admin
d703ab64e3
CI / docs-check (push) Canceled after 0s
CI / backend-test (push) Canceled after 0s
CI / service-test (push) Canceled after 0s
CI / frontend-test (push) Canceled after 0s
CI / rust-core (push) Canceled after 0s
CI / docs-check (pull_request) Canceled after 0s
CI / backend-test (pull_request) Canceled after 0s
CI / service-test (pull_request) Canceled after 0s
CI / frontend-test (pull_request) Canceled after 0s
CI / rust-core (pull_request) Canceled after 0s
190 lines
7.9 KiB
Python
190 lines
7.9 KiB
Python
"""安全的 AST 到 LaTeX 转换和绘图标签的矢量数学布局。"""
|
|
|
|
from __future__ import annotations
|
|
|
|
import ast
|
|
import html
|
|
import math
|
|
import threading
|
|
from dataclasses import dataclass
|
|
from functools import lru_cache
|
|
|
|
from matplotlib.font_manager import FontProperties
|
|
from matplotlib.mathtext import MathTextParser
|
|
from matplotlib.path import Path as MplPath
|
|
|
|
from app.plot.parser import parse_expression
|
|
|
|
_MATH_PARSER = MathTextParser("path")
|
|
_RASTER_PARSER = MathTextParser("agg")
|
|
_MATH_LOCK = threading.Lock()
|
|
|
|
|
|
def _number(value: int | float) -> str:
|
|
text = repr(value)
|
|
if "e" not in text.lower():
|
|
return text
|
|
mantissa, exponent = text.lower().split("e", 1)
|
|
return rf"{mantissa}\times 10^{{{int(exponent)}}}"
|
|
|
|
|
|
def _latex(node: ast.AST, parent_precedence: int = 0) -> str:
|
|
if isinstance(node, ast.Constant):
|
|
return _number(node.value)
|
|
if isinstance(node, ast.Name):
|
|
return r"\pi" if node.id == "pi" else node.id
|
|
if isinstance(node, ast.UnaryOp):
|
|
value = _latex(node.operand, 25)
|
|
result = ("-" if isinstance(node.op, ast.USub) else "+") + value
|
|
return rf"\left({result}\right)" if parent_precedence > 25 else result
|
|
if isinstance(node, ast.BinOp):
|
|
if isinstance(node.op, ast.Div):
|
|
return rf"\frac{{{_latex(node.left)}}}{{{_latex(node.right)}}}"
|
|
if isinstance(node.op, ast.Pow):
|
|
result = rf"{{{_latex(node.left, 30)}}}^{{{_latex(node.right)}}}"
|
|
return rf"\left({result}\right)" if parent_precedence > 30 else result
|
|
precedence = 20 if isinstance(node.op, ast.Mult) else 10
|
|
operator = r" \cdot " if isinstance(node.op, ast.Mult) else (" + " if isinstance(node.op, ast.Add) else " - ")
|
|
left = _latex(node.left, precedence)
|
|
right = _latex(node.right, precedence + (1 if isinstance(node.op, ast.Sub) else 0))
|
|
result = left + operator + right
|
|
return rf"\left({result}\right)" if parent_precedence > precedence else result
|
|
if isinstance(node, ast.Call) and isinstance(node.func, ast.Name):
|
|
argument = _latex(node.args[0])
|
|
name = node.func.id
|
|
if name == "sqrt":
|
|
return rf"\sqrt{{{argument}}}"
|
|
if name == "abs":
|
|
return rf"\left|{argument}\right|"
|
|
if name in {"log10", "log2"}:
|
|
return rf"\log_{{{name[3:]}}}\left({argument}\right)"
|
|
if name in {"asin", "acos", "atan"}:
|
|
return rf"\{name[1:]}^{{-1}}\left({argument}\right)"
|
|
command = "log" if name == "ln" else name
|
|
return rf"\{command}\left({argument}\right)"
|
|
raise ValueError(f"Unsupported validated expression node: {type(node).__name__}")
|
|
|
|
|
|
def expression_latex(expression: str) -> str:
|
|
"""将一个已支持的函数表达式转换为 MathText 兼容的 LaTeX。"""
|
|
return "y = " + _latex(parse_expression(expression).body)
|
|
|
|
|
|
@dataclass(frozen=True)
|
|
class VectorPath:
|
|
commands: tuple[tuple[str, tuple[float, ...]], ...]
|
|
|
|
|
|
@dataclass(frozen=True)
|
|
class MathLayout:
|
|
width: float
|
|
height: float
|
|
depth: float
|
|
paths: tuple[VectorPath, ...]
|
|
rects: tuple[tuple[float, float, float, float], ...]
|
|
|
|
|
|
def _offset(values: tuple[float, ...], x: float, y: float) -> tuple[float, ...]:
|
|
return tuple(value + (x if index % 2 == 0 else y) for index, value in enumerate(values))
|
|
|
|
|
|
@lru_cache(maxsize=256)
|
|
def math_layout(latex: str, size: float = 12.0) -> MathLayout:
|
|
"""将 LaTeX 布局为可重用的矢量路径； FT2Font 的调用被缓存和序列化。"""
|
|
with _MATH_LOCK:
|
|
parsed = _MATH_PARSER.parse(f"${latex}$", dpi=72, prop=FontProperties(size=size))
|
|
paths: list[VectorPath] = []
|
|
for font, font_size, _character, glyph, offset_x, offset_y in parsed.glyphs:
|
|
font.set_size(font_size, 72)
|
|
font.load_glyph(glyph)
|
|
vertices, codes = font.get_path()
|
|
commands: list[tuple[str, tuple[float, ...]]] = []
|
|
for values, code in MplPath(vertices, codes).iter_segments(curves=True, simplify=False):
|
|
command = {
|
|
MplPath.MOVETO: "M",
|
|
MplPath.LINETO: "L",
|
|
MplPath.CURVE3: "Q",
|
|
MplPath.CURVE4: "C",
|
|
MplPath.CLOSEPOLY: "Z",
|
|
}[code]
|
|
points = () if command == "Z" else _offset(tuple(float(value) for value in values), float(offset_x), float(offset_y))
|
|
commands.append((command, points))
|
|
paths.append(VectorPath(tuple(commands)))
|
|
rects = tuple(tuple(float(value) for value in rect) for rect in parsed.rects)
|
|
return MathLayout(float(parsed.width), float(parsed.height), float(parsed.depth), tuple(paths), rects)
|
|
|
|
|
|
def _svg_number(value: float) -> str:
|
|
if math.isclose(value, round(value), abs_tol=1e-8):
|
|
return str(int(round(value)))
|
|
return f"{value:.4f}".rstrip("0").rstrip(".")
|
|
|
|
|
|
def _svg_path(path: VectorPath) -> str:
|
|
return " ".join(command + (" " + " ".join(_svg_number(value) for value in values) if values else "") for command, values in path.commands)
|
|
|
|
|
|
def render_math_svg(latex: str, *, x: float, top: float, class_name: str, color: str) -> str:
|
|
"""返回包含 MathText 矢量字形的无脚本 SVG 组。"""
|
|
layout = math_layout(latex)
|
|
baseline = top + layout.height - layout.depth
|
|
accessible = html.escape(latex, quote=True)
|
|
parts = [
|
|
f'<g class="{class_name} plot-math-label" fill="{color}" '
|
|
f'transform="translate({_svg_number(x)} {_svg_number(baseline)}) scale(1 -1)" '
|
|
f'aria-label="{accessible}" data-latex="{accessible}">'
|
|
]
|
|
parts.extend(f'<path d="{_svg_path(path)}"/>' for path in layout.paths)
|
|
for rx, ry, width, height in layout.rects:
|
|
parts.append(
|
|
f'<path d="M {_svg_number(rx)} {_svg_number(ry)} h {_svg_number(width)} '
|
|
f'v {_svg_number(height)} h -{_svg_number(width)} Z"/>'
|
|
)
|
|
parts.append("</g>")
|
|
return "".join(parts)
|
|
|
|
|
|
def render_math_reportlab(latex: str, *, x: float, visual_top: float, color: object):
|
|
"""返回包含与 SVG 相同的 LaTeX 字形几何形状的 reportlab 组。"""
|
|
from reportlab.graphics.shapes import Group, Path, Rect
|
|
|
|
layout = math_layout(latex)
|
|
baseline = visual_top - (layout.height - layout.depth)
|
|
group = Group()
|
|
for vector in layout.paths:
|
|
path = Path(fillColor=color, strokeColor=None)
|
|
current = (0.0, 0.0)
|
|
start = current
|
|
for command, values in vector.commands:
|
|
if command == "M":
|
|
current = (values[0], values[1]); start = current
|
|
path.moveTo(*current)
|
|
elif command == "L":
|
|
current = (values[0], values[1]); path.lineTo(*current)
|
|
elif command == "Q":
|
|
control, end = (values[0], values[1]), (values[2], values[3])
|
|
first = (current[0] + 2 * (control[0] - current[0]) / 3,
|
|
current[1] + 2 * (control[1] - current[1]) / 3)
|
|
second = (end[0] + 2 * (control[0] - end[0]) / 3,
|
|
end[1] + 2 * (control[1] - end[1]) / 3)
|
|
path.curveTo(*first, *second, *end); current = end
|
|
elif command == "C":
|
|
path.curveTo(*values); current = (values[4], values[5])
|
|
else:
|
|
path.closePath(); current = start
|
|
group.add(path)
|
|
for rx, ry, width, height in layout.rects:
|
|
group.add(Rect(rx, ry, width, height, fillColor=color, strokeColor=None))
|
|
group.translate(x, baseline)
|
|
return group
|
|
|
|
|
|
@lru_cache(maxsize=256)
|
|
def render_math_mask(latex: str, size: float = 12.0, dpi: float = 144.0) -> tuple[int, int, bytes]:
|
|
"""将 LaTeX 光栅化为 8 位 alpha 掩码以用于 DOCX/PNG 导出。"""
|
|
with _MATH_LOCK:
|
|
parsed = _RASTER_PARSER.parse(f"${latex}$", dpi=dpi, prop=FontProperties(size=size))
|
|
image = parsed.image
|
|
height, width = image.shape
|
|
return int(width), int(height), image.tobytes()
|