feat(export): 函数图像静态渲染（function-plot → SVG）

- 新增 app/plot 包：白名单表达式解析（ast 无 eval）+ FunctionPlot 模型 + 静态 SVG 渲染 - HtmlExporter 的 function_plot 节点解析并内嵌 SVG，解析失败回退占位并转诊断 - 新增 test_plot.py（13 个测试）覆盖表达式安全、指令解析、SVG 输出与导出链路集成 Co-Authored-By: Claude Code <noreply@anthropic.com>
2026-09-04 22:41:35 +08:00
parent 64af1f5165
commit f49d1245a1
6 changed files with 804 additions and 5 deletions
@@ -0,0 +1,223 @@
+"""Function Plot → 静态 SVG 渲染。
+
+只输出纯几何与 <text> 的 SVG（无 script/foreignObject/内联事件），可安全内嵌 HTML。
+所有文本与颜色都经过转义/校验，不把用户输入直接拼进标记。
+"""
+
+from __future__ import annotations
+
+import html
+import math
+import re
+from typing import Callable
+
+from app.plot.model import FunctionPlot, StaticRenderResult
+from app.plot.parser import PlotParseError, evaluate, parse_expression
+
+_WIDTH = 640
+_HEIGHT = 480
+_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}$")
+
+
+def _safe_color(color: str | None, fallback: str) -> str:
+    return color.strip() if color and _COLOR_RE.match(color.strip()) else fallback
+
+
+def _fmt_num(v: float) -> str:
+    if v == 0:
+        return "0"
+    if abs(v) >= 1e6 or abs(v) < 1e-6:
+        return f"{v:.2e}"
+    return f"{v:.6g}"
+
+
+def _nice_step(span: float, target_ticks: int = 6) -> float:
+    raw = abs(span) / target_ticks
+    mag = 10 ** math.floor(math.log10(raw))
+    for m in (1, 2, 5, 10):
+        if raw <= m * mag:
+            return m * mag
+    return 10 * mag
+
+
+def _ticks(lo: float, hi: float, step: float) -> list[float]:
+    first = math.ceil(lo / step) * step
+    values: list[float] = []
+    v = first
+    while v <= hi + step * 1e-9:
+        values.append(v)
+        v += step
+    return values
+
+
+def _compute_range(
+    plot: FunctionPlot,
+    fns: list[tuple[object, object]],
+    xmin: float,
+    xmax: float,
+) -> tuple[float, float]:
+    """采样确定 y 范围；指定 range 则优先，否则取有限样本的 min/max 加 5% 余量。"""
+    if plot.range is not None:
+        return float(plot.range[0]), float(plot.range[1])
+
+    ys: list[float] = []
+    for _expr, tree in fns:
+        for i in range(_SAMPLES + 1):
+            x = xmin + (xmax - xmin) * i / _SAMPLES
+            try:
+                y = evaluate(tree, x)  # type: ignore[arg-type]
+            except (ValueError, ZeroDivisionError, OverflowError):
+                continue
+            if math.isfinite(y):
+                ys.append(y)
+
+    if not ys:
+        return -10.0, 10.0
+    lo, hi = min(ys), max(ys)
+    if lo == hi:
+        lo -= 1.0
+        hi += 1.0
+    pad = (hi - lo) * 0.05
+    return lo - pad, hi + pad
+
+
+def _polyline(
+    tree: object,
+    xmin: float,
+    xmax: float,
+    sx: Callable[[float], float],
+    sy: Callable[[float], float],
+    color: str,
+) -> str:
+    """采样并把非有限点处断开成多段 polyline，避免画穿渐近线。"""
+    segments: list[str] = []
+    points: list[str] = []
+    for i in range(_SAMPLES + 1):
+        x = xmin + (xmax - xmin) * i / _SAMPLES
+        try:
+            y = evaluate(tree, x)  # type: ignore[arg-type]
+        except (ValueError, ZeroDivisionError, OverflowError):
+            y = math.nan
+        if not math.isfinite(y):
+            if points:
+                segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
+                points = []
+            continue
+        px = sx(x)
+        py = sy(y)
+        points.append(f"{px:.2f},{py:.2f}")
+    if points:
+        segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
+    return "".join(segments)
+
+
+def _grid(
+    xmin: float,
+    xmax: float,
+    ymin: float,
+    ymax: float,
+    sx: Callable[[float], float],
+    sy: Callable[[float], float],
+) -> str:
+    parts: list[str] = []
+    for x in _ticks(xmin, xmax, _nice_step(xmax - xmin)):
+        parts.append(f'<line x1="{sx(x):.2f}" y1="{sy(ymin):.2f}" x2="{sx(x):.2f}" y2="{sy(ymax):.2f}" stroke="#eaeef2"/>')
+    for y in _ticks(ymin, ymax, _nice_step(ymax - ymin)):
+        parts.append(f'<line x1="{sx(xmin):.2f}" y1="{sy(y):.2f}" x2="{sx(xmax):.2f}" y2="{sy(y):.2f}" stroke="#eaeef2"/>')
+    return "".join(parts)
+
+
+def _axes(
+    xmin: float,
+    xmax: float,
+    ymin: float,
+    ymax: float,
+    sx: Callable[[float], float],
+    sy: Callable[[float], float],
+) -> str:
+    parts: list[str] = []
+    # 坐标轴：过原点则画在原点，否则贴边，保证始终有参照系
+    x_axis_y = 0.0 if ymin <= 0 <= ymax else ymin
+    y_axis_x = 0.0 if xmin <= 0 <= xmax else xmin
+    parts.append(
+        f'<line x1="{sx(xmin):.2f}" y1="{sy(x_axis_y):.2f}" x2="{sx(xmax):.2f}" y2="{sy(x_axis_y):.2f}" stroke="#57606a"/>'
+    )
+    parts.append(
+        f'<line x1="{sx(y_axis_x):.2f}" y1="{sy(ymin):.2f}" x2="{sx(y_axis_x):.2f}" y2="{sy(ymax):.2f}" stroke="#57606a"/>'
+    )
+    # x 轴刻度数字（画在轴下方）
+    for x in _ticks(xmin, xmax, _nice_step(xmax - xmin)):
+        parts.append(
+            f'<text x="{sx(x):.2f}" y="{sy(x_axis_y) + 14:.2f}" text-anchor="middle" font-size="10" fill="#57606a">{html.escape(_fmt_num(x))}</text>'
+        )
+    # y 轴刻度数字（画在轴左侧）
+    for y in _ticks(ymin, ymax, _nice_step(ymax - ymin)):
+        parts.append(
+            f'<text x="{sx(y_axis_x) - 6:.2f}" y="{sy(y) + 3:.2f}" text-anchor="end" font-size="10" fill="#57606a">{html.escape(_fmt_num(y))}</text>'
+        )
+    return "".join(parts)
+
+
+def _labels(plot: FunctionPlot, sx: Callable[[float], float], sy: Callable[[float], float]) -> str:
+    parts: list[str] = []
+    if plot.axes.xlabel:
+        parts.append(
+            f'<text x="{(_WIDTH / 2):.2f}" y="{_HEIGHT - 10:.2f}" text-anchor="middle" font-size="12" fill="#1f2328">{html.escape(plot.axes.xlabel)}</text>'
+        )
+    if plot.axes.ylabel:
+        parts.append(
+            f'<text x="16" y="{(_HEIGHT / 2):.2f}" text-anchor="middle" font-size="12" fill="#1f2328" transform="rotate(-90 16 {_HEIGHT / 2:.2f})">{html.escape(plot.axes.ylabel)}</text>'
+        )
+    return "".join(parts)
+
+
+def render_svg(plot: FunctionPlot) -> StaticRenderResult:
+    """把已解析的 FunctionPlot 渲染为内嵌 SVG。"""
+    warnings: list[str] = []
+    xmin, xmax = plot.domain
+    if xmin >= xmax:
+        warnings.append("domain 无效，回退到 [-10, 10]")
+        xmin, xmax = -10.0, 10.0
+
+    # 重新解析并编译表达式（parse_source 已校验，这里异常只在模型被绕过时触发）
+    fns: list[tuple[object, object]] = []
+    for expr in plot.expressions:
+        try:
+            tree = parse_expression(expr.expression)
+        except PlotParseError as exc:
+            warnings.append(f"表达式无法渲染，已跳过：{expr.expression}（{exc.diagnostic.message}）")
+            continue
+        fns.append((expr, tree))
+
+    ymin, ymax = _compute_range(plot, fns, xmin, xmax)
+    if plot.range is not None and plot.range[0] >= plot.range[1]:
+        warnings.append("range 无效，改用自动范围")
+        ymin, ymax = _compute_range(plot, fns, xmin, xmax)
+
+    def sx(x: float) -> float:
+        return _MARGIN + (x - xmin) / (xmax - xmin) * (_WIDTH - 2 * _MARGIN)
+
+    def sy(y: float) -> float:
+        return _HEIGHT - _MARGIN - (y - ymin) / (ymax - ymin) * (_HEIGHT - 2 * _MARGIN)
+
+    parts: list[str] = [
+        f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 {_WIDTH} {_HEIGHT}" role="img">'
+    ]
+    if plot.axes.grid:
+        parts.append(_grid(xmin, xmax, ymin, ymax, sx, sy))
+    parts.append(_axes(xmin, xmax, ymin, ymax, sx, sy))
+    for i, (expr, tree) in enumerate(fns):
+        color = _safe_color(expr.color, _PALETTE[i % len(_PALETTE)])
+        parts.append(_polyline(tree, xmin, xmax, sx, sy, color))
+    parts.append(_labels(plot, sx, sy))
+    parts.append("</svg>")
+
+    return StaticRenderResult(
+        content="".join(parts),
+        width=_WIDTH,
+        height=_HEIGHT,
+        warnings=warnings,
+    )