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Merged
merged 2 commits into from
Jun 11, 2021
Merged

Pathing issue #20395

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81a3cff
added check for collinearity
diegopetrola Jun 7, 2021
d811134
modified comments
diegopetrola Jun 11, 2021
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10 changes: 10 additions & 0 deletions lib/matplotlib/tests/test_path.py
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Original file line number Diff line number Diff line change
Expand Up @@ -410,6 +410,16 @@ def test_path_intersect_path(phi):
b = transform.transform_path(Path([(0, 1), (0, 2), (0, 5)]))
assert a.intersects_path(b) and b.intersects_path(a)

# a and b are collinear but do not intersect
a = transform.transform_path(Path([(1, -1), (0, -1)]))
b = transform.transform_path(Path([(0, 1), (0.9, 1)]))
assert not a.intersects_path(b) and not b.intersects_path(a)

# a and b are collinear but do not intersect
a = transform.transform_path(Path([(0., -5.), (1., -5.)]))
b = transform.transform_path(Path([(1., 5.), (0., 5.)]))
assert not a.intersects_path(b) and not b.intersects_path(a)


@pytest.mark.parametrize('offset', range(-720, 361, 45))
def test_full_arc(offset):
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33 changes: 21 additions & 12 deletions src/_path.h
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Original file line number Diff line number Diff line change
Expand Up @@ -833,21 +833,27 @@ inline bool segments_intersect(const double &x1,
// determinant
double den = ((y4 - y3) * (x2 - x1)) - ((x4 - x3) * (y2 - y1));

if (isclose(den, 0.0)) { // collinear segments
if (x1 == x2 && x2 == x3) { // segments have infinite slope (vertical lines)
// and lie on the same line
return (fmin(y1, y2) <= fmin(y3, y4) && fmin(y3, y4) <= fmax(y1, y2)) ||
(fmin(y3, y4) <= fmin(y1, y2) && fmin(y1, y2) <= fmax(y3, y4));
}
else {
double intercept = (y1*x2 - y2*x1)*(x4 - x3) - (y3*x4 - y4*x3)*(x1 - x2);
if (isclose(intercept, 0.0)) { // segments lie on the same line
// If den == 0 we have two possibilities:
if (isclose(den, 0.0)) {
float t_area = (x2*y3 - x3*y2) - x1*(y3 - y2) + y1*(x3 - x2);
// 1 - If the area of the triangle made by the 3 first points (2 from the first segment
// plus one from the second) is zero, they are collinear
if (isclose(t_area, 0.0)) {
if (x1 == x2 && x2 == x3) { // segments have infinite slope (vertical lines)
// and lie on the same line
return (fmin(y1, y2) <= fmin(y3, y4) && fmin(y3, y4) <= fmax(y1, y2)) ||
(fmin(y3, y4) <= fmin(y1, y2) && fmin(y1, y2) <= fmax(y3, y4));
}
else {
return (fmin(x1, x2) <= fmin(x3, x4) && fmin(x3, x4) <= fmax(x1, x2)) ||
(fmin(x3, x4) <= fmin(x1, x2) && fmin(x1, x2) <= fmax(x3, x4));
(fmin(x3, x4) <= fmin(x1, x2) && fmin(x1, x2) <= fmax(x3, x4));

}
}

return false;
// 2 - If t_area is not zero, the segments are parallel, but not collinear
else {
return false;
}
}

const double n1 = ((x4 - x3) * (y1 - y3)) - ((y4 - y3) * (x1 - x3));
Expand All @@ -865,6 +871,7 @@ inline bool segments_intersect(const double &x1,
template <class PathIterator1, class PathIterator2>
bool path_intersects_path(PathIterator1 &p1, PathIterator2 &p2)
{

typedef PathNanRemover<py::PathIterator> no_nans_t;
typedef agg::conv_curve<no_nans_t> curve_t;

Expand All @@ -889,12 +896,14 @@ bool path_intersects_path(PathIterator1 &p1, PathIterator2 &p2)
}
c2.rewind(0);
c2.vertex(&x21, &y21);


while (c2.vertex(&x22, &y22) != agg::path_cmd_stop) {
// if the segment in path 2 is (almost) 0 length, skip to next vertex
if ((isclose((x21 - x22) * (x21 - x22) + (y21 - y22) * (y21 - y22), 0))){
continue;
}

if (segments_intersect(x11, y11, x12, y12, x21, y21, x22, y22)) {
return true;
}
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