mockingbirdnest · Dec 11, 2019 · Dec 11, 2019 · Dec 11, 2019 · Dec 11, 2019 · Dec 11, 2019
diff --git a/astronomy/frames.hpp b/astronomy/frames.hpp
@@ -13,7 +13,9 @@ namespace astronomy {
 namespace internal_frames {
 
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
+using geometry::NonInertial;
 using geometry::Position;
 using quantities::si::ArcMinute;
 using quantities::si::ArcSecond;
@@ -46,7 +48,7 @@ using quantities::si::Degree;
 //   identified with TCB), we call this ICRS.
 using ICRS = Frame<serialization::Frame::SolarSystemTag,
                    serialization::Frame::ICRS,
-                   /*frame_is_inertial=*/true>;
+                   Inertial>;
 
 // The Geocentric Celestial Reference System.
 // The origin is the centre of mass of the whole Earth system, including oceans
@@ -65,7 +67,7 @@ using ICRS = Frame<serialization::Frame::SolarSystemTag,
 //   Principia's |Instant| is TT.
 using GCRS = Frame<serialization::Frame::SolarSystemTag,
                    serialization::Frame::GCRS,
-                   /*frame_is_inertial=*/false>;
+                   NonInertial>;
 
 // The International Terrestrial Reference System.
 // The origin is the centre of mass of the whole Earth system, including oceans
@@ -98,7 +100,7 @@ using GCRS = Frame<serialization::Frame::SolarSystemTag,
 //   http://etrs89.ensg.ign.fr/pub/EUREF-TN-1.pdf
 using ITRS = Frame<serialization::Frame::SolarSystemTag,
                    serialization::Frame::ITRS,
-                   /*frame_is_inertial=*/false>;
+                   NonInertial>;
 
 // The following two reference systems are both geocentric, and they share the
 // same z axis, the Celestial Intermediate Pole.  Their common xy plane is the
@@ -141,9 +143,9 @@ using CelestialIntermediateReferenceSystem = GCRS;
 // The xy plane is the plane of the sky.  The origin is at the barycentre of the
 // extrasolar system.  The z axis goes from the extrasolar system to the Earth.
 // The xz plane is (approximately) the plane of the extrasolar system.
-using Sky =
-    Frame<serialization::Frame::SolarSystemTag,
-          serialization::Frame::SKY, true>;
+using Sky = Frame<serialization::Frame::SolarSystemTag,
+                  serialization::Frame::SKY,
+                  Inertial>;
 
 }  // namespace internal_frames
 

diff --git a/astronomy/ksp_fingerprint_test.cpp b/astronomy/ksp_fingerprint_test.cpp
@@ -19,14 +19,15 @@ namespace astronomy {
 using base::Fingerprint2011;
 using base::SerializeAsBytes;
 using geometry::Frame;
+using geometry::Inertial;
 using physics::SolarSystem;
 using ::testing::Eq;
 
 class KSPFingerprintTest : public ::testing::Test {
  protected:
   using Barycentric = Frame<serialization::Frame::PluginTag,
                             serialization::Frame::BARYCENTRIC,
-                            true>;
+                            Inertial>;
 
   KSPFingerprintTest()
       : solar_system_(

diff --git a/astronomy/ksp_resonance_test.cpp b/astronomy/ksp_resonance_test.cpp
@@ -30,6 +30,7 @@ using base::OFStream;
 using geometry::AngularVelocity;
 using geometry::BarycentreCalculator;
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
 using geometry::OrthogonalMap;
 using geometry::Position;
@@ -73,7 +74,7 @@ class KSPResonanceTest : public ::testing::Test {
  protected:
   using KSP = Frame<serialization::Frame::TestTag,
                     serialization::Frame::TEST,
-                    /*frame_is_inertial=*/true>;
+                    Inertial>;
 
   using Periods = std::map<not_null<MassiveBody const*>, Time>;
 

diff --git a/astronomy/ksp_system_test.cpp b/astronomy/ksp_system_test.cpp
@@ -28,6 +28,7 @@ using base::not_null;
 using base::OFStream;
 using geometry::BarycentreCalculator;
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
 using geometry::Position;
 using geometry::Sign;
@@ -66,7 +67,7 @@ namespace astronomy {
 
 using KSP = Frame<serialization::Frame::TestTag,
                   serialization::Frame::TEST,
-                  /*frame_is_inertial=*/true>;
+                  Inertial>;
 
 class KSPSystem {
  protected:

diff --git a/astronomy/lunar_orbit_test.cpp b/astronomy/lunar_orbit_test.cpp
@@ -45,7 +45,9 @@ using base::OFStream;
 using geometry::AngularVelocity;
 using geometry::Displacement;
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
+using geometry::NonInertial;
 using geometry::OrthogonalMap;
 using geometry::Position;
 using geometry::Vector;
@@ -178,7 +180,7 @@ class LunarOrbitTest : public ::testing::TestWithParam<GeopotentialTruncation> {
   // Earth, see figure 1. of Russell and Lara (2006).
   using LunarSurface = Frame<LunarTag,
                              LunarTag::surface,
-                             /*frame_is_inertial=*/false>;
+                             NonInertial>;
 
   // This reference frame is non-rotating, with its origin at the selenocentre.
   // The axes are those of LunarSurface at J2000.
@@ -187,7 +189,7 @@ class LunarOrbitTest : public ::testing::TestWithParam<GeopotentialTruncation> {
   // |KeplerOrbit| should check that; this is good enough for a test.
   using Selenocentric = Frame<LunarTag,
                               LunarTag::selenocentric,
-                              /*frame_is_inertial=*/true>;
+                              Inertial>;
 
   // We do not use a |BodyCentredNonRotatingDynamicFrame| since that would use
   // ICRS axes.

diff --git a/astronomy/solar_system_dynamics_test.cpp b/astronomy/solar_system_dynamics_test.cpp
@@ -41,6 +41,7 @@ using geometry::Commutator;
 using geometry::DefinesFrame;
 using geometry::Displacement;
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
 using geometry::Position;
 using geometry::Rotation;
@@ -171,8 +172,8 @@ class SolarSystemDynamicsTest : public ::testing::Test {
     // of the Sun's axis.
     // TODO(egg): perhaps rotating bodies should export a rotation to their
     // celestial reference frame, we'll use that in the plugin too.
-    enum LocalFrameTag { tag };
-    using ParentEquator = Frame<LocalFrameTag, tag, /*frame_is_inertial=*/true>;
+    using ParentEquator =
+        Frame<enum class LocalFrameTag, LocalFrameTag{}, Inertial>;
     auto const z = Bivector<double, ICRS>({0, 0, 1});
     std::optional<Rotation<ICRS, ParentEquator>> rotation;
 

diff --git a/benchmarks/dynamic_frame.cpp b/benchmarks/dynamic_frame.cpp
@@ -65,7 +65,7 @@ const Length tolerance = 0.01 * Metre;
 }  // namespace
 
 using Rendering = Frame<serialization::Frame::TestTag,
-                        serialization::Frame::TEST, false>;
+                        serialization::Frame::TEST>;
 
 template<typename F, template<typename> class T>
 void FillLinearTrajectory(Position<F> const& initial,

diff --git a/benchmarks/embedded_explicit_runge_kutta_nyström_integrator.cpp b/benchmarks/embedded_explicit_runge_kutta_nyström_integrator.cpp
@@ -27,6 +27,7 @@ namespace principia {
 
 using geometry::Displacement;
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
 using geometry::Position;
 using geometry::Vector;
@@ -58,7 +59,7 @@ namespace integrators {
 namespace {
 
 using World = Frame<serialization::Frame::TestTag,
-                    serialization::Frame::TEST, true>;
+                    serialization::Frame::TEST, Inertial>;
 
 template<typename ODE>
 double HarmonicOscillatorToleranceRatio1D(

diff --git a/benchmarks/perspective.cpp b/benchmarks/perspective.cpp
@@ -26,9 +26,9 @@ using quantities::si::Radian;
 
 namespace {
 using World = Frame<serialization::Frame::TestTag,
-                    serialization::Frame::TEST1, false>;
+                    serialization::Frame::TEST1>;
 using Camera = Frame<serialization::Frame::TestTag,
-                     serialization::Frame::TEST2, false>;
+                     serialization::Frame::TEST2>;
 }  // namespace
 
 void RandomSegmentsBenchmark(

diff --git a/benchmarks/symplectic_runge_kutta_nyström_integrator.cpp b/benchmarks/symplectic_runge_kutta_nyström_integrator.cpp
@@ -29,6 +29,7 @@ namespace principia {
 using base::Status;
 using geometry::Displacement;
 using geometry::Frame;
+using geometry::Inertial;
 using geometry::Instant;
 using geometry::Position;
 using geometry::Vector;
@@ -58,7 +59,7 @@ namespace integrators {
 namespace {
 
 using World = Frame<serialization::Frame::TestTag,
-                    serialization::Frame::TEST, true>;
+                    serialization::Frame::TEST, Inertial>;
 
 }  // namespace
 

diff --git a/geometry/affine_map_test.cpp b/geometry/affine_map_test.cpp
@@ -34,7 +34,7 @@ using testing_utilities::RelativeError;
 class AffineMapTest : public testing::Test {
  protected:
   using World = Frame<serialization::Frame::TestTag,
-                      serialization::Frame::TEST, true>;
+                      serialization::Frame::TEST, Inertial>;
 
   using Orth = OrthogonalMap<World, World>;
   using Perm = Permutation<World, World>;

diff --git a/geometry/frame.hpp b/geometry/frame.hpp
@@ -16,12 +16,40 @@ namespace internal_frame {
 using base::not_constructible;
 using base::not_null;
 
-template<typename FrameTag, FrameTag frame_tag, bool frame_is_inertial>
+enum FrameMotion {
+  Inertial,
+  NonInertial,
+};
+
+enum class Handedness {
+  Left,
+  Right,
+};
+
+// The frame is serializable if and only if FrameTag is a protocol buffer enum.
+// To declare a local frame that does not need serialization, use the following
+// pattern:
+//   using MyFrame = Frame<enum class MyFrameTag>;
+//
+// or:
+//   using MyFrame = Frame<enum class MyFrameTag, MyFrameTag{}, Inertial>;
+//
+// By default, the frame is non-inertial and right-handed.
+// TODO(phl): Make the serialization check compile-time.
+template<typename FrameTag,
+         FrameTag tag_ = FrameTag{},
+         FrameMotion motion_ = NonInertial,
+         Handedness handedness_ = Handedness::Right>
 struct Frame : not_constructible {
+  static constexpr bool is_inertial = motion_ == Inertial;
+  static constexpr FrameMotion motion = motion_;
+  static constexpr Handedness handedness = handedness_;
+
+  static const Position<Frame> origin;
+  static const Velocity<Frame> unmoving;
+
   using Tag = FrameTag;
-  static Position<Frame> const origin;
-  static Tag const tag = frame_tag;
-  static bool const is_inertial = frame_is_inertial;
+  static constexpr Tag tag = tag_;
 
   static void WriteToMessage(not_null<serialization::Frame*> message);
 
@@ -38,6 +66,9 @@ void ReadFrameFromMessage(
 }  // namespace internal_frame
 
 using internal_frame::Frame;
+using internal_frame::Handedness;
+using internal_frame::Inertial;
+using internal_frame::NonInertial;
 using internal_frame::ReadFrameFromMessage;
 
 }  // namespace geometry

diff --git a/geometry/frame_body.hpp b/geometry/frame_body.hpp
@@ -20,37 +20,40 @@ inline uint32_t Fingerprint(std::string const& s) {
   return Fingerprint2011(s.c_str(), s.size()) & 0xFFFFFFFF;
 }
 
-template<typename FrameTag, FrameTag frame_tag, bool frame_is_inertial>
-void Frame<FrameTag, frame_tag, frame_is_inertial>::WriteToMessage(
-    not_null<serialization::Frame*> const message) {
+template<typename FrameTag, FrameTag tag_,
+         FrameMotion motion_, Handedness handedness_>
+void Frame<FrameTag, tag_, motion_, handedness_>::WriteToMessage(
+  not_null<serialization::Frame*> const message) {
   std::string const& tag_type_full_name =
       google::protobuf::GetEnumDescriptor<Tag>()->full_name();
 
   message->set_tag_type_fingerprint(Fingerprint(tag_type_full_name));
-  message->set_tag(tag);
+  message->set_tag(static_cast<int>(tag));
   message->set_is_inertial(is_inertial);
 }
 
-template<typename FrameTag, FrameTag frame_tag, bool frame_is_inertial>
-void Frame<FrameTag, frame_tag, frame_is_inertial>::ReadFromMessage(
-    serialization::Frame const& message) {
+template<typename FrameTag, FrameTag tag_,
+         FrameMotion motion_, Handedness handedness_>
+void Frame<FrameTag, tag_, motion_, handedness_>::ReadFromMessage(
+  serialization::Frame const& message) {
   std::string const& tag_type_full_name =
       google::protobuf::GetEnumDescriptor<Tag>()->full_name();
 
   CHECK_EQ(Fingerprint(tag_type_full_name), message.tag_type_fingerprint())
       << tag_type_full_name;
-  CHECK_EQ(tag, message.tag());
+  CHECK_EQ(static_cast<int>(tag), message.tag());
   CHECK_EQ(is_inertial, message.is_inertial());
 }
 
 // Default-initialized to {0, 0, 0}.
-template<typename FrameTag, FrameTag frame_tag, bool frame_is_inertial>
-Position<Frame<FrameTag, frame_tag, frame_is_inertial>> const
-Frame<FrameTag, frame_tag, frame_is_inertial>::origin;
-template<typename FrameTag, FrameTag frame_tag, bool frame_is_inertial>
-FrameTag const Frame<FrameTag, frame_tag, frame_is_inertial>::tag;
-template<typename FrameTag, FrameTag frame_tag, bool frame_is_inertial>
-bool const Frame<FrameTag, frame_tag, frame_is_inertial>::is_inertial;
+template<typename FrameTag, FrameTag tag_,
+         FrameMotion motion_, Handedness handedness_>
+Position<Frame<FrameTag, tag_, motion_, handedness_>> const
+Frame<FrameTag, tag_, motion_, handedness_>::origin;
+template<typename FrameTag, FrameTag tag_,
+         FrameMotion motion_, Handedness handedness_>
+Velocity<Frame<FrameTag, tag_, motion_, handedness_>> const
+Frame<FrameTag, tag_, motion_, handedness_>::unmoving;
 
 inline void ReadFrameFromMessage(
     serialization::Frame const& message,

diff --git a/geometry/frame_test.cpp b/geometry/frame_test.cpp
@@ -12,13 +12,28 @@ namespace geometry {
 class FrameTest : public testing::Test {
  protected:
   using World1 = Frame<serialization::Frame::TestTag,
-                       serialization::Frame::TEST1, true>;
+                       serialization::Frame::TEST1,
+                       Inertial,
+                       Handedness::Right>;
   using World2 = Frame<serialization::Frame::TestTag,
-                       serialization::Frame::TEST2, true>;
+                       serialization::Frame::TEST2,
+                       Inertial,
+                       Handedness::Right>;
   using World3 = Frame<serialization::Frame::TestTag,
-                       serialization::Frame::TEST1, false>;
+                       serialization::Frame::TEST1,
+                       NonInertial,
+                       Handedness::Right>;
   using World4 = Frame<serialization::Frame::SolarSystemTag,
-                       serialization::Frame::ICRS, true>;
+                       serialization::Frame::ICRS,
+                       Inertial,
+                       Handedness::Right>;
+
+  using F1 = Frame<enum class F1Tag>;
+  using F2 = Frame<enum class F2Tag>;
+  using F3 = Frame<enum class F3Tag, F3Tag{}, Inertial>;
+  static_assert(!std::is_same_v<F1, F2>);
+  static_assert(!std::is_same_v<F1, F3>);
+  static_assert(!std::is_same_v<F2, F3>);
 };
 
 using FrameDeathTest = FrameTest;
@@ -28,7 +43,7 @@ TEST_F(FrameDeathTest, SerializationError) {
     serialization::Frame message;
     World1::WriteToMessage(&message);
     World2::ReadFromMessage(message);
-  }, "tag ==");
+  }, R"(\(tag\) ==)");
   EXPECT_DEATH({
     serialization::Frame message;
     World1::WriteToMessage(&message);

diff --git a/geometry/grassmann.hpp b/geometry/grassmann.hpp
@@ -39,7 +39,7 @@ class Multivector;
 template<typename Scalar, typename Frame>
 class Multivector<Scalar, Frame, 1> final {
  public:
-  Multivector();
+  constexpr Multivector();
   explicit Multivector(R3Element<Scalar> const& coordinates);
 
   R3Element<Scalar> const& coordinates() const;
@@ -77,7 +77,7 @@ class Multivector<Scalar, Frame, 1> final {
 template<typename Scalar, typename Frame>
 class Multivector<Scalar, Frame, 2> final {
  public:
-  Multivector();
+  constexpr Multivector();
   explicit Multivector(R3Element<Scalar> const& coordinates);
 
   R3Element<Scalar> const& coordinates() const;
@@ -111,7 +111,7 @@ class Multivector<Scalar, Frame, 2> final {
 template<typename Scalar, typename Frame>
 class Multivector<Scalar, Frame, 3> final {
  public:
-  Multivector();
+  constexpr Multivector();
   explicit Multivector(Scalar const& coordinates);
 
   Scalar const& coordinates() const;