半圆菜单展开/收起代码如下：

import 'dart:math';

import 'package:flutter/material.dart';

class DemoFlowMenu extends StatefulWidget {
  @override
  _DemoFlowMenuState createState() => _DemoFlowMenuState();
}

class _DemoFlowMenuState extends State<DemoFlowMenu>
    with TickerProviderStateMixin {
  //动画需要这个类来混合
  //动画变量,以及初始化和销毁
  AnimationController _ctrlAnimationCircle;

  @override
  void initState() {
    super.initState();
    _ctrlAnimationCircle = AnimationController(
        //初始化动画变量
        lowerBound: 0,
        upperBound: 80,
        duration: Duration(milliseconds: 300),
        vsync: this);
    _ctrlAnimationCircle.addListener(() => setState(() {}));
  }

  @override
  void dispose() {
    _ctrlAnimationCircle.dispose(); //销毁变量,释放资源
    super.dispose();
  }

  //生成Flow的数据
  List<Widget> _buildFlowChildren() {
    return List.generate(
        5,
        (index) => Container(
              child: Icon(
                index.isEven ? Icons.timer : Icons.ac_unit,
                color: Colors.primaries[index % Colors.primaries.length],
              ),
            ));
  }

  @override
  Widget build(BuildContext context) {
    return Stack(
      children: <Widget>[
        Positioned.fill(
          child: Flow(
            delegate: FlowAnimatedCircle(_ctrlAnimationCircle.value),
            children: _buildFlowChildren(),
          ),
        ),
        Positioned.fill(
          child: IconButton(
            icon: Icon(Icons.menu),
            onPressed: () {
              setState(() {
                //点击后让动画可前行或回退
                _ctrlAnimationCircle.status == AnimationStatus.completed
                    ? _ctrlAnimationCircle.reverse()
                    : _ctrlAnimationCircle.forward();
              });
            },
          ),
        ),
      ],
    );
  }
}

FlowAnimatedCircle 代码如下：

class FlowAnimatedCircle extends FlowDelegate {
  final double radius; //绑定半径,让圆动起来
  FlowAnimatedCircle(this.radius);

  @override
  void paintChildren(FlowPaintingContext context) {
    if (radius == 0) {
      return;
    }
    double x = 0; //开始(0,0)在父组件的中心
    double y = 0;
    for (int i = 0; i < context.childCount; i++) {
      x = radius * cos(i * pi / (context.childCount - 1)); //根据数学得出坐标
      y = radius * sin(i * pi / (context.childCount - 1)); //根据数学得出坐标
      context.paintChild(i, transform: Matrix4.translationValues(x, -y, 0));
    } //使用Matrix定位每个子组件
  }

  @override
  bool shouldRepaint(FlowDelegate oldDelegate) => true;
}