Line-line intersection edge cases

Lib/fontTools/misc/bezierTools.py

@@ -1171,6 +1171,10 @@
     e1x, e1y = e1
     s2x, s2y = s2
     e2x, e2y = e2
+
+    def closepoints(pt1, pt2):
+        return math.isclose(pt1[0], pt2[0]) and math.isclose(pt1[1], pt2[1])
+
     if (
         math.isclose(s2x, e2x) and math.isclose(s1x, e1x) and not math.isclose(s1x, s2x)
     ):  # Parallel vertical
@@ -1179,11 +1183,20 @@
         math.isclose(s2y, e2y) and math.isclose(s1y, e1y) and not math.isclose(s1y, s2y)
     ):  # Parallel horizontal
         return []
-    if math.isclose(s2x, e2x) and math.isclose(s2y, e2y):  # Line segment is tiny
-        return []
-    if math.isclose(s1x, e1x) and math.isclose(s1y, e1y):  # Line segment is tiny
+    if closepoints(s2, e2) or closepoints(s1, e1):  # Line segment is tiny
         return []
+    if closepoints(s1, s2):  # Coincident at starts
+        return [Intersection(pt=s1, t1=0, t2=0)]
+    if closepoints(e1, e2):  # Coincident at ends
+        return [Intersection(pt=e1, t1=1, t2=1)]
+    if closepoints(s1, e2):
+        return [Intersection(pt=s1, t1=0, t2=1)]
+    if closepoints(s2, e1):
+        return [Intersection(pt=s2, t1=1, t2=0)]
+
     if math.isclose(e1x, s1x):
+        if math.isclose(e2x, s2x):
+            return []
         x = s1x
         slope34 = (e2y - s2y) / (e2x - s2x)
         y = slope34 * (x - s2x) + s2y
@@ -1194,6 +1207,8 @@
             )
         ]
     if math.isclose(s2x, e2x):
+        if math.isclose(s1x, e1x):
+            return []
         x = s2x
         slope12 = (e1y - s1y) / (e1x - s1x)
         y = slope12 * (x - s1x) + s1y

Tests/misc/bezierTools_test.py

@@ -5,6 +5,7 @@
     calcCubicBounds,
     curveLineIntersections,
     curveCurveIntersections,
+    lineLineIntersections,
     segmentPointAtT,
     splitLine,
     splitQuadratic,
@@ -197,3 +198,16 @@ def test_intersections_linelike():
     seg2 = [(0.0, 0.5), (0.25, 0.5), (0.75, 0.5), (1.0, 0.5)]
     pt = curveCurveIntersections(seg1, seg2)[0][0]
     assert pt == (0.0, 0.5)
+
+
+def test_intersections_samestart():
+    seg1 = [(250, 1000), (250, 810)]
+    seg2 = [(250, 1000), (250, 400)]
+    pt = lineLineIntersections(*seg1, *seg2)[0][0]
+    assert pt == (250.0, 1000.0)
+    # E1 == S2
+    seg3 = [(250, 810), (250, 500)]
+    pt = lineLineIntersections(*seg1, *seg3)[0][0]
+    assert pt == (250.0, 810.0)
+    # Entirely contained, give up
+    assert lineLineIntersections(*seg2, *seg3) == []