Integrate LiveKit SFU and harden booking workflow

lib/calendar/timezone.ts

@@ -1,5 +1,59 @@
 const BERLIN_TZ = "Europe/Berlin";
 
+export type CalendarDate = { year: number; month: number; day: number };
+
+export function berlinDateKey(date: Date): string {
+  const { year, month, day } = berlinParts(date);
+  return `${year}-${String(month).padStart(2, "0")}-${String(day).padStart(2, "0")}`;
+}
+
+export function formatBerlinDate(date: Date, options: Intl.DateTimeFormatOptions = {}): string {
+  return new Intl.DateTimeFormat("de-DE", { ...options, timeZone: BERLIN_TZ }).format(date);
+}
+
+export function formatBerlinTime(date: Date, options: Intl.DateTimeFormatOptions = {}): string {
+  return new Intl.DateTimeFormat("de-DE", { ...options, timeZone: BERLIN_TZ }).format(date);
+}
+
+export function berlinParts(date: Date): CalendarDate & { hour: number; minute: number } {
+  const parts = new Intl.DateTimeFormat("en-US", {
+    timeZone: BERLIN_TZ,
+    year: "numeric",
+    month: "2-digit",
+    day: "2-digit",
+    hour: "2-digit",
+    minute: "2-digit",
+    hourCycle: "h23",
+  }).formatToParts(date);
+  const get = (type: string) => Number(parts.find((part) => part.type === type)?.value ?? "0");
+  return { year: get("year"), month: get("month"), day: get("day"), hour: get("hour"), minute: get("minute") };
+}
+
+export function berlinOffsetMinutes(date: Date): number {
+  const tzName = new Intl.DateTimeFormat("en-US", { timeZone: BERLIN_TZ, timeZoneName: "shortOffset" })
+    .formatToParts(date)
+    .find((part) => part.type === "timeZoneName")?.value ?? "GMT+1";
+  const match = tzName.match(/GMT([+-]\d+)(?::(\d+))?/);
+  const hours = match ? Number(match[1]) : 1;
+  const minutes = match?.[2] ? Number(match[2]) : 0;
+  return hours * 60 + (hours < 0 ? -minutes : minutes);
+}
+
+/** Converts a Berlin wall-clock date/time into the UTC instant it represents. */
+export function berlinWallTimeToUTC(date: CalendarDate, hour: number, minute: number): Date {
+  const guess = Date.UTC(date.year, date.month - 1, date.day, hour, minute);
+  return new Date(guess - berlinOffsetMinutes(new Date(guess)) * 60_000);
+}
+
+export function berlinDayBounds(date: Date): { key: string; start: Date; end: Date } {
+  const current = berlinParts(date);
+  const nextCalendarDay = new Date(Date.UTC(current.year, current.month - 1, current.day + 1));
+  const next = berlinParts(nextCalendarDay);
+  const start = berlinWallTimeToUTC(current, 0, 0);
+  const nextStart = berlinWallTimeToUTC(next, 0, 0);
+  return { key: berlinDateKey(date), start, end: new Date(nextStart.getTime() - 1) };
+}
+
 /**
  * Converts a JS Date (a UTC instant) into its Europe/Berlin wall-clock
  * representation for iCalendar's local `TZID` date-time form