docs: 将仓库代码注释统一为中文

backend/app/plot/math_label.py

@@ -1,4 +1,4 @@
-"""Safe AST-to-LaTeX conversion and vector math layout for plot labels."""
+"""安全的 AST 到 LaTeX 转换和绘图标签的矢量数学布局。"""
 
 from __future__ import annotations
 
@@ -66,7 +66,7 @@ def _latex(node: ast.AST, parent_precedence: int = 0) -> str:
 
 
 def expression_latex(expression: str) -> str:
-    """Convert one already-supported function expression to MathText-compatible LaTeX."""
+    """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)
 
 
@@ -90,7 +90,7 @@ def _offset(values: tuple[float, ...], x: float, y: float) -> tuple[float, ...]:
 
 @lru_cache(maxsize=256)
 def math_layout(latex: str, size: float = 12.0) -> MathLayout:
-    """Lay out LaTeX as reusable vector paths; calls are cached and serialized for FT2Font."""
+    """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] = []
@@ -125,7 +125,7 @@ def _svg_path(path: VectorPath) -> str:
 
 
 def render_math_svg(latex: str, *, x: float, top: float, class_name: str, color: str) -> str:
-    """Return a script-free SVG group containing MathText vector glyphs."""
+    """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)
@@ -145,7 +145,7 @@ def render_math_svg(latex: str, *, x: float, top: float, class_name: str, color:
 
 
 def render_math_reportlab(latex: str, *, x: float, visual_top: float, color: object):
-    """Return a reportlab Group containing the same LaTeX glyph geometry as the SVG."""
+    """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)
@@ -181,7 +181,7 @@ def render_math_reportlab(latex: str, *, x: float, visual_top: float, color: obj
 
 @lru_cache(maxsize=256)
 def render_math_mask(latex: str, size: float = 12.0, dpi: float = 144.0) -> tuple[int, int, bytes]:
-    """Rasterize LaTeX to an 8-bit alpha mask for DOCX/PNG export."""
+    """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

backend/app/plot/render.py

@@ -226,13 +226,7 @@ _CURVE_MAX_REFINEMENT_EVALUATIONS = 8192
 
 
 def _refine_crossing(tree, left, right, ymin, ymax, budget=None):
-    """Adaptively check both halves of a crossing; None explicitly breaks a path.
-
-    A visible midpoint is not a continuity proof. Accept a visible chord only
-    when its midpoint error is within a quarter pixel; otherwise subdivide both
-    halves. Depth, evaluation and floating-point limits always break unresolved
-    intervals instead of joining them. Entirely off-screen triples can be culled.
-    """
+    """自适应检查路口的两半； None 明确中断了一条路径。可见的中点并不是连续性证明。仅当中点误差在四分之一像素以内时才接受可见弦；否则将两半细分。深度、求值和浮点限制总是打破未解决的间隔，而不是连接它们。完全不在屏幕外的三元组可以被剔除。"""
     remaining = _REFINE_MAX_EVALUATIONS
     if budget is None:
         budget = [_REFINE_MAX_EVALUATIONS]
@@ -255,12 +249,11 @@ def _refine_crossing(tree, left, right, ymin, ymax, budget=None):
         values = (a[1], y, b[1])
         if all(math.isfinite(v) for v in values):
             if max(values) < ymin or min(values) > ymax:
-                return [a, None, b]  # No visible chord; do not connect across it.
+                return [a, None, b]  # 无可见和弦；不要通过它连接。
             error = abs(y - (a[1] / 2 + b[1] / 2))
             if any(ymin <= v <= ymax for v in values) and error <= tolerance:
                 return [a, mid, b]
-        # Refine either side of a nonfinite midpoint too: dropping the whole
-        # interval would erase valid branches between the original samples.
+        # 也优化非有限中点的任一侧：删除整个间隔将擦除原始样本之间的有效分支。
         first = refine(a, mid, depth + 1)
         second = refine(mid, b, depth + 1)
         return first + second[1:]
@@ -309,7 +302,7 @@ def _sample_segments(
             continue
         if prev_y is not None:
             refined = _refine_crossing(tree, (prev_x, prev_y), (x, y), ymin, ymax, budget)
-            samples = refined[1:]  # The previous endpoint is already in points.
+            samples = refined[1:]  # 前一个端点已经以点为单位。
         else:
             samples = [(x, y)]
         for sample in samples: