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Line-line intersection edge cases #3396

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Line-line intersection edge cases #3396

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1b49270
Test for lines having same start/end
simoncozens Dec 15, 2023
8695d19
Provide intersections for lines with same start/end
simoncozens Dec 15, 2023
8811dfc
Handle more degenerate cases
simoncozens Dec 15, 2023
de466e8
Better way to do it
simoncozens Dec 15, 2023
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10 changes: 10 additions & 0 deletions Lib/fontTools/misc/bezierTools.py
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Expand Up @@ -1184,6 +1184,11 @@
if math.isclose(s1x, e1x) and math.isclose(s1y, e1y): # Line segment is tiny
return []
if math.isclose(e1x, s1x):
if math.isclose(e2x, s2x): # Same start
if math.isclose(s1y, s2y):
return [Intersection(pt=(s1x, s1y), t1=0, t2=0)]
# Degenerate coincident case
return []
x = s1x
slope34 = (e2y - s2y) / (e2x - s2x)
y = slope34 * (x - s2x) + s2y
Expand All @@ -1194,6 +1199,11 @@
)
]
if math.isclose(s2x, e2x):
if math.isclose(s1x, e1x):
if math.isclose(e1y, e2y): # Same end
return [Intersection(pt=(e1x, e1y), t1=1, t2=1)]

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# Degenerate coincident case
return []

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x = s2x
slope12 = (e1y - s1y) / (e1x - s1x)
y = slope12 * (x - s1x) + s1y
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10 changes: 10 additions & 0 deletions Tests/misc/bezierTools_test.py
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Expand Up @@ -5,6 +5,7 @@
calcCubicBounds,
curveLineIntersections,
curveCurveIntersections,
lineLineIntersections,
segmentPointAtT,
splitLine,
splitQuadratic,
Expand Down Expand Up @@ -197,3 +198,12 @@ 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)
seg3 = [(250, 810), (250, 500)]
assert lineLineIntersections(*seg1, *seg3) == []
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Don't seg1 and seg3 intersect at (250, 810)?

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oh sorry I see now (was typing from mobile), the segments actually are coincident, sitting on top of one another. In theory they intersect in all the points where they overlap, but since we need to return some finite results it's ok to return [] in this edge case

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Exactly.

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wait I'm still confused... I think you swapped the two cases.

all the three segments above seg1, seg2 and seg3 are parallel to one another and the Y axis, have the same x coordinate 250; seg1 and and seg2 are the ones that overlap one another, they also share the starting point but coincide for the entire length of seg1 (which is a subset of seg2). So I'd expect we would return [] in this case. Whereas you are returning (250.0, 1000.0) which is their starting point.

On the other hand, seg1 and seg2, while being parallel (x coordinates are all 250), they only touch where seg1 ends and seg3 starts, i.e. (250, 810) -- so I would expect the latter to be returned as their intersection, not []