yxxandClaude Code
b87f94551b
- P2 复杂表达式绕过异常回退：解析与渲染共同纳入局部异常回退； AST 深度/节点数上限拦截 RecursionError - P2 极端有限范围生成 nan SVG：校验坐标跨度有限且 >0，回退安全范围； _polyline 拒绝非有限像素坐标 - P3 更新接口契约文档：function-plot 静态 SVG 已实现 Co-Authored-By: Claude Code <noreply@anthropic.com>
259 lines
9.3 KiB
Python
259 lines
9.3 KiB
Python
"""Function Plot → 静态 SVG 渲染。
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只输出纯几何与 <text> 的 SVG（无 script/foreignObject/内联事件），可安全内嵌 HTML。
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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。
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"""
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from __future__ import annotations
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import html
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import math
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import re
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from typing import Callable
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from app.plot.model import FunctionPlot, StaticRenderResult
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from app.plot.parser import PlotParseError, evaluate, parse_expression
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_WIDTH = 640
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_HEIGHT = 480
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_MARGIN = 52 # 四周留白，放轴刻度与标签
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_SAMPLES = 400
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_PALETTE = ["#0969da", "#d1242f", "#1a7f37", "#8250df", "#bf8700", "#e36209"]
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_COLOR_RE = re.compile(r"^#[0-9a-fA-F]{3,8}$")
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def _safe_color(color: str | None, fallback: str) -> str:
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return color.strip() if color and _COLOR_RE.match(color.strip()) else fallback
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def _valid_span(lo: float, hi: float) -> bool:
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"""范围跨度有效：端点有限、跨度有限且大于零。
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端点相减可能溢出为 ``inf``（如 ``-1e308`` 到 ``1e308``），需单独校验跨度，
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否则后续坐标换算会生成含 ``nan`` 的 SVG。
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"""
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span = hi - lo
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return math.isfinite(lo) and math.isfinite(hi) and math.isfinite(span) and span > 0
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def _fmt_num(v: float) -> str:
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if v == 0:
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return "0"
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if abs(v) >= 1e6 or abs(v) < 1e-6:
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return f"{v:.2e}"
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return f"{v:.6g}"
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def _nice_step(span: float, target_ticks: int = 6) -> float:
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raw = abs(span) / target_ticks
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if not math.isfinite(raw) or raw <= 0:
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return 1.0 # 兜底步长，避免 span 为 0/inf 时产生非法刻度
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mag = 10 ** math.floor(math.log10(raw))
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for m in (1, 2, 5, 10):
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if raw <= m * mag:
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return m * mag
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return 10 * mag
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def _ticks(lo: float, hi: float, step: float) -> list[float]:
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# 防御：非法步长直接返回空，避免除零
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if not math.isfinite(step) or step <= 0:
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return []
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first = math.ceil(lo / step) * step
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values: list[float] = []
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v = first
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# 有上限的整数索引推进 + 步长推进校验，防止浮点精度导致 v+step==v 的死循环
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for _ in range(1000):
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if v > hi + step * 1e-9:
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break
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values.append(v)
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nxt = v + step
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if nxt <= v:
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break # 步长小于当前数值的浮点精度，已无法推进
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v = nxt
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return values
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def _compute_range(
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fns: list[tuple[object, object]],
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xmin: float,
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xmax: float,
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) -> tuple[float, float]:
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"""采样确定 y 范围；取有限样本的 min/max 加 5% 余量。"""
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ys: list[float] = []
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for _expr, tree in fns:
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for i in range(_SAMPLES + 1):
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x = xmin + (xmax - xmin) * i / _SAMPLES
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try:
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y = evaluate(tree, x) # type: ignore[arg-type]
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except (ValueError, ZeroDivisionError, OverflowError, TypeError):
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continue
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# 复数等非实数结果直接跳过，不参与范围统计
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if isinstance(y, (int, float)) and math.isfinite(y):
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ys.append(y)
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if not ys:
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return -10.0, 10.0
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lo, hi = min(ys), max(ys)
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if lo == hi:
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lo -= 1.0
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hi += 1.0
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pad = (hi - lo) * 0.05
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return lo - pad, hi + pad
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def _polyline(
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tree: object,
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xmin: float,
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xmax: float,
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sx: Callable[[float], float],
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sy: Callable[[float], float],
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color: str,
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) -> str:
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"""采样并把非有限点处断开成多段 polyline，避免画穿渐近线。"""
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segments: list[str] = []
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points: list[str] = []
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for i in range(_SAMPLES + 1):
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x = xmin + (xmax - xmin) * i / _SAMPLES
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try:
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y = evaluate(tree, x) # type: ignore[arg-type]
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except (ValueError, ZeroDivisionError, OverflowError, TypeError):
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y = math.nan
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if not isinstance(y, (int, float)) or not math.isfinite(y):
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if points:
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segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
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points = []
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continue
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px = sx(x)
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py = sy(y)
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# 映射后的坐标必须有限：显式 range 下极端 y 值可能让像素坐标溢出为 inf
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if not (math.isfinite(px) and math.isfinite(py)):
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if points:
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segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
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points = []
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continue
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points.append(f"{px:.2f},{py:.2f}")
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if points:
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segments.append(f'<polyline points="{" ".join(points)}" fill="none" stroke="{color}"/>')
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return "".join(segments)
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def _grid(
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xmin: float,
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xmax: float,
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ymin: float,
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ymax: float,
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sx: Callable[[float], float],
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sy: Callable[[float], float],
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) -> str:
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parts: list[str] = []
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for x in _ticks(xmin, xmax, _nice_step(xmax - xmin)):
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parts.append(f'<line x1="{sx(x):.2f}" y1="{sy(ymin):.2f}" x2="{sx(x):.2f}" y2="{sy(ymax):.2f}" stroke="#eaeef2"/>')
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for y in _ticks(ymin, ymax, _nice_step(ymax - ymin)):
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parts.append(f'<line x1="{sx(xmin):.2f}" y1="{sy(y):.2f}" x2="{sx(xmax):.2f}" y2="{sy(y):.2f}" stroke="#eaeef2"/>')
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return "".join(parts)
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def _axes(
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xmin: float,
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xmax: float,
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ymin: float,
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ymax: float,
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sx: Callable[[float], float],
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sy: Callable[[float], float],
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) -> str:
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parts: list[str] = []
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# 坐标轴：过原点则画在原点，否则贴边，保证始终有参照系
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x_axis_y = 0.0 if ymin <= 0 <= ymax else ymin
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y_axis_x = 0.0 if xmin <= 0 <= xmax else xmin
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parts.append(
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f'<line x1="{sx(xmin):.2f}" y1="{sy(x_axis_y):.2f}" x2="{sx(xmax):.2f}" y2="{sy(x_axis_y):.2f}" stroke="#57606a"/>'
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)
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parts.append(
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f'<line x1="{sx(y_axis_x):.2f}" y1="{sy(ymin):.2f}" x2="{sx(y_axis_x):.2f}" y2="{sy(ymax):.2f}" stroke="#57606a"/>'
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)
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# x 轴刻度数字（画在轴下方）
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for x in _ticks(xmin, xmax, _nice_step(xmax - xmin)):
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parts.append(
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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>'
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)
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# y 轴刻度数字（画在轴左侧）
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for y in _ticks(ymin, ymax, _nice_step(ymax - ymin)):
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parts.append(
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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>'
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)
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return "".join(parts)
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def _labels(plot: FunctionPlot, sx: Callable[[float], float], sy: Callable[[float], float]) -> str:
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parts: list[str] = []
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if plot.axes.xlabel:
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parts.append(
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f'<text x="{(_WIDTH / 2):.2f}" y="{_HEIGHT - 10:.2f}" text-anchor="middle" font-size="12" fill="#1f2328">{html.escape(plot.axes.xlabel)}</text>'
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)
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if plot.axes.ylabel:
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parts.append(
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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>'
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)
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return "".join(parts)
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def render_svg(plot: FunctionPlot) -> StaticRenderResult:
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"""把已解析的 FunctionPlot 渲染为内嵌 SVG。"""
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warnings: list[str] = []
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xmin, xmax = plot.domain
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if not _valid_span(xmin, xmax):
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warnings.append("domain 无效，回退到 [-10, 10]")
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xmin, xmax = -10.0, 10.0
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# 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）
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fns: list[tuple[object, object]] = []
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for expr in plot.expressions:
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try:
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tree = parse_expression(expr.expression)
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except PlotParseError as exc:
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warnings.append(f"表达式无法渲染，已跳过：{expr.expression}（{exc.diagnostic.message}）")
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continue
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fns.append((expr, tree))
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# 纵轴范围：显式 range 有效则用之；无效（退化/非有限/跨度溢出）丢弃并自动采样重算
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if plot.range is not None:
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lo, hi = float(plot.range[0]), float(plot.range[1])
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if _valid_span(lo, hi):
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ymin, ymax = lo, hi
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else:
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warnings.append("range 无效，改用自动范围")
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ymin, ymax = _compute_range(fns, xmin, xmax)
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else:
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ymin, ymax = _compute_range(fns, xmin, xmax)
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# 最终防线：自动范围在极端样本下也可能溢出，坐标映射前必须保证跨度有限且大于零
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if not _valid_span(ymin, ymax):
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warnings.append("y 范围跨度无法表示，回退到 [-10, 10]")
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ymin, ymax = -10.0, 10.0
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def sx(x: float) -> float:
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return _MARGIN + (x - xmin) / (xmax - xmin) * (_WIDTH - 2 * _MARGIN)
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def sy(y: float) -> float:
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return _HEIGHT - _MARGIN - (y - ymin) / (ymax - ymin) * (_HEIGHT - 2 * _MARGIN)
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parts: list[str] = [
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f'<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 {_WIDTH} {_HEIGHT}" role="img">'
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]
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if plot.axes.grid:
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parts.append(_grid(xmin, xmax, ymin, ymax, sx, sy))
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parts.append(_axes(xmin, xmax, ymin, ymax, sx, sy))
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for i, (expr, tree) in enumerate(fns):
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color = _safe_color(expr.color, _PALETTE[i % len(_PALETTE)])
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parts.append(_polyline(tree, xmin, xmax, sx, sy, color))
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parts.append(_labels(plot, sx, sy))
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parts.append("</svg>")
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return StaticRenderResult(
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content="".join(parts),
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width=_WIDTH,
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height=_HEIGHT,
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warnings=warnings,
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)
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