internal Pair <Vector2, Vector2> computeTangentsPoints(Agent observer, Agent agent)
{
// First element of the pair = left tangent
// Second element of the pair = right tangent
Pair <Vector2, Vector2> toReturn = new Pair <Vector2, Vector2>();
Vector2 centers = agent.position_ - observer.position_;
Vector2 r1a = Vector2.normalize(Vector2.rotation(centers, (float)-Math.PI / 2)) * observer.radius_;
Vector2 r1b = Vector2.normalize(Vector2.rotation(centers, (float)Math.PI / 2)) * observer.radius_;
// Compute intersection points between radius and circle
// Right one
Vector2 h1a = observer.position_ + r1a;
// Left one
Vector2 h1b = observer.position_ + r1b;
// If the radius is the same, tangents points are perpendicular to centers vector
if (Math.Abs(observer.radius_ - agent.radius_) < RVO_EPSILON)
{
toReturn.First = h1a;
toReturn.Second = h1b;
}
else
{
Vector2 r2a = Vector2.normalize(Vector2.rotation(centers, (float)-Math.PI / 2)) * agent.radius_;
Vector2 r2b = Vector2.normalize(Vector2.rotation(centers, (float)Math.PI / 2)) * agent.radius_;
Vector2 h2a = agent.position_ + r2a;
Vector2 h2b = agent.position_ + r2b;
// If tangents are parallel, radius are the same, i.e. there is no intersection point.
if (Math.Abs(Vector2.det(h1a - h2a, h1b - h2b)) < RVO_EPSILON)
{
Console.Write("Problem while computing tangent points\n SHALL NOT HAPPEN !!! \n");
toReturn.First = h1a;
toReturn.Second = h1b;
}
else
{
Vector2 intersectionPoint = Vector2.intersectOf2Lines(h1a, h2a, h1b, h2b);
// Equivalent to :
Vector2 circleCenter = (intersectionPoint + observer.position_) / 2;
toReturn = Vector2.intersectOf2Circles(circleCenter, Vector2.abs(circleCenter - observer.position_), observer.position_, observer.radius_);
// Test angles to know which one is right & which one is left
if (Vector2.isOnTheLeftSide(toReturn.First - observer.position_, centers))
{
Vector2 temp = toReturn.First;
toReturn.First = toReturn.Second;
toReturn.Second = temp;
}
}
}
return(toReturn);
}
internal SuperAgent representGroup(Agent observer)
{
// Compute the left & right tangent points obtained for each agent of the group
// First element of the pair = right tangent
// Second element of the pair = left tangent
IList <Pair <Vector2, Vector2> > tangents = new List <Pair <Vector2, Vector2> >();
IList <Pair <Vector2, Vector2> > radii = new List <Pair <Vector2, Vector2> >();
for (int i = 0; i < agents_.Count; i++)
{
tangents.Add(computeTangentsPoints(observer, agents_[i]));
Pair <Vector2, Vector2> rads = new Pair <Vector2, Vector2>();
rads.First = tangents[i].First - observer.position_;
rads.Second = tangents[i].Second - observer.position_;
radii.Add(rads);
}
// Compute the group tangent points (extrema)
int rightExtremumId = 0;
int leftExtremumId = 0;
for (int i = 1; i < tangents.Count; i++)
{
// Comparison
if (Vector2.isOnTheLeftSide(radii[rightExtremumId].First, radii[i].First))
{
rightExtremumId = i;
}
if (Vector2.isOnTheLeftSide(radii[i].Second, radii[leftExtremumId].Second))
{
leftExtremumId = i;
}
}
// If the tangent are taking more than 180°, cannot be considered as a group
for (int i = 0; i < agents_.Count; i++)
{
if (Vector2.isOnTheLeftSide(radii[rightExtremumId].First, radii[i].First))
{
//std::cout << "Problem representing groups : tangent angle > 180°\n";
return(new SuperAgent(null));
}
if (Vector2.isOnTheLeftSide(radii[i].Second, radii[leftExtremumId].Second))
{
//std::cout << "Problem representing groups : tangent angle > 180°\n";
return(new SuperAgent(null));
}
}
// Compute bisector
Vector2 rightTangent = Vector2.rotation(radii[rightExtremumId].First, (float)Math.PI / 2);
Vector2 leftTangent = Vector2.rotation(radii[leftExtremumId].Second, -(float)Math.PI / 2);
Vector2 intersectionPoint = Vector2.intersectOf2Lines(tangents[rightExtremumId].First, tangents[rightExtremumId].First + rightTangent,
tangents[leftExtremumId].Second, tangents[leftExtremumId].Second + leftTangent);
// alpha/2 is more usefull than alpha
float alpha2 = Vector2.angle(Vector2.rotation(tangents[leftExtremumId].Second - intersectionPoint, -Vector2.angle(tangents[rightExtremumId].First - intersectionPoint))) / 2;
if (alpha2 < 0)
{
//std::cout << "Problem representing groups : angle computation\n SHALL NOT HAPPEN !!! \n";
// But if radii are different or if
return(new SuperAgent(null));
}
Vector2 bisector_normalize_vector = Vector2.normalize(observer.position_ - intersectionPoint);
// Compute circle
// The distance between the observer and the circle (along the bisector axis)
float d = Single.PositiveInfinity;
float a, b, c, delta, x;
int constrainingAgent = 0;
for (int i = 0; i < agents_.Count; i++)
{
Vector2 ic1 = agents_[i].position_ - intersectionPoint;
a = 1 - Vector2.sqr((float)Math.Sin(alpha2));
b = 2 * (agents_[i].radius_ * (float)Math.Sin(alpha2) - ic1 * bisector_normalize_vector);
c = Vector2.absSq(ic1) - Vector2.sqr(agents_[i].radius_);
delta = Vector2.sqr(b) - 4 * a * c;
if (delta <= 0)
{
if (delta < -4 * RVO_EPSILON * c)
{
return(new SuperAgent(null));
}
else
{
delta = 0;
}
}
x = (-b + (float)Math.Sqrt(delta)) / (2 * a);
if (x < d)
{
d = x;
constrainingAgent = i;
}
}
if (d < Vector2.abs(observer.position_ - intersectionPoint) + observer.radius_ + d * Math.Sin(alpha2))
{
return(new SuperAgent(null));
}
SuperAgent toReturn = new SuperAgent(sim_);
toReturn.position_ = intersectionPoint + bisector_normalize_vector * d;
toReturn.radius_ = d * (float)Math.Sin(alpha2);
toReturn.velocity_ = agents_[constrainingAgent].velocity_;
return(toReturn);
}