Fix findIntersection() for overlapping segments. (#2)

ctessum · May 10, 2019 · 81284b8 · 81284b8
1 parent fcff711
commit 81284b8
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Showing 3 changed files with 122 additions and 43 deletions.
diff --git a/bugs_test.go b/bugs_test.go
@@ -57,10 +57,31 @@ func dump(poly polyclip.Polygon) string {
 	return fmt.Sprintf("%v", normalize(poly))
 }
 
+type testCase struct {
+	op       polyclip.Op
+	subject  polyclip.Polygon
+	clipping polyclip.Polygon
+	result   polyclip.Polygon
+}
+
+type testCases []testCase
+
+func (cases testCases) verify(t *T) {
+	t.Helper()
+	for i, c := range cases {
+		result := dump(c.subject.Construct(c.op, c.clipping))
+		if result != dump(c.result) {
+			t.Errorf("case %d: %v\nsubject:  %v\nclipping: %v\nexpected: %v\ngot:      %v",
+				i, c.op, c.subject, c.clipping, c.result, result)
+		}
+	}
+}
+
 func TestBug3(t *T) {
-	cases := []struct{ subject, clipping, result polyclip.Polygon }{
+	testCases{
 		// original reported github issue #3
 		{
+			op:      polyclip.UNION,
 			subject: polyclip.Polygon{{{1, 1}, {1, 2}, {2, 2}, {2, 1}}},
 			clipping: polyclip.Polygon{
 				{{2, 1}, {2, 2}, {3, 2}, {3, 1}},
@@ -74,6 +95,7 @@ func TestBug3(t *T) {
 		},
 		// simplified variant of issue #3, for easier debugging
 		{
+			op:      polyclip.UNION,
 			subject: polyclip.Polygon{{{1, 2}, {2, 2}, {2, 1}}},
 			clipping: polyclip.Polygon{
 				{{2, 1}, {2, 2}, {3, 2}},
@@ -82,6 +104,7 @@ func TestBug3(t *T) {
 			result: polyclip.Polygon{{{1, 2}, {2, 3}, {3, 2}, {2, 1}}},
 		},
 		{
+			op:      polyclip.UNION,
 			subject: polyclip.Polygon{{{1, 2}, {2, 2}, {2, 1}}},
 			clipping: polyclip.Polygon{
 				{{1, 2}, {2, 3}, {2, 2}},
@@ -90,12 +113,14 @@ func TestBug3(t *T) {
 		},
 		// another variation, now with single degenerated curve
 		{
+			op:      polyclip.UNION,
 			subject: polyclip.Polygon{{{1, 2}, {2, 2}, {2, 1}}},
 			clipping: polyclip.Polygon{
 				{{1, 2}, {2, 3}, {2, 2}, {2, 3}, {3, 2}}},
 			result: polyclip.Polygon{{{1, 2}, {2, 3}, {3, 2}, {2, 2}, {2, 1}}},
 		},
 		{
+			op:      polyclip.UNION,
 			subject: polyclip.Polygon{{{1, 2}, {2, 2}, {2, 1}}},
 			clipping: polyclip.Polygon{
 				{{2, 1}, {2, 2}, {2, 3}, {3, 2}},
@@ -104,18 +129,52 @@ func TestBug3(t *T) {
 		},
 		// "union" with effectively empty polygon (wholly self-intersecting)
 		{
+			op:       polyclip.UNION,
 			subject:  polyclip.Polygon{{{1, 2}, {2, 2}, {2, 1}}},
 			clipping: polyclip.Polygon{{{1, 2}, {2, 2}, {2, 3}, {1, 2}, {2, 2}, {2, 3}}},
 			result:   polyclip.Polygon{{{1, 2}, {2, 2}, {2, 1}}},
 		},
-	}
-	for _, c := range cases {
-		result := dump(c.subject.Construct(polyclip.UNION, c.clipping))
-		if result != dump(c.result) {
-			t.Errorf("case UNION:\nsubject:  %v\nclipping: %v\nexpected: %v\ngot:      %v",
-				c.subject, c.clipping, c.result, result)
-		}
-	}
+	}.verify(t)
+}
+
+func TestSelfIntersectionAvoidance(t *T) {
+	testCases{
+		{
+			op: polyclip.DIFFERENCE,
+			subject: polyclip.Polygon{{
+				{38.5721239031346, 172.33955556881023},
+				{39.99999999999999, 171.3397459621556},
+				{41.57979856674331, 170.60307379214092},
+				{43.2635182233307, 170.15192246987792},
+				{45, 170},
+				{46.7364817766693, 170.15192246987792},
+				{48.42020143325668, 170.60307379214092},
+				{50, 171.3397459621556},
+				{51.42787609686539, 172.33955556881023},
+			}},
+			clipping: polyclip.Polygon{{
+				{51.42787609686539, 172.33955556881023},
+				{50, 171.3397459621556},
+				{48.42020143325668, 170.60307379214092},
+				{46.7364817766693, 170.15192246987792},
+				{45, 170},
+				{43.2635182233307, 170.15192246987792},
+				{42.78116786015871, 170.28116786015872},
+				{42.65192246987792, 170.7635182233307},
+				{42.5, 172},
+			}},
+			result: polyclip.Polygon{{
+				{51.42787609686539, 172.33955556881023},
+				{42.5, 172},
+				{42.65192246987792, 170.7635182233307},
+				{42.78116786015871, 170.28116786015872},
+				// Should not contain this point: {43.2635182233307, 170.15192246987792},
+				{41.57979856674331, 170.60307379214092},
+				{39.99999999999999, 171.3397459621556},
+				{38.5721239031346, 172.33955556881023},
+			}},
+		},
+	}.verify(t)
 }
 
 func TestNonReductiveSegmentDivisions(t *T) {
@@ -304,35 +363,25 @@ func TestBug5(t *T) {
 	rect := polyclip.Polygon{{{24, 7}, {36, 7}, {36, 23}, {24, 23}}}
 	circle := polyclip.Polygon{{{24, 7}, {24.83622770614123, 7.043824837053814}, {25.66329352654208, 7.174819194129555}, {26.472135954999587, 7.391547869638773}, {27.253893144606412, 7.691636338859195}, {28.00000000000001, 8.071796769724493}, {28.702282018339798, 8.527864045000424}, {29.35304485087088, 9.054841396180851}, {29.94515860381917, 9.646955149129141}, {30.472135954999597, 10.297717981660224}, {30.92820323027553, 11.00000000000001}, {31.308363661140827, 11.746106855393611}, {31.60845213036125, 12.527864045000435}, {31.825180805870467, 13.33670647345794}, {31.95617516294621, 14.16377229385879}, {32.00000000000002, 15.00000000000002}, {31.95617516294621, 15.83622770614125}, {31.825180805870467, 16.6632935265421}, {31.60845213036125, 17.472135954999604}, {31.308363661140827, 18.25389314460643}, {30.92820323027553, 19.00000000000003}, {30.472135954999597, 19.702282018339815}, {29.94515860381917, 20.353044850870898}, {29.35304485087088, 20.945158603819188}, {28.702282018339798, 21.472135954999615}, {28.00000000000001, 21.928203230275546}, {27.253893144606412, 22.308363661140845}, {26.472135954999587, 22.608452130361268}, {25.66329352654208, 22.825180805870485}, {24.83622770614123, 22.956175162946227}, {24, 23.00000000000004}, {23.16377229385877, 22.956175162946227}, {22.33670647345792, 22.825180805870485}, {21.527864045000413, 22.608452130361268}, {20.746106855393588, 22.308363661140845}, {19.99999999999999, 21.928203230275546}, {19.297717981660202, 21.472135954999615}, {18.64695514912912, 20.945158603819188}, {18.05484139618083, 20.353044850870898}, {17.527864045000403, 19.702282018339815}, {17.07179676972447, 19.00000000000003}, {16.691636338859173, 18.25389314460643}, {16.39154786963875, 17.472135954999604}, {16.174819194129533, 16.6632935265421}, {16.04382483705379, 15.83622770614125}, {15.999999999999977, 15.00000000000002}, {16.04382483705379, 14.16377229385879}, {16.174819194129533, 13.33670647345794}, {16.39154786963875, 12.527864045000435}, {16.691636338859173, 11.746106855393611}, {17.07179676972447, 11.00000000000001}, {17.527864045000403, 10.297717981660224}, {18.05484139618083, 9.646955149129141}, {18.64695514912912, 9.054841396180851}, {19.297717981660202, 8.527864045000424}, {19.99999999999999, 8.071796769724493}, {20.746106855393588, 7.691636338859194}, {21.527864045000413, 7.391547869638772}, {22.33670647345792, 7.1748191941295545}, {23.16377229385877, 7.043824837053813}}}
 
-	expected := []struct {
-		op     polyclip.Op
-		result polyclip.Polygon
-	}{
+	testCases{
 		{
-			polyclip.UNION,
+			polyclip.UNION, rect, circle,
 			polyclip.Polygon{{{36, 23}, {36, 7}, {24, 7}, {23.16377229385877, 7.043824837053813}, {22.33670647345792, 7.1748191941295545}, {21.527864045000413, 7.391547869638772}, {20.746106855393588, 7.691636338859194}, {19.99999999999999, 8.071796769724493}, {19.297717981660202, 8.527864045000424}, {18.64695514912912, 9.054841396180851}, {18.05484139618083, 9.646955149129141}, {17.527864045000403, 10.297717981660224}, {17.07179676972447, 11.00000000000001}, {16.691636338859173, 11.746106855393611}, {16.39154786963875, 12.527864045000435}, {16.174819194129533, 13.33670647345794}, {16.04382483705379, 14.16377229385879}, {15.999999999999977, 15.00000000000002}, {16.04382483705379, 15.83622770614125}, {16.174819194129533, 16.6632935265421}, {16.39154786963875, 17.472135954999604}, {16.691636338859173, 18.25389314460643}, {17.07179676972447, 19.00000000000003}, {17.527864045000403, 19.702282018339815}, {18.05484139618083, 20.353044850870898}, {18.64695514912912, 20.945158603819188}, {19.297717981660202, 21.472135954999615}, {19.99999999999999, 21.928203230275546}, {20.746106855393588, 22.308363661140845}, {21.527864045000413, 22.608452130361268}, {22.33670647345792, 22.825180805870485}, {23.16377229385877, 22.956175162946227}, {24, 23.00000000000004}, {24.000000000000746, 23}}},
 		},
 		{
-			polyclip.INTERSECTION,
+			polyclip.INTERSECTION, rect, circle,
 			polyclip.Polygon{{{31.95617516294621, 15.83622770614125}, {31.825180805870467, 16.6632935265421}, {31.60845213036125, 17.472135954999604}, {31.308363661140827, 18.25389314460643}, {30.92820323027553, 19.00000000000003}, {30.472135954999597, 19.702282018339815}, {29.94515860381917, 20.353044850870898}, {29.35304485087088, 20.945158603819188}, {28.702282018339798, 21.472135954999615}, {28.00000000000001, 21.928203230275546}, {27.253893144606412, 22.308363661140845}, {26.472135954999587, 22.608452130361268}, {25.66329352654208, 22.825180805870485}, {24.83622770614123, 22.956175162946227}, {24.000000000000746, 23}, {24, 23}, {24, 7}, {24.83622770614123, 7.043824837053814}, {25.66329352654208, 7.174819194129555}, {26.472135954999587, 7.391547869638773}, {27.253893144606412, 7.691636338859195}, {28.00000000000001, 8.071796769724493}, {28.702282018339798, 8.527864045000424}, {29.35304485087088, 9.054841396180851}, {29.94515860381917, 9.646955149129141}, {30.472135954999597, 10.297717981660224}, {30.92820323027553, 11.00000000000001}, {31.308363661140827, 11.746106855393611}, {31.60845213036125, 12.527864045000435}, {31.825180805870467, 13.33670647345794}, {31.95617516294621, 14.16377229385879}, {32.00000000000002, 15.00000000000002}}},
 		},
 		{
-			polyclip.DIFFERENCE,
+			polyclip.DIFFERENCE, rect, circle,
 			polyclip.Polygon{{{24.000000000000746, 23}, {24.83622770614123, 22.956175162946227}, {25.66329352654208, 22.825180805870485}, {26.472135954999587, 22.608452130361268}, {27.253893144606412, 22.308363661140845}, {28.00000000000001, 21.928203230275546}, {28.702282018339798, 21.472135954999615}, {29.35304485087088, 20.945158603819188}, {29.94515860381917, 20.353044850870898}, {30.472135954999597, 19.702282018339815}, {30.92820323027553, 19.00000000000003}, {31.308363661140827, 18.25389314460643}, {31.60845213036125, 17.472135954999604}, {31.825180805870467, 16.6632935265421}, {31.95617516294621, 15.83622770614125}, {32.00000000000002, 15.00000000000002}, {31.95617516294621, 14.16377229385879}, {31.825180805870467, 13.33670647345794}, {31.60845213036125, 12.527864045000435}, {31.308363661140827, 11.746106855393611}, {30.92820323027553, 11.00000000000001}, {30.472135954999597, 10.297717981660224}, {29.94515860381917, 9.646955149129141}, {29.35304485087088, 9.054841396180851}, {28.702282018339798, 8.527864045000424}, {28.00000000000001, 8.071796769724493}, {27.253893144606412, 7.691636338859195}, {26.472135954999587, 7.391547869638773}, {25.66329352654208, 7.174819194129555}, {24.83622770614123, 7.043824837053814}, {24, 7}, {36, 7}, {36, 23}}},
 		},
 		{
-			polyclip.XOR,
+			polyclip.XOR, rect, circle,
 			polyclip.Polygon{
 				{{24.000000000000746, 23}, {24, 23}, {24, 7}, {23.16377229385877, 7.043824837053813}, {22.33670647345792, 7.1748191941295545}, {21.527864045000413, 7.391547869638772}, {20.746106855393588, 7.691636338859194}, {19.99999999999999, 8.071796769724493}, {19.297717981660202, 8.527864045000424}, {18.64695514912912, 9.054841396180851}, {18.05484139618083, 9.646955149129141}, {17.527864045000403, 10.297717981660224}, {17.07179676972447, 11.00000000000001}, {16.691636338859173, 11.746106855393611}, {16.39154786963875, 12.527864045000435}, {16.174819194129533, 13.33670647345794}, {16.04382483705379, 14.16377229385879}, {15.999999999999977, 15.00000000000002}, {16.04382483705379, 15.83622770614125}, {16.174819194129533, 16.6632935265421}, {16.39154786963875, 17.472135954999604}, {16.691636338859173, 18.25389314460643}, {17.07179676972447, 19.00000000000003}, {17.527864045000403, 19.702282018339815}, {18.05484139618083, 20.353044850870898}, {18.64695514912912, 20.945158603819188}, {19.297717981660202, 21.472135954999615}, {19.99999999999999, 21.928203230275546}, {20.746106855393588, 22.308363661140845}, {21.527864045000413, 22.608452130361268}, {22.33670647345792, 22.825180805870485}, {23.16377229385877, 22.956175162946227}, {24, 23.00000000000004}},
 				{{24.000000000000746, 23}, {24.83622770614123, 22.956175162946227}, {25.66329352654208, 22.825180805870485}, {26.472135954999587, 22.608452130361268}, {27.253893144606412, 22.308363661140845}, {28.00000000000001, 21.928203230275546}, {28.702282018339798, 21.472135954999615}, {29.35304485087088, 20.945158603819188}, {29.94515860381917, 20.353044850870898}, {30.472135954999597, 19.702282018339815}, {30.92820323027553, 19.00000000000003}, {31.308363661140827, 18.25389314460643}, {31.60845213036125, 17.472135954999604}, {31.825180805870467, 16.6632935265421}, {31.95617516294621, 15.83622770614125}, {32.00000000000002, 15.00000000000002}, {31.95617516294621, 14.16377229385879}, {31.825180805870467, 13.33670647345794}, {31.60845213036125, 12.527864045000435}, {31.308363661140827, 11.746106855393611}, {30.92820323027553, 11.00000000000001}, {30.472135954999597, 10.297717981660224}, {29.94515860381917, 9.646955149129141}, {29.35304485087088, 9.054841396180851}, {28.702282018339798, 8.527864045000424}, {28.00000000000001, 8.071796769724493}, {27.253893144606412, 7.691636338859195}, {26.472135954999587, 7.391547869638773}, {25.66329352654208, 7.174819194129555}, {24.83622770614123, 7.043824837053814}, {24, 7}, {36, 7}, {36, 23}},
 			},
 		},
-	}
-
-	for _, e := range expected {
-		result := rect.Construct(e.op, circle)
-		if dump(result) != dump(e.result) {
-			t.Errorf("case %d expected:\n%v\ngot:\n%v", e.op, dump(e.result), dump(result))
-		}
-	}
+	}.verify(t)
 }
diff --git a/clipper.go b/clipper.go
@@ -278,7 +278,7 @@ func (c *clipper) compute(operation Op) Polygon {
 	return connector.toPolygon()
 }
 
-func findIntersection(seg0, seg1 segment) (int, Point, Point) {
+func findIntersection(seg0, seg1 segment, tryBothDirections bool) (int, Point, Point) {
 	var pi0, pi1 Point
 	p0 := seg0.start
 	d0 := Point{seg0.end.X - p0.X, seg0.end.Y - p0.Y}
@@ -332,13 +332,18 @@ func findIntersection(seg0, seg1 segment) (int, Point, Point) {
 	if imax > 0 {
 		pi0.X = p0.X + w[0]*d0.X
 		pi0.Y = p0.Y + w[0]*d0.Y
-
-		// [MC: commented fragment removed]
-
-		if imax > 1 {
-			pi1.X = p0.X + w[1]*d0.X
-			pi1.Y = p0.Y + w[1]*d0.Y
+	}
+	// For same-segment scenarios, this should be the case.
+	if imax > 1 {
+		pi1.X = p0.X + w[1]*d0.X
+		pi1.Y = p0.Y + w[1]*d0.Y
+
+	} else if tryBothDirections {
+		// However, findIntersection() is not symmetric and sometimes fails in one direction. Try the other.
+		if otherImax, otherPi0, otherPi1 := findIntersection(seg1, seg0, false); otherImax > imax {
+			return otherImax, otherPi0, otherPi1
 		}
+		_DBG(func() { fmt.Printf("WARNING: Could not find overlap in segments %v, %v\n", seg0, seg1) })
 	}
 
 	return imax, pi0, pi1
@@ -378,7 +383,7 @@ func findIntersection2(u0, u1, v0, v1 float64, w *[]float64) int {
 func (c *clipper) possibleIntersection(e1, e2 *endpoint) {
 	// [MC]: commented fragment removed
 
-	numIntersections, ip1, _ := findIntersection(e1.segment(), e2.segment())
+	numIntersections, ip1, _ := findIntersection(e1.segment(), e2.segment(), true)
 
 	if numIntersections == 0 {
 		return

diff --git a/intersection_test.go b/intersection_test.go
@@ -6,59 +6,84 @@ func TestFindIntersection(t *testing.T) {
 	cases := []struct {
 		s1, s2           segment
 		numIntersections int
-		ip1, ip2         Point
+		ip1              Point
 	}{
 		{
 			// Almost (but not) parallel lines
 			segment{Point{0, 0}, Point{100, 0.0001}},
 			segment{Point{1, 0}, Point{100, 0}},
-			0, Point{}, Point{},
+			0, Point{},
 		},
 		{
 			// Almost (but not) parallel lines
 			segment{Point{0, 0}, Point{100, 0.0000001}},
 			segment{Point{1, 0}, Point{100, 0}},
-			0, Point{}, Point{},
+			0, Point{},
 		},
 		{
 			// Cross
 			segment{Point{1, 0}, Point{1, 3}},
 			segment{Point{0, 1}, Point{3, 1}},
-			1, Point{1, 1}, Point{},
+			1, Point{1, 1},
 		},
 		{
 			// Rays
 			segment{Point{0, 1}, Point{1, 3}},
 			segment{Point{0, 1}, Point{3, 1}},
-			1, Point{0, 1}, Point{},
+			1, Point{0, 1},
 		},
 		{
 			// Colinear rays
 			segment{Point{2, 1}, Point{0, 1}},
 			segment{Point{2, 1}, Point{1, 1}},
-			2, Point{2, 1}, Point{}, // Why isn't this 2 intersections at {1,1} {2,1}?
+			2, Point{2, 1},
 		},
 		{
 			// Colinear rays
 			segment{Point{0, 3}, Point{0, 1}},
 			segment{Point{0, 3}, Point{0, 2}},
-			2, Point{0, 3}, Point{}, // Why isn't this 2 intersections at {0,2}, {0,3}?
+			2, Point{0, 3},
 		},
 		{
 			// Overlapping segments
 			segment{Point{0, 1}, Point{3, 1}},
 			segment{Point{1, 1}, Point{2, 1}},
-			1, Point{3, 1}, Point{}, // Why isn't this 2 intersections at {1,1} {2,1}?
+			2, Point{1, 1},
 		},
 		{
 			// Overlapping segments
 			segment{Point{0, 1}, Point{0, 4}},
 			segment{Point{0, 2}, Point{0, 3}},
-			1, Point{0, 4}, Point{}, // Why isn't this 2 intersections at {0,2}, {0,3}?
+			2, Point{0, 2},
+		},
+		{ // Overlapping segments
+			segment{Point{43.2635182233307, 170.15192246987792}, Point{41.57979856674331, 170.60307379214092}},
+			segment{Point{43.2635182233307, 170.15192246987792}, Point{42.78116786015871, 170.28116786015872}},
+			2, Point{43.2635182233307, 170.15192246987792},
+		},
+		{ // Overlapping segments
+			segment{Point{41.57979856674331, 170.60307379214092}, Point{43.2635182233307, 170.15192246987792}},
+			segment{Point{42.78116786015871, 170.28116786015872}, Point{43.2635182233307, 170.15192246987792}},
+			2, Point{42.78116786015871, 170.28116786015872},
+		},
+		{ // Overlapping segments
+			segment{Point{43.2635182233307, 170.15192246987792}, Point{41.57979856674331, 170.60307379214092}},
+			segment{Point{42.78116786015871, 170.28116786015872}, Point{43.2635182233307, 170.15192246987792}},
+			2, Point{43.2635182233307, 170.15192246987792},
+		},
+		{ // Overlapping segments
+			segment{Point{41.57979856674331, 170.60307379214092}, Point{43.2635182233307, 170.15192246987792}},
+			segment{Point{43.2635182233307, 170.15192246987792}, Point{42.78116786015871, 170.28116786015872}},
+			2, Point{43.2635182233307, 170.15192246987792},
+		},
+		{ // Identical segments
+			segment{Point{66, 160}, Point{67.1242262770966, 147.15003485264717}},
+			segment{Point{66, 160}, Point{67.1242262770966, 147.15003485264717}},
+			2, Point{66, 160},
 		},
 	}
 	for i, v := range cases {
-		num, ip1, _ := findIntersection(v.s1, v.s2)
+		num, ip1, _ := findIntersection(v.s1, v.s2, true)
 		verify(t, num == v.numIntersections, "Case %d: Expected numIntersections to be %d, but got %d", i, v.numIntersections, num)
 		verify(t, ip1.Equals(v.ip1), "Case %d: Expected ip1 to be %v, but got %v", i, v.ip1, ip1)
 	}