fix(plot): 渐近点落在采样点之间时断段，避免伪竖线

相邻有限采样点分居可见范围上下两侧时说明中间夹着竖直渐近线，
此前只对非有限值断段，会被 Liang-Barsky 裁剪成贯穿绘图区的伪竖线；
现在在共享几何层断段，并新增回归测试断言不存在跨越上下边界的伪连接线段。

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

backend/app/plot/render.py

@@ -226,9 +226,14 @@ def _sample_segments(
     ymin: float,
     ymax: float,
 ) -> list[list[tuple[float, float]]]:
-    """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。"""
+    """采样并映射为像素点段，再裁剪到绘图矩形。
+
+    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
+    （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）。
+    """
     segments: list[list[tuple[float, float]]] = []
     points: list[tuple[float, float]] = []
+    prev_y: float | None = None
     for i in range(_SAMPLES + 1):
         x = xmin + (xmax - xmin) * i / _SAMPLES
         try:
@@ -239,6 +244,7 @@ def _sample_segments(
             if points:
                 segments.append(points)
                 points = []
+            prev_y = None
             continue
         px = _sx(x, xmin, xmax)
         py = _sy(y, ymin, ymax)
@@ -247,8 +253,18 @@ def _sample_segments(
             if points:
                 segments.append(points)
                 points = []
+            prev_y = None
             continue
+        # 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），
+        # 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
+        if prev_y is not None and (
+            (prev_y < ymin and y > ymax) or (prev_y > ymax and y < ymin)
+        ):
+            if points:
+                segments.append(points)
+                points = []
         points.append((px, py))
+        prev_y = y
     if points:
         segments.append(points)
 

backend/tests/test_plot.py

@@ -425,3 +425,19 @@ def test_render_reportlab_ylabel_within_drawing_bounds() -> None:
     x0, y0, x1, y1 = ylabel_groups[0].getBounds()
     assert 0 <= x0 <= x1 <= 640
     assert 0 <= y0 <= y1 <= 480
+
+
+def test_compute_geometry_breaks_at_asymptote() -> None:
+    # P2：渐近点落在两个采样点之间时，两侧采样仍有限，若不断段会被 Liang-Barsky
+    # 裁剪成贯穿绘图区的伪竖线；这里断言不存在跨越上下边界的伪连接线段。
+    from app.plot.render import _PLOT_Y0, _PLOT_Y1, compute_geometry
+
+    plot = parse_source("domain: -1, 1\nrange: -10, 10\ny = 1/(x-0.013)").plot
+    geo = compute_geometry(plot)
+    assert any(geo.polylines)  # 渐近线两侧的曲线分支仍在绘图区内可见
+    full_height = _PLOT_Y1 - _PLOT_Y0
+    for segments in geo.polylines:
+        for seg in segments:
+            # 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
+            for (_, py0), (_, py1) in zip(seg, seg[1:]):
+                assert abs(py1 - py0) < full_height * 0.5