| public static normalize ( Vector2 vector ) : Vector2 | ||
| vector | Vector2 | The two-dimensional vector whose normalization * is to be computed. |
| return | Vector2 | |
/**
* <summary>Solves a two-dimensional linear program subject to linear
* constraints defined by lines and a circular constraint.</summary>
*
* <param name="lines">Lines defining the linear constraints.</param>
* <param name="numObstLines">Count of obstacle lines.</param>
* <param name="beginLine">The line on which the 2-d linear program
* failed.</param>
* <param name="radius">The radius of the circular constraint.</param>
* <param name="result">A reference to the result of the linear program.
* </param>
*/
private void linearProgram3(IList <Line> lines, int numObstLines, int beginLine, float radius, ref Vector2 result)
{
float distance = 0.0f;
for (int i = beginLine; i < lines.Count; ++i)
{
if (RVOMath.det(lines[i].direction, lines[i].point - result) > distance)
{
/* Result does not satisfy constraint of line i. */
IList <Line> projLines = new List <Line>();
for (int ii = 0; ii < numObstLines; ++ii)
{
projLines.Add(lines[ii]);
}
for (int j = numObstLines; j < i; ++j)
{
Line line;
float determinant = RVOMath.det(lines[i].direction, lines[j].direction);
if (RVOMath.fabs(determinant) <= RVOMath.RVO_EPSILON)
{
/* Line i and line j are parallel. */
if (Vector2.Dot(lines[i].direction, lines[j].direction) > 0.0f)
{
/* Line i and line j point in the same direction. */
continue;
}
else
{
/* Line i and line j point in opposite direction. */
line.point = 0.5f * (lines[i].point + lines[j].point);
}
}
else
{
line.point = lines[i].point + (RVOMath.det(lines[j].direction, lines[i].point - lines[j].point) / determinant) * lines[i].direction;
}
line.direction = RVOMath.normalize(lines[j].direction - lines[i].direction);
projLines.Add(line);
}
Vector2 tempResult = result;
if (linearProgram2(projLines, radius, new Vector2(-lines[i].direction.y, lines[i].direction.x), true, ref result) < projLines.Count)
{
/*
* This should in principle not happen. The result is by
* definition already in the feasible region of this
* linear program. If it fails, it is due to small
* floating point error, and the current result is kept.
*/
result = tempResult;
}
distance = RVOMath.det(lines[i].direction, lines[i].point - result);
}
}
}
void setPreferredVelocities()
{
/*
* Set the preferred velocity to be a vector of unit magnitude
* (speed) in the direction of the goal.
*/
for (int i = 0; i < Simulator.Instance.getNumAgents(); ++i)
{
Vector2 goalVector = goals[i] - Simulator.Instance.getAgentPosition(i);
if (RVOMath.absSq(goalVector) > 1.0f)
{
goalVector = RVOMath.normalize(goalVector);
}
Simulator.Instance.setAgentPrefVelocity(i, goalVector);
/* Perturb a little to avoid deadlocks due to perfect symmetry. */
float angle = (float)random.NextDouble() * 2.0f * (float)Math.PI;
float dist = (float)random.NextDouble() * 0.0001f;
Simulator.Instance.setAgentPrefVelocity(i, Simulator.Instance.getAgentPrefVelocity(i) +
dist * new Vector2((float)Math.Cos(angle), (float)Math.Sin(angle)));
}
}
public void setPreferred()
{
goalDirection = new Vector2(0.0f, 0.0f);
if (path != null && pathStatus < path.corners.Length)
{
goalDirection = new Vector2(path.corners[pathStatus].x, path.corners[pathStatus].z) - new Vector2(transform.position.x, transform.position.z);
if (RVOMath.absSq(goalDirection) < goalOffset)
{
pathStatus++;
}
if (RVOMath.absSq(goalDirection) > AgentReference.maxSpeed_ * 0.9)
{
//Choose between two; max speed or less. (This provides somewhat smooth movement)
// float speed = userCoefficient * (float)((RVOMath.abs(RVOMath.normalize(goalDirection) / 1f) > 0.1) ? 0.1 : RVOMath.abs(RVOMath.normalize(goalDirection) / 1f));
float speed = (float)((RVOMath.abs(RVOMath.normalize(goalDirection)) > AgentReference.maxSpeed_ * 0.9) ? AgentReference.maxSpeed_ * 0.9 : RVOMath.abs(RVOMath.normalize(goalDirection)) * AgentReference.maxSpeed_);
goalDirection = new Vector2(RVOMath.normalize(goalDirection).x() * speed, RVOMath.normalize(goalDirection).y() * speed);
}
}
else
{
pathStatus = -1;
path = null;
//setDestination(transform.position);
}
AgentReference.prefVelocity_ = goalDirection * RVOMagnify.Magnify;
}
public void addObstacle(KInt2 a, KInt2 b)
{
Obstacle first = new Obstacle();
first.convex_ = true;
Obstacle second = new Obstacle();
second.convex_ = true;
first.previous_ = second;
second.previous_ = first;
first.next_ = second;
second.next_ = first;
first.point_ = a;
second.point_ = b;
first.direction_ = RVOMath.normalize(KInt2.ToInt2(b.x - a.x, b.y - a.y));
second.direction_ = -first.direction_;
first.id_ = obstacles_.Count;
obstacles_.Add(first);
second.id_ = obstacles_.Count;
obstacles_.Add(second);
}
/**
* <summary>Adds a new obstacle to the simulation.</summary>
*
* <returns>The number of the first vertex of the obstacle, or -1 when
* the number of vertices is less than two.</returns>
*
* <param name="vertices">List of the vertices of the polygonal obstacle
* in counterclockwise order.</param>
*
* <remarks>To add a "negative" obstacle, e.g. a bounding polygon around
* the environment, the vertices should be listed in clockwise order.
* </remarks>
*/
public int addObstacle(IList <Vector3> vertices3, float height)
{
List <Vector2> vertices = new List <Vector2>();
List <float> yPos = new List <float>();
foreach (Vector3 avertex3 in vertices3)
{
vertices.Add(new Vector2(avertex3.x, avertex3.z));
yPos.Add(avertex3.y);
}
if (vertices.Count < 2)
{
return(-1);
}
int obstacleNo = obstacles_.Count;
for (int i = 0; i < vertices.Count; ++i)
{
Obstacle obstacle = new Obstacle();
obstacle.point_ = vertices[i];
obstacle.curHeight_ = yPos[i];
if (i != 0)
{
obstacle.previous_ = obstacles_[obstacles_.Count - 1];
obstacle.previous_.next_ = obstacle;
}
if (i == vertices.Count - 1)
{
obstacle.next_ = obstacles_[obstacleNo];
obstacle.next_.previous_ = obstacle;
}
obstacle.direction_ = RVOMath.normalize(vertices[(i == vertices.Count - 1 ? 0 : i + 1)] - vertices[i]);
if (vertices.Count == 2)
{
obstacle.convex_ = true;
}
else
{
obstacle.convex_ = (RVOMath.leftOf(vertices[(i == 0 ? vertices.Count - 1 : i - 1)], vertices[i], vertices[(i == vertices.Count - 1 ? 0 : i + 1)]) >= 0.0f);
}
obstacle.ObsHeight_ = height;
obstacle.id_ = obstacles_.Count;
obstacles_.Add(obstacle);
}
RefreshList();
return(obstacleNo);
}
/**
* <summary>Adds a new obstacle to the simulation.</summary>
*
* <returns>The number of the first vertex of the obstacle, or -1 when
* the number of vertices is less than two.</returns>
*
* <param name="vertices">List of the vertices of the polygonal obstacle
* in counterclockwise order.</param>
*
* <remarks>To add a "negative" obstacle, e.g. a bounding polygon around
* the environment, the vertices should be listed in clockwise order.
* </remarks>
*/
public Obstacle addObstacle(IList <Vector2> vertices, bool _isMapBound)
{
if (vertices.Count < 2)
{
return(null);
}
int obstacleNo = obstacles_.Count;
Obstacle result = null;
for (int i = 0; i < vertices.Count; ++i)
{
Obstacle obstacle = new Obstacle();
obstacle.isMapBound = _isMapBound;
if (result == null)
{
result = obstacle;
}
obstacle.point_ = vertices[i];
if (i != 0)
{
obstacle.previous_ = obstacles_[obstacles_.Count - 1];
obstacle.previous_.next_ = obstacle;
}
if (i == vertices.Count - 1)
{
obstacle.next_ = obstacles_[obstacleNo];
obstacle.next_.previous_ = obstacle;
}
obstacle.direction_ = RVOMath.normalize(vertices[(i == vertices.Count - 1 ? 0 : i + 1)] - vertices[i]);
if (vertices.Count == 2)
{
obstacle.convex_ = true;
}
else
{
obstacle.convex_ = (RVOMath.leftOf(vertices[(i == 0 ? vertices.Count - 1 : i - 1)], vertices[i], vertices[(i == vertices.Count - 1 ? 0 : i + 1)]) >= 0.0);
}
obstacles_.Add(obstacle);
}
return(result);
}
/**
* <summary>Solves a two-dimensional linear program subject to linear
* constraints defined by lines and a circular constraint.</summary>
* 解决一个二维线性规划问题，由直线和一个圆形约束定义的线性约束
*
* <returns>The number of the line it fails on, and the number of lines
* if successful.</returns>
*
* <param name="lines">Lines defining the linear constraints.</param>
* <param name="radius">The radius of the circular constraint.</param>
* <param name="optVelocity">The optimization velocity.</param>
* <param name="directionOpt">True if the direction should be optimized.
* </param>
* <param name="result">A reference to the result of the linear program.
* </param>
*/
private int linearProgram2(IList <Line> lines, float radius, Vector2 optVelocity, bool directionOpt, ref Vector2 result)
{
if (directionOpt)
{
/*
* Optimize direction. Note that the optimization velocity is of
* unit length in this case.
* 优化方向。注意，在这种情况下，优化速度是单位长度的
*/
result = optVelocity * radius;
}
else if (RVOMath.absSq(optVelocity) > RVOMath.sqr(radius))
{
/* Optimize closest point and outside circle.
* 优化圆外最接近的点 当单位速度大小大于最大速度时，即速度在圆外
*/
result = RVOMath.normalize(optVelocity) * radius;
}
else
{
/* Optimize closest point and inside circle.
* 优化圆内最接近的点 当单位速度小于最大速度时，即速度在圆内
*/
result = optVelocity;
}
for (int i = 0; i < lines.Count; ++i)
{
if (RVOMath.det(lines[i].direction, lines[i].point - result) > 0.0f)
{
/* Result does not satisfy constraint i. Compute new optimal result.
* 结果不满足约束i，计算新的最优结果
*/
Vector2 tempResult = result;
if (!linearProgram1(lines, i, radius, optVelocity, directionOpt, ref result))
{
result = tempResult;
return(i);
}
}
}
return(lines.Count);
}
/**
* <summary>Adds a new obstacle to the simulation.</summary>
*
* <returns>The number of the first vertex of the obstacle, or -1 when
* the number of vertices is less than two.</returns>
*
* <param name="vertices">List of the vertices of the polygonal obstacle
* in counterclockwise order.</param>
*
* <remarks>To add a "negative" obstacle, e.g. a bounding polygon around
* the environment, the vertices should be listed in clockwise order.
* </remarks>
*/
public int addObstacle(IList <Vector2> vertices)
{
if (vertices.Count < 2)
{
return(-1);
}
int obstacleNo = obstacles_.Count;
for (int i = 0; i < vertices.Count; ++i)
{
Obstacle obstacle = new Obstacle();
obstacle.point_ = vertices[i];
if (i != 0)
{
obstacle.previous_ = obstacles_[obstacles_.Count - 1];
obstacle.previous_.next_ = obstacle;
}
if (i == vertices.Count - 1)
{
obstacle.next_ = obstacles_[obstacleNo];
obstacle.next_.previous_ = obstacle;
}
obstacle.direction_ = RVOMath.normalize(vertices[(i == vertices.Count - 1 ? 0 : i + 1)] - vertices[i]);
if (vertices.Count == 2)
{
obstacle.convex_ = true;
}
else
{
obstacle.convex_ = RVOMath.leftOf(vertices[(i == 0 ? vertices.Count - 1 : i - 1)],
vertices[i],
vertices[(i == vertices.Count - 1 ? 0 : i + 1)]) >= 0.0f;
}
obstacle.id_ = obstacles_.Count;
obstacles_.Add(obstacle);
}
return(obstacleNo);
}
void setPreferredVelocities()
{
/*
* Set the preferred velocity to be a vector of unit magnitude
* (speed) in the direction of the goal.
*/
for (int i = 0; i < Simulator.Instance.getNumAgents(); ++i)
{
Vector3 goalVector = goals[i] - Simulator.Instance.getAgentPosition(i);
if (RVOMath.absSq(goalVector) > 1.0f)
{
goalVector = RVOMath.normalize(goalVector);
}
Simulator.Instance.setAgentPrefVelocity(i, goalVector);
}
}
public void RunTest()
{
//Blocks blocks = new Blocks();
///* Set up the scenario. */
//blocks.setupScenario();
Parallel.For(0, Simulator.Instance.getNumAgents(), i =>
// for (int i = 0; i < Simulator.Instance.getNumAgents(); i++)
{
Simulator.Instance.DoTree();
Vector2 goalVector = goals[i] - Simulator.Instance.getAgentPosition(i);
if (RVOMath.absSq(goalVector) > 1.0f)
{
goalVector = RVOMath.normalize(goalVector);
}
Simulator.Instance.setAgentPrefVelocity(i, goalVector);
/* Perturb a little to avoid deadlocks due to perfect symmetry. */
float angle = (float)random.NextDouble() * 2.0f * (float)Math.PI;
float dist = (float)random.NextDouble() * 0.0001f;
Simulator.Instance.setAgentPrefVelocity(i, Simulator.Instance.getAgentPrefVelocity(i) +
dist * new Vector2((float)Math.Cos(angle), (float)Math.Sin(angle)));
Simulator.Instance.Compute(i);
Simulator.Instance.Update(i);
}
);
// blocks.setPreferredVelocities();
// Simulator.Instance.doStep();
//}
//while (!blocks.reachedGoal());
}
/**
* <summary>Solves a two-dimensional linear program subject to linear
* constraints defined by lines and a circular constraint.</summary>
*
* <returns>The number of the line it fails on, and the number of lines
* if successful.</returns>
*
* <param name="lines">Lines defining the linear constraints.</param>
* <param name="radius">The radius of the circular constraint.</param>
* <param name="optVelocity">The optimization velocity.</param>
* <param name="directionOpt">True if the direction should be optimized.
* </param>
* <param name="result">A reference to the result of the linear program.
* </param>
*/
private int linearProgram2(IList <Line> lines, float radius, Vector2 optVelocity, bool directionOpt, ref Vector2 result)
{
// directionOpt 第一次为false，第二次为true，directionOpt主要用在 linearProgram1 里面
if (directionOpt)
{
/*
* Optimize direction. Note that the optimization velocity is of
* unit length in this case.
*/
// 1.这个其实没什么用，只是因为velocity是归一化的所以直接乘 radius
result = optVelocity * radius;
}
else if (RVOMath.absSq(optVelocity) > RVOMath.sqr(radius))
{
/* Optimize closest point and outside circle. */
// 2.当 optVelocity 太大时，先归一化optVelocity，再乘 radius
result = RVOMath.normalize(optVelocity) * radius;
}
else
{
/* Optimize closest point and inside circle. */
// 3.当 optVelocity 小于maxSpeed时
result = optVelocity;
}
for (int i = 0; i < lines.Count; ++i)
{
if (RVOMath.det(lines[i].direction, lines[i].point - result) > 0.0f)
{
/* Result does not satisfy constraint i. Compute new optimal result. */
Vector2 tempResult = result;
if (!linearProgram1(lines, i, radius, optVelocity, directionOpt, ref result))
{
result = tempResult;
return(i);
}
}
}
return(lines.Count);
}
/**
* <summary>Solves a two-dimensional linear program subject to linear
* constraints defined by lines and a circular constraint.</summary>
*
* <returns>The number of the line it fails on, and the number of lines
* if successful.</returns>
*
* <param name="lines">Lines defining the linear constraints.</param>
* <param name="radius">The radius of the circular constraint.</param>
* <param name="optVelocity">The optimization velocity.</param>
* <param name="directionOpt">True if the direction should be optimized.
* </param>
* <param name="result">A reference to the result of the linear program.
* </param>
*/
private int linearProgram2(IList <Line> lines, float radius, Vector3 optVelocity, bool directionOpt, ref Vector3 result)
{
if (directionOpt)
{
/*
* Optimize direction. Note that the optimization velocity is of
* unit length in this case.
*/
result = optVelocity * radius;
}
else if (RVOMath.absSq(optVelocity) > RVOMath.sqr(radius))
{
/* Optimize closest point and outside circle. */
result = RVOMath.normalize(optVelocity) * radius;
}
else
{
/* Optimize closest point and inside circle. */
result = optVelocity;
}
for (int i = 0; i < lines.Count; ++i)
{
if (RVOMath.det(lines[i].direction, lines[i].point - result) > 0.0f)
{
/* Result does not satisfy constraint i. Compute new optimal result. */
Vector3 tempResult = result;
if (!linearProgram1(lines, i, radius, optVelocity, directionOpt, ref result))
{
result = tempResult;
return(i);
}
}
}
return(lines.Count);
}
/**
* <summary>Computes the new velocity of this agent.</summary>
*/
internal void computeNewVelocity()
{
orcaLines_.Clear();
//KInt invTimeHorizonObst = 1 / timeHorizonObst_;
KInt tempradius = radius_ / timeHorizonObst_;
/* Create obstacle ORCA lines. */
for (int i = 0; i < obstacleNeighbors_.Count; ++i)
{
Obstacle obstacle1 = obstacleNeighbors_[i].Value;
Obstacle obstacle2 = obstacle1.next_;
KInt2 relativePosition1 = obstacle1.point_ - position_;
KInt2 relativePosition2 = obstacle2.point_ - position_;
/*
* Check if velocity obstacle of obstacle is already taken care
* of by previously constructed obstacle ORCA lines.
*/
bool alreadyCovered = false;
for (int j = 0; j < orcaLines_.Count; ++j)
{
if (RVOMath.det(relativePosition1 / timeHorizonObst_ - orcaLines_[j].point, orcaLines_[j].direction) - tempradius >= 0 && RVOMath.det(relativePosition2 / timeHorizonObst_ - orcaLines_[j].point, orcaLines_[j].direction) - tempradius >= 0)
{
alreadyCovered = true;
break;
}
}
if (alreadyCovered)
{
continue;
}
/* Not yet covered. Check for collisions. */
KInt distSq1 = RVOMath.absSq(relativePosition1);
KInt distSq2 = RVOMath.absSq(relativePosition2);
KInt radiusSq = RVOMath.sqr(radius_);
KInt2 obstacleVector = obstacle2.point_ - obstacle1.point_;
KInt s = (-RVOMath.Dot(relativePosition1, obstacleVector)) / RVOMath.absSq(obstacleVector);
KInt distSqLine = RVOMath.absSq(-relativePosition1 - s * obstacleVector);
Line line = new Line();
if (s < 0 && distSq1 <= radiusSq)
{
/* Collision with left vertex. Ignore if non-convex. */
if (obstacle1.convex_)
{
line.point = KInt2.zero;
line.direction = RVOMath.normalize(KInt2.ToInt2(-relativePosition1.IntY, relativePosition1.IntX));
orcaLines_.Add(line);
}
continue;
}
else if (s > 1 && distSq2 <= radiusSq)
{
/*
* Collision with right vertex. Ignore if non-convex or if
* it will be taken care of by neighboring obstacle.
*/
if (obstacle2.convex_ && RVOMath.det(relativePosition2, obstacle2.direction_) >= 0)
{
line.point = KInt2.zero;
line.direction = RVOMath.normalize(KInt2.ToInt2(-relativePosition2.IntY, relativePosition2.IntX));
orcaLines_.Add(line);
}
continue;
}
else if (s >= 0 && s < 1 && distSqLine <= radiusSq)
{
/* Collision with obstacle segment. */
line.point = KInt2.zero;
line.direction = -obstacle1.direction_;
orcaLines_.Add(line);
continue;
}
/*
* No collision. Compute legs. When obliquely viewed, both legs
* can come from a single vertex. Legs extend cut-off line when
* non-convex vertex.
*/
KInt2 leftLegDirection, rightLegDirection;
if (s < 0 && distSqLine <= radiusSq)
{
/*
* Obstacle viewed obliquely so that left vertex
* defines velocity obstacle.
*/
if (!obstacle1.convex_)
{
/* Ignore obstacle. */
continue;
}
obstacle2 = obstacle1;
KInt leg1 = RVOMath.sqrt(distSq1 - radiusSq);
leftLegDirection = KInt2.ToInt2(relativePosition1.IntX * leg1 - relativePosition1.IntY * radius_, relativePosition1.IntX * radius_ + relativePosition1.IntY * leg1) / distSq1;
rightLegDirection = KInt2.ToInt2(relativePosition1.IntX * leg1 + relativePosition1.IntY * radius_, -relativePosition1.IntX * radius_ + relativePosition1.IntY * leg1) / distSq1;
if (isover(leftLegDirection) || isover(rightLegDirection))
{
LogMgr.LogError("!!!");
}
}
else if (s > 1 && distSqLine <= radiusSq)
{
/*
* Obstacle viewed obliquely so that
* right vertex defines velocity obstacle.
*/
if (!obstacle2.convex_)
{
/* Ignore obstacle. */
continue;
}
obstacle1 = obstacle2;
KInt leg2 = RVOMath.sqrt(distSq2 - radiusSq);
leftLegDirection = KInt2.ToInt2(relativePosition2.IntX * leg2 - relativePosition2.IntY * radius_, relativePosition2.IntX * radius_ + relativePosition2.IntY * leg2) / distSq2;
rightLegDirection = KInt2.ToInt2(relativePosition2.IntX * leg2 + relativePosition2.IntY * radius_, -relativePosition2.IntX * radius_ + relativePosition2.IntY * leg2) / distSq2;
if (isover(leftLegDirection) || isover(rightLegDirection))
{
LogMgr.LogError("!!!");
}
}
else
{
/* Usual situation. */
if (obstacle1.convex_)
{
KInt leg1 = RVOMath.sqrt(distSq1 - radiusSq);
leftLegDirection = KInt2.ToInt2(relativePosition1.IntX * leg1 - relativePosition1.IntY * radius_, relativePosition1.IntX * radius_ + relativePosition1.IntY * leg1) / distSq1;
if (isover(leftLegDirection))
{
LogMgr.LogError("!!!");
}
}
else
{
/* Left vertex non-convex; left leg extends cut-off line. */
leftLegDirection = -obstacle1.direction_;
if (isover(leftLegDirection))
{
LogMgr.LogError("!!!");
}
}
if (obstacle2.convex_)
{
KInt leg2 = RVOMath.sqrt(distSq2 - radiusSq);
rightLegDirection = KInt2.ToInt2(relativePosition2.IntX * leg2 + relativePosition2.IntY * radius_, -relativePosition2.IntX * radius_ + relativePosition2.IntY * leg2) / distSq2;
if (isover(rightLegDirection))
{
LogMgr.LogError("!!!");
}
}
else
{
/* Right vertex non-convex; right leg extends cut-off line. */
rightLegDirection = obstacle1.direction_;
if (isover(rightLegDirection))
{
LogMgr.LogError("!!!");
}
}
}
/*
* Legs can never point into neighboring edge when convex
* vertex, take cutoff-line of neighboring edge instead. If
* velocity projected on "foreign" leg, no constraint is added.
*/
Obstacle leftNeighbor = obstacle1.previous_;
bool isLeftLegForeign = false;
bool isRightLegForeign = false;
if (obstacle1.convex_ && RVOMath.det(leftLegDirection, -leftNeighbor.direction_) >= 0)
{
/* Left leg points into obstacle. */
leftLegDirection = -leftNeighbor.direction_;
if (isover(leftLegDirection))
{
LogMgr.LogError("!!!");
}
isLeftLegForeign = true;
}
if (obstacle2.convex_ && RVOMath.det(rightLegDirection, obstacle2.direction_) <= 0)
{
/* Right leg points into obstacle. */
rightLegDirection = obstacle2.direction_;
isRightLegForeign = true;
if (isover(rightLegDirection))
{
LogMgr.LogError("!!!");
}
}
/* Compute cut-off centers. */
KInt2 leftCutOff = (obstacle1.point_ - position_) / timeHorizonObst_;
KInt2 rightCutOff = (obstacle2.point_ - position_) / timeHorizonObst_;
KInt2 cutOffVector = rightCutOff - leftCutOff;
/* Project current velocity on velocity obstacle. */
/* Check if current velocity is projected on cutoff circles. */
KInt sqvalue = RVOMath.absSq(cutOffVector);
KInt t = KInt.ToInt(KInt.divscale / 2);
if (obstacle1 != obstacle2)
{
if (sqvalue == 0)
{
t = KInt.MaxValue;
}
else
{
t = RVOMath.Dot((velocity_ - leftCutOff), cutOffVector) / sqvalue;
}
}
KInt tLeft = RVOMath.Dot((velocity_ - leftCutOff), leftLegDirection);
KInt tRight = RVOMath.Dot((velocity_ - rightCutOff), rightLegDirection);
if ((t < 0 && tLeft < 0) || (obstacle1 == obstacle2 && tLeft < 0 && tRight < 0))
{
/* Project on left cut-off circle. */
KInt2 unitW = RVOMath.normalize((velocity_ - leftCutOff));
line.direction = KInt2.ToInt2(unitW.IntY, -unitW.IntX);
line.point = leftCutOff + radius_ * unitW / timeHorizonObst_;
orcaLines_.Add(line);
continue;
}
else if (t > 1 && tRight < 0)
{
/* Project on right cut-off circle. */
KInt2 unitW = RVOMath.normalize((velocity_ - rightCutOff));
line.direction = KInt2.ToInt2(unitW.IntY, -unitW.IntX);
line.point = rightCutOff + radius_ * unitW / timeHorizonObst_;
orcaLines_.Add(line);
continue;
}
/*
* Project on left leg, right leg, or cut-off line, whichever is
* closest to velocity.
*/
KInt distSqCutoff = (t < 0 || t > 1 || obstacle1 == obstacle2) ? KInt.MaxValue : RVOMath.absSq(velocity_ - (leftCutOff + t * cutOffVector));
KInt distSqLeft = tLeft < 0 ? KInt.MaxValue : RVOMath.absSq(velocity_ - (leftCutOff + tLeft * leftLegDirection));
KInt distSqRight = tRight < 0 ? KInt.MaxValue : RVOMath.absSq(velocity_ - (rightCutOff + tRight * rightLegDirection));
if (distSqCutoff <= distSqLeft && distSqCutoff <= distSqRight)
{
/* Project on cut-off line. */
line.direction = -obstacle1.direction_;
line.point = leftCutOff + radius_ * KInt2.ToInt2(-line.direction.IntY, line.direction.IntX) / timeHorizonObst_;
orcaLines_.Add(line);
continue;
}
if (distSqLeft <= distSqRight)
{
/* Project on left leg. */
if (isLeftLegForeign)
{
continue;
}
line.direction = leftLegDirection;
line.point = leftCutOff + radius_ * KInt2.ToInt2(-line.direction.IntY, line.direction.IntX) / timeHorizonObst_;
orcaLines_.Add(line);
continue;
}
/* Project on right leg. */
if (isRightLegForeign)
{
continue;
}
line.direction = -rightLegDirection;
line.point = rightCutOff + radius_ * KInt2.ToInt2(-line.direction.IntY, line.direction.IntX) / timeHorizonObst_;
orcaLines_.Add(line);
}
int numObstLines = orcaLines_.Count;
//KInt invTimeHorizon = 1 / timeHorizon_;
/* Create agent ORCA lines. */
for (int i = 0; i < agentNeighbors_.Count; ++i)
{
Agent other = agentNeighbors_[i].Value;
KInt2 relativePosition = other.position_ - position_;
KInt2 relativeVelocity = velocity_ - other.velocity_;
KInt distSq = RVOMath.absSq(relativePosition);
KInt combinedRadius = radius_ + other.radius_;
KInt combinedRadiusSq = RVOMath.sqr(combinedRadius);
Line line = new Line();
KInt2 u;
if (distSq > combinedRadiusSq)
{
/* No collision. */
KInt2 w = relativeVelocity - relativePosition / timeHorizon_;
/* Vector from cutoff center to relative velocity. */
KInt wLengthSq = RVOMath.absSq(w);
KInt dotProduct1 = RVOMath.Dot(w, relativePosition);
if (dotProduct1 < 0 && RVOMath.sqr(dotProduct1) > combinedRadiusSq * wLengthSq)
{
/* Project on cut-off circle. */
KInt wLength = RVOMath.sqrt(wLengthSq);
if (wLength == 0)
{
continue;
}
KInt2 unitW = w / wLength;
line.direction = KInt2.ToInt2(unitW.IntY, -unitW.IntX);
u = (combinedRadius / timeHorizon_ - wLength) * unitW;
}
else
{
/* Project on legs. */
KInt leg = RVOMath.sqrt(distSq - combinedRadiusSq);
if (RVOMath.det(relativePosition, w) > 0)
{
/* Project on left leg. */
line.direction = KInt2.ToInt2(relativePosition.IntX * leg - relativePosition.IntY * combinedRadius, relativePosition.IntX * combinedRadius + relativePosition.IntY * leg) / distSq;
}
else
{
/* Project on right leg. */
line.direction = -KInt2.ToInt2(relativePosition.IntX * leg + relativePosition.IntY * combinedRadius, -relativePosition.IntX * combinedRadius + relativePosition.IntY * leg) / distSq;
}
KInt dotProduct2 = RVOMath.Dot(relativeVelocity, line.direction);
u = dotProduct2 * line.direction - relativeVelocity;
}
}
else
{
/* Collision. Project on cut-off circle of time timeStep. */
//KInt invTimeStep = 1 / Simulator.Instance.timeStep_;
/* Vector from cutoff center to relative velocity. */
KInt2 w = relativeVelocity - relativePosition / Simulator.Instance.timeStep_;
KInt wLength = RVOMath.abs(w);
if (wLength == 0)
{
continue;
}
KInt2 unitW = w / wLength;
line.direction = KInt2.ToInt2(unitW.IntY, -unitW.IntX);
u = (combinedRadius / Simulator.Instance.timeStep_ - wLength) * unitW;
}
line.point = velocity_ + u / 2;
orcaLines_.Add(line);
}
int lineFail = linearProgram2(orcaLines_, maxSpeed_, prefVelocity_, false, ref newVelocity_);
if (lineFail < orcaLines_.Count)
{
linearProgram3(orcaLines_, numObstLines, lineFail, maxSpeed_, ref newVelocity_);
}
}
/**
* <summary>Computes the new velocity of this agent.</summary>
*/
internal void computeNewVelocity()
{
orcaLines_.Clear();
Fix64 invTimeHorizonObst = Fix64.One / timeHorizonObst_;
/* Create obstacle ORCA lines. */
for (int i = 0; i < obstacleNeighbors_.Count; ++i)
{
Obstacle obstacle1 = obstacleNeighbors_[i].Value;
Obstacle obstacle2 = obstacle1.next_;
Vec2 relativePosition1 = obstacle1.point_ - position_;
Vec2 relativePosition2 = obstacle2.point_ - position_;
/*
* Check if velocity obstacle of obstacle is already taken care
* of by previously constructed obstacle ORCA lines.
*/
bool alreadyCovered = false;
for (int j = 0; j < orcaLines_.Count; ++j)
{
if (RVOMath.det(invTimeHorizonObst * relativePosition1 - orcaLines_[j].point, orcaLines_[j].direction) - invTimeHorizonObst * radius_ >= -RVOMath.RVO_EPSILON && RVOMath.det(invTimeHorizonObst * relativePosition2 - orcaLines_[j].point, orcaLines_[j].direction) - invTimeHorizonObst * radius_ >= -RVOMath.RVO_EPSILON)
{
alreadyCovered = true;
break;
}
}
if (alreadyCovered)
{
continue;
}
/* Not yet covered. Check for collisions. */
Fix64 distSq1 = RVOMath.absSq(relativePosition1);
Fix64 distSq2 = RVOMath.absSq(relativePosition2);
Fix64 radiusSq = RVOMath.sqr(radius_);
Vec2 obstacleVector = obstacle2.point_ - obstacle1.point_;
Fix64 obstacleVectorSq = RVOMath.absSq(obstacleVector);
Fix64 s = obstacleVectorSq == Fix64.Zero ? Fix64.One : (-relativePosition1 * obstacleVector) / obstacleVectorSq;
Fix64 distSqLine = RVOMath.absSq(-relativePosition1 - s * obstacleVector);
Line line;
if (s < Fix64.Zero && distSq1 <= radiusSq)
{
/* Collision with left vertex. Ignore if non-convex. */
if (obstacle1.convex_)
{
line.point = Vec2.Zero;
line.direction = RVOMath.normalize(new Vec2(-relativePosition1.y, relativePosition1.x));
orcaLines_.Add(line);
}
continue;
}
else if (s > Fix64.One && distSq2 <= radiusSq)
{
/*
* Collision with right vertex. Ignore if non-convex or if
* it will be taken care of by neighboring obstacle.
*/
if (obstacle2.convex_ && RVOMath.det(relativePosition2, obstacle2.direction_) >= Fix64.Zero)
{
line.point = Vec2.Zero;
line.direction = RVOMath.normalize(new Vec2(-relativePosition2.y, relativePosition2.x));
orcaLines_.Add(line);
}
continue;
}
else if (s >= Fix64.Zero && s < Fix64.One && distSqLine <= radiusSq)
{
/* Collision with obstacle segment. */
line.point = Vec2.Zero;
line.direction = -obstacle1.direction_;
orcaLines_.Add(line);
continue;
}
/*
* No collision. Compute legs. When obliquely viewed, both legs
* can come from a single vertex. Legs extend cut-off line when
* non-convex vertex.
*/
Vec2 leftLegDirection, rightLegDirection;
if (s < Fix64.Zero && distSqLine <= radiusSq)
{
/*
* Obstacle viewed obliquely so that left vertex
* defines velocity obstacle.
*/
if (!obstacle1.convex_)
{
/* Ignore obstacle. */
continue;
}
obstacle2 = obstacle1;
Fix64 leg1 = RVOMath.sqrt((distSq1 - radiusSq).Clamp(Fix64.Zero, Fix64.MaxValue));
leftLegDirection = new Vec2(relativePosition1.x * leg1 - relativePosition1.y * radius_, relativePosition1.x * radius_ + relativePosition1.y * leg1) / distSq1;
rightLegDirection = new Vec2(relativePosition1.x * leg1 + relativePosition1.y * radius_, -relativePosition1.x * radius_ + relativePosition1.y * leg1) / distSq1;
}
else if (s > Fix64.One && distSqLine <= radiusSq)
{
/*
* Obstacle viewed obliquely so that
* right vertex defines velocity obstacle.
*/
if (!obstacle2.convex_)
{
/* Ignore obstacle. */
continue;
}
obstacle1 = obstacle2;
Fix64 leg2 = RVOMath.sqrt((distSq2 - radiusSq).Clamp(Fix64.Zero, Fix64.MaxValue));
leftLegDirection = new Vec2(relativePosition2.x * leg2 - relativePosition2.y * radius_, relativePosition2.x * radius_ + relativePosition2.y * leg2) / distSq2;
rightLegDirection = new Vec2(relativePosition2.x * leg2 + relativePosition2.y * radius_, -relativePosition2.x * radius_ + relativePosition2.y * leg2) / distSq2;
}
else
{
/* Usual situation. */
if (obstacle1.convex_)
{
Fix64 leg1 = RVOMath.sqrt((distSq1 - radiusSq).Clamp(Fix64.Zero, Fix64.MaxValue));
leftLegDirection = new Vec2(relativePosition1.x * leg1 - relativePosition1.y * radius_, relativePosition1.x * radius_ + relativePosition1.y * leg1) / distSq1;
}
else
{
/* Left vertex non-convex; left leg extends cut-off line. */
leftLegDirection = -obstacle1.direction_;
}
if (obstacle2.convex_)
{
Fix64 leg2 = RVOMath.sqrt((distSq2 - radiusSq).Clamp(Fix64.Zero, Fix64.MaxValue));
rightLegDirection = new Vec2(relativePosition2.x * leg2 + relativePosition2.y * radius_, -relativePosition2.x * radius_ + relativePosition2.y * leg2) / distSq2;
}
else
{
/* Right vertex non-convex; right leg extends cut-off line. */
rightLegDirection = obstacle1.direction_;
}
}
/*
* Legs can never point into neighboring edge when convex
* vertex, take cutoff-line of neighboring edge instead. If
* velocity projected on "foreign" leg, no constraint is added.
*/
Obstacle leftNeighbor = obstacle1.previous_;
bool isLeftLegForeign = false;
bool isRightLegForeign = false;
if (obstacle1.convex_ && RVOMath.det(leftLegDirection, -leftNeighbor.direction_) >= Fix64.Zero)
{
/* Left leg points into obstacle. */
leftLegDirection = -leftNeighbor.direction_;
isLeftLegForeign = true;
}
if (obstacle2.convex_ && RVOMath.det(rightLegDirection, obstacle2.direction_) <= Fix64.Zero)
{
/* Right leg points into obstacle. */
rightLegDirection = obstacle2.direction_;
isRightLegForeign = true;
}
/* Compute cut-off centers. */
Vec2 leftCutOff = invTimeHorizonObst * (obstacle1.point_ - position_);
Vec2 rightCutOff = invTimeHorizonObst * (obstacle2.point_ - position_);
Vec2 cutOffVector = rightCutOff - leftCutOff;
/* Project current velocity on velocity obstacle. */
/* Check if current velocity is projected on cutoff circles. */
Fix64 cutOffVectorSq = RVOMath.absSq(cutOffVector);
Fix64 t = obstacle1 == obstacle2 || cutOffVectorSq == Fix64.Zero ? 0.5f : ((velocity_ - leftCutOff) * cutOffVector) / cutOffVectorSq;
Fix64 tLeft = (velocity_ - leftCutOff) * leftLegDirection;
Fix64 tRight = (velocity_ - rightCutOff) * rightLegDirection;
if ((t < Fix64.Zero && tLeft < Fix64.Zero) || (obstacle1 == obstacle2 && tLeft < Fix64.Zero && tRight < Fix64.Zero))
{
/* Project on left cut-off circle. */
Vec2 unitW = RVOMath.normalize(velocity_ - leftCutOff);
line.direction = new Vec2(unitW.y, -unitW.x);
line.point = leftCutOff + radius_ * invTimeHorizonObst * unitW;
orcaLines_.Add(line);
continue;
}
else if (t > Fix64.One && tRight < Fix64.Zero)
{
/* Project on right cut-off circle. */
Vec2 unitW = RVOMath.normalize(velocity_ - rightCutOff);
line.direction = new Vec2(unitW.y, -unitW.x);
line.point = rightCutOff + radius_ * invTimeHorizonObst * unitW;
orcaLines_.Add(line);
continue;
}
/*
* Project on left leg, right leg, or cut-off line, whichever is
* closest to velocity.
*/
Fix64 distSqCutoff = (t <Fix64.Zero || t> Fix64.One || obstacle1 == obstacle2) ? Fix64.MaxValue : RVOMath.absSq(velocity_ - (leftCutOff + t * cutOffVector));
Fix64 distSqLeft = tLeft < Fix64.Zero ? Fix64.MaxValue : RVOMath.absSq(velocity_ - (leftCutOff + tLeft * leftLegDirection));
Fix64 distSqRight = tRight < Fix64.Zero ? Fix64.MaxValue : RVOMath.absSq(velocity_ - (rightCutOff + tRight * rightLegDirection));
if (distSqCutoff <= distSqLeft && distSqCutoff <= distSqRight)
{
/* Project on cut-off line. */
line.direction = -obstacle1.direction_;
line.point = leftCutOff + radius_ * invTimeHorizonObst * new Vec2(-line.direction.y, line.direction.x);
orcaLines_.Add(line);
continue;
}
if (distSqLeft <= distSqRight)
{
/* Project on left leg. */
if (isLeftLegForeign)
{
continue;
}
line.direction = leftLegDirection;
line.point = leftCutOff + radius_ * invTimeHorizonObst * new Vec2(-line.direction.y, line.direction.x);
orcaLines_.Add(line);
continue;
}
/* Project on right leg. */
if (isRightLegForeign)
{
continue;
}
line.direction = -rightLegDirection;
line.point = rightCutOff + radius_ * invTimeHorizonObst * new Vec2(-line.direction.y, line.direction.x);
orcaLines_.Add(line);
}
int numObstLines = orcaLines_.Count;
Fix64 invTimeHorizon = Fix64.One / timeHorizon_;
/* Create agent ORCA lines. */
for (int i = 0; i < agentNeighbors_.Count; ++i)
{
Agent other = agentNeighbors_[i].Value;
Vec2 relativePosition = other.position_ - position_;
Vec2 relativeVelocity = velocity_ - other.velocity_;
Fix64 distSq = RVOMath.absSq(relativePosition);
Fix64 combinedRadius = radius_ + other.radius_;
Fix64 combinedRadiusSq = RVOMath.sqr(combinedRadius);
Line line;
Vec2 u;
if (distSq > combinedRadiusSq)
{
/* No collision. */
Vec2 w = relativeVelocity - invTimeHorizon * relativePosition;
/* the w has a change to be zero exactly.
* for example: the two objects are at the exactly same position and with the exactly same velocity
* so we have to make some perturbation to separate them */
if (w == Vec2.Zero)
{
w = id_ > other.id_ ? Vec2.Left : Vec2.Right;
}
/* Vector from cutoff center to relative velocity. */
Fix64 wLengthSq = RVOMath.absSq(w);
Fix64 dotProduct1 = w * relativePosition;
if (dotProduct1 < Fix64.Zero && RVOMath.sqr(dotProduct1) > combinedRadiusSq * wLengthSq)
{
/* Project on cut-off circle. */
Fix64 wLength = RVOMath.sqrt(wLengthSq);
Vec2 unitW = w / wLength;
line.direction = new Vec2(unitW.y, -unitW.x);
u = (combinedRadius * invTimeHorizon - wLength) * unitW;
}
else
{
/* Project on legs. */
Fix64 leg = RVOMath.sqrt(distSq - combinedRadiusSq);
if (RVOMath.det(relativePosition, w) > Fix64.Zero)
{
/* Project on left leg. */
line.direction = new Vec2(relativePosition.x * leg - relativePosition.y * combinedRadius, relativePosition.x * combinedRadius + relativePosition.y * leg) / distSq;
}
else
{
/* Project on right leg. */
line.direction = -new Vec2(relativePosition.x * leg + relativePosition.y * combinedRadius, -relativePosition.x * combinedRadius + relativePosition.y * leg) / distSq;
}
Fix64 dotProduct2 = relativeVelocity * line.direction;
u = dotProduct2 * line.direction - relativeVelocity;
}
}
else
{
/* Collision. Project on cut-off circle of time timeStep. */
Fix64 invTimeStep = Fix64.One / simulator_.timeStep_;
/* Vector from cutoff center to relative velocity. */
Vec2 w = relativeVelocity - invTimeStep * relativePosition;
/* the w has a change to be zero exactly.
* for example: the two objects are at the exactly same position and with the exactly same velocity
* so we have to make some perturbation to separate them */
if (w == Vec2.Zero)
{
w = id_ > other.id_ ? Vec2.Left : Vec2.Right;
}
Fix64 wLength = RVOMath.abs(w);
Vec2 unitW = wLength == Fix64.Zero ? Vec2.Zero : w / wLength;
line.direction = new Vec2(unitW.y, -unitW.x);
u = (combinedRadius * invTimeStep - wLength) * unitW;
}
line.point = velocity_ + 0.5f * u;
orcaLines_.Add(line);
}
int lineFail = linearProgram2(orcaLines_, maxSpeed_, prefVelocity_, false, ref newVelocity_);
if (lineFail < orcaLines_.Count)
{
linearProgram3(orcaLines_, numObstLines, lineFail, maxSpeed_, ref newVelocity_);
}
}
/**
* <summary>Computes the new velocity of this agent.</summary>
*/
internal void computeNewVelocity()
{
if (isKinematic)
{
newVelocity_ = prefVelocity_ / prefVelocity_.magnitude * maxSpeed_;
return;
}
orcaLines_.Clear();
float invTimeHorizonObst = 1.0f / timeHorizonObst_;
/* Create obstacle ORCA lines. */
for (int i = 0; i < obstacleNeighbors_.Count; ++i)
{
Obstacle obstacle1 = obstacleNeighbors_[i].Value;
Obstacle obstacle2 = obstacle1.next_;
Vector2 relativePosition1 = obstacle1.point_ - position_;
Vector2 relativePosition2 = obstacle2.point_ - position_;
/*
* Check if velocity obstacle of obstacle is already taken care
* of by previously constructed obstacle ORCA lines.
*/
bool alreadyCovered = false;
for (int j = 0; j < orcaLines_.Count; ++j)
{
if (RVOMath.det(invTimeHorizonObst * relativePosition1 - orcaLines_[j].point, orcaLines_[j].direction) - invTimeHorizonObst * radius_ >= -RVOMath.RVO_EPSILON && RVOMath.det(invTimeHorizonObst * relativePosition2 - orcaLines_[j].point, orcaLines_[j].direction) - invTimeHorizonObst * radius_ >= -RVOMath.RVO_EPSILON)
{
alreadyCovered = true;
break;
}
}
if (alreadyCovered)
{
continue;
}
/* Not yet covered. Check for collisions. */
float distSq1 = RVOMath.absSq(relativePosition1);
float distSq2 = RVOMath.absSq(relativePosition2);
float radiusSq = RVOMath.sqr(radius_);
Vector2 obstacleVector = obstacle2.point_ - obstacle1.point_;
float s = Vector2.Dot(-relativePosition1, obstacleVector) / RVOMath.absSq(obstacleVector);
float distSqLine = RVOMath.absSq(-relativePosition1 - s * obstacleVector);
Line line;
if (s < 0.0f && distSq1 <= radiusSq)
{
/* Collision with left vertex. Ignore if non-convex. */
if (obstacle1.convex_)
{
line.point = new Vector2(0.0f, 0.0f);
line.direction = RVOMath.normalize(new Vector2(-relativePosition1.y, relativePosition1.x));
orcaLines_.Add(line);
}
continue;
}
else if (s > 1.0f && distSq2 <= radiusSq)
{
/*
* Collision with right vertex. Ignore if non-convex or if
* it will be taken care of by neighboring obstacle.
*/
if (obstacle2.convex_ && RVOMath.det(relativePosition2, obstacle2.direction_) >= 0.0f)
{
line.point = new Vector2(0.0f, 0.0f);
line.direction = RVOMath.normalize(new Vector2(-relativePosition2.y, relativePosition2.x));
orcaLines_.Add(line);
}
continue;
}
else if (s >= 0.0f && s < 1.0f && distSqLine <= radiusSq)
{
/* Collision with obstacle segment. */
line.point = new Vector2(0.0f, 0.0f);
line.direction = -obstacle1.direction_;
orcaLines_.Add(line);
continue;
}
/*
* No collision. Compute legs. When obliquely viewed, both legs
* can come from a single vertex. Legs extend cut-off line when
* non-convex vertex.
*/
Vector2 leftLegDirection, rightLegDirection;
if (s < 0.0f && distSqLine <= radiusSq)
{
/*
* Obstacle viewed obliquely so that left vertex
* defines velocity obstacle.
*/
if (!obstacle1.convex_)
{
/* Ignore obstacle. */
continue;
}
obstacle2 = obstacle1;
float leg1 = RVOMath.sqrt(distSq1 - radiusSq);
leftLegDirection = new Vector2(relativePosition1.x * leg1 - relativePosition1.y * radius_, relativePosition1.x * radius_ + relativePosition1.y * leg1) / distSq1;
rightLegDirection = new Vector2(relativePosition1.x * leg1 + relativePosition1.y * radius_, -relativePosition1.x * radius_ + relativePosition1.y * leg1) / distSq1;
}
else if (s > 1.0f && distSqLine <= radiusSq)
{
/*
* Obstacle viewed obliquely so that
* right vertex defines velocity obstacle.
*/
if (!obstacle2.convex_)
{
/* Ignore obstacle. */
continue;
}
obstacle1 = obstacle2;
float leg2 = RVOMath.sqrt(distSq2 - radiusSq);
leftLegDirection = new Vector2(relativePosition2.x * leg2 - relativePosition2.y * radius_, relativePosition2.x * radius_ + relativePosition2.y * leg2) / distSq2;
rightLegDirection = new Vector2(relativePosition2.x * leg2 + relativePosition2.y * radius_, -relativePosition2.x * radius_ + relativePosition2.y * leg2) / distSq2;
}
else
{
/* Usual situation. */
if (obstacle1.convex_)
{
float leg1 = RVOMath.sqrt(distSq1 - radiusSq);
leftLegDirection = new Vector2(relativePosition1.x * leg1 - relativePosition1.y * radius_, relativePosition1.x * radius_ + relativePosition1.y * leg1) / distSq1;
}
else
{
/* Left vertex non-convex; left leg extends cut-off line. */
leftLegDirection = -obstacle1.direction_;
}
if (obstacle2.convex_)
{
float leg2 = RVOMath.sqrt(distSq2 - radiusSq);
rightLegDirection = new Vector2(relativePosition2.x * leg2 + relativePosition2.y * radius_, -relativePosition2.x * radius_ + relativePosition2.y * leg2) / distSq2;
}
else
{
/* Right vertex non-convex; right leg extends cut-off line. */
rightLegDirection = obstacle1.direction_;
}
}
/*
* Legs can never point into neighboring edge when convex
* vertex, take cutoff-line of neighboring edge instead. If
* velocity projected on "foreign" leg, no constraint is added.
*/
Obstacle leftNeighbor = obstacle1.previous_;
bool isLeftLegForeign = false;
bool isRightLegForeign = false;
if (obstacle1.convex_ && RVOMath.det(leftLegDirection, -leftNeighbor.direction_) >= 0.0f)
{
/* Left leg points into obstacle. */
leftLegDirection = -leftNeighbor.direction_;
isLeftLegForeign = true;
}
if (obstacle2.convex_ && RVOMath.det(rightLegDirection, obstacle2.direction_) <= 0.0f)
{
/* Right leg points into obstacle. */
rightLegDirection = obstacle2.direction_;
isRightLegForeign = true;
}
/* Compute cut-off centers. */
Vector2 leftCutOff = invTimeHorizonObst * (obstacle1.point_ - position_);
Vector2 rightCutOff = invTimeHorizonObst * (obstacle2.point_ - position_);
Vector2 cutOffVector = rightCutOff - leftCutOff;
/* Project current velocity on velocity obstacle. */
/* Check if current velocity is projected on cutoff circles. */
float t = obstacle1 == obstacle2 ? 0.5f : Vector2.Dot((velocity_ - leftCutOff), cutOffVector) / RVOMath.absSq(cutOffVector);
float tLeft = Vector2.Dot(velocity_ - leftCutOff, leftLegDirection);
float tRight = Vector2.Dot(velocity_ - rightCutOff, rightLegDirection);
if ((t < 0.0f && tLeft < 0.0f) || (obstacle1 == obstacle2 && tLeft < 0.0f && tRight < 0.0f))
{
/* Project on left cut-off circle. */
Vector2 unitW = RVOMath.normalize(velocity_ - leftCutOff);
line.direction = new Vector2(unitW.y, -unitW.x);
line.point = leftCutOff + radius_ * invTimeHorizonObst * unitW;
orcaLines_.Add(line);
continue;
}
else if (t > 1.0f && tRight < 0.0f)
{
/* Project on right cut-off circle. */
Vector2 unitW = RVOMath.normalize(velocity_ - rightCutOff);
line.direction = new Vector2(unitW.y, -unitW.x);
line.point = rightCutOff + radius_ * invTimeHorizonObst * unitW;
orcaLines_.Add(line);
continue;
}
/*
* Project on left leg, right leg, or cut-off line, whichever is
* closest to velocity.
*/
float distSqCutoff = (t <0.0f || t> 1.0f || obstacle1 == obstacle2) ? float.PositiveInfinity : RVOMath.absSq(velocity_ - (leftCutOff + t * cutOffVector));
float distSqLeft = tLeft < 0.0f ? float.PositiveInfinity : RVOMath.absSq(velocity_ - (leftCutOff + tLeft * leftLegDirection));
float distSqRight = tRight < 0.0f ? float.PositiveInfinity : RVOMath.absSq(velocity_ - (rightCutOff + tRight * rightLegDirection));
if (distSqCutoff <= distSqLeft && distSqCutoff <= distSqRight)
{
/* Project on cut-off line. */
line.direction = -obstacle1.direction_;
line.point = leftCutOff + radius_ * invTimeHorizonObst * new Vector2(-line.direction.y, line.direction.x);
orcaLines_.Add(line);
continue;
}
if (distSqLeft <= distSqRight)
{
/* Project on left leg. */
if (isLeftLegForeign)
{
continue;
}
line.direction = leftLegDirection;
line.point = leftCutOff + radius_ * invTimeHorizonObst * new Vector2(-line.direction.y, line.direction.x);
orcaLines_.Add(line);
continue;
}
/* Project on right leg. */
if (isRightLegForeign)
{
continue;
}
line.direction = -rightLegDirection;
line.point = rightCutOff + radius_ * invTimeHorizonObst * new Vector2(-line.direction.y, line.direction.x);
orcaLines_.Add(line);
}
int numObstLines = orcaLines_.Count;
float invTimeHorizon = 1.0f / timeHorizon_;
/* Create agent ORCA lines. */
for (int i = 0; i < agentNeighbors_.Count; ++i)
{
Agent other = agentNeighbors_[i].Value;
Vector2 relativePosition = other.position_ - position_;
Vector2 relativeVelocity = velocity_ - other.velocity_;
float distSq = RVOMath.absSq(relativePosition);
float combinedRadius = radius_ + other.radius_;
float combinedRadiusSq = RVOMath.sqr(combinedRadius);
Line line;
Vector2 u;
if (distSq > combinedRadiusSq)
{
/* No collision. */
Vector2 w = relativeVelocity - invTimeHorizon * relativePosition;
/* Vector from cutoff center to relative velocity. */
float wLengthSq = RVOMath.absSq(w);
float dotProduct1 = Vector2.Dot(w, relativePosition);
if (dotProduct1 < 0.0f && RVOMath.sqr(dotProduct1) > combinedRadiusSq * wLengthSq)
{
/* Project on cut-off circle. */
float wLength = RVOMath.sqrt(wLengthSq);
Vector2 unitW = w / wLength;
line.direction = new Vector2(unitW.y, -unitW.x);
u = (combinedRadius * invTimeHorizon - wLength) * unitW;
}
else
{
/* Project on legs. */
float leg = RVOMath.sqrt(distSq - combinedRadiusSq);
if (RVOMath.det(relativePosition, w) > 0.0f)
{
/* Project on left leg. */
line.direction = new Vector2(relativePosition.x * leg - relativePosition.y * combinedRadius, relativePosition.x * combinedRadius + relativePosition.y * leg) / distSq;
}
else
{
/* Project on right leg. */
line.direction = -new Vector2(relativePosition.x * leg + relativePosition.y * combinedRadius, -relativePosition.x * combinedRadius + relativePosition.y * leg) / distSq;
}
float dotProduct2 = Vector2.Dot(relativeVelocity, line.direction);
u = dotProduct2 * line.direction - relativeVelocity;
}
}
else
{
/* Collision. Project on cut-off circle of time timeStep. */
float invTimeStep = 1.0f / Simulator.Instance.timeStep_;
/* Vector from cutoff center to relative velocity. */
Vector2 w = relativeVelocity - invTimeStep * relativePosition;
float wLength = RVOMath.abs(w);
Vector2 unitW = w / wLength;
line.direction = new Vector2(unitW.y, -unitW.x);
u = (combinedRadius * invTimeStep - wLength) * unitW;
}
if (!other.isKinematic)
{
line.point = velocity_ + 0.5f * u;
}
else
{
line.point = relativeVelocity;
}
orcaLines_.Add(line);
}
int lineFail = linearProgram2(orcaLines_, maxSpeed_, prefVelocity_, false, ref newVelocity_);
if (lineFail < orcaLines_.Count)
{
linearProgram3(orcaLines_, numObstLines, lineFail, maxSpeed_, ref newVelocity_);
}
}
private void acceleratedProgram(Vector2 velocity, ref Vector2 result)
{
//Debug.Log(velocity.ToString() + " " + result.ToString());
float speed = RVOMath.abs(velocity);
float maxSpeed = RVOMath.Min(speed + accelerated_, maxSpeed_);
float minSpeed = RVOMath.Max(speed - accelerated_, 0.0f);
Vector2 tempResult = result;
//Debug.Log(speed);
if (speed >= minSpeedToTurn_)
{
Vector2 leftVerticalVelocity = new Vector2(-velocity.y_, velocity.x_);
Vector2 rightVerticalVelocity = new Vector2(velocity.y_, -velocity.x_);
leftVerticalVelocity = RVOMath.normalize(leftVerticalVelocity) * speed * angularSpeed_;
rightVerticalVelocity = RVOMath.normalize(rightVerticalVelocity) * speed * angularSpeed_;
Vector2 leftMin = RVOMath.normalize(velocity + leftVerticalVelocity) * minSpeed;
Vector2 leftMax = RVOMath.normalize(velocity + leftVerticalVelocity) * maxSpeed;
Vector2 rightMin = RVOMath.normalize(velocity + rightVerticalVelocity) * minSpeed;
Vector2 rightMax = RVOMath.normalize(velocity + rightVerticalVelocity) * maxSpeed;
Vector2 leftVector2 = leftMax - leftMin;
Vector2 rightVector2 = rightMax - rightMin;
if (RVOMath.det(leftVector2, result) < 0.0f && RVOMath.det(rightVector2, result) > 0.0f) //middle
{
float resultSpeed = RVOMath.abs(result);
if (resultSpeed > maxSpeed)
{
tempResult = RVOMath.normalize(result) * maxSpeed;
}
if (resultSpeed < minSpeed)
{
tempResult = RVOMath.normalize(result) * minSpeed;
}
}
else
{
if (RVOMath.det(leftVector2, result) > 0.0f) //left
{
float r = ((result - leftMin) * (leftMax - leftMin)) / RVOMath.absSq(leftMax - leftMin);
if (id_ == 2)
{
Debug.Log(r);
}
if (r < 0.0f)
{
tempResult = RVOMath.normalize(leftVector2) * minSpeed;
}
if (r > 1.0f)
{
tempResult = RVOMath.normalize(leftVector2) * maxSpeed;
}
if (r >= 0.0f && r <= 1.0f)
{
float resultSpeed = RVOMath.absSq(result) - RVOMath.distSqPointLineSegment(leftMin, leftMax, result);
resultSpeed = RVOMath.sqrt(resultSpeed);
if (resultSpeed > maxSpeed)
{
tempResult = RVOMath.normalize(leftVector2) * maxSpeed;
}
if (resultSpeed < minSpeed)
{
tempResult = RVOMath.normalize(leftVector2) * minSpeed;
}
if (resultSpeed >= minSpeed && resultSpeed <= maxSpeed)
{
tempResult = RVOMath.normalize(leftVector2) * resultSpeed;
}
}
}
if (RVOMath.det(rightVector2, result) < 0.0f) //right
{
float r = ((result - rightMin) * (rightMax - rightMin)) / RVOMath.absSq(rightMax - rightMin);
if (r < 0.0f)
{
tempResult = RVOMath.normalize(rightVector2) * minSpeed;
}
if (r > 1.0f)
{
tempResult = RVOMath.normalize(rightVector2) * maxSpeed;
}
if (r >= 0.0f && r <= 1.0f)
{
float resultSpeed = RVOMath.absSq(result) - RVOMath.distSqPointLineSegment(rightMin, rightMax, result);
resultSpeed = RVOMath.sqrt(resultSpeed);
if (resultSpeed > maxSpeed)
{
tempResult = RVOMath.normalize(rightVector2) * maxSpeed;
}
if (resultSpeed < minSpeed)
{
tempResult = RVOMath.normalize(rightVector2) * minSpeed;
}
if (resultSpeed >= minSpeed && resultSpeed <= maxSpeed)
{
tempResult = RVOMath.normalize(rightVector2) * resultSpeed;
}
}
}
}
}
else
{
float resultSpeed = RVOMath.abs(result);
if (resultSpeed > maxSpeed)
{
if (RVOMath.abs(velocity) < 1e-6f)
{
tempResult = RVOMath.normalize(prefVelocity_) * maxSpeed;
}
else
{
tempResult = RVOMath.normalize(velocity) * maxSpeed;
}
}
if (resultSpeed < minSpeed)
{
tempResult = RVOMath.normalize(velocity) * minSpeed;
}
}
result = tempResult;
}
/**
* <summary>Solves a two-dimensional linear program subject to linear
* constraints defined by lines and a circular constraint.</summary>
*
* <param name="lines">Lines defining the linear constraints.</param>
* <param name="numObstLines">Count of obstacle lines.</param>
* <param name="beginLine">The line on which the 2-d linear program
* failed.</param>
* <param name="radius">The radius of the circular constraint.</param>
* <param name="result">A reference to the result of the linear program.
* </param>
*/
private void linearProgram3(IList <Line> lines, int numObstLines, int beginLine, float radius, ref Vector2 result)
{
if (mass_ != 1)
{
Debug.Log("linearProgram3 beginLine:" + beginLine);
}
float distance = 0.0f;
// 遍历所有剩余ORCA线
for (int i = beginLine; i < lines.Count; ++i)
{
// 每一条 ORCA 线都需要精确的做出处理，distance 为 最大违规的速度
if (RVOMath.det(lines[i].direction, lines[i].point - result) > distance)
{
/* Result does not satisfy constraint of line i. */
IList <Line> projLines = new List <Line>();
// 1.静态阻挡的orca线直接加到projLines中
for (int ii = 0; ii < numObstLines; ++ii)
{
projLines.Add(lines[ii]);
}
// 2.动态阻挡的orca线需要重新计算line，从第一个非静态阻挡到当前的orca线
for (int j = numObstLines; j < i; ++j)
{
Line line;
float determinant = RVOMath.det(lines[i].direction, lines[j].direction);
if (RVOMath.fabs(determinant) <= RVOMath.RVO_EPSILON)
{
/* Line i and line j are parallel. */
if (lines[i].direction * lines[j].direction > 0.0f)
{
/* Line i and line j point in the same direction. */
// 2-1 两条线平行且同向
continue;
}
else
{
/* Line i and line j point in opposite direction. */
// 2-2 两条线平行且反向
line.point = 0.5f * (lines[i].point + lines[j].point);
}
}
else
{
// 2-3 两条线不平行
line.point = lines[i].point + (RVOMath.det(lines[j].direction, lines[i].point - lines[j].point) / determinant) * lines[i].direction;
}
// 计算ORCA线的方向
line.direction = RVOMath.normalize(lines[j].direction - lines[i].direction);
projLines.Add(line);
}
// 3.再次计算最优速度
Vector2 tempResult = result;
// 注意这里的 new Vector2(-lines[i].direction.y(), lines[i].direction.x()) 是方向向量
if (linearProgram2(projLines, radius, new Vector2(-lines[i].direction.y(), lines[i].direction.x()), true, ref result) < projLines.Count)
{
/*
* This should in principle not happen. The result is by
* definition already in the feasible region of this
* linear program. If it fails, it is due to small
* floating point error, and the current result is kept.
*/
result = tempResult;
}
distance = RVOMath.det(lines[i].direction, lines[i].point - result);
}
}
}