added function to test containment

Containment uses the sumOfTri to determine if a point is inside of the
rectangle, r1.  It checks all four points of r2 (p1, p2, p3, p4) against
r1.  If they are all inside, then the rectangle is contained.

rectangle.go

@@ -54,6 +54,40 @@ func (r Rectangle) Size() float64 {
 	return distance(r.P1, n1) * distance(r.P1, n2)
 }
 
-//
+func sumOfTri(r Rectangle, p Point) bool {
-//func Containment(r1, r2, Rectangle) bool {
+	rsize := r.Size()
-//}
+	n1, n2 := r.Neighbors(r.P1)
+	x1, x2 := Point{}, Point{}
+	accross := &Point{}
+	if r.P2 != n1 || r.P2 != n2 {
+		accross = &r.P2
+		x1, x2 = r.Neighbors(r.P2)
+	}
+	if r.P3 != n1 || r.P3 != n2 {
+		accross = &r.P3
+		x1, x2 = r.Neighbors(r.P3)
+	}
+	if r.P4 != n1 || r.P4 != n2 {
+		accross = &r.P4
+		x1, x2 = r.Neighbors(r.P4)
+	}
+	sumTri := SizeTriangle(r.P1, n1, p) +
+		SizeTriangle(r.P1, n2, p) +
+		SizeTriangle(*accross, x1, p) +
+		SizeTriangle(*accross, x2, p)
+	if rsize == sumTri {
+		return true
+	}
+	return false
+}
+
+// Containment returns whether r2 is contained inside of r1
+func Containment(r1, r2 Rectangle) bool {
+	if r1.Size() <= r2.Size() {
+		return false
+	}
+	if sumOfTri(r1, r2.P1) && sumOfTri(r1, r2.P2) && sumOfTri(r1, r2.P3) && sumOfTri(r1, r2.P4) {
+		return true
+	}
+	return false
+}

rectangle_test.go

@@ -52,3 +52,46 @@ func TestSize(t *testing.T) {
 
 	}
 }
+
+func TestContainment(t *testing.T) {
+	var containmentTest = []struct {
+		r        []Rectangle
+		expected bool
+	}{
+		{
+			[]Rectangle{
+				Rectangle{Point{0, 0}, Point{0, 3}, Point{3, 0}, Point{3, 3}},
+				Rectangle{Point{1, 1}, Point{1, 2}, Point{2, 1}, Point{2, 2}}},
+			true,
+		},
+		{
+			[]Rectangle{
+				Rectangle{Point{0, 0}, Point{0, 3}, Point{3, 0}, Point{3, 3}},
+				Rectangle{Point{1, 1}, Point{1, 2}, Point{2, 1}, Point{2, 2}}},
+			true,
+		},
+		{
+			[]Rectangle{
+				Rectangle{Point{0, 0}, Point{0, 3}, Point{3, 0}, Point{3, 3}},
+				Rectangle{Point{0, 0}, Point{0, 3}, Point{3, 0}, Point{3, 3}}},
+			false,
+		},
+		{
+			[]Rectangle{
+				Rectangle{Point{0, 0}, Point{0, 3}, Point{3, 0}, Point{3, 3}},
+				Rectangle{Point{3, 3}, Point{3, 4}, Point{4, 3}, Point{4, 4}}},
+			false,
+		},
+	}
+	for _, rt := range containmentTest {
+		actual := Containment(rt.r[0], rt.r[1])
+		if actual != rt.expected {
+			t.Errorf(
+				"failed spiral:\n\texpected: %d\n\t  actual: %d",
+				rt.expected,
+				actual,
+			)
+		}
+
+	}
+}