Move hand cutouts ahead to where the hands will be

The tracked hands arrive 30-60 ms after the cameras saw them and reach the
displays later still, so holes trailed moving hands. Track each hand's palm
velocity in the room and move its capsules ahead to about when the frame is
on the displays, every tick, so the holes also move smoothly between tracker
updates. Slow hands aren't moved (their velocity is noise). The control
socket gets cutouts predict on|off and cutouts lead <ms>.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

screens/handcut.h

@@ -8,6 +8,10 @@
 // sees them on a panel, and Renderer draws the panel's client buffer into a side-by-side
 // buffer (left eye | right eye) with those spots transparent. A panel shows that buffer,
 // with the overlay's SideBySide_Parallel flag, only while a hand is in front of it.
+//
+// The hands arrive some 30-60 ms after the cameras saw them, and show up on the displays
+// later still, so Hands moves each hand ahead along its velocity in the room to where it
+// will be when the frame reaches the eyes.
 #pragma once
 
 #include "vr.h"
@@ -46,14 +50,27 @@ public:
     // Once per tick: the head pose now, CLOCK_MONOTONIC ns. Re-reads the hands file when
     // it changed. Returns true while fresh hands are known.
     bool Update(const Mat &head, int64_t nowNs);
+    // Where the hands will be `lead` after now (see SetPrediction).
     const std::vector<Capsule> &capsules() const { return world_; }
+    // Predict the hands' motion (on by default) to now + leadMs: about how long a frame
+    // takes from here to the displays.
+    void SetPrediction(bool on, double leadMs);
+    bool predicting() const { return predict_; }
+    double leadMs() const { return leadNs_ / 1e6; }
 
 private:
     bool Read();
     Mat HeadAt(int64_t ns) const;
     struct Past { int64_t ns; Mat head; };
+    struct Motion { int64_t ns = 0; double palm[3]{}, v[3]{}; };   // a hand's palm, in the room
     std::vector<Past> history_;   // the last second of head poses
-    std::vector<Capsule> world_;
+    std::vector<Capsule> base_;   // the capsules at capture time, in the room
+    std::vector<int> owner_;      // each capsule's hand (index into ids_), or -1
+    std::vector<uint32_t> ids_;   // the hands in the file
+    std::map<uint32_t, Motion> motion_;
+    std::vector<Capsule> world_;  // base_, moved ahead
+    bool predict_ = true;
+    int64_t leadNs_ = 25'000'000;
     int fd_ = -1;
     const void *map_ = nullptr;
     uint64_t seq_ = 0;