Flutter cursor wheel widget auto positioning with animation

You should use AnimationController to animate position of the items and you must set the correct position of menu item in the onPanEnd method, i completely review your code and finally fixed it as below:

import 'dart:math';

import 'package:flutter/material.dart';

void main() {
  runApp(MyApp());
}

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      debugShowCheckedModeBanner: false,
      theme: ThemeData(
        primarySwatch: Colors.blue,
      ),
      home: RotateText(),
    );
  }
}

class RotateText extends StatefulWidget {
  RotateText({Key key}) : super(key: key); // changed

  @override
  _RotateTextState createState() => _RotateTextState();
}

class _RotateTextState extends State<RotateText>
    with SingleTickerProviderStateMixin {
  double finalAngle = 0.0;
  double offsetAngle = 0.0;

  Tween<double> _tween;
  Animation<double> _animation;
  AnimationController _animationController;

  @override
  void initState() {
    super.initState();
    _animationController =
        AnimationController(duration: Duration(milliseconds: 700), vsync: this);
    _tween = Tween(begin: 0.0, end: finalAngle);
    _animation = _tween.animate(CurvedAnimation(
        parent: _animationController, curve: Curves.easeOut))
      ..addListener(() {
        setState(() {});
      });
  }

  void updateFinalAngle(double angle, [bool withDuration = false]) {
    _tween.begin = _tween.end;
    _animationController.reset();
    _tween.end = angle;
    _animationController.forward();
  }

  @override
  Widget build(BuildContext context) {
    return _defaultApp(context);
  }

  _defaultApp(BuildContext context) {
    var radius = 300.0;
    var left = MediaQuery.of(context).size.width / 2 - radius;
    var size = 1.6 * radius;
    var place = 60;
    var item = 100.0;
    var distance = 180;

    return Scaffold(
        appBar: AppBar(
          title: Text('Single finger Rotate text'), // changed
        ),
        body: Stack(children: <Widget>[
          Positioned(
              left: left,
              bottom: place - radius,
              child: Container(
                width: 2 * radius,
                height: 2 * radius,
                decoration: BoxDecoration(
                  shape: BoxShape.circle,
                  color: Colors.grey,
                ),
                child: LayoutBuilder(
                  builder: (context, constraints) {
                    return GestureDetector(
                      behavior: HitTestBehavior.translucent,
                      onPanStart: (details) {
                        Offset centerOfGestureDetector = Offset(
                            constraints.maxWidth / 2,
                            constraints.maxHeight / 2);
                        final touchPositionFromCenter =
                            details.localPosition - centerOfGestureDetector;
                        offsetAngle =
                            touchPositionFromCenter.direction - finalAngle;
                      },
                      onPanUpdate: (details) {
                        Offset centerOfGestureDetector = Offset(
                            constraints.maxWidth / 2,
                            constraints.maxHeight / 2);
                        final touchPositionFromCenter =
                            details.localPosition - centerOfGestureDetector;
                        setState(() {
                          finalAngle =
                              touchPositionFromCenter.direction - offsetAngle;
                          updateFinalAngle(finalAngle);
                        });
                      },
                      onPanEnd: (detail) {
                        double fixedAngle = _calcFinalAngle(finalAngle);
                        finalAngle = fixedAngle;
                        updateFinalAngle(finalAngle, true);
                      },
                      child: Transform.rotate(
                        angle: _animation.value,
                        child: Icon(
                          Icons.settings,
                          color: Colors.white,
                          size: size,
                        ),
                      ),
                    );
                  },
                ),
              )),
          Positioned(
              left: left +
                  radius / 2 +
                  item +
                  distance * cos(_animation.value - pi / 2),
              bottom:
                  place - item / 2 - distance * sin(_animation.value - pi / 2),
              child: Container(
                height: item,
                width: item,
                child: Image.network(
                  'https://picsum.photos/250?image=9',
                ),
              )),
        ]));
  }

  double _calcFinalAngle(double radianAngle) {
    int degreeAngle =
        double.parse((radianAngle * (180 / pi)).toStringAsFixed(2)).round();

    int criticalAngle = 60;
    int criticalOffset = 30;
    bool isNegative = false;
    if (degreeAngle < 0) isNegative = true;
    degreeAngle = degreeAngle.abs();
    int rem60 = degreeAngle % criticalAngle;

    if (rem60 >= criticalOffset) {
      degreeAngle += (60 - rem60);
    } else {
      degreeAngle -= rem60;
    }

    double resultAngleInRad = degreeAngle * (pi / 180);

    return isNegative ? -resultAngleInRad : resultAngleInRad;
  }
}