Include line moment when constructing a plane from a line and point (#281)

Plane3.LinePoint currently computes the normal as w cross p, omitting
the line moment. This only gives the intended plane when the line passes
through the origin. For example a line through [1,2,3] in direction
[1,0,0] and a point [1,4,3] should define z=3; the current result does
not contain the supplied point or line.

Subtract the moment v from w cross p, obtaining w cross (p-anchor). The
constant term v dot p remains unchanged. Regression tests check the
plane equation directly, independently of the separate Plane3.contains
fix in #280, using translated and origin-passing lines and rescaled
directions.

Validation: six new cases fail and three pass on unchanged code. With
this fix the full tests directory reports 482 passed, 3 skipped, 63
subtests passed (Python 3.11, NumPy 2). No other pending geometry fixes
are included.

AI assistance was used to investigate, implement and test this change.

Author: xixihaha-ha

spatialmath/geom3d.py

@@ -95,7 +95,7 @@ def LinePoint(cls, l: Line3, p: ArrayLike3) -> Self:
 
         :seealso: :meth:`PointNormal`  :meth:`ThreePoints`
         """
-        n = np.cross(l.w, p)
+        n = np.cross(l.w, p) - l.v
         d = np.dot(l.v, p)
 
         return cls(np.r_[n, d])

tests/test_plane_line_point.py

@@ -0,0 +1,26 @@
+import numpy as np
+import pytest
+
+from spatialmath import Line3, Plane3
+
+
+@pytest.mark.parametrize(
+    "anchor,direction,point",
+    [
+        ([1, 2, 3], [1, 0, 0], [1, 4, 3]),
+        ([2, -1, 4], [1, 2, -1], [3, 2, 5]),
+        ([0, 0, 0], [0, 0, 1], [2, 3, 4]),
+    ],
+)
+@pytest.mark.parametrize("scale", [1, -2, 0.25])
+def test_line_point_plane_contains_translated_line(anchor, direction, point, scale):
+    anchor = np.asarray(anchor, dtype=float)
+    direction = np.asarray(direction, dtype=float) * scale
+    line = Line3.PointDir(anchor, direction)
+    plane = Plane3.LinePoint(line, np.asarray(point, dtype=float))
+
+    # Use the plane equation directly, independent of Plane3.contains.
+    for p in [point, anchor, anchor + direction, anchor - 3 * direction]:
+        np.testing.assert_allclose(plane.n @ p + plane.d, 0, atol=1e-12)
+    expected_normal = np.cross(direction, np.asarray(point) - anchor)
+    np.testing.assert_allclose(plane.n, expected_normal, atol=1e-12)