backend/app/export/exporters/pdf.py

@@ -1,9 +1,9 @@
 """PdfExporter：Document AST → PDF（reportlab platypus）。
 
 v1 为文本优先：标题/段落/行内强调与链接/列表/引用/表格/代码块/数学文本均可导出；
-function_plot 与 mermaid 保留源码占位并记 warning。中文字体用 reportlab 内置
-STSong-Light CID 字体，避免外部字体依赖。CID 字体无独立 bold/italic 字重，
-故行内强调退化为普通文本（内容不丢、样式简化），标题靠字号区分层级。
+function_plot 内嵌为矢量图（reportlab Drawing），mermaid 保留源码占位并记 warning。
+中文字体用 reportlab 内置 STSong-Light CID 字体，避免外部字体依赖。CID 字体无独立
+bold/italic 字重，故行内强调退化为普通文本（内容不丢、样式简化），标题靠字号区分层级。
 """
 
 from __future__ import annotations

backend/app/plot/render.py

@@ -24,6 +24,11 @@ _MARGIN = 52  # 四周留白，放轴刻度与标签
 _SAMPLES = 400
 _PALETTE = ["#0969da", "#d1242f", "#1a7f37", "#8250df", "#bf8700", "#e36209"]
 _COLOR_RE = re.compile(r"^#[0-9a-fA-F]{3,8}$")
+# 绘图矩形（像素，SVG y-down）：曲线与坐标轴所在区域，坐标轴/网格均在此范围内
+_PLOT_X0 = _MARGIN
+_PLOT_Y0 = _MARGIN
+_PLOT_X1 = _WIDTH - _MARGIN
+_PLOT_Y1 = _HEIGHT - _MARGIN
 
 
 def _safe_color(color: str | None, fallback: str) -> str:
@@ -141,6 +146,79 @@ class PlotGeometry:
     warnings: list[str]
 
 
+def _clip_segment(
+    p0: tuple[float, float],
+    p1: tuple[float, float],
+    x0: float,
+    y0: float,
+    x1: float,
+    y1: float,
+) -> tuple[tuple[float, float], tuple[float, float]] | None:
+    """Liang-Barsky：把线段裁剪到轴对齐矩形 [x0,x1]×[y0,y1]，完全在外返回 None。"""
+    dx = p1[0] - p0[0]
+    dy = p1[1] - p0[1]
+    p = (-dx, dx, -dy, dy)
+    q = (p0[0] - x0, x1 - p0[0], p0[1] - y0, y1 - p0[1])
+    u1, u2 = 0.0, 1.0
+    for pk, qk in zip(p, q):
+        if pk == 0:
+            if qk < 0:
+                return None
+        else:
+            r = qk / pk
+            if pk < 0:
+                if r > u2:
+                    return None
+                if r > u1:
+                    u1 = r
+            else:
+                if r < u1:
+                    return None
+                if r < u2:
+                    u2 = r
+    if u1 > u2:
+        return None
+    return (p0[0] + u1 * dx, p0[1] + u1 * dy), (p0[0] + u2 * dx, p0[1] + u2 * dy)
+
+
+def _points_close(
+    a: tuple[float, float], b: tuple[float, float], eps: float = 1e-9
+) -> bool:
+    return abs(a[0] - b[0]) < eps and abs(a[1] - b[1]) < eps
+
+
+def _clip_polyline(
+    points: list[tuple[float, float]],
+    x0: float,
+    y0: float,
+    x1: float,
+    y1: float,
+) -> list[list[tuple[float, float]]]:
+    """把折线裁剪到矩形，返回若干连续子段；相邻点不衔接处自动断段。"""
+    if not points:
+        return []
+    segments: list[list[tuple[float, float]]] = []
+    current: list[tuple[float, float]] = []
+    for i in range(len(points) - 1):
+        clipped = _clip_segment(points[i], points[i + 1], x0, y0, x1, y1)
+        if clipped is None:
+            if current:
+                segments.append(current)
+                current = []
+            continue
+        a, b = clipped
+        # 共享点被裁剪修改（折线短暂越界后折返）时，a 与上一段末点不衔接，需断段
+        if current and not _points_close(a, current[-1]):
+            segments.append(current)
+            current = []
+        if not current:
+            current.append(a)
+        current.append(b)
+    if current:
+        segments.append(current)
+    return segments
+
+
 def _sample_segments(
     tree: object,
     xmin: float,
@@ -148,7 +226,7 @@ def _sample_segments(
     ymin: float,
     ymax: float,
 ) -> list[list[tuple[float, float]]]:
-    """采样并映射为像素点段；非有限点处断段，避免画穿渐近线。"""
+    """采样并映射为像素点段，再裁剪到绘图矩形；非有限点处断段，避免画穿渐近线。"""
     segments: list[list[tuple[float, float]]] = []
     points: list[tuple[float, float]] = []
     for i in range(_SAMPLES + 1):
@@ -173,7 +251,13 @@ def _sample_segments(
         points.append((px, py))
     if points:
         segments.append(points)
-    return segments
+
+    # 裁剪到绘图矩形：reportlab 无 SVG viewport 那样的自动裁剪，超出显式 range 的
+    # 曲线会覆盖页面其他内容，故在共享几何层统一裁剪（SVG 也一并收敛到绘图区）。
+    clipped: list[list[tuple[float, float]]] = []
+    for seg in segments:
+        clipped.extend(_clip_polyline(seg, _PLOT_X0, _PLOT_Y0, _PLOT_X1, _PLOT_Y1))
+    return clipped
 
 
 def compute_geometry(plot: FunctionPlot) -> PlotGeometry:

backend/app/plot/render_reportlab.py

@@ -89,15 +89,19 @@ def _build_drawing(geo: PlotGeometry) -> Drawing:
             )
         )
     if geo.ylabel:
-        # 竖向标签：rotate(90) 在 y-up 坐标下等价于 SVG 的 rotate(-90)
+        # 竖向标签：Group.rotate(90) 在 y-up 坐标下等价于 SVG 的 rotate(-90)。
+        # 文本放在组内局部坐标 (0,0)，先平移后旋转得到 T·R（先绕原点旋转、再平移到
+        # 目标位置），避免用绝对坐标定位又用相同坐标当旋转中心造成的重复变换，
+        # 后者会把标签甩到画布之外（负 x 区域）。
         label = Group()
         label.add(
             String(
-                16, geo.height / 2, geo.ylabel,
+                0, 0, geo.ylabel,
                 fontName=_FONT, fontSize=_LABEL_FONT_SIZE, fillColor=_LABEL_COLOR, textAnchor="middle",
             )
         )
-        label.rotate(90, 16, geo.height / 2)
+        label.translate(16, geo.height / 2)
+        label.rotate(90)
         drawing.add(label)
 
     return drawing

backend/tests/test_plot.py

@@ -383,3 +383,45 @@ def test_render_reportlab_curves_are_finite_and_bounded() -> None:
             assert math.isfinite(x) and math.isfinite(y)
             assert 0 <= x <= 640
             assert 0 <= y <= 480
+
+
+def test_compute_geometry_clips_curves_to_plot_rect() -> None:
+    # P2：显式 range 外的曲线应裁剪到绘图矩形，避免 PDF 中曲线覆盖页面其他内容
+    from app.plot.render import (
+        _PLOT_X0,
+        _PLOT_X1,
+        _PLOT_Y0,
+        _PLOT_Y1,
+        compute_geometry,
+    )
+
+    plot = parse_source("range: -1, 1\ny = 10*x").plot
+    geo = compute_geometry(plot)
+    assert geo.polylines
+    assert any(geo.polylines)  # 曲线穿越 range 后在绘图区内仍有可见段
+    for segments in geo.polylines:
+        for seg in segments:
+            assert seg
+            for px, py in seg:
+                assert _PLOT_X0 <= px <= _PLOT_X1
+                assert _PLOT_Y0 <= py <= _PLOT_Y1
+
+
+def test_render_reportlab_ylabel_within_drawing_bounds() -> None:
+    # P2：纵轴标签旋转后边界应落在 Drawing 范围内，不能甩到负 x 区域
+    from reportlab.graphics.shapes import Group, String
+
+    from app.plot.render_reportlab import render_drawing
+
+    plot = parse_source("ylabel: 数值\ny = x").plot
+    drawing = render_drawing(plot)
+    groups = [c for c in drawing.contents if isinstance(c, Group)]
+    ylabel_groups = [
+        g
+        for g in groups
+        if any(isinstance(s, String) and s.text == "数值" for s in g.contents)
+    ]
+    assert ylabel_groups
+    x0, y0, x1, y1 = ylabel_groups[0].getBounds()
+    assert 0 <= x0 <= x1 <= 640
+    assert 0 <= y0 <= y1 <= 480