flutter_clock/lib/pages/main_page.dart

import 'package:flutter/material.dart';
import 'dart:async';
import 'dart:math' as math;
import 'package:intl/intl.dart';

class MainPage extends StatefulWidget {
  @override
  State<StatefulWidget> createState() {
    @override
    _MainPageState createState() => _MainPageState();
  }
}

class _MainPageState extends State<MainPage> {
  final _utcMidnightRadiansOffset = radiansFromDegrees(-64);
  static const _secondsInDay = 86400;
  DateTime _localTime = DateTime.now();

  @override
  void initState() {
    super.initState();
    Timer.periodic(Duration(seconds: 1),
        (_) => setState(() => _localTime = DateTime.now()));
  }

  @override
  Widget build(BuildContext context) => Scaffold(
        backgroundColor: Colors.white,
        appBar: AppBar(title: Text('xkcd clock')),
        body: Column(
          children: [
            Stack(
              children: [
                Image.asset('assets/face.png'),
                Transform.rotate(
                  angle: -(radiansFromTime(_localTime.toUtc()) +
                      _utcMidnightRadiansOffset),
                  child: ClipOval(
                    clipper: InnerFaceClipper(),
                    child: Image.asset('assets/face.png'),
                  ),
                ),
              ],
            ),
            Text(DateFormat.EEEE().format(_localTime),
                style: TextStyle(fontSize: 48)),
            Text(DateFormat.yMMMMd().format(_localTime),
                style: TextStyle(fontSize: 20)),
            Text(DateFormat.jm().format(_localTime),
                style: TextStyle(fontSize: 42)),
          ],
        ),
      );

  static double radiansFromDegrees(double degrees) => degrees * math.pi / 180;
  static double radiansFromTime(DateTime time) {
    final midnightToday = DateTime(time.year, time.month, time.day);
    final secondsSinceMidnight = midnightToday.difference(time).inSeconds;
    final percent = secondsSinceMidnight / _secondsInDay;
    final degrees = percent * 360;
    return radiansFromDegrees(degrees);
  }
}

class InnerFaceClipper extends CustomClipper<Rect> {
  final percent = 0.85;

  @override
  Rect getClip(Size size) => Rect.fromCenter(
        center: size.center(Offset(0, 0)),
        width: size.width * percent,
        height: size.height * percent,
      );

  @override
  bool shouldReclip(CustomClipper oldClipper) => true;
}