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QuLogic merged 3 commits into from
Feb 7, 2026
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Implement TeX's fraction and script alignment #31046

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94ff452
Implement TeX's fraction and script alignment
tfpf Jul 17, 2022
4bfa0f9
Fix positioning of mathtext Rules
anntzer Feb 1, 2026
1cd8510
Fix up mathtext constants for fraction/script alignment
QuLogic Feb 6, 2026
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256 changes: 203 additions & 53 deletions lib/matplotlib/_mathtext.py
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Original file line number Diff line number Diff line change
Expand Up @@ -306,6 +306,12 @@ def render_rect_filled(self, output: Output,
"""
output.rects.append((x, y, w, h))

def get_axis_height(self, font: str, fontsize: float, dpi: float) -> float:
"""
Get the axis height for the given *font* and *fontsize*.
"""
raise NotImplementedError()

def get_xheight(self, font: str, fontsize: float, dpi: float) -> float:
"""
Get the xheight for the given *font* and *fontsize*.
Expand Down Expand Up @@ -407,17 +413,19 @@ def _get_info(self, fontname: str, font_class: str, sym: str, fontsize: float,
offset=offset
)

def get_axis_height(self, fontname: str, fontsize: float, dpi: float) -> float:
# The fraction line (if present) must be aligned with the minus sign. Therefore,
# the height of the latter from the baseline is the axis height.
metrics = self.get_metrics(
fontname, mpl.rcParams['mathtext.default'], '\u2212', fontsize, dpi)
return (metrics.ymax + metrics.ymin) / 2

def get_xheight(self, fontname: str, fontsize: float, dpi: float) -> float:
font = self._get_font(fontname)

@anntzer anntzer Feb 1, 2026

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What is the rationale for not reading the x-height from pclt anymore? (+ see comment re: tfm params for actually directly using hardcoding tfm params instead).

@tfpf tfpf Feb 2, 2026 •
edited
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The algorithm breaks for the bundled Computer Modern font, because the x-height obtained from pclt is much greater than the rendered x-height. The other fonts don't have a font table, if I recall correctly.

If, however, the correct parameters could be added to the files, the x-height (and many other parameters, including the axis height, as you pointed out below) could definitely be read therefrom.

@anntzer anntzer Feb 3, 2026

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OK, so let's not bother with this too much for now and fix this later once when revisiting xheight/axis_height reading?

font.set_size(fontsize, dpi)
pclt = font.get_sfnt_table('pclt')
if pclt is None:
# Some fonts don't store the xHeight, so we do a poor man's xHeight
metrics = self.get_metrics(
fontname, mpl.rcParams['mathtext.default'], 'x', fontsize, dpi)
return metrics.iceberg
x_height = (pclt['xHeight'] / 64) * (fontsize / 12) * (dpi / 100)
return x_height
# Some fonts report the wrong x-height, while some don't store it, so
# we do a poor man's x-height.
metrics = self.get_metrics(
fontname, mpl.rcParams['mathtext.default'], 'x', fontsize, dpi)
return metrics.iceberg

def get_underline_thickness(self, font: str, fontsize: float, dpi: float) -> float:
# This function used to grab underline thickness from the font
Expand Down Expand Up @@ -895,7 +903,10 @@ class FontConstantsBase:
# Percentage of x-height of additional horiz. space after sub/superscripts
script_space: T.ClassVar[float] = 0.05

# Percentage of x-height that sub/superscripts drop below the baseline
# Percentage of x-height that superscripts drop below the top of large box
supdrop: T.ClassVar[float] = 0.4

# Percentage of x-height that subscripts drop below the bottom of large box
subdrop: T.ClassVar[float] = 0.4

# Percentage of x-height that superscripts are raised from the baseline
Expand All @@ -921,40 +932,109 @@ class FontConstantsBase:
# integrals
delta_integral: T.ClassVar[float] = 0.1

# Percentage of x-height the numerator is shifted up in display style.
num1: T.ClassVar[float] = 1.4

# Percentage of x-height the numerator is shifted up in text, script and
# scriptscript styles if there is a fraction line.
num2: T.ClassVar[float] = 1.5

# Percentage of x-height the numerator is shifted up in text, script and
# scriptscript styles if there is no fraction line.
num3: T.ClassVar[float] = 1.3

# Percentage of x-height the denominator is shifted down in display style.
denom1: T.ClassVar[float] = 1.3

# Percentage of x-height the denominator is shifted down in text, script
# and scriptscript styles.
denom2: T.ClassVar[float] = 1.1


class ComputerModernFontConstants(FontConstantsBase):
script_space = 0.075
subdrop = 0.2
sup1 = 0.45
sub1 = 0.2
sub2 = 0.3
delta = 0.075
# Previously, the x-height of Computer Modern was obtained from the font
# table. However, that x-height was greater than the the actual (rendered)
# x-height by a factor of 1.771484375 (at font size 12, DPI 100 and hinting
# type 32). Now that we're using the rendered x-height, some font constants
# have been increased by the same factor to compensate.
script_space = 0.132861328125
delta = 0.132861328125
delta_slanted = 0.3
delta_integral = 0.3
_x_height = 451470
# These all come from the cmsy10.tfm metrics, divided by the design xheight from
# there, since we multiply these values by the scaled xheight later.
supdrop = 404864 / _x_height
subdrop = 52429 / _x_height
sup1 = 432949 / _x_height
sub1 = 157286 / _x_height
sub2 = 259226 / _x_height
num1 = 709370 / _x_height
num2 = 412858 / _x_height
num3 = 465286 / _x_height
denom1 = 719272 / _x_height
denom2 = 361592 / _x_height


class STIXFontConstants(FontConstantsBase):
script_space = 0.1
sup1 = 0.8
sub2 = 0.6
delta = 0.05
delta_slanted = 0.3
delta_integral = 0.3


class STIXSansFontConstants(FontConstantsBase):
# These values are extracted from the TeX table of STIXGeneral.ttf using FreeType,

@QuLogic QuLogic Feb 7, 2026

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This should have said FontForge, not FreeType; I'll fix it in a followup.

# and then divided by design xheight, since we multiply these values by the scaled
# xheight later.
_x_height = 450
supdrop = 386 / _x_height
subdrop = 50.0002 / _x_height
sup1 = 413 / _x_height
sub1 = 150 / _x_height
sub2 = 309 / _x_height
num1 = 747 / _x_height
num2 = 424 / _x_height
num3 = 474 / _x_height
denom1 = 756 / _x_height
denom2 = 375 / _x_height


class STIXSansFontConstants(STIXFontConstants):
script_space = 0.05
sup1 = 0.8
delta_slanted = 0.6
delta_integral = 0.3


class DejaVuSerifFontConstants(FontConstantsBase):
pass
# These values are extracted from the TeX table of DejaVuSerif.ttf using FreeType,
# and then divided by design xheight, since we multiply these values by the scaled
# xheight later.
_x_height = 1063
supdrop = 790.527 / _x_height
subdrop = 102.4 / _x_height
sup1 = 845.824 / _x_height
sub1 = 307.199 / _x_height
sub2 = 632.832 / _x_height
num1 = 1529.86 / _x_height
num2 = 868.352 / _x_height
num3 = 970.752 / _x_height
denom1 = 1548.29 / _x_height
denom2 = 768 / _x_height


class DejaVuSansFontConstants(FontConstantsBase):
pass
# These values are extracted from the TeX table of DejaVuSans.ttf using FreeType,
# and then divided by design xheight, since we multiply these values by the scaled
# xheight later.
_x_height = 1120
supdrop = 790.527 / _x_height
subdrop = 102.4 / _x_height
sup1 = 845.824 / _x_height
sub1 = 307.199 / _x_height
sub2 = 632.832 / _x_height
num1 = 1529.86 / _x_height
num2 = 868.352 / _x_height
num3 = 970.752 / _x_height
denom1 = 1548.29 / _x_height
denom2 = 768 / _x_height


# Maps font family names to the FontConstantBase subclass to use
Expand Down Expand Up @@ -1015,6 +1095,15 @@ def shrink(self) -> None:
def render(self, output: Output, x: float, y: float) -> None:
"""Render this node."""

def is_char_node(self) -> bool:
# TeX defines a `char_node` as one which represents a single character,
# but also states that a `char_node` will never appear in a `Vlist`
# (node134). Further, nuclei made of one `Char` and nuclei made of
# multiple `Char`s have their superscripts and subscripts shifted by
# the same amount. In order to make Mathtext behave similarly, just
# check whether this node is a `Vlist` or has any `Vlist` descendants.
return True


class Box(Node):
"""A node with a physical location."""
Expand Down Expand Up @@ -1204,6 +1293,10 @@ def __init__(self, elements: T.Sequence[Node], w: float = 0.0,
self.kern()
self.hpack(w=w, m=m)

def is_char_node(self) -> bool:
# See description in Node.is_char_node.
return all(map(lambda node: node.is_char_node(), self.children))

def kern(self) -> None:
"""
Insert `Kern` nodes between `Char` nodes to set kerning.
Expand Down Expand Up @@ -1295,6 +1388,10 @@ def __init__(self, elements: T.Sequence[Node], h: float = 0.0,
super().__init__(elements)
self.vpack(h=h, m=m)

def is_char_node(self) -> bool:
# See description in Node.is_char_node.
return False

def vpack(self, h: float = 0.0,
m: T.Literal['additional', 'exactly'] = 'additional',
l: float = np.inf) -> None:
Expand Down Expand Up @@ -1386,7 +1483,7 @@ def __init__(self, width: float, height: float, depth: float, state: ParserState

def render(self, output: Output, # type: ignore[override]
x: float, y: float, w: float, h: float) -> None:
self.fontset.render_rect_filled(output, x, y, w, h)
self.fontset.render_rect_filled(output, x, y - h, w, h)


class Hrule(Rule):
Expand Down Expand Up @@ -2111,6 +2208,7 @@ def csnames(group: str, names: Iterable[str]) -> Regex:
| p.text
| p.boldsymbol
| p.substack
| p.auto_delim
)

mdelim = r"\middle" - (p.delim("mdelim") | Error("Expected a delimiter"))
Expand Down Expand Up @@ -2440,8 +2538,7 @@ def subsuper(self, s: str, loc: int, toks: ParseResults) -> T.Any:
state = self.get_state()
rule_thickness = state.fontset.get_underline_thickness(
state.font, state.fontsize, state.dpi)
x_height = state.fontset.get_xheight(
state.font, state.fontsize, state.dpi)
x_height = state.fontset.get_xheight(state.font, state.fontsize, state.dpi)

if napostrophes:
if super is None:
Expand Down Expand Up @@ -2530,9 +2627,19 @@ def subsuper(self, s: str, loc: int, toks: ParseResults) -> T.Any:
else:
subkern = 0

# Set the minimum shifts for the superscript and subscript (node756).
if nucleus.is_char_node():
shift_up = 0.0
shift_down = 0.0
else:
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shrunk_x_height = state.fontset.get_xheight(
state.font, state.fontsize * SHRINK_FACTOR, state.dpi)
shift_up = nucleus.height - consts.supdrop * shrunk_x_height
shift_down = nucleus.depth + consts.subdrop * shrunk_x_height

x: List
if super is None:
# node757
# Align subscript without superscript (node757).
# Note: One of super or sub must be a Node if we're in this function, but
# mypy can't know this, since it can't interpret pyparsing expressions,
# hence the cast.
Expand All @@ -2541,29 +2648,37 @@ def subsuper(self, s: str, loc: int, toks: ParseResults) -> T.Any:
if self.is_dropsub(last_char):
shift_down = lc_baseline + consts.subdrop * x_height
else:
shift_down = consts.sub1 * x_height
shift_down = max(shift_down, consts.sub1 * x_height,
x.height - x_height * 4 / 5)
x.shift_amount = shift_down
else:
# Align superscript (node758).
x = Hlist([Kern(superkern), super])
x.shrink()
if self.is_dropsub(last_char):
shift_up = lc_height - consts.subdrop * x_height
else:
shift_up = consts.sup1 * x_height
shift_up = max(shift_up, consts.sup1 * x_height, x.depth + x_height / 4)
if sub is None:
x.shift_amount = -shift_up
else: # Both sub and superscript
else:
# Align subscript with superscript (node759).
y = Hlist([Kern(subkern), sub])
y.shrink()
if self.is_dropsub(last_char):
shift_down = lc_baseline + consts.subdrop * x_height
else:
shift_down = consts.sub2 * x_height
# If sub and superscript collide, move super up
clr = (2 * rule_thickness -
shift_down = max(shift_down, consts.sub2 * x_height)
# If the subscript and superscript are too close to each other,
# move the subscript down.
clr = (4 * rule_thickness -
((shift_up - x.depth) - (y.height - shift_down)))
if clr > 0.:
shift_up += clr
shift_down += clr
clr = x_height * 4 / 5 - shift_up + x.depth
if clr > 0:
shift_up += clr
shift_down -= clr
x = Vlist([
x,
Kern((shift_up - x.depth) - (y.height - shift_down)),
Expand All @@ -2586,32 +2701,67 @@ def _genfrac(self, ldelim: str, rdelim: str, rule: float | None, style: _MathSty
state = self.get_state()
thickness = state.get_current_underline_thickness()

axis_height = state.fontset.get_axis_height(
state.font, state.fontsize, state.dpi)
consts = _get_font_constant_set(state)
x_height = state.fontset.get_xheight(state.font, state.fontsize, state.dpi)

for _ in range(style.value):
x_height *= SHRINK_FACTOR
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num.shrink()
den.shrink()
cnum = HCentered([num])
cden = HCentered([den])
width = max(num.width, den.width)
cnum.hpack(width, 'exactly')
cden.hpack(width, 'exactly')
vlist = Vlist([
cnum, # numerator
Vbox(0, 2 * thickness), # space
Hrule(state, rule), # rule
Vbox(0, 2 * thickness), # space
cden, # denominator
])

# Shift so the fraction line sits in the middle of the
# equals sign
metrics = state.fontset.get_metrics(
state.font, mpl.rcParams['mathtext.default'],
'=', state.fontsize, state.dpi)
shift = (cden.height -
((metrics.ymax + metrics.ymin) / 2 - 3 * thickness))
vlist.shift_amount = shift

result: list[Box | Char | str] = [Hlist([vlist, Hbox(2 * thickness)])]
# Align the fraction with a fraction line (node743, node744 and node746).
if rule:
if style is self._MathStyle.DISPLAYSTYLE:
num_shift_up = consts.num1 * x_height
den_shift_down = consts.denom1 * x_height
clr = 3 * rule # The minimum clearance.
else:
num_shift_up = consts.num2 * x_height
den_shift_down = consts.denom2 * x_height
clr = rule # The minimum clearance.
delta = rule / 2
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num_clr = max((num_shift_up - cnum.depth) - (axis_height + delta), clr)
den_clr = max((axis_height - delta) - (cden.height - den_shift_down), clr)
vlist = Vlist([cnum, # numerator
Vbox(0, num_clr), # space
Hrule(state, rule), # rule
Vbox(0, den_clr), # space
cden # denominator
])
vlist.shift_amount = cden.height + den_clr + delta - axis_height

# Align the fraction without a fraction line (node743, node744 and node745).
else:
if style is self._MathStyle.DISPLAYSTYLE:
num_shift_up = consts.num1 * x_height
den_shift_down = consts.denom1 * x_height
min_clr = 7 * thickness # The minimum clearance.
else:
num_shift_up = consts.num3 * x_height
den_shift_down = consts.denom2 * x_height
min_clr = 3 * thickness # The minimum clearance.
def_clr = (num_shift_up - cnum.depth) - (cden.height - den_shift_down)
clr = max(def_clr, min_clr)
vlist = Vlist([cnum, # numerator
Vbox(0, clr), # space
cden # denominator
])
vlist.shift_amount = den_shift_down
if def_clr < min_clr:
vlist.shift_amount += (min_clr - def_clr) / 2

result: list[Box | Char | str] = [Hlist([
Hbox(thickness),
vlist,
Hbox(thickness)
])]
if ldelim or rdelim:
return self._auto_sized_delimiter(ldelim or ".", result, rdelim or ".")
return result
Expand Down
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