');
// Assume default values.
// depth + height should be less than 1.0 em
return {
defaultMetrics: true,
depth: .20,
height: .70,
italic: 0,
skew: 0
}
}
if (metrics) {
return {
depth: metrics[0],
height: metrics[1],
italic: metrics[2],
skew: metrics[3]
}
}
return null;
}
/**
*
* @param {number|string} value If value is a string, it may be suffixed
* with a unit, which will override the `unit` paramter
* @param {string} unit
* @param {number} precision
* @private
*/
function convertDimenToEm(value, unit, precision) {
if (typeof value === 'string') {
const m = value.match(/([-+]?[0-9.]*)\s*([a-zA-Z]+)/);
if (!m) {
value = parseFloat(value);
} else {
value = parseFloat(m[1]);
unit = m[2].toLowerCase();
}
}
// If the units are missing, TeX assumes 'pt'
const f = {
'pt': 1.0,
'mm': 7227 / 2540,
'cm': 7227 / 254,
'ex': 35271 / 8192,
'px': 3.0 / 4.0,
'em': METRICS.ptPerEm,
'bp': 803 / 800,
'dd': 1238 / 1157,
'pc': 12.0,
'in': 72.27,
'mu': 10 / 18,
}[unit] || 1.0
if (isFinite(precision)) {
const factor = Math.pow(10, precision);
return Math.round((value / METRICS.ptPerEm) * f * factor) / factor;
}
return (value / METRICS.ptPerEm) * f;
}
function convertDimenToPx(value, unit) {
return convertDimenToEm(value, unit) * (4.0 / 3.0) * METRICS.ptPerEm;
}
export default {
toEm : convertDimenToEm,
toPx: convertDimenToPx,
METRICS,
SIGMAS,
getCharacterMetrics
}