geom/segment: add segment-segment intersection test

cruft/util/geom/segment.cpp

@@ -69,6 +69,72 @@ cruft::geom::intersects (cruft::geom::segment2i seg, cruft::region2i rect)
 }
 
 
+///////////////////////////////////////////////////////////////////////////////
+template <>
+bool
+cruft::geom::intersects (cruft::geom::segment2f ab, cruft::point2f p)
+{
+    auto const hi = max (ab.a, ab.b);
+    auto const lo = min (ab.a, ab.b);
+
+    return all (p <= hi) and all (p >= lo);
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
+// segment-segment intersection in 2D is derived from
+//    https://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect
+//
+// The idea is to check the winding of 4 triangles created by the segment.
+//
+// Co-linear segments need some additional tests to determine if points of one segment lie on the other.
+
+
+/// \return 0 if colinear, 1 for clockwise, -1 for counter-clockwise
+static int
+winding (
+    cruft::point2f const p,
+    cruft::point2f const q,
+    cruft::point2f const r
+) {
+    auto const qp = q - p;
+    auto const rq = r - q;
+
+    auto const c = cross (qp, rq);
+
+    if (cruft::exactly_zero (c))
+        return 0;
+    else if (c > 0)
+        return 1;
+    else
+        return -1;
+}
+
+
+//-----------------------------------------------------------------------------
+template <>
+bool
+cruft::geom::intersects (
+    cruft::geom::segment2f const s0,
+    cruft::geom::segment2f const s1
+) {
+    auto const w0 = winding (s0.a, s0.b, s1.a);
+    auto const w1 = winding (s0.a, s0.b, s1.b);
+    auto const w2 = winding (s1.a, s1.b, s0.a);
+    auto const w3 = winding (s1.a, s1.b, s0.b);
+
+    if (w0 != w1 and w2 != w3)
+        return true;
+
+    if (w0 == 0 and intersects (s0, s1.a)) return true;
+    if (w1 == 0 and intersects (s0, s1.b)) return true;
+    if (w2 == 0 and intersects (s1, s0.a)) return true;
+    if (w3 == 0 and intersects (s1, s0.b)) return true;
+
+    return false;
+}
+
+
 ///////////////////////////////////////////////////////////////////////////////
 template <>
 cruft::geom::aabb3f

test/geom/segment.cpp

@@ -6,7 +6,8 @@
 
 
 ///////////////////////////////////////////////////////////////////////////////
-void test_point_distance (cruft::TAP::logger &tap)
+void
+test_point_distance (cruft::TAP::logger &tap)
 {
     static struct {
         cruft::point3f a, b;
@@ -27,8 +28,9 @@ void test_point_distance (cruft::TAP::logger &tap)
 }
 
 
-//-----------------------------------------------------------------------------
+///////////////////////////////////////////////////////////////////////////////
-void test_region_intersection (cruft::TAP::logger &tap)
+void
+test_region_intersection (cruft::TAP::logger &tap)
 {
     using p = cruft::point2i;
 
@@ -70,7 +72,58 @@ void test_region_intersection (cruft::TAP::logger &tap)
 
 
 ///////////////////////////////////////////////////////////////////////////////
-void test_bresenham (cruft::TAP::logger &tap)
+void
+test_segment_intersection (cruft::TAP::logger &tap)
+{
+    using cruft::geom::segment2f;
+    using cruft::point2f;
+
+    static struct {
+        segment2f a;
+        segment2f b;
+        bool expected;
+        char const *message;
+    } TESTS[] = {
+        {
+            .a = { { 1, 1 }, { 10, 1 } },
+            .b = { { 1, 2 }, { 10, 2 } },
+            .expected = false,
+            .message = "parallel"
+        },
+        {
+            .a = { { 10, 0 }, {  0, 10 } },
+            .b = { {  0, 0 }, { 10, 10 } },
+            .expected = true,
+            .message = "right angles"
+        },
+        {
+            .a = { { -5, -5 }, {  0,  0 } },
+            .b = { {  1,  1 }, { 10, 10 } },
+            .expected = false,
+            .message = "co-linear stopping early",
+        },
+        {
+            .a = { { -5, -5 }, {  5,  5 } },
+            .b = { {  0,  0 }, { 10, 10 } },
+            .expected = true,
+            .message = "co-linear stopping midway",
+        },
+    };
+
+    for (auto const &t: TESTS) {
+        tap.expect_eq (
+            t.expected,
+            intersects (t.a, t.b),
+            "segment-segment {}",
+            t.message
+        );
+    }
+}
+
+
+///////////////////////////////////////////////////////////////////////////////
+void
+test_bresenham (cruft::TAP::logger &tap)
 {
     static struct {
         cruft::point2i a;
@@ -120,6 +173,7 @@ main (int, char**)
     cruft::TAP::logger tap;
     test_point_distance (tap);
     test_region_intersection (tap);
+    test_segment_intersection (tap);
     test_bresenham (tap);
     return tap.status ();
 }