Add a comet trail animation

The frame glides from waypoint to waypoint and drops a screenshot of
itself every frame-width or so. The stills stay where they were taken
and fade over a few seconds, so the live video reads as the head of a
comet whose tail is its own recent past.

The steering caps how fast the heading may change: an instant turn would
lay the stills out in straight dotted lines, and it is the curve that
makes a tail read as one. Drops are spaced by distance travelled rather
than by a timer, so they stay even however the frame is turning.

Since the capture is a crop of the tab, a still lying under the frame
would be photographed into the next one. A drop waits until the frame is
clear of the tail, keeping the invariant corners already relies on.

Also picks up the FRAME_SCALE, BOUNCE_SPEED and CORNER_INTERVAL_SECONDS
tuning sitting in the tree.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Tg15tLAuT6NrCE1ZxKVgDB

public/player/motion.js

@@ -14,6 +14,11 @@ import {
   DRAG_FRAME_SCALE,
   DRAG_MIN_SCALE,
   DRAG_MAX_SCALE,
+  TRAIL_SPEED,
+  TRAIL_TURN_RATE,
+  TRAIL_SPACING,
+  TRAIL_LENGTH,
+  TRAIL_FADE_SECONDS,
   AUTO_ANIMATION,
 } from '/config.js';
 
@@ -299,6 +304,224 @@ export function startCorners(context) {
   };
 }
 
+// --- trail --------------------------------------------------------------
+
+// The frame glides along a curving path and drops a photograph of itself every
+// so often. Each still stays where it was taken and fades, so the live video
+// reads as the head of a comet whose tail is its own recent past.
+
+/**
+ * Steering toward a waypoint at constant speed, with a cap on how fast the
+ * heading may change. The cap is the whole point: an instant turn would lay the
+ * stills out in straight dotted lines, and it is the curve that makes a tail
+ * read as one. Pure apart from the injected RNG, so the path can be exercised
+ * without a browser.
+ */
+export function createGlider({ x = 0, y = 0 } = {}, random = Math.random) {
+  // How close counts as arrived. Anything tighter than the turn radius
+  // (speed / turn rate) risks the glider circling a waypoint forever, unable to
+  // steer hard enough to land on it.
+  const reach = TRAIL_SPEED / TRAIL_TURN_RATE;
+
+  function normalise(angle) {
+    return Math.atan2(Math.sin(angle), Math.cos(angle));
+  }
+
+  const glider = {
+    x,
+    y,
+    heading: random() * Math.PI * 2,
+    target: null,
+
+    retarget(bounds) {
+      glider.target = {
+        x: random() * Math.max(0, bounds.width),
+        y: random() * Math.max(0, bounds.height),
+      };
+      return glider.target;
+    },
+
+    step(dt, bounds) {
+      const maxX = Math.max(0, bounds.width);
+      const maxY = Math.max(0, bounds.height);
+
+      if (!glider.target) glider.retarget(bounds);
+      if (Math.hypot(glider.target.x - glider.x, glider.target.y - glider.y) < reach) {
+        glider.retarget(bounds);
+      }
+
+      // Shortest way round to the bearing of the waypoint, then take at most
+      // this step's share of the turn rate.
+      const bearing = Math.atan2(glider.target.y - glider.y, glider.target.x - glider.x);
+      const turn = normalise(bearing - glider.heading);
+      glider.heading = normalise(
+        glider.heading + clamp(turn, -TRAIL_TURN_RATE * dt, TRAIL_TURN_RATE * dt),
+      );
+
+      glider.x += Math.cos(glider.heading) * TRAIL_SPEED * dt;
+      glider.y += Math.sin(glider.heading) * TRAIL_SPEED * dt;
+
+      // Reflect off the edges rather than clamping and sliding along them. The
+      // waypoint is always inside the bounds, so steering picks up from there
+      // and pulls the glider back inward instead of straight into the wall.
+      if (glider.x < 0 || glider.x > maxX) {
+        glider.x = clamp(glider.x, 0, maxX);
+        glider.heading = normalise(Math.PI - glider.heading);
+      }
+      if (glider.y < 0 || glider.y > maxY) {
+        glider.y = clamp(glider.y, 0, maxY);
+        glider.heading = normalise(-glider.heading);
+      }
+
+      return glider;
+    },
+  };
+
+  return glider;
+}
+
+export function startTrail(context) {
+  const { element } = context;
+  const layer = document.getElementById('stills');
+
+  let size = applyFrameSize(element);
+  const glider = createGlider({
+    x: (window.innerWidth - size.width) / 2,
+    y: (window.innerHeight - size.height) / 2,
+  });
+
+  // A ring buffer: the tail is a fixed number of images, and the oldest one is
+  // what the next drop reuses. `rect` doubles as the "currently showing" flag.
+  const cells = [];
+  for (let i = 0; i < TRAIL_LENGTH; i += 1) {
+    const img = document.createElement('img');
+    img.classList.add('trail');
+    layer.appendChild(img);
+    cells.push({ img, born: 0, rect: null });
+  }
+
+  let next = 0;
+  let travelled = 0;
+
+  function bounds() {
+    return {
+      width: window.innerWidth - size.width,
+      height: window.innerHeight - size.height,
+    };
+  }
+
+  function measure() {
+    size = applyFrameSize(element);
+
+    const limit = bounds();
+    glider.x = Math.min(glider.x, Math.max(0, limit.width));
+    glider.y = Math.min(glider.y, Math.max(0, limit.height));
+  }
+
+  /** True when the frame overlaps nothing that is still showing in the tail. */
+  function clearOfTail(rect) {
+    for (const cell of cells) {
+      const other = cell.rect;
+      if (!other) continue;
+      if (
+        rect.left < other.right &&
+        rect.right > other.left &&
+        rect.top < other.bottom &&
+        rect.bottom > other.top
+      ) {
+        return false;
+      }
+    }
+
+    return true;
+  }
+
+  /** Photograph the frame where it stands. Reports whether a still landed. */
+  function drop(now) {
+    // Read late: the capture handle may still be waiting on the operator to
+    // answer the screen-share prompt when this animation starts.
+    if (!context.capture) return false;
+
+    const rect = element.getBoundingClientRect();
+
+    // The capture is a crop of the tab, so an older still lying under the frame
+    // would be photographed into the new one. Skip this drop instead; the
+    // travelled distance is not spent, so it happens as soon as the frame is
+    // back in the clear.
+    if (!clearOfTail(rect)) return false;
+
+    const shot = context.capture.grab(rect);
+    if (!shot) return false;
+
+    const cell = cells[next];
+    cell.img.src = shot;
+    cell.img.style.width = `${rect.width}px`;
+    cell.img.style.height = `${rect.height}px`;
+    place(cell.img, rect.left, rect.top);
+    cell.born = now;
+    cell.rect = { left: rect.left, top: rect.top, right: rect.right, bottom: rect.bottom };
+    // Re-append so the freshest still paints over the rest of the tail.
+    layer.appendChild(cell.img);
+
+    next = (next + 1) % cells.length;
+    return true;
+  }
+
+  function fade(now) {
+    for (const cell of cells) {
+      if (!cell.rect) continue;
+
+      const life = 1 - (now - cell.born) / 1000 / TRAIL_FADE_SECONDS;
+      if (life <= 0) {
+        cell.img.style.opacity = '0';
+        // Gone, so it stops holding up drops that pass over its old spot.
+        cell.rect = null;
+        continue;
+      }
+
+      // Squared: a still holds its brightness for a moment and then goes
+      // quickly, which thins the tail out instead of trailing a long grey smear.
+      cell.img.style.opacity = (life * life).toFixed(3);
+    }
+  }
+
+  place(element, glider.x, glider.y);
+  window.addEventListener('resize', measure);
+
+  let last = performance.now();
+  let handle = 0;
+  let stopped = false;
+
+  function frame(now) {
+    if (stopped) return;
+
+    const dt = Math.min((now - last) / 1000, 0.05);
+    last = now;
+
+    const wasX = glider.x;
+    const wasY = glider.y;
+    glider.step(dt, bounds());
+    place(element, glider.x, glider.y);
+
+    // Spacing by distance rather than by a timer keeps the stills evenly spread
+    // however the frame is turning.
+    travelled += Math.hypot(glider.x - wasX, glider.y - wasY);
+    if (travelled >= size.width * TRAIL_SPACING && drop(now)) travelled = 0;
+
+    fade(now);
+    handle = requestAnimationFrame(frame);
+  }
+
+  handle = requestAnimationFrame(frame);
+
+  return function stop() {
+    stopped = true;
+    cancelAnimationFrame(handle);
+    window.removeEventListener('resize', measure);
+    for (const cell of cells) cell.img.remove();
+  };
+}
+
 // --- drag and resize ----------------------------------------------------
 
 // Someone shoving a video window around a desktop: a pointer travels to the
@@ -687,6 +910,7 @@ export const ANIMATIONS = {
   bounce: startBounce,
   corners: startCorners,
   drag: startDragResize,
+  trail: startTrail,
 };
 
 const NAMES = Object.keys(ANIMATIONS);