C# 二维平面运动引擎

C# 二维平面运动引擎主要用于实现游戏中物体在平面上的运动、碰撞检测、物理效果等功能。以下是一个简单的二维平面运动引擎示例：

public class Vector2D
{
    public float X { get; set; }
    public float Y { get; set; }

    public Vector2D(float x, float y)
    {
        X = x;
        Y = y;
    }

    public static Vector2D operator +(Vector2D a, Vector2D b)
    {
        return new Vector2D(a.X + b.X, a.Y + b.Y);
    }

    public static Vector2D operator -(Vector2D a, Vector2D b)
    {
        return new Vector2D(a.X - b.X, a.Y - b.Y);
    }

    public static Vector2D operator *(Vector2D a, float scalar)
    {
        return new Vector2D(a.X * scalar, a.Y * scalar);
    }

    public static Vector2D operator /(Vector2D a, float scalar)
    {
        return new Vector2D(a.X / scalar, a.Y / scalar);
    }

    public float Length()
    {
        return (float)Math.Sqrt(X * X + Y * Y);
    }

    public Vector2D Normalize()
    {
        float length = Length();
        return new Vector2D(X / length, Y / length);
    }

    public float Dot(Vector2D other)
    {
        return X * other.X + Y * other.Y;
    }

    public float Cross(Vector2D other)
    {
        return X * other.Y - Y * other.X;
    }
}

public class GameObject
{
    public Vector2D Position { get; set; }
    public Vector2D Velocity { get; set; }
    public float Mass { get; set; }
    public float Radius { get; set; }

    public void Update(float deltaTime)
    {
        Position += Velocity * deltaTime;
    }

    public bool IsColliding(GameObject other)
    {
        float distance = (Position - other.Position).Length();
        return distance < Radius + other.Radius;
    }

    public void ResolveCollision(GameObject other)
    {
        Vector2D normal = (other.Position - Position).Normalize();
        Vector2D relativeVelocity = other.Velocity - Velocity;
        float impulse = -2 * relativeVelocity.Dot(normal) / (Mass + other.Mass);
        Velocity -= impulse * other.Mass * normal;
        other.Velocity += impulse * Mass * normal;
    }
}

public class PhysicsEngine
{
    private List<GameObject> objects = new List<GameObject>();

    public void AddObject(GameObject obj)
    {
        objects.Add(obj);
    }

    public void RemoveObject(GameObject obj)
    {
        objects.Remove(obj);
    }

    public void Update(float deltaTime)
    {
        for (int i = 0; i < objects.Count; i++)
        {
            objects[i].Update(deltaTime);
        }

        for (int i = 0; i < objects.Count; i++)
        {
            for (int j = i + 1; j < objects.Count; j++)
            {
                if (objects[i].IsColliding(objects[j]))
                {
                    objects[i].ResolveCollision(objects[j]);
                }
            }
        }
    }
}

这个引擎包含了三个类：`Vector2D`、`GameObject` 和 `PhysicsEngine`。`Vector2D` 类表示平面上的二维向量，包含了向量加、减、乘、除、求长度、归一化、点积、叉积等基本操作。`GameObject` 类表示游戏中的物体，包含了位置、速度、质量、半径等属性，以及更新、碰撞检测、碰撞响应等方法。`PhysicsEngine` 类表示物理引擎，包含了游戏中所有物体的列表，以及更新物体位置、检测碰撞、响应碰撞等方法。

使用时，可以先创建一个物理引擎实例，然后向其中添加物体，每帧调用引擎的 `Update` 方法更新物体位置、检测碰撞、响应碰撞等操作。例如：

PhysicsEngine engine = new PhysicsEngine();

GameObject ball1 = new GameObject();
ball1.Position = new Vector2D(100, 100);
ball1.Velocity = new Vector2D(50, 0);
ball1.Mass = 1;
ball1.Radius = 10;

GameObject ball2 = new GameObject();
ball2.Position = new Vector2D(200, 100);
ball2.Velocity = new Vector2D(-50, 0);
ball2.Mass = 1;
ball2.Radius = 10;

engine.AddObject(ball1);
engine.AddObject(ball2);

while (true)
{
    engine.Update(0.01f);
    // 渲染物体...
}

这个示例创建了两个球体，分别从左右两侧向中间运动，当两个球体碰撞时会发生弹性碰撞并反弹。