c# - 如何解决与不可移动物体的二维碰撞？

Question

我正在创建一个 2D 物理引擎，但我在处理可移动和不可移动物体之间的某种类型的碰撞时遇到了问题。我所说的可移动的意思是 (x,y) 值可以改变，而不是参照系可以改变或不能改变。

例如，球撞到墙上就是可移动的物体与不可移动的物体发生碰撞。

我相信在这种情况下我需要使用法向力之类的东西，但我不确定如何使用它来找到碰撞的结果。

这是我目前的代码。这段代码用于两个移动实体之间的碰撞，但我需要为一个不移动的实体添加一个案例:

private static void UpdateEntities(PhysicsEntity a, PhysicsEntity b)
    {
        var collisionAngle = Math.Atan2(a.Position.Y - b.Position.Y, a.Position.X - b.Position.X);
        var angleA = a.Velocity.Direction - collisionAngle;
        var angleB = b.Velocity.Direction - collisionAngle;

        var vAx = a.Velocity.Magnitude * Math.Cos(angleA);
        var vAy = a.Velocity.Magnitude * Math.Sin(angleA);
        var vBx = b.Velocity.Magnitude * Math.Cos(angleB);
        var vBy = b.Velocity.Magnitude * Math.Sin(angleB);

        var vfAx = ((vAx * (a.Mass - b.Mass) + 2 * b.Mass * vBx) / (a.Mass + b.Mass)) * a.Material.Elasticity;
        var vfBx = ((vBx * (b.Mass - a.Mass) + 2 * a.Mass * vAx) / (a.Mass + b.Mass)) * b.Material.Elasticity;
        var vfAy = vAy * a.Material.Elasticity;
        var vfBy = vBy * b.Material.Elasticity;

        var magA = Math.Sqrt(Math.Pow(vfAx, 2) + Math.Pow(vfAy, 2));
        var magB = Math.Sqrt(Math.Pow(vfBx, 2) + Math.Pow(vfBy, 2));
        var dirA = Math.Atan2(vfAy, vfAx) + collisionAngle;
        var dirB = Math.Atan2(vfBy, vfBx) + collisionAngle;

        a.Velocity.X = magA * Math.Cos(dirA);
        a.Velocity.Y = magA * Math.Sin(dirA);
        b.Velocity.X = magB * Math.Cos(dirB);
        b.Velocity.Y = magB * Math.Sin(dirB);

    }

我尝试将不可移动物体的速度设置为与可移动物体的速度相反，但这会导致物体相互相位。

Answer 1

我从一个 friend 那里得到了帮助，我们制定了这个算法，让物体在碰撞过程中从不动的物体上反射出来。

修改后的原始函数:

private static void UpdateEntities(PhysicsEntity a, PhysicsEntity b)
    {
        var collisionAngle = Math.Atan2(a.Position.Y - b.Position.Y, a.Position.X - b.Position.X);

        if (a.IsMoveable && b.IsMoveable)
        {
            var angleA = a.Velocity.Direction - collisionAngle;
            var angleB = b.Velocity.Direction - collisionAngle;

            var vAx = a.Velocity.Magnitude * Math.Cos(angleA);
            var vAy = a.Velocity.Magnitude * Math.Sin(angleA);
            var vBx = b.Velocity.Magnitude * Math.Cos(angleB);
            var vBy = b.Velocity.Magnitude * Math.Sin(angleB);

            var vfAx = ((vAx * (a.Mass - b.Mass) + 2 * b.Mass * vBx) / (a.Mass + b.Mass)) * a.Material.Elasticity;
            var vfBx = ((vBx * (b.Mass - a.Mass) + 2 * a.Mass * vAx) / (a.Mass + b.Mass)) * b.Material.Elasticity;
            var vfAy = vAy * a.Material.Elasticity;
            var vfBy = vBy * b.Material.Elasticity;

            var magA = Math.Sqrt(Math.Pow(vfAx, 2) + Math.Pow(vfAy, 2));
            var magB = Math.Sqrt(Math.Pow(vfBx, 2) + Math.Pow(vfBy, 2));
            var dirA = Math.Atan2(vfAy, vfAx) + collisionAngle;
            var dirB = Math.Atan2(vfBy, vfBx) + collisionAngle;

            a.Velocity.X = magA * Math.Cos(dirA);
            a.Velocity.Y = magA * Math.Sin(dirA);
            b.Velocity.X = magB * Math.Cos(dirB);
            b.Velocity.Y = magB * Math.Sin(dirB);
        }
        else
        {
            var sign = Math.Sign(collisionAngle);
            collisionAngle *= sign;
            while (collisionAngle > Math.PI/2)
            {
                collisionAngle -= Math.PI / 2;
            }
            collisionAngle *= sign;
            if (a.IsMoveable)
            {
                Reflection(ref a, b, collisionAngle);
            }
            else
            {
                Reflection(ref b, a, collisionAngle);
            }
        }
    }

反射函数:

        private static void Reflection(ref PhysicsEntity movable, PhysicsEntity immovable, double collisionAngle)
    {
        if (Math.Abs(collisionAngle - Math.PI / 2) < Universe.Epsilon)
        {
            // take the velocity vector, rotate it 180 degrees, scale it
            movable.Velocity.X *= -1;
            movable.Velocity.Y *= -1;
        }
        else if (Math.Abs(movable.Position.Y - immovable.Position.Y) < Universe.Epsilon ||
                 (movable.Position.X > movable.CollisionPoint.X ^ movable.Position.Y < movable.CollisionPoint.Y))
        {
            //take velocity vector, rotate CCW by 2*collisionAngle, scale it
            var rotateAngle = 2 * collisionAngle;
            var xPrime = movable.Velocity.X * Math.Cos(rotateAngle) - movable.Velocity.Y * Math.Sin(rotateAngle);
            var yPrime = movable.Velocity.Y * Math.Cos(rotateAngle) - movable.Velocity.X * Math.Sin(rotateAngle);
            movable.Velocity.X = xPrime;
            movable.Velocity.Y = yPrime;
        }
        else
        {
            //take the vector, rotate it CCW by 360-2*collisionAngle, scale it
            var rotateAngle = 2 * (Math.PI - collisionAngle);
            var xPrime = movable.Velocity.X * Math.Cos(rotateAngle) - movable.Velocity.Y * Math.Sin(rotateAngle);
            var yPrime = movable.Velocity.Y * Math.Cos(rotateAngle) - movable.Velocity.X * Math.Sin(rotateAngle);
            movable.Velocity.X = xPrime;
            movable.Velocity.Y = yPrime;
        }

        movable.Velocity.X *= movable.Material.Elasticity;
        movable.Velocity.Y *= movable.Material.Elasticity;
    }