fix(plot): bound adaptive sampling and preserve curve discontinuities
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+75
-12
@@ -219,21 +219,72 @@ def _clip_polyline(
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return segments
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_REFINE_MAX_DEPTH = 24
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_REFINE_MAX_EVALUATIONS = 256
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_CURVE_MAX_REFINEMENT_EVALUATIONS = 8192
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def _refine_crossing(tree, left, right, ymin, ymax, budget=None):
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"""Adaptively check both halves of a crossing; None explicitly breaks a path.
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A visible midpoint is not a continuity proof. Accept a visible chord only
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when its midpoint error is within a quarter pixel; otherwise subdivide both
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halves. Depth, evaluation and floating-point limits always break unresolved
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intervals instead of joining them. Entirely off-screen triples can be culled.
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"""
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remaining = _REFINE_MAX_EVALUATIONS
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if budget is None:
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budget = [_REFINE_MAX_EVALUATIONS]
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tolerance = (ymax - ymin) / (_PLOT_Y1 - _PLOT_Y0) / 4
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def refine(a, b, depth):
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nonlocal remaining
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x = a[0] + (b[0] - a[0]) / 2
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if depth >= _REFINE_MAX_DEPTH or remaining == 0 or budget[0] == 0 or not a[0] < x < b[0]:
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return [a, None, b]
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remaining -= 1
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budget[0] -= 1
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try:
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y = evaluate(tree, x)
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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)):
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y = math.nan
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mid = (x, y)
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values = (a[1], y, b[1])
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if all(math.isfinite(v) for v in values):
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if max(values) < ymin or min(values) > ymax:
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return [a, None, b] # No visible chord; do not connect across it.
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error = abs(y - (a[1] / 2 + b[1] / 2))
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if any(ymin <= v <= ymax for v in values) and error <= tolerance:
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return [a, mid, b]
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# Refine either side of a nonfinite midpoint too: dropping the whole
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# interval would erase valid branches between the original samples.
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first = refine(a, mid, depth + 1)
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second = refine(mid, b, depth + 1)
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return first + second[1:]
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return refine(left, right, 0)
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def _sample_segments(
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tree: object,
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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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warnings: list[str] | None = None,
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) -> list[list[tuple[float, float]]]:
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"""采样并映射为像素点段，再裁剪到绘图矩形。
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两处断段：非有限点处（画穿渐近线）；相邻有限采样点横跨可见范围上下两侧时
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（渐近点恰好落在两个采样点之间，否则会被裁剪成贯穿绘图区的伪竖线）。
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每个相邻有限采样区间都检查中点，避免端点在可见范围内的渐近线漏判。
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自适应细分受区间与整条曲线预算限制，未解析区间以断点保守处理。
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"""
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segments: list[list[tuple[float, float]]] = []
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points: list[tuple[float, float]] = []
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prev_y: float | None = None
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prev_x = xmin
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budget = [_CURVE_MAX_REFINEMENT_EVALUATIONS]
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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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@@ -255,19 +306,31 @@ def _sample_segments(
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points = []
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prev_y = None
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continue
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# 渐近线检测：相邻有限采样点分居可见范围上下两侧（一个 < ymin、一个 > ymax），
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# 说明两者之间夹着竖直渐近线，断段避免被 Liang-Barsky 裁剪成贯穿绘图区的伪竖线
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if prev_y is not None and (
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(prev_y < ymin and y > ymax) or (prev_y > ymax and y < ymin)
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):
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if points:
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segments.append(points)
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points = []
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points.append((px, py))
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if prev_y is not None:
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refined = _refine_crossing(tree, (prev_x, prev_y), (x, y), ymin, ymax, budget)
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samples = refined[1:] # The previous endpoint is already in points.
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else:
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samples = [(x, y)]
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for sample in samples:
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mapped = None if sample is None else (
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_sx(sample[0], xmin, xmax), _sy(sample[1], ymin, ymax)
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)
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if mapped is None or not all(math.isfinite(value) for value in mapped):
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if points:
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segments.append(points)
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points = []
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else:
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points.append(mapped)
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prev_y = y
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prev_x = x
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if points:
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segments.append(points)
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if budget[0] == 0 and warnings is not None:
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warning = "曲线细分达到求值上限，未解析区间已断开；请缩小 domain 后重试"
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if warning not in warnings:
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warnings.append(warning)
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# 裁剪到绘图矩形：reportlab 无 SVG viewport 那样的自动裁剪，超出显式 range 的
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# 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）。
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clipped: list[list[tuple[float, float]]] = []
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@@ -320,7 +383,7 @@ def compute_geometry(plot: FunctionPlot) -> PlotGeometry:
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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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colors.append(color)
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polylines.append(_sample_segments(tree, xmin, xmax, ymin, ymax))
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polylines.append(_sample_segments(tree, xmin, xmax, ymin, ymax, warnings))
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return PlotGeometry(
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width=_WIDTH,
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@@ -441,3 +441,119 @@ def test_compute_geometry_breaks_at_asymptote() -> None:
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# 相邻点垂直跨度若接近整个绘图区高度，即为渐近线伪连接
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for (_, py0), (_, py1) in zip(seg, seg[1:]):
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assert abs(py1 - py0) < full_height * 0.5
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@pytest.mark.parametrize('slope,root', [(1000, 0.0025), (-1000, 0.0025), (1000000, 0.002731)])
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def test_steep_continuous_crossing_survives_svg_and_pdf(slope, root):
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from app.plot.render import compute_geometry, _PLOT_Y0, _PLOT_Y1, _PLOT_X0, _PLOT_X1
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from app.plot.render_reportlab import render_drawing
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from reportlab.graphics.shapes import PolyLine
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plot = parse_source(f'domain: -1, 1\nrange: -1, 1\ny = {slope}*(x-{root})').plot
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segments = compute_geometry(plot).polylines[0]
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assert len(segments) == 1
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points = segments[0]
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assert min(y for x,y in points) == pytest.approx(_PLOT_Y0)
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assert max(y for x,y in points) == pytest.approx(_PLOT_Y1)
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for x,y in points:
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data_x = (x-_PLOT_X0)/(_PLOT_X1-_PLOT_X0)*2-1
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data_y = 1-(y-_PLOT_Y0)/(_PLOT_Y1-_PLOT_Y0)*2
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assert data_y == pytest.approx(slope*(data_x-root),abs=1e-7)
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assert '<polyline ' in render_svg(plot).content
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assert any(isinstance(item,PolyLine) for item in render_drawing(plot).contents)
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def test_crossing_refinement_has_bounded_work(monkeypatch):
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import app.plot.render as rendering
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calls = []
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def jump(tree, x):
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calls.append(x)
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return -2 if x < 0.123456789 else 2
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monkeypatch.setattr(rendering, 'evaluate', jump)
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samples = rendering._refine_crossing(None, (0,-2), (1,2), -1,1)
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assert None in samples
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assert len(calls) <= rendering._REFINE_MAX_EVALUATIONS
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def test_visible_midpoint_does_not_bridge_a_pole():
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from app.plot.render import compute_geometry, _PLOT_Y0, _PLOT_Y1, _PLOT_X0, _PLOT_X1
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plot = parse_source('domain: 0, 2\nrange: -1, 1\ny = 1000*(x-0.0025)+0.001/(x-0.001)').plot
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segments = compute_geometry(plot).polylines[0]
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assert segments
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for seg in segments:
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for px, py in seg:
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x = (px-_PLOT_X0)/(_PLOT_X1-_PLOT_X0)*2
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y = 1-(py-_PLOT_Y0)/(_PLOT_Y1-_PLOT_Y0)*2
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# On the visible branch, 1000*t + .001/t - 1.5 >= .5.
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assert x > .001
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assert y >= .5-1e-8
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assert y == pytest.approx(1000*(x-.0025)+.001/(x-.001),abs=.002)
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def test_refined_extreme_samples_never_emit_nonfinite_coordinates():
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from app.plot.render import compute_geometry
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from app.plot.render_reportlab import render_drawing
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from reportlab.graphics.shapes import PolyLine
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plot = parse_source('domain: 0, 2\nrange: -1e-308, 1e-308\ny = 1e-304*(x-0.00125)-1e308*x*(x-0.005)*(x-0.00125)').plot
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geo = compute_geometry(plot)
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for segments in geo.polylines:
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for seg in segments:
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assert all(math.isfinite(v) for point in seg for v in point)
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svg = render_svg(plot).content
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assert 'nan' not in svg and 'inf' not in svg
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for shape in render_drawing(plot).contents:
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if isinstance(shape, PolyLine):
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assert all(math.isfinite(v) for v in shape.points)
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def test_refinement_budget_is_shared_by_both_subtrees(monkeypatch):
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import app.plot.render as rendering
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calls = []
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def oscillate(tree, x):
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calls.append(x)
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return .9*math.sin(1e9*x)
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monkeypatch.setattr(rendering, 'evaluate', oscillate)
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samples = rendering._refine_crossing(None, (0,-2), (1,2), -1,1)
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assert len(calls) == rendering._REFINE_MAX_EVALUATIONS
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assert None in samples # Exhaustion leaves gaps, never unchecked chords.
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@pytest.mark.parametrize('factor,pole', [(0.0001,.001),(-0.0001,.001),(.001,.001),(.0001,.0025),(.0001,.00419)])
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def test_visible_endpoints_do_not_hide_a_pole(factor, pole):
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from app.plot.render import compute_geometry, _PLOT_X0, _PLOT_X1
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plot = parse_source(f'domain: 0, 2\nrange: -1, 1\ny = {factor}/(x-{pole})').plot
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segments = compute_geometry(plot).polylines[0]
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assert segments
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left = right = False
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for segment in segments:
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xs = [(px-_PLOT_X0)/(_PLOT_X1-_PLOT_X0)*2 for px,py in segment]
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assert not min(xs) < pole < max(xs)
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left |= max(xs) < pole
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right |= min(xs) > pole
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assert left and right
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@pytest.mark.parametrize('expression', ['x', 'x^2', 'sin(x)', 'exp(x)', 'sqrt(x)', 'log(x)'])
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def test_smooth_and_domain_limited_curves_remain_visible(expression):
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from app.plot.render import compute_geometry, _PLOT_X0, _PLOT_X1, _PLOT_Y0, _PLOT_Y1
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plot = parse_source(f'domain: -2, 2\nrange: -2, 5\ny = {expression}').plot
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geometry = compute_geometry(plot)
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assert geometry.polylines[0]
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assert not geometry.warnings
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for segment in geometry.polylines[0]:
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for x,y in segment:
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assert math.isfinite(x) and math.isfinite(y)
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assert _PLOT_X0-1e-8 <= x <= _PLOT_X1+1e-8
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assert _PLOT_Y0-1e-8 <= y <= _PLOT_Y1+1e-8
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def test_curve_refinement_has_one_shared_budget(monkeypatch):
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import app.plot.render as rendering
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calls=[]
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def oscillate(tree, x):
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calls.append(x)
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return .9*math.sin(1e9*x)
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monkeypatch.setattr(rendering,'evaluate',oscillate)
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warnings=[]
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rendering._sample_segments(None,0,2,-1,1,warnings)
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assert len(calls) <= rendering._SAMPLES+1+rendering._CURVE_MAX_REFINEMENT_EVALUATIONS
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assert len(warnings)==1
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@@ -131,3 +131,13 @@ uv run pytest -q
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- DOCX 内嵌函数图像（需栅格化为 PNG，本轮范围外，仅 PDF 内嵌矢量图）。
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- 函数图像交互预览与缩放（前端 JS Renderer 负责，后端仅提供静态 SVG）。
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- 代码语法高亮（当前仅 CSS class 占位）。
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### PR #41：陡峭连续曲线与渐近线区分（2026-09-07）
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每个相邻有限采样区间都会检查中点，不再要求端点分别位于 range 上下两侧，也不因找到一个可见中点就连接整个区间。共享几何层检查中点与弦的偏差：有可见点且误差不超过四分之一像素时保留子段，否则继续细分左右两侧。每个区间最多额外求值 256 次、深度最多 24 层；同一表达式全部区间共享 8192 次额外求值预算，避免全区间检查导致无界增长。达到限制或无法继续推进浮点坐标时，以显式断点隔开未验证子段。遇到非有限中点仍检查它的两侧，保留有效分支，但不跨过非有限点连接。整条曲线耗尽预算时返回 warning，提示缩小 domain 后重试。
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采样三点全在同一不可见侧的子段直接舍弃。细分点与普通点一样检查映射后坐标是否有限，再统一裁剪。SVG 与 PDF 使用相同结果。这是有界数值采样，不是任意函数连续性的数学证明；高频或极窄特征仍受采样与精度限制。
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回归覆盖陡峭正负直线、百万斜率、可见中点混合极点、极小纵轴范围、两端均在可见范围内的极点、极点恰好位于中点、常见连续函数及 log/sqrt 定义域边界；验证区间与整条曲线共享求值预算，耗尽后保留断点和 warning，SVG/PDF 曲线坐标不得包含 NaN/Infinity。
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补充检测：36 组不同系数和极点位置的几何检查通过。一次本机测量中，百万斜率直线和普通倒数曲线约 3 ms，高频 `sin(1000000000*x)` 达到预算并返回 warning，约 45 ms；该数据用于验证有界退出，不作为性能承诺。
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