spatial/r3: implement Vec.Cross

spatial/r3/vector.go

@@ -38,6 +38,15 @@ func (p Vec) Dot(q Vec) float64 {
 	return p.X*q.X + p.Y*q.Y + p.Z*q.Z
 }
 
+// Cross returns the cross product p×q.
+func (p Vec) Cross(q Vec) Vec {
+	return Vec{
+		p.Y*q.Z - p.Z*q.Y,
+		p.Z*q.X - p.X*q.Z,
+		p.X*q.Y - p.Y*q.X,
+	}
+}
+
 // Box is a 3D bounding box.
 type Box struct {
 	Min, Max Vec

spatial/r3/vector_test.go

@@ -112,3 +112,26 @@ func TestDot(t *testing.T) {
 		})
 	}
 }
+
+func TestCross(t *testing.T) {
+	for _, test := range []struct {
+		v1, v2, want Vec
+	}{
+		{Vec{1, 0, 0}, Vec{1, 0, 0}, Vec{0, 0, 0}},
+		{Vec{1, 0, 0}, Vec{0, 1, 0}, Vec{0, 0, 1}},
+		{Vec{0, 1, 0}, Vec{1, 0, 0}, Vec{0, 0, -1}},
+		{Vec{1, 2, 3}, Vec{-4, 5, -6}, Vec{-27, -6, 13}},
+		{Vec{1, 2, 3}, Vec{1, 2, 3}, Vec{}},
+		{Vec{1, 2, 3}, Vec{2, 3, 4}, Vec{-1, 2, -1}},
+	} {
+		t.Run("", func(t *testing.T) {
+			got := test.v1.Cross(test.v2)
+			if got != test.want {
+				t.Fatalf(
+					"error: %v × %v = %v, want %v",
+					test.v1, test.v2, got, test.want,
+				)
+			}
+		})
+	}
+}