fix(splash): 배경 아이콘 겹침 최소화

lib/presentation/pages/splash/splash_screen.dart

@@ -19,6 +19,8 @@ class _SplashScreenState extends State<SplashScreen>
   late List<AnimationController> _foodControllers;
   late AnimationController _questionMarkController;
   late AnimationController _centerIconController;
+  List<Offset>? _iconPositions;
+  Size? _lastScreenSize;
 
   final List<IconData> foodIcons = [
     Icons.rice_bowl,
@@ -62,6 +64,64 @@ class _SplashScreenState extends State<SplashScreen>
     )..repeat(reverse: true);
   }
 
+  List<Offset> _generateIconPositions(Size screenSize) {
+    final random = math.Random();
+    const iconSize = 40.0;
+    const maxScale = 1.5;
+    const margin = iconSize * maxScale;
+    const overlapThreshold = 0.3;
+    final effectiveSize = iconSize * maxScale;
+    final center = Offset(screenSize.width / 2, screenSize.height / 2);
+    final centerSafeRadius =
+        math.min(screenSize.width, screenSize.height) * 0.18;
+
+    Offset randomPosition() {
+      final x =
+          margin +
+          random.nextDouble() * (screenSize.width - margin * 2).clamp(1, 9999);
+      final y =
+          margin +
+          random.nextDouble() * (screenSize.height - margin * 2).clamp(1, 9999);
+      return Offset(x, y);
+    }
+
+    final positions = <Offset>[];
+    var attempts = 0;
+    const maxAttempts = 500;
+
+    while (positions.length < foodIcons.length && attempts < maxAttempts) {
+      attempts++;
+      final candidate = randomPosition();
+      if ((candidate - center).distance < centerSafeRadius) {
+        continue;
+      }
+      final hasHeavyOverlap = positions.any(
+        (p) => _isOverlapTooHigh(p, candidate, effectiveSize, overlapThreshold),
+      );
+      if (hasHeavyOverlap) {
+        continue;
+      }
+      positions.add(candidate);
+    }
+
+    while (positions.length < foodIcons.length) {
+      positions.add(randomPosition());
+    }
+
+    return positions;
+  }
+
+  bool _isOverlapTooHigh(Offset a, Offset b, double size, double maxRatio) {
+    final dx = (a.dx - b.dx).abs();
+    final dy = (a.dy - b.dy).abs();
+    final overlapX = math.max(0.0, size - dx);
+    final overlapY = math.max(0.0, size - dy);
+    final overlapArea = overlapX * overlapY;
+    final maxArea = size * size;
+    if (maxArea == 0) return false;
+    return overlapArea / maxArea > maxRatio;
+  }
+
   @override
   Widget build(BuildContext context) {
     final isDark = Theme.of(context).brightness == Brightness.dark;
@@ -145,15 +205,22 @@ class _SplashScreenState extends State<SplashScreen>
   }
 
   List<Widget> _buildFoodIcons() {
-    final random = math.Random();
+    final screenSize = MediaQuery.of(context).size;
+    final sameSize =
+        _lastScreenSize != null &&
+        (_lastScreenSize!.width - screenSize.width).abs() < 1 &&
+        (_lastScreenSize!.height - screenSize.height).abs() < 1;
+    if (_iconPositions == null || !sameSize) {
+      _iconPositions = _generateIconPositions(screenSize);
+      _lastScreenSize = screenSize;
+    }
 
     return List.generate(foodIcons.length, (index) {
-      final left = random.nextDouble() * 0.8 + 0.1;
+      final position = _iconPositions![index];
-      final top = random.nextDouble() * 0.7 + 0.1;
 
       return Positioned(
-        left: MediaQuery.of(context).size.width * left,
+        left: position.dx,
-        top: MediaQuery.of(context).size.height * top,
+        top: position.dy,
         child: FadeTransition(
           opacity: Tween(begin: 0.2, end: 0.8).animate(
             CurvedAnimation(