本の内容が理解できず困っています。

[たぬき]

実例で学ぶゲームAIプログラミングという本の障害物を避けるという項目の横力の説明部分の計算が、よく理解できず困っています。（本103・104ページ）

具体的には、下のコードのlateral forceの部分です。
初歩的基礎的な勘違いや理解不足の類かと思うんですが、
障害物の半径－ヴィークルのローカル座標のｙという式だと、yがマイナスのとき大きくなり、プラスのとき小さくなりバランスが悪い気がするのと、それ以前に半径イコールyであった場合など、衝突するのではないかと思ってしまい混乱しています。
理解できず質問するのは大変お恥ずかしいのですが、よろしくお願いいたします。

コード:

Vector2D SteeringBehavior::ObstacleAvoidance(const std::vector<BaseGameEntity*>& obstacles)
{
  //the detection box length is proportional to the agent's velocity
  m_dDBoxLength = Prm.MinDetectionBoxLength + 
                  (m_pVehicle->Speed()/m_pVehicle->MaxSpeed()) *
                  Prm.MinDetectionBoxLength;

  //tag all obstacles within range of the box for processing
  m_pVehicle->World()->TagObstaclesWithinViewRange(m_pVehicle, m_dDBoxLength);

  //this will keep track of the closest intersecting obstacle (CIB)
  BaseGameEntity* ClosestIntersectingObstacle = NULL;
 
  //this will be used to track the distance to the CIB
  double DistToClosestIP = MaxDouble;

  //this will record the transformed local coordinates of the CIB
  Vector2D LocalPosOfClosestObstacle;

  std::vector<BaseGameEntity*>::const_iterator curOb = obstacles.begin();

  while(curOb != obstacles.end())
  {
    //if the obstacle has been tagged within range proceed
    if ((*curOb)->IsTagged())
    {
      //calculate this obstacle's position in local space
      Vector2D LocalPos = PointToLocalSpace((*curOb)->Pos(),
                                             m_pVehicle->Heading(),
                                             m_pVehicle->Side(),
                                             m_pVehicle->Pos());

      //if the local position has a negative x value then it must lay
      //behind the agent. (in which case it can be ignored)
      if (LocalPos.x >= 0)
      {
        //if the distance from the x axis to the object's position is less
        //than its radius + half the width of the detection box then there
        //is a potential intersection.
        double ExpandedRadius = (*curOb)->BRadius() + m_pVehicle->BRadius();

        if (fabs(LocalPos.y) < ExpandedRadius)
        {
          //now to do a line/circle intersection test. The center of the 
          //circle is represented by (cX, cY). The intersection points are 
          //given by the formula x = cX +/-sqrt(r^2-cY^2) for y=0. 
          //We only need to look at the smallest positive value of x because
          //that will be the closest point of intersection.
          double cX = LocalPos.x;
          double cY = LocalPos.y;
          
          //we only need to calculate the sqrt part of the above equation once
          double SqrtPart = sqrt(ExpandedRadius*ExpandedRadius - cY*cY);

          double ip = cX - SqrtPart;

          if (ip <= 0.0)
          {
            ip = cX + SqrtPart;
          }

          //test to see if this is the closest so far. If it is keep a
          //record of the obstacle and its local coordinates
          if (ip < DistToClosestIP)
          {
            DistToClosestIP = ip;

            ClosestIntersectingObstacle = *curOb;

            LocalPosOfClosestObstacle = LocalPos;
          }         
        }
      }
    }

    ++curOb;
  }

  //if we have found an intersecting obstacle, calculate a steering 
  //force away from it
  Vector2D SteeringForce;

  if (ClosestIntersectingObstacle)
  {
    //the closer the agent is to an object, the stronger the 
    //steering force should be
    double multiplier = 1.0 + (m_dDBoxLength - LocalPosOfClosestObstacle.x) /
                        m_dDBoxLength;

    //calculate the lateral force
    SteeringForce.y = (ClosestIntersectingObstacle->BRadius()-
                       LocalPosOfClosestObstacle.y)  * multiplier;   

    //apply a braking force proportional to the obstacles distance from
    //the vehicle. 
    const double BrakingWeight = 0.2;

    SteeringForce.x = (ClosestIntersectingObstacle->BRadius() - 
                       LocalPosOfClosestObstacle.x) * 
                       BrakingWeight;
  }

  //finally, convert the steering vector from local to world space
  return VectorToWorldSpace(SteeringForce,
                            m_pVehicle->Heading(),
                            m_pVehicle->Side());
}

[Math]

https://books.google.co.jp/books?id=JuF ... B0&f=false
をみると高校の数学・物理の入門レベルから説明してあるので（103,104ページも日本語であるし）じっくりと読めばわかるとおもいますね。