feat: create ellipses from geometry

lib/game/components/pathway.dart

@@ -144,6 +144,47 @@ class Pathway extends BodyComponent with InitialPosition, Layered {
     );
   }
 
+  /// Creates an ellipse [Pathway].
+  ///
+  /// Does so with two [ChainShape] separated by a [width]. Can
+  /// be rotated by a given [rotation] in radians.
+  ///
+  /// If [singleWall] is true, just one [ChainShape] is created.
+  factory Pathway.ellipse({
+    Color? color,
+    required Vector2 center,
+    required double width,
+    required double bigRadius,
+    required double smallRadius,
+    required double angle,
+    double rotation = 0,
+    bool singleWall = false,
+  }) {
+    final paths = <List<Vector2>>[];
+
+    // TODO(ruialonso): Refactor repetitive logic
+    final outerWall = calculateEllipse(
+      center: center,
+      bigRadius: bigRadius,
+      smallRadius: smallRadius,
+    ).map((vector) => vector..rotate(rotation)).toList();
+    paths.add(outerWall);
+
+    if (!singleWall) {
+      final innerWall = calculateEllipse(
+        center: center,
+        bigRadius: bigRadius - width,
+        smallRadius: smallRadius - width,
+      ).map((vector) => vector..rotate(rotation)).toList();
+      paths.add(innerWall);
+    }
+
+    return Pathway._(
+      color: color,
+      paths: paths,
+    );
+  }
+
   final List<List<Vector2>> _paths;
 
   /// Constructs different [ChainShape]s to form the [Pathway] shape.

lib/game/pinball_game.dart

@@ -1,5 +1,5 @@
 // ignore_for_file: public_member_api_docs
-
+import 'dart:math' as math;
 import 'dart:async';
 import 'package:flame/extensions.dart';
 import 'package:flame/input.dart';

packages/geometry/lib/src/geometry.dart

@@ -33,6 +33,43 @@ List<Vector2> calculateArc({
   return points;
 }
 
+/// Calculates all [Vector2]s of an ellipse.
+///
+/// An ellipse can be achieved by specifying a [center], a [bigRadius] and a
+/// [smallRadius].
+/// In addition, a semi-ellipse can be achieved by specifying its [angle] and an
+/// [offsetAngle] (both in radians).
+///
+/// The higher the [precision], the more [Vector2]s will be calculated;
+/// achieving a more rounded ellipse.
+///
+/// For more information read: https://en.wikipedia.org/wiki/Ellipse.
+List<Vector2> calculateEllipse({
+  required Vector2 center,
+  required double bigRadius,
+  required double smallRadius,
+  int precision = 100,
+}) {
+  assert(
+    0 < smallRadius && smallRadius <= bigRadius,
+    'smallRadius ($smallRadius) and bigRadius ($bigRadius) must be in '
+    'range 0 < smallRadius <= bigRadius',
+  );
+
+  final stepAngle = 2 * math.pi / (precision - 1);
+
+  final points = <Vector2>[];
+  for (var i = 0; i < precision; i++) {
+    final xCoord = center.x + smallRadius * math.cos(stepAngle * i);
+    final yCoord = center.y - bigRadius * math.sin(stepAngle * i);
+
+    final point = Vector2(xCoord, yCoord);
+    points.add(point);
+  }
+
+  return points;
+}
+
 /// Calculates all [Vector2]s of a bezier curve.
 ///
 /// A bezier curve of [controlPoints] that say how to create this curve.