feat(export): PDF 内嵌函数图像矢量图

- 抽取 render.py 共享几何：新增 PlotGeometry + compute_geometry，render_svg
  改为薄序列化层，SVG 输出与重构前逐字节一致（8 组用例回归验证）
- 新增 app/plot/render_reportlab.py：消费共享几何产出 reportlab 矢量 Drawing
  （网格/坐标轴 Line、曲线 PolyLine、刻度/标签 String、ylabel Group 旋转），
  复用 STSong-Light 渲染中文，按页面内容宽 renderScale 缩放
- pdf.py _block_function_plot 改为内嵌矢量图（解析/渲染失败或超预算回退占位，
  单图失败不阻断整篇）；mermaid 仍占位
- 抽取 FunctionPlotBudget + format_plot_diagnostic 到 _common.py，html/pdf 共用
- 文档同步：PDF 已内嵌函数图像，DOCX 仍占位（栅格化范围外）

Co-Authored-By: Claude Code <noreply@anthropic.com>

backend/tests/test_export.py

@@ -311,16 +311,50 @@ def test_export_docx_completes_with_zip_magic_bytes() -> None:
     assert path.read_bytes()[:2] == b"PK"
 
 
-def test_pdf_exporter_marks_plot_and_mermaid_as_placeholders() -> None:
+def test_pdf_exporter_embeds_function_plot_and_marks_mermaid() -> None:
     from app.export.exporters.pdf import PdfExporter
 
     md = "```mermaid\ngraph LR\n```\n\n```function_plot\ny = x\n```"
     result = asyncio.run(PdfExporter().export(parse_document(md), ExportOptions()))
     assert result.content[:4] == b"%PDF"
     assert any("mermaid" in w for w in result.warnings)
+    # function_plot 已内嵌为矢量图，不再产生「函数图像占位」warning
+    assert not any("函数图像" in w for w in result.warnings)
+    # 绘图用 STSong-Light 渲染刻度/标签，字体应嵌入 PDF
+    assert b"STSong-Light" in result.content
+
+
+def test_pdf_exporter_function_plot_fallback_on_error() -> None:
+    from app.export.exporters.pdf import PdfExporter
+
+    # 解析失败（不安全表达式）应回退源码占位并记 warning，不阻断整篇导出
+    md = "```function_plot\ny = os.system('x')\n```"
+    result = asyncio.run(PdfExporter().export(parse_document(md), ExportOptions()))
+    assert result.content[:4] == b"%PDF"
     assert any("函数图像" in w for w in result.warnings)
 
 
+def test_pdf_exporter_limits_function_plot_count() -> None:
+    from app.export.exporters.pdf import PdfExporter
+
+    blocks = "\n\n".join("```function-plot\ny = x\n```" for _ in range(20))
+    result = asyncio.run(PdfExporter().export(parse_document(blocks), ExportOptions()))
+    assert result.content[:4] == b"%PDF"
+    # 超出数量上限的图块回退占位并记 warning
+    assert any("数量超过上限" in w for w in result.warnings)
+
+
+def test_pdf_exporter_limits_total_plot_nodes(monkeypatch) -> None:
+    import app.export.exporters._common as common_mod
+    from app.export.exporters.pdf import PdfExporter
+
+    monkeypatch.setattr(common_mod, "MAX_TOTAL_PLOT_NODES", 5)
+    md = "```function-plot\ny = x\n```\n\n```function-plot\ny = x + x + x + x\n```"
+    result = asyncio.run(PdfExporter().export(parse_document(md), ExportOptions()))
+    assert result.content[:4] == b"%PDF"
+    assert any("累计复杂度" in w for w in result.warnings)
+
+
 def test_docx_exporter_marks_plot_and_mermaid_as_placeholders() -> None:
     from app.export.exporters.docx import DocxExporter
 

backend/tests/test_plot.py

@@ -278,9 +278,9 @@ def test_html_exporter_limits_function_plot_count() -> None:
 
 def test_html_exporter_limits_total_plot_nodes(monkeypatch) -> None:
     # P1：文档级累计 AST 节点预算超限后，后续图像回退占位，防止组合复杂度耗尽 CPU
-    import app.export.exporters.html as html_mod
+    import app.export.exporters._common as common_mod
 
-    monkeypatch.setattr(html_mod, "_MAX_TOTAL_PLOT_NODES", 5)
+    monkeypatch.setattr(common_mod, "MAX_TOTAL_PLOT_NODES", 5)
     # 第一个图块 y=x（1 节点）在预算内；第二个图块 y=x+x+x+x（7 节点）累计超限
     md = "```function-plot\ny = x\n```\n\n```function-plot\ny = x + x + x + x\n```"
     result = asyncio.run(HtmlExporter().export(parse_document(md), ExportOptions()))
@@ -322,3 +322,64 @@ def test_mermaid_static_renderer_returns_placeholder() -> None:
     result = renderer.render(StaticRenderRequest(kind="mermaid", source="graph LR"))
     assert result.content == ""
     assert any("mermaid" in w for w in result.warnings)
+
+
+# --------------------------------------------------------------------------- #
+# 共享几何与 reportlab 后端（PDF 内嵌函数图像）
+# --------------------------------------------------------------------------- #
+def test_compute_geometry_shares_pixel_segments() -> None:
+    from app.plot.render import compute_geometry
+
+    plot = parse_source("y = x^2\ny = sin(x)").plot
+    geo = compute_geometry(plot)
+    assert geo.width == 640
+    assert geo.height == 480
+    assert len(geo.polylines) == 2
+    assert geo.colors == ["#0969da", "#d1242f"]
+    assert geo.xticks and geo.yticks
+    for segments in geo.polylines:
+        assert segments
+        for seg in segments:
+            assert seg
+            for px, py in seg:
+                assert math.isfinite(px) and math.isfinite(py)
+                assert 0 <= px <= geo.width
+                assert 0 <= py <= geo.height
+
+
+def test_render_reportlab_builds_drawing() -> None:
+    from reportlab.graphics.shapes import Drawing, Group, Line, PolyLine, String
+
+    from app.plot.render_reportlab import render_drawing
+
+    plot = parse_source("xlabel: 时间\nylabel: 数值\ny = x^2").plot
+    drawing = render_drawing(plot, width=480)
+    assert isinstance(drawing, Drawing)
+    assert drawing.renderScale == 0.75  # 480 / 640
+    kinds = {type(c).__name__ for c in drawing.contents}
+    assert {"Line", "PolyLine", "String", "Group"} <= kinds
+    strings = [c for c in drawing.contents if isinstance(c, String)]
+    assert any(s.fontName == "STSong-Light" for s in strings)
+    assert any(s.text == "时间" for s in strings)
+    # ylabel 在旋转 Group 内
+    groups = [c for c in drawing.contents if isinstance(c, Group)]
+    assert groups
+    group_texts = [s.text for g in groups for s in g.contents if isinstance(s, String)]
+    assert "数值" in group_texts
+
+
+def test_render_reportlab_curves_are_finite_and_bounded() -> None:
+    from reportlab.graphics.shapes import PolyLine
+
+    from app.plot.render_reportlab import render_drawing
+
+    plot = parse_source("y = x").plot
+    drawing = render_drawing(plot)
+    polylines = [c for c in drawing.contents if isinstance(c, PolyLine)]
+    assert polylines
+    for pl in polylines:
+        pts = pl.points  # 扁平 [x0,y0,x1,y1,...]
+        for x, y in zip(pts[0::2], pts[1::2]):
+            assert math.isfinite(x) and math.isfinite(y)
+            assert 0 <= x <= 640
+            assert 0 <= y <= 480