diff --git a/masque/shapes/path.py b/masque/shapes/path.py
index a7b0ac6..ff1c6e9 100644
--- a/masque/shapes/path.py
+++ b/masque/shapes/path.py
@@ -344,11 +344,11 @@ class Path(Shape):
         bs = v[1:-1] - v[:-2] + perp[1:] - perp[:-1]
         ds = v[1:-1] - v[:-2] - perp[1:] + perp[:-1]
 
-        rp = numpy.linalg.solve(As, bs[:, :, None])[:, 0]
-        rn = numpy.linalg.solve(As, ds[:, :, None])[:, 0]
+        rp = numpy.linalg.lstsq(As, bs[:, :, None], rcond=1e-12)[0][:, 0, 0]
+        rn = numpy.linalg.lstsq(As, ds[:, :, None], rcond=1e-12)[0][:, 0, 0]
 
-        intersection_p = v[:-2] + rp * dv[:-1] + perp[:-1]
-        intersection_n = v[:-2] + rn * dv[:-1] - perp[:-1]
+        intersection_p = v[:-2] + rp[:, None] * dv[:-1] + perp[:-1]
+        intersection_n = v[:-2] + rn[:, None] * dv[:-1] - perp[:-1]
 
         towards_perp = (dv[1:] * perp[:-1]).sum(axis=1) > 0  # path bends towards previous perp?
 #       straight = (dv[1:] * perp[:-1]).sum(axis=1) == 0     # path is straight