WebVR: add angular velocity estimate to pose

chrome/browser/android/vr_shell/vr_shell.cc

Index: chrome/browser/android/vr_shell/vr_shell.cc
diff --git a/chrome/browser/android/vr_shell/vr_shell.cc b/chrome/browser/android/vr_shell/vr_shell.cc
index edcbb68f0fe05e2c0f75e96229e281b9e33a5b32..103e7278bc0e5ec10fd757e24e4ef581d94ec8ef 100644
--- a/chrome/browser/android/vr_shell/vr_shell.cc
+++ b/chrome/browser/android/vr_shell/vr_shell.cc
@@ -655,7 +655,9 @@ void VrShell::RegisterGamepadDataFetcher(
 }
 
 /* static */
-device::mojom::VRPosePtr VrShell::VRPosePtrFromGvrPose(gvr::Mat4f head_mat) {
+device::mojom::VRPosePtr VrShell::VRPosePtrFromGvrPose(gvr::Mat4f head_mat,
+                                                       gvr::Mat4f head_mat_2,
+                                                       int64_t epsilon_nanos) {
   device::mojom::VRPosePtr pose = device::mojom::VRPose::New();
 
   pose->orientation.emplace(4);
@@ -682,6 +684,37 @@ device::mojom::VRPosePtr VrShell::VRPosePtrFromGvrPose(gvr::Mat4f head_mat) {
     pose->position.value()[2] = decomposed_transform.translate[2];
   }
 
+  // The angular velocity is a 3-element vector pointing along the rotation
+  // axis with magnitude equal to rotation speed in radians/second.
+  //
+  // The spec isn't very clear on details, clarification requested in
+  // https://github.com/w3c/webvr/issues/212 .
+  //
+  // Assume we're using right-hand rule for direction and a headset-attached
+  // frame of reference with +X to the right, +Y up, and +Z backwards (towards
+  // back of head).
+  //
+  // Examples:
+  // - "look up" motion: (positive, 0, 0)
+  // - "turn left" motion: (0, positive, 0)
+  // - "lean head left" motion: (0, 0, positive)
+  //
+  // Assuming that pose prediction is simply based on adding a time * angular
+  // velocity rotation to the pose, we can approximate the angular velocity
+  // from the difference between two successive poses. This is a first order
+  // estimate that assumes small enough rotations so that we can do linear
+  // approximation.
+  pose->angularVelocity.emplace(3);
+  // Assume that epsilon is nonzero since it's a compile-time constant
+  // provided by the caller.
+  double epsilon_seconds = epsilon_nanos * 1e-9;
+  pose->angularVelocity.value()[0] =

[billorr, 2017/03/24 22:52:51]

can you explain the math here in a comment?  Looking at
https://en.wikipedia.org/wiki/Rotation_matrix#Determining_the_axis, the formula
you have isn't quite the same.

We are basically trying to find the axis of the rotation part of
(head_mat_2-head_mat), which is a rotation matrix (ignoring the translation
component).

[klausw, 2017/03/27 02:25:52]

I'm using
https://en.wikipedia.org/wiki/Angular_velocity#Calculation_from_the_orientati...
, I added a link to that in a comment.

My original calculation wasn't quite correct, it was missing a multiplication
with the inverse of the first matrix. I added that, in addition to an additional
rotation to transform it into seated space.

+      (head_mat_2.m[1][2] - head_mat.m[1][2]) / epsilon_seconds;
+  pose->angularVelocity.value()[1] =
+      -(head_mat_2.m[0][2] - head_mat.m[0][2]) / epsilon_seconds;
+  pose->angularVelocity.value()[2] =
+      (head_mat_2.m[0][1] - head_mat.m[0][1]) / epsilon_seconds;
+
   return pose;
 }