diff --git a/doc/flame/components.md b/doc/flame/components.md
index 655339a278..06afa86c02 100644
--- a/doc/flame/components.md
+++ b/doc/flame/components.md
@@ -340,6 +340,12 @@ void onDragUpdate(DragUpdateInfo info) {
 
 ### PositionType
 
+```{note}
+If you are using the `CameraComponent` you should not use `PositionType`, but
+instead adding your components directly to the viewport for example if you
+want to use them as a HUD.
+```
+
 If you want to create a HUD (Head-up display) or another component that isn't positioned in relation
 to the game coordinates, you can change the `PositionType` of the component.
 The default `PositionType` is `positionType = PositionType.game` and that can be changed to
@@ -810,6 +816,44 @@ class ButtonComponent extends SpriteGroupComponent<ButtonState>
 ```
 
 
+## SpawnComponent
+
+This component is a non-visual component that spawns other components inside of the parent of the
+`SpawnComponent`. It's great if you for example want to spawn enemies or power-ups randomly within
+an area.
+
+The `SpawnComponent` takes a factory function that it uses to create new components and an area
+where the components should be spawned within (or along the edges of).
+
+For the area, you can use the `Circle`, `Rectangle` or `Polygon` class, and if you want to only
+spawn components along the edges of the shape set the `within` argument to false (defaults to true).
+
+This would for example spawn new components of the type `MyComponent` every 0.5 seconds randomly
+within the defined circle:
+
+```dart
+SpawnComponent(
+  factory: () => MyComponent(size: Vector2(10, 20)),
+  period: 0.5,
+  area: Circle(Vector2(100, 200), 150),
+);
+```
+
+If you don't want the spawning rate to be static, you can use the `SpawnComponent.periodRange`
+constructor with the `minPeriod` and `maxPeriod` arguments instead.
+In the following example the component would be spawned randomly within the circle and the time
+between each new spawned component is between 0.5 to 10 seconds.
+
+```dart
+SpawnComponent.periodRange(
+  factory: () => MyComponent(size: Vector2(10, 20)),
+  minPeriod: 0.5,
+  maxPeriod: 10,
+  area: Circle(Vector2(100, 200), 150),
+);
+```
+
+
 ## SvgComponent
 
 **Note**: To use SVG with Flame, use the [`flame_svg`](https://github.com/flame-engine/flame_svg)
diff --git a/doc/flame/examples/lib/drag_events.dart b/doc/flame/examples/lib/drag_events.dart
index 625745fd95..1ae5701c00 100644
--- a/doc/flame/examples/lib/drag_events.dart
+++ b/doc/flame/examples/lib/drag_events.dart
@@ -3,6 +3,7 @@ import 'dart:math';
 import 'package:flame/components.dart';
 import 'package:flame/events.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flutter/rendering.dart';
 
 class DragEventsGame extends FlameGame {
@@ -242,5 +243,3 @@ class Star extends PositionComponent with DragCallbacks {
     position += event.delta;
   }
 }
-
-const tau = 2 * pi;
diff --git a/doc/flame/examples/lib/router.dart b/doc/flame/examples/lib/router.dart
index fd91457b83..bfb854050b 100644
--- a/doc/flame/examples/lib/router.dart
+++ b/doc/flame/examples/lib/router.dart
@@ -2,6 +2,7 @@ import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
 import 'package:flame/events.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame/rendering.dart';
 import 'package:flutter/rendering.dart';
 
@@ -355,7 +356,7 @@ class Orbit extends PositionComponent {
 
   @override
   void update(double dt) {
-    _angle += dt / revolutionPeriod * Transform2D.tau;
+    _angle += dt / revolutionPeriod * tau;
     planet.position = Vector2(radius, 0)..rotate(_angle);
   }
 }
diff --git a/doc/flame/examples/lib/value_route.dart b/doc/flame/examples/lib/value_route.dart
index e34a618fc6..20af955d5a 100644
--- a/doc/flame/examples/lib/value_route.dart
+++ b/doc/flame/examples/lib/value_route.dart
@@ -6,6 +6,7 @@ import 'package:flame/components.dart';
 import 'package:flame/events.dart';
 import 'package:flame/experimental.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 
 class ValueRouteExample extends FlameGame {
   late final RouterComponent router;
@@ -130,5 +131,3 @@ class Star extends PositionComponent with TapCallbacks {
     }
   }
 }
-
-const tau = pi * 2;
diff --git a/examples/lib/stories/camera_and_viewport/camera_component_example.dart b/examples/lib/stories/camera_and_viewport/camera_component_example.dart
index a107bc8044..76f4ae9215 100644
--- a/examples/lib/stories/camera_and_viewport/camera_component_example.dart
+++ b/examples/lib/stories/camera_and_viewport/camera_component_example.dart
@@ -4,6 +4,7 @@ import 'package:flame/camera.dart';
 import 'package:flame/components.dart';
 import 'package:flame/extensions.dart' show OffsetExtension;
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame/input.dart';
 import 'package:flutter/painting.dart';
 
@@ -258,7 +259,6 @@ class Ant extends PositionComponent {
   late final Color color;
   final Random random;
   static const black = Color(0xFF000000);
-  static const tau = Transform2D.tau;
   late final Paint bodyPaint;
   late final Paint eyesPaint;
   late final Paint legsPaint;
diff --git a/examples/lib/stories/components/components.dart b/examples/lib/stories/components/components.dart
index ed0c31c28e..1b7aad0aed 100644
--- a/examples/lib/stories/components/components.dart
+++ b/examples/lib/stories/components/components.dart
@@ -10,6 +10,7 @@ import 'package:examples/stories/components/keys_example.dart';
 import 'package:examples/stories/components/look_at_example.dart';
 import 'package:examples/stories/components/look_at_smooth_example.dart';
 import 'package:examples/stories/components/priority_example.dart';
+import 'package:examples/stories/components/spawn_component_example.dart';
 import 'package:examples/stories/components/time_scale_example.dart';
 import 'package:flame/game.dart';
 
@@ -64,6 +65,14 @@ void addComponentsStories(Dashbook dashbook) {
           baseLink('components/components_notifier_provider_example.dart'),
       info: ComponentsNotifierProviderExampleWidget.description,
     )
+    ..add(
+      'Spawn Component',
+      (_) => const GameWidget.controlled(
+        gameFactory: SpawnComponentExample.new,
+      ),
+      codeLink: baseLink('components/spawn_component_example.dart'),
+      info: SpawnComponentExample.description,
+    )
     ..add(
       'Time Scale',
       (_) => const GameWidget.controlled(
diff --git a/examples/lib/stories/components/spawn_component_example.dart b/examples/lib/stories/components/spawn_component_example.dart
new file mode 100644
index 0000000000..315496b045
--- /dev/null
+++ b/examples/lib/stories/components/spawn_component_example.dart
@@ -0,0 +1,60 @@
+import 'package:examples/commons/ember.dart';
+import 'package:flame/components.dart';
+import 'package:flame/experimental.dart';
+import 'package:flame/extensions.dart';
+import 'package:flame/game.dart';
+import 'package:flame/input.dart';
+import 'package:flame/math.dart';
+
+class SpawnComponentExample extends FlameGame with TapDetector {
+  static String description =
+      'Tap on the screen to start spawning Embers within different shapes.';
+
+  @override
+  void onTapDown(TapDownInfo info) {
+    final shapeType = Shapes.values.random();
+    final Shape shape;
+    final position = info.eventPosition.game;
+    switch (shapeType) {
+      case Shapes.rectangle:
+        shape = Rectangle.fromCenter(
+          center: info.eventPosition.game,
+          size: Vector2.all(200),
+        );
+      case Shapes.circle:
+        shape = Circle(info.eventPosition.game, 150);
+      case Shapes.polygon:
+        shape = Polygon(
+          [
+            Vector2(-1.0, 0.0),
+            Vector2(-0.8, 0.6),
+            Vector2(0.0, 1.0),
+            Vector2(0.6, 0.9),
+            Vector2(1.0, 0.0),
+            Vector2(0.3, -0.2),
+            Vector2(0.0, -1.0),
+            Vector2(-0.8, -0.5),
+          ].map((vertex) {
+            return vertex
+              ..scale(200)
+              ..add(position);
+          }).toList(),
+        );
+    }
+
+    add(
+      SpawnComponent(
+        factory: (_) => Ember(),
+        period: 0.5,
+        area: shape,
+        within: randomFallback.nextBool(),
+      ),
+    );
+  }
+}
+
+enum Shapes {
+  rectangle,
+  circle,
+  polygon,
+}
diff --git a/examples/lib/stories/effects/move_effect_example.dart b/examples/lib/stories/effects/move_effect_example.dart
index 56396968e6..025b603211 100644
--- a/examples/lib/stories/effects/move_effect_example.dart
+++ b/examples/lib/stories/effects/move_effect_example.dart
@@ -3,6 +3,7 @@ import 'dart:math';
 import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame_noise/flame_noise.dart';
 import 'package:flutter/material.dart';
 
@@ -26,7 +27,6 @@ class MoveEffectExample extends FlameGame {
 
   @override
   void onLoad() {
-    const tau = Transform2D.tau;
     cameraComponent = CameraComponent.withFixedResolution(
       world: world,
       width: 400,
diff --git a/examples/lib/stories/effects/rotate_effect_example.dart b/examples/lib/stories/effects/rotate_effect_example.dart
index ce18df38bf..51d32dd6f6 100644
--- a/examples/lib/stories/effects/rotate_effect_example.dart
+++ b/examples/lib/stories/effects/rotate_effect_example.dart
@@ -4,6 +4,7 @@ import 'dart:ui';
 import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flutter/animation.dart';
 
 class RotateEffectExample extends FlameGame {
@@ -45,7 +46,7 @@ class RotateEffectExample extends FlameGame {
     compass.arrow
       ..add(
         RotateEffect.to(
-          Transform2D.tau,
+          tau,
           EffectController(
             duration: 20,
             infinite: true,
@@ -54,7 +55,7 @@ class RotateEffectExample extends FlameGame {
       )
       ..add(
         RotateEffect.by(
-          Transform2D.tau * 0.015,
+          tau * 0.015,
           EffectController(
             duration: 0.1,
             reverseDuration: 0.1,
@@ -64,7 +65,7 @@ class RotateEffectExample extends FlameGame {
       )
       ..add(
         RotateEffect.by(
-          Transform2D.tau * 0.021,
+          tau * 0.021,
           EffectController(
             duration: 0.13,
             reverseDuration: 0.13,
@@ -98,7 +99,7 @@ class Compass extends PositionComponent {
   Future<void> onLoad() async {
     _marksPath = Path();
     for (var i = 0; i < 12; i++) {
-      final angle = Transform2D.tau * (i / 12);
+      final angle = tau * (i / 12);
       // Note: rim takes up 0.1radius, so the lengths must be > than that
       final markLength = (i % 3 == 0) ? _radius * 0.2 : _radius * 0.15;
       _marksPath.moveTo(
@@ -189,7 +190,7 @@ class CompassRim extends PositionComponent {
     final innerRadius = _radius - _width;
     final midRadius = _radius - _width / 3;
     for (var i = 0; i < numberOfNotches; i++) {
-      final angle = Transform2D.tau * (i / numberOfNotches);
+      final angle = tau * (i / numberOfNotches);
       _marksPath.moveTo(
         _radius + innerRadius * sin(angle),
         _radius + innerRadius * cos(angle),
diff --git a/examples/lib/stories/effects/scale_effect_example.dart b/examples/lib/stories/effects/scale_effect_example.dart
index 866fed31c4..3f6921e9f1 100644
--- a/examples/lib/stories/effects/scale_effect_example.dart
+++ b/examples/lib/stories/effects/scale_effect_example.dart
@@ -4,6 +4,7 @@ import 'dart:ui';
 import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame/input.dart';
 import 'package:flame/palette.dart';
 import 'package:flutter/animation.dart';
@@ -76,7 +77,6 @@ class Star extends PositionComponent {
   Star() {
     const smallR = 15.0;
     const bigR = 30.0;
-    const tau = 2 * pi;
     shape = Path()..moveTo(bigR, 0);
     for (var i = 1; i < 10; i++) {
       final r = i.isEven ? bigR : smallR;
diff --git a/examples/lib/stories/effects/sequence_effect_example.dart b/examples/lib/stories/effects/sequence_effect_example.dart
index 5995837cd4..ea3f15e73b 100644
--- a/examples/lib/stories/effects/sequence_effect_example.dart
+++ b/examples/lib/stories/effects/sequence_effect_example.dart
@@ -3,6 +3,7 @@ import 'dart:ui';
 import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 
 class SequenceEffectExample extends FlameGame {
   static const String description = '''
@@ -14,7 +15,6 @@ class SequenceEffectExample extends FlameGame {
 
   @override
   Future<void> onLoad() async {
-    const tau = Transform2D.tau;
     EffectController duration(double x) => EffectController(duration: x);
     add(
       Player()
diff --git a/packages/flame/lib/components.dart b/packages/flame/lib/components.dart
index ecd77d16a7..49855532ba 100644
--- a/packages/flame/lib/components.dart
+++ b/packages/flame/lib/components.dart
@@ -35,6 +35,7 @@ export 'src/components/nine_tile_box_component.dart';
 export 'src/components/parallax_component.dart';
 export 'src/components/particle_system_component.dart';
 export 'src/components/position_component.dart';
+export 'src/components/spawn_component.dart';
 export 'src/components/sprite_animation_component.dart';
 export 'src/components/sprite_animation_group_component.dart';
 export 'src/components/sprite_batch_component.dart';
diff --git a/packages/flame/lib/math.dart b/packages/flame/lib/math.dart
new file mode 100644
index 0000000000..10309074e8
--- /dev/null
+++ b/packages/flame/lib/math.dart
@@ -0,0 +1,3 @@
+export 'src/math/random_fallback.dart';
+export 'src/math/solve_cubic.dart';
+export 'src/math/solve_quadratic.dart';
diff --git a/packages/flame/lib/src/components/spawn_component.dart b/packages/flame/lib/src/components/spawn_component.dart
new file mode 100644
index 0000000000..4c72abaa65
--- /dev/null
+++ b/packages/flame/lib/src/components/spawn_component.dart
@@ -0,0 +1,135 @@
+import 'dart:async';
+import 'dart:math';
+
+import 'package:flame/components.dart';
+import 'package:flame/effects.dart';
+import 'package:flame/experimental.dart';
+import 'package:flame/math.dart';
+
+/// {@template spawn_component}
+/// The [SpawnComponent] is a non-visual component which can spawn
+/// [PositionComponent]s randomly within a set [area]. If [area] is not set it
+/// will use the size of the nearest ancestor that provides a size.
+/// [period] will set the static time interval for when it will spawn new
+/// components.
+/// If you want to use a non static time interval, use the
+/// [SpawnComponent.periodRange] constructor.
+/// {@endremplate}
+class SpawnComponent extends Component {
+  /// {@macro spawn_component}
+  SpawnComponent({
+    required this.factory,
+    required double period,
+    this.area,
+    this.within = true,
+    Random? random,
+    super.key,
+  })  : _period = period,
+        _random = random ?? randomFallback;
+
+  /// Use this constructor if you want your components to spawn within an
+  /// interval time range.
+  /// [minPeriod] will be the minimum amount of time before the next component
+  /// spawns and [maxPeriod] will be the maximum amount of time before it
+  /// spawns.
+  SpawnComponent.periodRange({
+    required this.factory,
+    required double minPeriod,
+    required double maxPeriod,
+    this.area,
+    this.within = true,
+    Random? random,
+    super.key,
+  })  : _period = minPeriod +
+            (random ?? randomFallback).nextDouble() * (maxPeriod - minPeriod),
+        _random = random ?? randomFallback;
+
+  /// The function used to create new components to spawn.
+  ///
+  /// [amount] is the amount of components that the [SpawnComponent] has spawned
+  /// so far.
+  PositionComponent Function(int amount) factory;
+
+  /// The area where the components should be spawned.
+  Shape? area;
+
+  /// Whether the random point should be within the [area] or along its edges.
+  bool within;
+
+  /// The timer that is used to control when components are spawned.
+  late final Timer timer;
+
+  /// The time between each component is spawned.
+  double get period => _period;
+  set period(double newPeriod) {
+    _period = newPeriod;
+    timer.limit = _period;
+  }
+
+  double _period;
+
+  /// The minimum amount of time that has to pass until the next component is
+  /// spawned.
+  double? minPeriod;
+
+  /// The maximum amount of time that has to pass until the next component is
+  /// spawned.
+  double? maxPeriod;
+
+  /// Whether it is spawning components within a random time frame or at a
+  /// static rate.
+  bool get hasRandomPeriod => minPeriod != null;
+
+  final Random _random;
+
+  /// The amount of spawned components.
+  int amount = 0;
+
+  @override
+  FutureOr<void> onLoad() async {
+    if (area == null) {
+      final parentPosition =
+          ancestors().whereType<PositionProvider>().firstOrNull?.position ??
+              Vector2.zero();
+      final parentSize =
+          ancestors().whereType<ReadOnlySizeProvider>().firstOrNull?.size ??
+              Vector2.zero();
+      assert(
+        !parentSize.isZero(),
+        'The SpawnComponent needs an ancestor with a size if area is not '
+        'provided.',
+      );
+      area = Rectangle.fromLTWH(
+        parentPosition.x,
+        parentPosition.y,
+        parentSize.x,
+        parentSize.y,
+      );
+    }
+
+    void updatePeriod() {
+      if (hasRandomPeriod) {
+        period = minPeriod! + _random.nextDouble() * (maxPeriod! - minPeriod!);
+      }
+    }
+
+    updatePeriod();
+
+    final timerComponent = TimerComponent(
+      period: _period,
+      repeat: true,
+      onTick: () {
+        final component = factory(amount);
+        component.position = area!.randomPoint(
+          random: _random,
+          within: within,
+        );
+        parent?.add(component);
+        updatePeriod();
+        amount++;
+      },
+    );
+    timer = timerComponent.timer;
+    add(timerComponent);
+  }
+}
diff --git a/packages/flame/lib/src/effects/controllers/sine_effect_controller.dart b/packages/flame/lib/src/effects/controllers/sine_effect_controller.dart
index ccd0a85982..4b69d7073e 100644
--- a/packages/flame/lib/src/effects/controllers/sine_effect_controller.dart
+++ b/packages/flame/lib/src/effects/controllers/sine_effect_controller.dart
@@ -1,4 +1,5 @@
 import 'dart:math' as math;
+import 'package:flame/geometry.dart';
 import 'package:flame/src/effects/controllers/duration_effect_controller.dart';
 import 'package:flame/src/effects/controllers/infinite_effect_controller.dart';
 import 'package:flame/src/effects/controllers/repeated_effect_controller.dart';
@@ -17,7 +18,6 @@ class SineEffectController extends DurationEffectController {
 
   @override
   double get progress {
-    const tau = math.pi * 2;
     return math.sin(tau * timer / duration);
   }
 }
diff --git a/packages/flame/lib/src/experimental/geometry/shapes/circle.dart b/packages/flame/lib/src/experimental/geometry/shapes/circle.dart
index 1a3e999133..9b7e859162 100644
--- a/packages/flame/lib/src/experimental/geometry/shapes/circle.dart
+++ b/packages/flame/lib/src/experimental/geometry/shapes/circle.dart
@@ -2,9 +2,11 @@ import 'dart:math';
 import 'dart:ui';
 
 import 'package:flame/geometry.dart';
+import 'package:flame/math.dart';
 import 'package:flame/src/experimental/geometry/shapes/shape.dart';
 import 'package:flame/src/extensions/vector2.dart';
 import 'package:flame/src/game/transform2d.dart';
+import 'package:flame/src/math/random_fallback.dart';
 
 /// The circle with a given [center] and a [radius].
 ///
@@ -49,7 +51,11 @@ class Circle extends Shape {
 
   @override
   bool containsPoint(Vector2 point) {
-    return (point - _center).length2 <= _radius * _radius;
+    return (_tmpResult
+              ..setFrom(point)
+              ..sub(_center))
+            .length2 <=
+        _radius * _radius;
   }
 
   @override
@@ -97,6 +103,17 @@ class Circle extends Shape {
       ..add(_center);
   }
 
+  @override
+  Vector2 randomPoint({Random? random, bool within = true}) {
+    final randomGenerator = random ?? randomFallback;
+    final theta = randomGenerator.nextDouble() * tau;
+    final radius = within ? randomGenerator.nextDouble() * _radius : _radius;
+    final x = radius * cos(theta);
+    final y = radius * sin(theta);
+
+    return Vector2(_center.x + x, _center.y + y);
+  }
+
   @override
   String toString() => 'Circle([${_center.x}, ${_center.y}], $_radius)';
 
diff --git a/packages/flame/lib/src/experimental/geometry/shapes/polygon.dart b/packages/flame/lib/src/experimental/geometry/shapes/polygon.dart
index 6d32764437..809788b960 100644
--- a/packages/flame/lib/src/experimental/geometry/shapes/polygon.dart
+++ b/packages/flame/lib/src/experimental/geometry/shapes/polygon.dart
@@ -1,9 +1,12 @@
+import 'dart:math';
 import 'dart:ui';
 
 import 'package:collection/collection.dart';
+import 'package:flame/components.dart';
+import 'package:flame/math.dart';
 import 'package:flame/src/experimental/geometry/shapes/shape.dart';
 import 'package:flame/src/game/transform2d.dart';
-import 'package:vector_math/vector_math_64.dart';
+import 'package:flame/src/math/tmp_vector2.dart';
 
 /// An arbitrary polygon with 3 or more vertices.
 ///
@@ -241,4 +244,62 @@ class Polygon extends Shape {
 
   @override
   String toString() => 'Polygon($vertices)';
+
+  @override
+  Vector2 randomPoint({Random? random, bool within = true}) {
+    final randomGenerator = random ?? randomFallback;
+    if (within) {
+      final result = Vector2.zero();
+      final min = aabb.min;
+      final max = aabb.max;
+
+      while (true) {
+        final randomX = min.x + randomGenerator.nextDouble() * (max.x - min.x);
+        final randomY = min.y + randomGenerator.nextDouble() * (max.y - min.y);
+        result.setValues(randomX, randomY);
+
+        if (containsPoint(result)) {
+          return result;
+        }
+      }
+    } else {
+      return Polygon.randomPointAlongEdges(_vertices, random: randomGenerator);
+    }
+  }
+
+  /// Returns a random point on the [vertices].
+  static Vector2 randomPointAlongEdges(
+    List<Vector2> vertices, {
+    Random? random,
+  }) {
+    final randomGenerator = random ?? randomFallback;
+    final verticesLengths = <double>[];
+    var totalLength = 0.0;
+    for (final (i, startPoint) in vertices.indexed) {
+      final endPoint = vertices[(i + 1) % vertices.length];
+      final length = startPoint.distanceTo(endPoint);
+      verticesLengths.add(length);
+      totalLength += length;
+    }
+    final pointOnEdges = randomGenerator.nextDouble() * totalLength;
+    var vertexIndex = 0;
+    var currentEndPoint = 0.0;
+    late final double localEdgePoint;
+    while (vertexIndex < verticesLengths.length) {
+      final lastEndPoint = currentEndPoint;
+      currentEndPoint += verticesLengths[vertexIndex];
+      if (currentEndPoint >= pointOnEdges) {
+        localEdgePoint = pointOnEdges - lastEndPoint;
+        break;
+      }
+      vertexIndex++;
+    }
+    final startPoint = vertices[vertexIndex];
+    final endPoint = vertices[(vertexIndex + 1) % vertices.length];
+    tmpVector2
+      ..setFrom(endPoint)
+      ..sub(startPoint)
+      ..scaleTo(localEdgePoint);
+    return startPoint + tmpVector2;
+  }
 }
diff --git a/packages/flame/lib/src/experimental/geometry/shapes/rectangle.dart b/packages/flame/lib/src/experimental/geometry/shapes/rectangle.dart
index 41bb076dc7..b390ec5795 100644
--- a/packages/flame/lib/src/experimental/geometry/shapes/rectangle.dart
+++ b/packages/flame/lib/src/experimental/geometry/shapes/rectangle.dart
@@ -1,10 +1,13 @@
 import 'dart:math';
 import 'dart:ui';
 
+import 'package:flame/extensions.dart';
 import 'package:flame/geometry.dart';
+import 'package:flame/src/experimental/geometry/shapes/polygon.dart';
 import 'package:flame/src/experimental/geometry/shapes/shape.dart';
 import 'package:flame/src/game/transform2d.dart';
-import 'package:vector_math/vector_math_64.dart';
+import 'package:flame/src/math/random_fallback.dart';
+import 'package:flutter/cupertino.dart';
 
 /// An axis-aligned rectangle.
 ///
@@ -161,6 +164,19 @@ class Rectangle extends Shape {
     return edges.expand((e) => e.intersections(line)).toSet();
   }
 
+  @override
+  Vector2 randomPoint({Random? random, bool within = true}) {
+    final randomGenerator = random ?? randomFallback;
+    if (within) {
+      return Vector2(
+        left + randomGenerator.nextDouble() * width,
+        top + randomGenerator.nextDouble() * height,
+      );
+    } else {
+      return Polygon.randomPointAlongEdges(vertices, random: randomGenerator);
+    }
+  }
+
   /// The 4 edges of this rectangle, returned in a clockwise fashion.
   List<LineSegment> get edges => [topEdge, rightEdge, bottomEdge, leftEdge];
 
diff --git a/packages/flame/lib/src/experimental/geometry/shapes/rounded_rectangle.dart b/packages/flame/lib/src/experimental/geometry/shapes/rounded_rectangle.dart
index 7af244fb5f..00d652756d 100644
--- a/packages/flame/lib/src/experimental/geometry/shapes/rounded_rectangle.dart
+++ b/packages/flame/lib/src/experimental/geometry/shapes/rounded_rectangle.dart
@@ -1,9 +1,10 @@
 import 'dart:math';
 import 'dart:ui';
 
+import 'package:flame/geometry.dart';
+import 'package:flame/math.dart';
 import 'package:flame/src/experimental/geometry/shapes/shape.dart';
 import 'package:flame/src/game/transform2d.dart';
-import 'package:meta/meta.dart';
 import 'package:vector_math/vector_math_64.dart';
 
 /// An axis-aligned rectangle with rounded corners.
@@ -197,7 +198,27 @@ class RoundedRectangle extends Shape {
   @override
   String toString() =>
       'RoundedRectangle([$_left, $_top], [$_right, $_bottom], $_radius)';
-}
 
-@internal
-const tau = Transform2D.tau; // 2π
+  @override
+  Vector2 randomPoint({Random? random, bool within = true}) {
+    assert(
+      within,
+      'It is not possible to get a point only along the edges of a '
+      'rounded rectangle.',
+    );
+    final randomGenerator = random ?? randomFallback;
+    final result = Vector2.zero();
+    final min = aabb.min;
+    final max = aabb.max;
+
+    while (true) {
+      final randomX = min.x + randomGenerator.nextDouble() * (max.x - min.x);
+      final randomY = min.y + randomGenerator.nextDouble() * (max.y - min.y);
+      result.setValues(randomX, randomY);
+
+      if (containsPoint(result)) {
+        return result;
+      }
+    }
+  }
+}
diff --git a/packages/flame/lib/src/experimental/geometry/shapes/shape.dart b/packages/flame/lib/src/experimental/geometry/shapes/shape.dart
index abaca8fa69..e905e5c998 100644
--- a/packages/flame/lib/src/experimental/geometry/shapes/shape.dart
+++ b/packages/flame/lib/src/experimental/geometry/shapes/shape.dart
@@ -1,3 +1,4 @@
+import 'dart:math';
 import 'dart:ui';
 
 import 'package:flame/src/experimental/geometry/shapes/circle.dart';
@@ -93,4 +94,11 @@ abstract class Shape {
   /// not get ownership of the returned object: they must treat it as an
   /// immutable short-lived object.
   Vector2 nearestPoint(Vector2 point);
+
+  /// Returns a random point within the shape if [within] is true (default) and
+  /// otherwise a point along the edges of the shape.
+  /// Do note that [within]=true also includes the edges.
+  ///
+  /// If [isClosed] is false, the [within] value does not make a difference.
+  Vector2 randomPoint({Random? random, bool within = true});
 }
diff --git a/packages/flame/lib/src/extensions/list.dart b/packages/flame/lib/src/extensions/list.dart
index 9ff1f802d2..2952ff8516 100644
--- a/packages/flame/lib/src/extensions/list.dart
+++ b/packages/flame/lib/src/extensions/list.dart
@@ -1,3 +1,7 @@
+import 'dart:math';
+
+import 'package:flame/math.dart';
+
 extension ListExtension<E> on List<E> {
   /// Reverses the list in-place.
   void reverse() {
@@ -7,4 +11,11 @@ extension ListExtension<E> on List<E> {
       this[j] = temp;
     }
   }
+
+  /// Returns a random element from the list.
+  E random([Random? random]) {
+    assert(isNotEmpty, "Can't get a random element from an empty list");
+    final randomGenerator = random ?? randomFallback;
+    return this[randomGenerator.nextInt(length)];
+  }
 }
diff --git a/packages/flame/lib/src/extensions/rect.dart b/packages/flame/lib/src/extensions/rect.dart
index 462a409058..063a1d3d53 100644
--- a/packages/flame/lib/src/extensions/rect.dart
+++ b/packages/flame/lib/src/extensions/rect.dart
@@ -1,4 +1,4 @@
-import 'dart:math' show min, max;
+import 'dart:math' show Random, max, min;
 import 'dart:math' as math;
 import 'dart:ui';
 
@@ -7,6 +7,7 @@ import 'package:flame/geometry.dart';
 import 'package:flame/src/extensions/matrix4.dart';
 import 'package:flame/src/extensions/offset.dart';
 import 'package:flame/src/extensions/vector2.dart';
+import 'package:flame/src/math/random_fallback.dart';
 
 export 'dart:ui' show Rect;
 
@@ -79,6 +80,15 @@ extension RectExtension on Rect {
     );
   }
 
+  /// Generates a random point within the bounds of this [Rect].
+  Vector2 randomPoint([Random? random]) {
+    final randomGenerator = random ?? randomFallback;
+    return Vector2(
+      left + randomGenerator.nextDouble() * width,
+      top + randomGenerator.nextDouble() * height,
+    );
+  }
+
   /// Creates a [Rect] that represents the bounds of the list [pts].
   static Rect getBounds(List<Vector2> pts) {
     final xPoints = pts.map((e) => e.x);
diff --git a/packages/flame/lib/src/game/transform2d.dart b/packages/flame/lib/src/game/transform2d.dart
index b957d27a47..3d0f868d56 100644
--- a/packages/flame/lib/src/game/transform2d.dart
+++ b/packages/flame/lib/src/game/transform2d.dart
@@ -1,5 +1,6 @@
 import 'dart:math' as math;
 
+import 'package:flame/geometry.dart' as geometry;
 import 'package:flame/src/game/notifying_vector2.dart';
 import 'package:flutter/foundation.dart';
 import 'package:vector_math/vector_math_64.dart';
@@ -34,6 +35,8 @@ class Transform2D extends ChangeNotifier {
   final NotifyingVector2 _position;
   final NotifyingVector2 _scale;
   final NotifyingVector2 _offset;
+  @Deprecated('Use tau from the package:flame/geometry.dart export instead, '
+      'this field will be removed in Flame v1.10.0')
   static const tau = 2 * math.pi;
 
   Transform2D()
@@ -73,9 +76,10 @@ class Transform2D extends ChangeNotifier {
   ///
   /// The [tolerance] parameter is in absolute units, not relative.
   bool closeTo(Transform2D other, {double tolerance = 1e-10}) {
-    final deltaAngle = (angle - other.angle) % tau;
+    final deltaAngle = (angle - other.angle) % geometry.tau;
     assert(deltaAngle >= 0);
-    return (deltaAngle <= tolerance || deltaAngle >= tau - tolerance) &&
+    return (deltaAngle <= tolerance ||
+            deltaAngle >= geometry.tau - tolerance) &&
         (position.x - other.position.x).abs() <= tolerance &&
         (position.y - other.position.y).abs() <= tolerance &&
         (scale.x - other.scale.x).abs() <= tolerance &&
@@ -110,9 +114,9 @@ class Transform2D extends ChangeNotifier {
   }
 
   /// Similar to [angle], but uses degrees instead of radians.
-  double get angleDegrees => _angle * (360 / tau);
+  double get angleDegrees => _angle * (360 / geometry.tau);
   set angleDegrees(double a) {
-    _angle = a * (tau / 360);
+    _angle = a * (geometry.tau / 360);
     _markAsModified();
   }
 
diff --git a/packages/flame/lib/src/geometry/circle_component.dart b/packages/flame/lib/src/geometry/circle_component.dart
index 34d90b5175..1cfb56d76f 100644
--- a/packages/flame/lib/src/geometry/circle_component.dart
+++ b/packages/flame/lib/src/geometry/circle_component.dart
@@ -4,7 +4,7 @@ import 'package:flame/components.dart';
 import 'package:flame/extensions.dart';
 import 'package:flame/geometry.dart';
 import 'package:flame/src/effects/provider_interfaces.dart';
-import 'package:flame/src/utils/solve_quadratic.dart';
+import 'package:flame/src/math/solve_quadratic.dart';
 import 'package:meta/meta.dart';
 
 class CircleComponent extends ShapeComponent implements SizeProvider {
diff --git a/packages/flame/lib/src/math/random_fallback.dart b/packages/flame/lib/src/math/random_fallback.dart
new file mode 100644
index 0000000000..3666100eaf
--- /dev/null
+++ b/packages/flame/lib/src/math/random_fallback.dart
@@ -0,0 +1,5 @@
+import 'dart:math';
+
+/// When you don't care about what [Random] object you have and don't want to
+/// create an unnecessary object you can use this pre-created object.
+final Random randomFallback = Random();
diff --git a/packages/flame/lib/src/utils/solve_cubic.dart b/packages/flame/lib/src/math/solve_cubic.dart
similarity index 95%
rename from packages/flame/lib/src/utils/solve_cubic.dart
rename to packages/flame/lib/src/math/solve_cubic.dart
index 6d40bdd970..9cc332f889 100644
--- a/packages/flame/lib/src/utils/solve_cubic.dart
+++ b/packages/flame/lib/src/math/solve_cubic.dart
@@ -1,6 +1,7 @@
 import 'dart:math';
 
-import 'package:flame/src/utils/solve_quadratic.dart';
+import 'package:flame/geometry.dart';
+import 'package:flame/src/math/solve_quadratic.dart';
 
 /// Solves cubic equation `ax³ + bx² + cx + d == 0`.
 ///
@@ -56,4 +57,3 @@ double _cubicRoot(double x) {
 }
 
 const discriminantEpsilon = 1e-15;
-const tau = 2 * pi;
diff --git a/packages/flame/lib/src/utils/solve_quadratic.dart b/packages/flame/lib/src/math/solve_quadratic.dart
similarity index 100%
rename from packages/flame/lib/src/utils/solve_quadratic.dart
rename to packages/flame/lib/src/math/solve_quadratic.dart
diff --git a/packages/flame/lib/src/math/tmp_vector2.dart b/packages/flame/lib/src/math/tmp_vector2.dart
new file mode 100644
index 0000000000..d3d112550d
--- /dev/null
+++ b/packages/flame/lib/src/math/tmp_vector2.dart
@@ -0,0 +1,7 @@
+import 'package:meta/meta.dart';
+import 'package:vector_math/vector_math_64.dart';
+
+/// Use internally when you need a temporary [Vector2] object but don't want to
+/// instantiate a new one due to performance.
+@internal
+final Vector2 tmpVector2 = Vector2.zero();
diff --git a/packages/flame/lib/src/rendering/rotate3d_decorator.dart b/packages/flame/lib/src/rendering/rotate3d_decorator.dart
index bba660fa9c..83e0030aa7 100644
--- a/packages/flame/lib/src/rendering/rotate3d_decorator.dart
+++ b/packages/flame/lib/src/rendering/rotate3d_decorator.dart
@@ -1,6 +1,6 @@
-import 'dart:math';
 import 'dart:ui';
 
+import 'package:flame/geometry.dart';
 import 'package:flame/src/rendering/decorator.dart';
 import 'package:vector_math/vector_math_64.dart';
 
@@ -46,7 +46,6 @@ class Rotate3DDecorator extends Decorator {
   /// "back" side is shows if the component is rotated 180º degree around either
   /// the X or Y axis.
   bool get isFlipped {
-    const tau = 2 * pi;
     final phaseX = (angleX / tau - 0.25) % 1.0;
     final phaseY = (angleY / tau - 0.25) % 1.0;
     return (phaseX > 0.5) ^ (phaseY > 0.5);
diff --git a/packages/flame/lib/util.dart b/packages/flame/lib/util.dart
new file mode 100644
index 0000000000..717d52013d
--- /dev/null
+++ b/packages/flame/lib/util.dart
@@ -0,0 +1,6 @@
+@Deprecated(
+  'Import math.dart instead, this file will be removed in a Flame v1.10.0',
+)
+export 'src/math/random_fallback.dart';
+export 'src/math/solve_cubic.dart';
+export 'src/math/solve_quadratic.dart';
diff --git a/packages/flame/test/components/position_component_test.dart b/packages/flame/test/components/position_component_test.dart
index a9324b7b7d..38d3e072c4 100644
--- a/packages/flame/test/components/position_component_test.dart
+++ b/packages/flame/test/components/position_component_test.dart
@@ -5,6 +5,7 @@ import 'package:canvas_test/canvas_test.dart';
 import 'package:flame/collisions.dart';
 import 'package:flame/components.dart';
 import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame_test/flame_test.dart';
 import 'package:test/test.dart';
 
@@ -1001,7 +1002,7 @@ void main() {
         const h = 2.0;
         final component = PositionComponent(size: Vector2(w, h));
         for (var i = 0; i < 10; i++) {
-          final a = (i / 10) * Transform2D.tau / 4;
+          final a = (i / 10) * tau / 4;
           component.angle = a;
           expect(
             component.toRect(),
diff --git a/packages/flame/test/components/spawn_component_test.dart b/packages/flame/test/components/spawn_component_test.dart
new file mode 100644
index 0000000000..3f44f98696
--- /dev/null
+++ b/packages/flame/test/components/spawn_component_test.dart
@@ -0,0 +1,111 @@
+import 'dart:math';
+
+import 'package:flame/components.dart';
+import 'package:flame/experimental.dart';
+import 'package:flame_test/flame_test.dart';
+import 'package:test/test.dart';
+
+void main() {
+  group('SpawnComponent', () {
+    testWithFlameGame('Spawns components within rectangle', (game) async {
+      final random = Random(0);
+      final shape = Rectangle.fromCenter(
+        center: Vector2(100, 200),
+        size: Vector2.all(200),
+      );
+      final spawn = SpawnComponent(
+        factory: (_) => PositionComponent(),
+        period: 1,
+        area: shape,
+        random: random,
+      );
+      await game.ensureAdd(spawn);
+      game.update(0.5);
+      expect(game.children.length, 1);
+      game.update(0.5);
+      game.update(0.0);
+      expect(game.children.length, 2);
+      game.update(1.0);
+      game.update(0.0);
+      expect(game.children.length, 3);
+
+      for (var i = 0; i < 1000; i++) {
+        game.update(random.nextDouble());
+      }
+      expect(
+        game.children
+            .query<PositionComponent>()
+            .every((c) => shape.containsPoint(c.position)),
+        isTrue,
+      );
+    });
+
+    testWithFlameGame('Spawns components within circle', (game) async {
+      final random = Random(0);
+      final shape = Circle(Vector2(100, 200), 100);
+      expect(shape.containsPoint(Vector2.all(200)), isTrue);
+      final spawn = SpawnComponent(
+        factory: (_) => PositionComponent(),
+        period: 1,
+        area: shape,
+        random: random,
+      );
+      await game.ensureAdd(spawn);
+      game.update(0.5);
+      expect(game.children.length, 1);
+      game.update(0.5);
+      game.update(0.0);
+      expect(game.children.length, 2);
+      game.update(1.0);
+      game.update(0.0);
+      expect(game.children.length, 3);
+
+      for (var i = 0; i < 1000; i++) {
+        game.update(random.nextDouble());
+      }
+      expect(
+        game.children
+            .query<PositionComponent>()
+            .every((c) => shape.containsPoint(c.position)),
+        isTrue,
+      );
+    });
+
+    testWithFlameGame('Spawns components within polygon', (game) async {
+      final random = Random(0);
+      final shape = Polygon(
+        [
+          Vector2(100, 100),
+          Vector2(200, 100),
+          Vector2(150, 200),
+        ],
+      );
+      expect(shape.containsPoint(Vector2.all(150)), isTrue);
+      final spawn = SpawnComponent(
+        factory: (_) => PositionComponent(),
+        period: 1,
+        area: shape,
+        random: random,
+      );
+      await game.ensureAdd(spawn);
+      game.update(0.5);
+      expect(game.children.length, 1);
+      game.update(0.5);
+      game.update(0.0);
+      expect(game.children.length, 2);
+      game.update(1.0);
+      game.update(0.0);
+      expect(game.children.length, 3);
+
+      for (var i = 0; i < 1000; i++) {
+        game.update(random.nextDouble());
+      }
+      expect(
+        game.children
+            .query<PositionComponent>()
+            .every((c) => shape.containsPoint(c.position)),
+        isTrue,
+      );
+    });
+  });
+}
diff --git a/packages/flame/test/effects/controllers/speed_effect_controller_test.dart b/packages/flame/test/effects/controllers/speed_effect_controller_test.dart
index 100562634b..55b9d3c35a 100644
--- a/packages/flame/test/effects/controllers/speed_effect_controller_test.dart
+++ b/packages/flame/test/effects/controllers/speed_effect_controller_test.dart
@@ -2,7 +2,7 @@ import 'dart:ui';
 
 import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
-import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame/src/effects/measurable_effect.dart';
 import 'package:flame_test/flame_test.dart';
 import 'package:flutter_test/flutter_test.dart';
@@ -91,7 +91,6 @@ void main() {
       });
 
       testWithFlameGame('speed on RotateEffect', (game) async {
-        const tau = Transform2D.tau;
         final effect = RotateEffect.to(tau, EffectController(speed: 1));
         final component = PositionComponent(position: Vector2(5, 8));
         component.add(effect);
diff --git a/packages/flame/test/effects/move_along_path_effect_test.dart b/packages/flame/test/effects/move_along_path_effect_test.dart
index c46b5a0612..9927f23e02 100644
--- a/packages/flame/test/effects/move_along_path_effect_test.dart
+++ b/packages/flame/test/effects/move_along_path_effect_test.dart
@@ -3,14 +3,13 @@ import 'dart:ui';
 
 import 'package:flame/components.dart';
 import 'package:flame/effects.dart';
-import 'package:flame/game.dart';
+import 'package:flame/geometry.dart';
 import 'package:flame_test/flame_test.dart';
 import 'package:flutter_test/flutter_test.dart';
 
 void main() {
   group('MoveAlongPathEffect', () {
     testWithFlameGame('relative path', (game) async {
-      const tau = Transform2D.tau;
       const x0 = 32.5;
       const y0 = 14.88;
       final component = PositionComponent(position: Vector2(x0, y0));
diff --git a/packages/flame/test/extensions/list_test.dart b/packages/flame/test/extensions/list_test.dart
new file mode 100644
index 0000000000..310d7e6ed4
--- /dev/null
+++ b/packages/flame/test/extensions/list_test.dart
@@ -0,0 +1,26 @@
+import 'dart:math';
+
+import 'package:flame/extensions.dart';
+import 'package:test/test.dart';
+
+void main() {
+  group('ListExtension', () {
+    test('reverse', () {
+      final list = [1, 3, 3, 7];
+      list.reverse();
+      expect(list, [7, 3, 3, 1]);
+      list.insert(1, 4);
+      list.reverse();
+      expect(list, [1, 3, 3, 4, 7]);
+    });
+
+    test('random', () {
+      final list = [1, 3, 3, 7];
+      final random = Random(0);
+      final element1 = list.random(random);
+      expect(element1, 7);
+      final element2 = list.random(random);
+      expect(element2, 3);
+    });
+  });
+}
diff --git a/packages/flame/test/game/transform2d_test.dart b/packages/flame/test/game/transform2d_test.dart
index d68ab15a82..bfc5e5f660 100644
--- a/packages/flame/test/game/transform2d_test.dart
+++ b/packages/flame/test/game/transform2d_test.dart
@@ -1,5 +1,6 @@
 import 'dart:math' as math;
 
+import 'package:flame/geometry.dart';
 import 'package:flame/src/game/transform2d.dart';
 import 'package:test/test.dart';
 import 'package:vector_math/vector_math_64.dart';
@@ -90,7 +91,6 @@ void main() {
     });
 
     test('angle', () {
-      const tau = Transform2D.tau;
       final t = Transform2D();
       t.angle = tau / 6;
       expect(t.angleDegrees, closeTo(60, 1e-10));
diff --git a/packages/flame/test/utils/recycled_queue_test.dart b/packages/flame/test/math/recycled_queue_test.dart
similarity index 100%
rename from packages/flame/test/utils/recycled_queue_test.dart
rename to packages/flame/test/math/recycled_queue_test.dart
diff --git a/packages/flame/test/utils/solve_cubic_test.dart b/packages/flame/test/math/solve_cubic_test.dart
similarity index 98%
rename from packages/flame/test/utils/solve_cubic_test.dart
rename to packages/flame/test/math/solve_cubic_test.dart
index b4a72e5bda..47e7802fc4 100644
--- a/packages/flame/test/utils/solve_cubic_test.dart
+++ b/packages/flame/test/math/solve_cubic_test.dart
@@ -1,4 +1,4 @@
-import 'package:flame/src/utils/solve_cubic.dart';
+import 'package:flame/math.dart';
 import 'package:flame_test/flame_test.dart';
 import 'package:test/test.dart';
 
diff --git a/packages/flame/test/utils/solve_quadratic_test.dart b/packages/flame/test/math/solve_quadratic_test.dart
similarity index 97%
rename from packages/flame/test/utils/solve_quadratic_test.dart
rename to packages/flame/test/math/solve_quadratic_test.dart
index 15f607b9f2..9e39569b56 100644
--- a/packages/flame/test/utils/solve_quadratic_test.dart
+++ b/packages/flame/test/math/solve_quadratic_test.dart
@@ -1,6 +1,6 @@
 import 'dart:math';
 
-import 'package:flame/src/utils/solve_quadratic.dart';
+import 'package:flame/math.dart';
 import 'package:flame_test/flame_test.dart';
 import 'package:test/test.dart';