fix: segments intersection bug.

Unit test also added.

include/igl/segment_segment_intersect.cpp

@@ -53,7 +53,7 @@ IGL_INLINE bool igl::segments_intersect(
     t = t1.norm() / rxs.norm();
     t = t * sign;
 
-    if (t < -eps || fabs(t) < eps)
+	if ((t - 1.) > eps || t < -eps)
         return false;
 
     a_t = t;

tests/include/igl/segment_segment_intersect.cpp

@@ -0,0 +1,39 @@
+#include <test_common.h>
+#include <igl/segment_segment_intersect.h>
+
+TEST_CASE("segment_segment_intersect: examples", "[igl]")
+{
+	// example 1
+	// https://github.com/libigl/libigl/issues/965
+
+	auto s1 = Eigen::RowVector3d(581, 388, -54);
+	auto dir1 = Eigen::RowVector3d(0.75, -4.36, 0.64);
+
+	auto s2 = Eigen::RowVector3d(636, 77, -10);
+	auto dir2 = Eigen::RowVector3d(-2.79, 0.96, 0.39);
+
+	double a1, a2;
+	bool sect1 = igl::segments_intersect(s1, dir1, s2, dir2, a1, a2);
+
+	bool intersectCondition1 = (a1 >= 0 && a1 <= 1 && a2 >= 0 && a2 <= 1);
+
+	REQUIRE(sect1 == false);
+	REQUIRE(intersectCondition1 == false);
+
+	// example 2
+	// https://github.com/libigl/libigl/issues/957
+
+	auto s3 = Eigen::RowVector3d(-56.6, 0, -201.7);
+	auto dir3 = Eigen::RowVector3d(0, 0, 1);
+
+	auto s4 = Eigen::RowVector3d(-65.6, 0, 258.8);
+	auto dir4 = Eigen::RowVector3d(15.4, 0, 1.9);
+
+	double a3, a4;
+	bool sect2 = igl::segments_intersect(s3, dir3, s4, dir4, a3, a4);
+
+	bool intersectCondition2 = (a3 >= 0 && a3 <= 1 && a4 >= 0 && a4 <= 1);
+
+	REQUIRE(sect2 == false);
+	REQUIRE(intersectCondition2 == false);
+}