feat: show playable charts with score hover and special-start markers

src/lib/engine/score-timeline.ts

@@ -0,0 +1,40 @@
+import type { NoteScorePoint } from './types.ts';
+
+export type ScorePoint = {
+  timeSeconds: number;
+  averageScore: number;
+  maximumScore: number;
+  maximumProbability?: number;
+};
+
+export function buildScorePoints(notes: readonly NoteScorePoint[], probabilities: readonly number[]): ScorePoint[] {
+  let averageScore = 0;
+  let maximumScore = 0;
+  return [{ timeSeconds: 0, averageScore: 0, maximumScore: 0, maximumProbability: 1 }, ...notes.map((note, index) => {
+    averageScore += note.expectedScore;
+    maximumScore += note.theoreticalMaxScore;
+    return { timeSeconds: note.timeSeconds, averageScore, maximumScore, maximumProbability: probabilities[index] };
+  })];
+}
+
+/** Include every simultaneous judgement, exactly as in the cumulative score graph. */
+export function scorePointAtTime(points: readonly ScorePoint[], timeSeconds: number): ScorePoint {
+  let low = 0;
+  let high = points.length - 1;
+  while (low < high) {
+    const middle = Math.ceil((low + high) / 2);
+    if (points[middle].timeSeconds <= timeSeconds) low = middle;
+    else high = middle - 1;
+  }
+  return points[low] ?? { timeSeconds: 0, averageScore: 0, maximumScore: 0 };
+}
+
+export function formatTimelineScore(score: number): string {
+  return Math.round(score).toLocaleString('ko-KR');
+}
+
+export function formatTimelineProbability(probability: number | undefined): string {
+  if (probability === undefined) return '—';
+  if (probability > 0 && probability < 0.000001) return '<0.0001%';
+  return `${(probability * 100).toLocaleString('ko-KR', { maximumFractionDigits: probability < 0.0001 ? 4 : 2 })}%`;
+}