/// <summary>
/// Time to collision of a ray to a disc.
/// </summary>
/// <param name="p">The start position of the ray</param>
/// <param name="v">The velocity vector of the ray</param>
/// <param name="p2">The center position of the disc</param>
/// <param name="radius">The radius of the disc</param>
/// <param name="collision">Specifies whether the time to collision is computed (false), or the time from collision (true).计算将要发生碰撞的时间，或者发生碰撞后经过的时间</param>
/// <returns>Returns the time to collision of ray p + tv to disc D(p2, radius), and #RVO_INFTY when the disc is not hit. If collision is true, the value is negative.</returns>
//点到直线距离公式：d = |AX0+BY0+C|/sqrt(A*A+B*B)
//直线AX+BY+C=0,A=-V.y B=V.x C =P.x*V.y-V.x*P.y
//可能碰撞：d<r=>d*d-r*r<0
//p2带入AX0+BY0+C
//AX0+BY0+C = -v.y*p2.x+v.x*p2.y+p.x*v.y-v.x*p.y=v.x(p2.y-p.y)-v.y(p2.x-p.x)=det(v, ba)
//d*d = det(v, ba)*det(v, ba)/absSq(v)
//r*r-d*d>0 => r*r-det(v, ba)*det(v, ba)/absSq(v)>0 => discr = r*r*absSq(v) - det(v, ba)*det(v, ba)>0
//
private float time2Collision(Vector2 p, Vector2 v, Vector2 p2, float radius, bool collision)
{
Vector2 ba = p2 - p;
float sq_diam = radius * radius;
float time;
float discr = -RVOMath.Sqr(RVOMath.Det(v, ba)) + sq_diam * RVOMath.AbsSq(v);
if (discr > 0)
{
if (collision)
{
time = (Vector2.Dot(v, ba) + Mathf.Sqrt(discr)) / RVOMath.AbsSq(v);//脱落碰撞需要的时间
if (time < 0)
{
time = -float.MaxValue; //
Debug.LogError("isCollide time < 0 "); //?
}
}
else
{
time = (Vector2.Dot(v, ba) - Mathf.Sqrt(discr)) / RVOMath.AbsSq(v);//将要发生碰撞的时间
if (time < 0)
{
time = float.MaxValue;//永远不会发生碰撞
}
}
}
else
{//不碰撞
if (collision)
{
time = -float.MaxValue;
}
else
{
time = float.MaxValue;
}
}
return(time);
}