Offer a new page after a finger fling past the page edge

A quick one-finger flick toward a free side of the active page, once
that edge is on screen, highlights and pulses the plus button on that
side for three seconds. It never adds a page by itself, so ordinary
panning can't create pages; a tap on the highlighted plus does.

Fling detection lives in ink/fling.ts with tests.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01GaoZtJQZwLXkEgWs8twCia

src/lib/ink/fling.ts

@@ -0,0 +1,41 @@
+// Fling detection for one-finger pans: a quick flick that ends the drag.
+
+import type { Dir } from '$lib/model/tree';
+
+export interface Sample {
+	x: number;
+	y: number;
+	t: number;
+}
+
+/** Only the last stretch of the drag counts. */
+const WINDOW_MS = 100;
+/** px/ms; a slow drag that stops is not a fling. */
+const MIN_SPEED = 0.6;
+/** The main axis must dominate by this much. */
+const MIN_RATIO = 2;
+
+/**
+ * Side of the canvas a fling heads for, or null. Moving the finger left pulls in
+ * what's on the right, so a leftward flick returns 'right'.
+ */
+export function flingDir(samples: readonly Sample[]): Dir | null {
+	const last = samples.at(-1);
+	if (!last) return null;
+	const first = samples.find((s) => last.t - s.t <= WINDOW_MS);
+	if (!first || first === last) return null;
+	const dt = last.t - first.t;
+	if (dt <= 0) return null;
+	const dx = last.x - first.x;
+	const dy = last.y - first.y;
+	if (Math.hypot(dx, dy) / dt < MIN_SPEED) return null;
+	if (Math.abs(dx) >= Math.abs(dy) * MIN_RATIO) return dx < 0 ? 'right' : 'left';
+	if (Math.abs(dy) >= Math.abs(dx) * MIN_RATIO) return dy < 0 ? 'down' : 'up';
+	return null;
+}
+
+/** Keeps a short trail of pointer samples for flingDir. */
+export function pushSample(samples: Sample[], s: Sample) {
+	samples.push(s);
+	while (samples.length > 2 && s.t - samples[0].t > WINDOW_MS * 2) samples.shift();
+}