Grahpics overhaul and predicting bullets

Scripts/Utils/MathFunctions.cs

@@ -0,0 +1,32 @@
+using Godot;
+
+namespace Cirno.Scripts.Utils;
+
+public static class MathFunctions
+{
+    public static Vector2? PredictInterceptPosition(Vector2 shooterPos, Vector2 targetPos, Vector2 targetVel, float projectileSpeed)
+    {
+        Vector2 displacement = targetPos - shooterPos;
+        float a = targetVel.LengthSquared() - projectileSpeed * projectileSpeed;
+        float b = 2 * displacement.Dot(targetVel);
+        float c = displacement.LengthSquared();
+
+        float discriminant = b * b - 4 * a * c;
+
+        if (discriminant < 0 || Mathf.Abs(a) < 0.001f)
+            return null; // No solution or projectile too slow
+
+        float sqrtDisc = Mathf.Sqrt(discriminant);
+        float t1 = (-b - sqrtDisc) / (2 * a);
+        float t2 = (-b + sqrtDisc) / (2 * a);
+
+        float t = Mathf.Min(t1, t2);
+        if (t < 0)
+            t = Mathf.Max(t1, t2);
+
+        if (t < 0)
+            return null; // No valid positive time
+
+        return targetPos + targetVel * t;
+    }
+}