feat: Add vector projection and inversion (#1787)

Adding projection, ìnvert and inverted to the vector extension.

packages/flame/lib/src/extensions/vector2.dart

@@ -80,6 +80,26 @@ extension Vector2Extension on Vector2 {
     }
   }
 
+  /// Project this onto [other].
+  ///
+  /// [other] needs to have a length > 0;
+  /// If [out] is specified, it will be used to provide the result.
+  Vector2 projection(Vector2 other, {Vector2? out}) {
+    assert(other.length2 > 0, 'other needs to have a length > 0');
+    final dotProduct = dot(other);
+    final result = (out?..setFrom(other)) ?? other.clone();
+    return result..scale(dotProduct / other.length2);
+  }
+
+  /// Inverts the vector.
+  void invert() {
+    x *= -1;
+    y *= -1;
+  }
+
+  /// Returns the inverse of this vector.
+  Vector2 inverted() => Vector2(-x, -y);
+
   /// Smoothly moves this [Vector2] in the direction [target] by a displacement
   /// given by a distance [ds] in that direction.
   ///

packages/flame/test/extensions/vector2_test.dart

@@ -208,4 +208,59 @@ void main() {
       expectDouble(position.screenAngle(), math.pi / 2);
     });
   });
+
+  group('projection', () {
+    test('Project onto longer vector', () {
+      final u = Vector2(5, 2);
+      final v = Vector2(10, 0);
+      final result = u.projection(v);
+      expect(result, Vector2(5, 0));
+    });
+
+    test('Project onto shorter vector', () {
+      final u = Vector2(5, 2);
+      final v = Vector2(2, 0);
+      final result = u.projection(v);
+      expect(result, Vector2(5, 0));
+    });
+
+    test('Project onto vector in other direction', () {
+      final u = Vector2(5, 2);
+      final v = Vector2(-10, 0);
+      final result = u.projection(v);
+      expect(result, Vector2(5, 0));
+    });
+
+    test('Project onto vector with out', () {
+      final out = Vector2.zero();
+      final u = Vector2(5, 2);
+      final v = Vector2(-10, 0);
+      final result = u.projection(v, out: out);
+      expect(result, Vector2(5, 0));
+      expect(out, Vector2(5, 0));
+    });
+
+    test('Project onto vector with out as sane return and argument', () {
+      var out = Vector2.zero();
+      final u = Vector2(5, 2);
+      final v = Vector2(-10, 0);
+      out = u.projection(v, out: out);
+      expect(out, Vector2(5, 0));
+    });
+  });
+
+  group('inversion', () {
+    test('invert', () {
+      final v = Vector2.all(1);
+      v.invert();
+      expect(v, Vector2.all(-1));
+    });
+
+    test('inverted', () {
+      final v = Vector2.all(1);
+      final w = v.inverted();
+      expect(v, Vector2.all(1));
+      expect(w, Vector2.all(-1));
+    });
+  });
 }