Place external source/exit pills near their connection targets

Replace count-sorted, group-centered rows with a spring-like placement:
pills order by their weighted median target x and settle by clamped
coordinate descent, minimizing weighted horizontal connection distance
while keeping the minimum pill spacing.

frontend/src/analytics/transitions.js

@@ -18,7 +18,9 @@
  * connections. Animated beads flow along every edge in each direction,
  * emitted at time intervals inversely proportional (linear) to the
  * directional count.
- * External sources appear as nodes in a row above the map. Sources are
+ * External sources appear as nodes in a row above the map, each pill
+ * slid sideways toward the pages it connects to (weighted by count,
+ * minimum spacing kept). Sources are
  * identified from visit records in this order: utm_campaign, utm_source,
  * referer, then other utm_* tags. Visits with a UTM tag are grouped under
  * that tag's value, not under the referer domain. A UTM source node only
@@ -700,6 +702,51 @@ function buildInternalEdges(pairs, byPath, dayScale = 1) {
   return { edges, flows }
 }
 
+/**
+ * Weighted median of {x, w} targets: the x minimizing Σ w|x − t| —
+ * the spot where a pill's total horizontal connection pull balances.
+ */
+function weightedMedian(targets) {
+  const ts = [...targets].sort((a, b) => a.x - b.x)
+  let total = 0
+  for (const t of ts) total += t.w
+  let acc = 0
+  for (const t of ts) {
+    acc += t.w
+    if (acc >= total / 2) return t.x
+  }
+  return ts[ts.length - 1].x
+}
+
+/**
+ * Slide the pills of an external row sideways so each sits as close as
+ * possible to the pages it connects to: minimize Σ w|pill.x − target.x|
+ * over all drawn connections (weight = count), subject to a minimum
+ * center `spacing` (no overlap). Pills are ordered by their weighted
+ * median target (swapping any inverted adjacent pair can only add
+ * crossing distance), then positioned by coordinate descent on this
+ * convex objective: each pass snaps a pill to its weighted median,
+ * clamped to the spacing window between its current neighbors.
+ */
+function placeRow(items, spacing) {
+  items.sort((a, b) => a.anchor - b.anchor)
+  const n = items.length
+  for (const it of items) it.x = it.anchor
+  for (let pass = 0; pass < 40; pass++) {
+    let moved = 0
+    const sweep = (i) => {
+      const lo = i > 0 ? items[i - 1].x + spacing : -Infinity
+      const hi = i < n - 1 ? items[i + 1].x - spacing : Infinity
+      const x = Math.min(Math.max(items[i].anchor, lo), hi)
+      moved = Math.max(moved, Math.abs(x - items[i].x))
+      items[i].x = x
+    }
+    for (let i = 0; i < n; i++) sweep(i)
+    for (let i = n - 1; i >= 0; i--) sweep(i)
+    if (moved < 0.01) break
+  }
+}
+
 const UTM_PRIORITY = ['utm_campaign', 'utm_source']
 const UTM_FALLBACK = ['utm_medium', 'utm_content', 'utm_term', 'utm_id']
 
@@ -764,10 +811,12 @@ function collectSourcePairs(visits) {
  * Place external source and exit nodes and build their edges and bead
  * flows.
  * Sources (incoming links) are derived from visit UTM/referer data and form
- * a row centered above the map, hottest first; exits come from the
- * transition matrix and form a matching row centered below the map, so
+ * a row above the map; exits come from the
+ * transition matrix and form a matching row below the map, so
  * the site itself stays in the middle. Both rows sit EXT_GAP beyond the
- * map's bounds.
+ * map's bounds. Within a row the pills slide sideways toward the pages
+ * they connect to (placeRow), minimizing the weighted horizontal
+ * connection distance while keeping a minimum center spacing.
  * Widths and pruning use the same log scale and traffic-share rule as
  * internal connections.
  */
@@ -785,9 +834,10 @@ function buildExternal({ sources, exits }, byPath, innerBounds, dayScale = 1) {
 
   const width = (count) => scaledWidth(count * dayScale)
 
-  // Incoming: one source node per identified source, in a row centered
-  // above the map, with an edge to each page that source led to. A source
-  // whose connectors are all culled (below MIN_WMID) is dropped itself.
+  // Incoming: one source node per identified source, in a row above the
+  // map, with an edge to each page that source led to. A source whose
+  // connectors are all culled (below MIN_WMID) is dropped itself. Pills
+  // slide sideways toward their connection targets (see placeRow).
   const bySource = new Map() // source -> pairs, sorted by total incoming count
   for (const p of liveSources.filter((p) => p.in >= minCount)) {
     const g = bySource.get(p.source) || []
@@ -804,20 +854,25 @@ function buildExternal({ sources, exits }, byPath, innerBounds, dayScale = 1) {
     }))
     .sort((a, b) => b.total - a.total)
     .slice(0, MAX_EXT_IN)
-    .filter(({ ps }) =>
-      ps.some((p) => !byPath.get(p.page).hidden && width(p.in) >= MIN_WMID))
+    .map((o) => ({
+      ...o,
+      // Anchoring targets: the drawn (non-culled) connections only.
+      targets: o.ps
+        .filter((p) => !byPath.get(p.page).hidden && width(p.in) >= MIN_WMID)
+        .map((p) => ({ x: byPath.get(p.page).x, w: p.in })),
+    }))
+    .filter((o) => o.targets.length)
   if (origins.length) {
-    const cx = (innerBounds.x0 + innerBounds.x1) / 2
     const y = innerBounds.y0 - TNODE_BOUND - EXT_GAP
-    const spacing = TNODE_W + 44
-    const x0 = cx - ((origins.length - 1) * spacing) / 2
-    origins.forEach(({ source, ps, total, href, isUtm }, i) => {
+    for (const o of origins) o.anchor = weightedMedian(o.targets)
+    placeRow(origins, TNODE_W + 44)
+    origins.forEach(({ source, ps, total, href, isUtm, x }) => {
       const label = isUtm ? source : extLabel(source)
       const xn = {
         path: source,
         href,
         label, // clipped at the pill border on render
-        x: x0 + i * spacing,
+        x,
         y,
         count: total,
         kind: 'source',
@@ -836,10 +891,11 @@ function buildExternal({ sources, exits }, byPath, innerBounds, dayScale = 1) {
 
   // Outgoing: one exit node per distinct full URL (so several links to
   // the same domain stay distinct), showing the total count across all
-  // pages linking to it, in a row centered below the map (hottest
-  // first), mirroring the source row above. Each (URL, page) pair
-  // contributes an edge from that page. An exit whose connectors are all
-  // culled (below MIN_WMID) is dropped itself.
+  // pages linking to it, in a row below the map mirroring the source row
+  // above. Each (URL, page) pair contributes an edge from that page. An
+  // exit whose connectors are all culled (below MIN_WMID) is dropped
+  // itself. Pills slide sideways toward their connection targets (see
+  // placeRow).
   const byExt = new Map() // full URL -> { ext, out, pairs }
   for (const p of liveExits.filter((p) => p.out >= minCount)) {
     const g = byExt.get(p.ext) || { ext: p.ext, out: 0, pairs: [] }
@@ -850,19 +906,23 @@ function buildExternal({ sources, exits }, byPath, innerBounds, dayScale = 1) {
   const targets = [...byExt.values()]
     .sort((a, b) => b.out - a.out)
     .slice(0, MAX_EXT_OUT)
-    .filter(({ pairs }) =>
-      pairs.some((p) => !byPath.get(p.page).hidden && width(p.out) >= MIN_WMID))
+    .map((t) => ({
+      ...t,
+      targets: t.pairs
+        .filter((p) => !byPath.get(p.page).hidden && width(p.out) >= MIN_WMID)
+        .map((p) => ({ x: byPath.get(p.page).x, w: p.out })),
+    }))
+    .filter((t) => t.targets.length)
   if (targets.length) {
-    const cx = (innerBounds.x0 + innerBounds.x1) / 2
     const y = innerBounds.y1 + TNODE_BOUND + EXT_GAP
-    const spacing = TNODE_W + 44
-    const x0 = cx - ((targets.length - 1) * spacing) / 2
-    targets.forEach(({ ext, out, pairs }, i) => {
+    for (const t of targets) t.anchor = weightedMedian(t.targets)
+    placeRow(targets, TNODE_W + 44)
+    targets.forEach(({ ext, out, pairs, x }) => {
       const xn = {
         path: ext,
         href: ext,
         label: extLabel(ext),
-        x: x0 + i * spacing,
+        x,
         y,
         count: out,
         kind: 'exit',