从位置向量获取速度向量 [英] Getting the velocity vector from position vectors

问题描述

我看了一堆类似的问题，但似乎找不到一个特别能回答我问题的问题.我正在编写一个简单的3d游戏，并且试图允许玩家拾取并在我的地图上移动实体.我本质上是想获得一个速度矢量，该矢量将物理"对象推"到与玩家眼睛无关的位置，无论他们在看什么.这是在另一个游戏中完成的示例(玩家将椅子实体举在眼前).

I looked at a bunch of similar questions, and I cannot seem to find one that particularly answers my question. I am coding a simple 3d game, and I am trying to allow the player to pick up and move entities around my map. I essentially want to get a velocity vector that will "push" the physics object a distance from the player's eyes, wherever they are looking. Here's an example of this being done in another game (the player is holding a chair entity in front of his eyes).

为此，我先找出玩家的眼睛角度，然后从这些角度获取前向矢量，然后计算物体的速度.这是我的工作代码:

To do this, I find out the player's eye angles, then get the forward vector from the angles, then calculate the velocity of the object. Here is my working code:

void Player::PickupOtherEntity( Entity& HoldingEntity )
{
    QAngle eyeAngles = this->GetPlayerEyeAngles();
    Vector3 vecPos = this->GetEyePosition();
    Vector3 vecDir = eyeAngles.Forward();

    Vector3 holdingEntPos = HoldingEntity.GetLocation();

    // update object by holding it a distance away
    vecPos.x += vecDir.x * DISTANCE_TO_HOLD;
    vecPos.y += vecDir.y * DISTANCE_TO_HOLD;
    vecPos.z += vecDir.z * DISTANCE_TO_HOLD;

    Vector3 vecVel = vecPos - holdingEntPos;
    vecVel = vecVel.Scale(OBJECT_SPEED_TO_MOVE);

    // set the entity's velocity as to "push" it to be in front of the player's eyes
    // at a distance of DISTANCE_TO_HOLD away
    HoldingEntity.SetVelocity(vecVel);
}

所有这些都很棒，但是我想转换数学公式以便可以施加冲动.我不想为对象设置一个全新的速度，而是要向其现有速度添加"一些速度.因此，假设我具有当前速度，我需要什么样的数学运算来增加"速度?这本质上是一个游戏物理问题.谢谢！

All that is great, but I want to convert my math so that I can apply an impulse. Instead of setting a completely new velocity to the object, I want to "add" some velocity to its existing velocity. So supposing I have its current velocity, what kind of math do I need to "add" velocity? This is essentially a game physics question. Thank you!

推荐答案

基本牛顿理论/达朗贝尔物理学规定:

basic Newtonian/D'Alembert physics dictate:

derivate(position)=velocity
derivate(velocity)=acceleration

，也向后:

integrate(acceleration)=velocity
integrate(velocity)=position

因此对于您的引擎，您可以使用:

so for your engine you can use:

矩形求和而不是积分(积分的数值解).定义时间常数dt [seconds]，它是两次更新之间的间隔(定时器或1/fps).因此，更新代码(必须每隔dt定期调用一次:

rectangle summation instead of integration (numerical solution of integral). Define time constant dt [seconds] which is the interval between updates (timer or 1/fps). So the update code (must be periodically called every dt:

vx+=ax*dt;
vy+=ay*dt;
vz+=az*dt;
 x+=vx*dt;
 y+=vy*dt;
 z+=vz*dt;

其中:

• a{x,y,z} [m/s^2]是实际加速度(在您的情况下，方向矢量缩放为a=Force/mass)
• v{x,y,z} [m/s]是实际速度

• x,y,z [m]是实际位置

• a{x,y,z} [m/s^2] is actual acceleration (in your case direction vector scaled to a=Force/mass)
• v{x,y,z} [m/s] is actual velocity

• x,y,z [m] is actual position

1. 必须将这些值初始化为a,v零，并且将x,y,z初始化为初始位置
2. 所有对象/玩家...都有自己的变量
3. 完全停止由v=0; a=0;
完成
4. 仅通过更改a
即可驱动对象
5. 在通过碰撞normal碰撞的碰撞镜v向量的情况下

1. These values have to be initialized a,v to zero and x,y,z to init position
2. all objects/players... have their own variables
3. full stop is done by v=0; a=0;
4. driving of objects is done only by change of a
5. in case of collision mirror v vector by collision normal

，并可能乘以k<1.0(例如0.95)来计算能量对冲击的损失

and maybe multiply by some k<1.0 (0.95 for example) to account energy loss on impact

您可以通过添加g向量来添加重力或任何其他力场:

You can add gravity or any other force field by adding g vector:

vx+=ax*dt+gx*dt;
vy+=ay*dt+gy*dt;
vz+=az*dt+gz*dt;

您还可以添加摩擦力和其他任何需要的东西

also You can add friction and anything else you need

PS.角度也一样，只是使用angle/omega/epsilon/I而不是x/a/v/m

PS. the same goes for angles just use angle/omega/epsilon/I instead of x/a/v/m

通过角度I平均绕质量中心旋转(pitch,yaw,roll)清晰

to be clear by angles I mean rotation (pitch,yaw,roll) around mass center

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