- Integrated NavigationServer and Navigation2DServer.

- Added Navigation Agents and Obstacles.
- Integrated Collision Avoidance.

This work has been kindly sponsored by IMVU.

10 files changed, 1923 insertions, 0 deletions

diff --git a/thirdparty/rvo2/LICENSE b/thirdparty/rvo2/LICENSE
new file mode 100644
index 0000000000..d645695673
--- /dev/null
+++ b/thirdparty/rvo2/LICENSE
@@ -0,0 +1,202 @@
+
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diff --git a/thirdparty/rvo2/README.md b/thirdparty/rvo2/README.md
new file mode 100644
index 0000000000..96af597cb6
--- /dev/null
+++ b/thirdparty/rvo2/README.md
@@ -0,0 +1,32 @@
+Optimal Reciprocal Collision Avoidance in Three Dimensions
+==========================================================
+
+<http://gamma.cs.unc.edu/RVO2/>
+
+[![Build Status](https://travis-ci.org/snape/RVO2-3D.png?branch=master)](https://travis-ci.org/snape/RVO2-3D)
+[![Build status](https://ci.appveyor.com/api/projects/status/ov8ec3igv588wpx7/branch/master?svg=true)](https://ci.appveyor.com/project/snape/rvo2-3d)
+
+Copyright 2008 University of North Carolina at Chapel Hill
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+<http://www.apache.org/licenses/LICENSE-2.0>
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+Please send all bug reports to [geom@cs.unc.edu](mailto:geom@cs.unc.edu).
+
+The authors may be contacted via:
+
+Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, and Dinesh Manocha  
+Dept. of Computer Science  
+201 S. Columbia St.  
+Frederick P. Brooks, Jr. Computer Science Bldg.  
+Chapel Hill, N.C. 27599-3175  
+United States of America
diff --git a/thirdparty/rvo2/src/API.h b/thirdparty/rvo2/src/API.h
new file mode 100644
index 0000000000..c63a5a383c
--- /dev/null
+++ b/thirdparty/rvo2/src/API.h
@@ -0,0 +1,71 @@
+/*
+ * API.h
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+/**
+ * \file    API.h
+ * \brief   Contains definitions related to Microsoft Windows.
+ */
+
+#ifndef RVO_API_H_
+#define RVO_API_H_
+
+#ifdef _WIN32
+#include <SDKDDKVer.h>
+#define WIN32_LEAN_AND_MEAN
+#define NOCOMM
+#define NOIMAGE
+#define NOIME
+#define NOKANJI
+#define NOMCX
+#ifndef NOMINMAX
+#define NOMINMAX
+#endif
+#define NOPROXYSTUB
+#define NOSERVICE
+#define NOSOUND
+#define NOTAPE
+#define NORPC
+#define _USE_MATH_DEFINES
+#include <windows.h>
+#undef CONNECT_DEFERRED // Avoid collision with the Godot Object class
+#undef CreateDialog // Avoid collision with the Godot CreateDialog class
+#endif
+
+#ifdef RVO_EXPORTS
+#define RVO_API __declspec(dllexport)
+#elif defined(RVO_IMPORTS)
+#define RVO_API __declspec(dllimport)
+#else
+#define RVO_API
+#endif
+
+#endif /* RVO_API_H_ */
diff --git a/thirdparty/rvo2/src/Agent.cpp b/thirdparty/rvo2/src/Agent.cpp
new file mode 100644
index 0000000000..851d780758
--- /dev/null
+++ b/thirdparty/rvo2/src/Agent.cpp
@@ -0,0 +1,425 @@
+/*
+ * Agent.cpp
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+#include "Agent.h"
+
+#include <algorithm>
+#include <cmath>
+
+#include "Definitions.h"
+#include "KdTree.h"
+
+namespace RVO {
+/**
+	 * \brief   A sufficiently small positive number.
+	 */
+const float RVO_EPSILON = 0.00001f;
+
+/**
+	 * \brief   Defines a directed line.
+	 */
+class Line {
+public:
+    /**
+		 * \brief   The direction of the directed line.
+		 */
+    Vector3 direction;
+
+    /**
+		 * \brief   A point on the directed line.
+		 */
+    Vector3 point;
+};
+
+/**
+	 * \brief   Solves a one-dimensional linear program on a specified line subject to linear constraints defined by planes and a spherical constraint.
+	 * \param   planes        Planes defining the linear constraints.
+	 * \param   planeNo       The plane on which the line lies.
+	 * \param   line          The line on which the 1-d linear program is solved
+	 * \param   radius        The radius of the spherical constraint.
+	 * \param   optVelocity   The optimization velocity.
+	 * \param   directionOpt  True if the direction should be optimized.
+	 * \param   result        A reference to the result of the linear program.
+	 * \return  True if successful.
+	 */
+bool linearProgram1(const std::vector<Plane> &planes, size_t planeNo, const Line &line, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result);
+
+/**
+	 * \brief   Solves a two-dimensional linear program on a specified plane subject to linear constraints defined by planes and a spherical constraint.
+	 * \param   planes        Planes defining the linear constraints.
+	 * \param   planeNo       The plane on which the 2-d linear program is solved
+	 * \param   radius        The radius of the spherical constraint.
+	 * \param   optVelocity   The optimization velocity.
+	 * \param   directionOpt  True if the direction should be optimized.
+	 * \param   result        A reference to the result of the linear program.
+	 * \return  True if successful.
+	 */
+bool linearProgram2(const std::vector<Plane> &planes, size_t planeNo, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result);
+
+/**
+	 * \brief   Solves a three-dimensional linear program subject to linear constraints defined by planes and a spherical constraint.
+	 * \param   planes        Planes defining the linear constraints.
+	 * \param   radius        The radius of the spherical constraint.
+	 * \param   optVelocity   The optimization velocity.
+	 * \param   directionOpt  True if the direction should be optimized.
+	 * \param   result        A reference to the result of the linear program.
+	 * \return  The number of the plane it fails on, and the number of planes if successful.
+	 */
+size_t linearProgram3(const std::vector<Plane> &planes, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result);
+
+/**
+	 * \brief   Solves a four-dimensional linear program subject to linear constraints defined by planes and a spherical constraint.
+	 * \param   planes     Planes defining the linear constraints.
+	 * \param   beginPlane The plane on which the 3-d linear program failed.
+	 * \param   radius     The radius of the spherical constraint.
+	 * \param   result     A reference to the result of the linear program.
+	 */
+void linearProgram4(const std::vector<Plane> &planes, size_t beginPlane, float radius, Vector3 &result);
+
+Agent::Agent() :
+        id_(0), maxNeighbors_(0), maxSpeed_(0.0f), neighborDist_(0.0f), radius_(0.0f), timeHorizon_(0.0f), ignore_y_(false) {}
+
+void Agent::computeNeighbors(KdTree *kdTree_) {
+    agentNeighbors_.clear();
+    if (maxNeighbors_ > 0) {
+        kdTree_->computeAgentNeighbors(this, neighborDist_ * neighborDist_);
+    }
+}
+
+#define ABS(m_v) (((m_v) < 0) ? (-(m_v)) : (m_v))
+void Agent::computeNewVelocity(float timeStep) {
+    orcaPlanes_.clear();
+    const float invTimeHorizon = 1.0f / timeHorizon_;
+
+    /* Create agent ORCA planes. */
+    for (size_t i = 0; i < agentNeighbors_.size(); ++i) {
+        const Agent *const other = agentNeighbors_[i].second;
+
+        Vector3 relativePosition = other->position_ - position_;
+        Vector3 relativeVelocity = velocity_ - other->velocity_;
+        const float combinedRadius = radius_ + other->radius_;
+
+        // This is a Godot feature that allow the agents to avoid the collision
+        // by moving only on the horizontal plane relative to the player velocity.
+        if (ignore_y_) {
+            // Skip if these are in two different heights
+            if (ABS(relativePosition[1]) > combinedRadius * 2) {
+                continue;
+            }
+            relativePosition[1] = 0;
+            relativeVelocity[1] = 0;
+        }
+
+        const float distSq = absSq(relativePosition);
+        const float combinedRadiusSq = sqr(combinedRadius);
+
+        Plane plane;
+        Vector3 u;
+
+        if (distSq > combinedRadiusSq) {
+            /* No collision. */
+            const Vector3 w = relativeVelocity - invTimeHorizon * relativePosition;
+            /* Vector from cutoff center to relative velocity. */
+            const float wLengthSq = absSq(w);
+
+            const float dotProduct = w * relativePosition;
+
+            if (dotProduct < 0.0f && sqr(dotProduct) > combinedRadiusSq * wLengthSq) {
+                /* Project on cut-off circle. */
+                const float wLength = std::sqrt(wLengthSq);
+                const Vector3 unitW = w / wLength;
+
+                plane.normal = unitW;
+                u = (combinedRadius * invTimeHorizon - wLength) * unitW;
+            } else {
+                /* Project on cone. */
+                const float a = distSq;
+                const float b = relativePosition * relativeVelocity;
+                const float c = absSq(relativeVelocity) - absSq(cross(relativePosition, relativeVelocity)) / (distSq - combinedRadiusSq);
+                const float t = (b + std::sqrt(sqr(b) - a * c)) / a;
+                const Vector3 w = relativeVelocity - t * relativePosition;
+				const float wLength = abs(w);
+				const Vector3 unitW = w / wLength;
+
+				plane.normal = unitW;
+                u = (combinedRadius * t - wLength) * unitW;
+			}
+        } else {
+            /* Collision. */
+            const float invTimeStep = 1.0f / timeStep;
+            const Vector3 w = relativeVelocity - invTimeStep * relativePosition;
+            const float wLength = abs(w);
+            const Vector3 unitW = w / wLength;
+
+            plane.normal = unitW;
+            u = (combinedRadius * invTimeStep - wLength) * unitW;
+		}
+
+        plane.point = velocity_ + 0.5f * u;
+        orcaPlanes_.push_back(plane);
+    }
+
+    const size_t planeFail = linearProgram3(orcaPlanes_, maxSpeed_, prefVelocity_, false, newVelocity_);
+
+    if (planeFail < orcaPlanes_.size()) {
+        linearProgram4(orcaPlanes_, planeFail, maxSpeed_, newVelocity_);
+    }
+
+    if (ignore_y_) {
+        // Not 100% necessary, but better to have.
+        newVelocity_[1] = prefVelocity_[1];
+    }
+}
+
+void Agent::insertAgentNeighbor(const Agent *agent, float &rangeSq) {
+    if (this != agent) {
+        const float distSq = absSq(position_ - agent->position_);
+
+        if (distSq < rangeSq) {
+            if (agentNeighbors_.size() < maxNeighbors_) {
+                agentNeighbors_.push_back(std::make_pair(distSq, agent));
+            }
+
+            size_t i = agentNeighbors_.size() - 1;
+
+            while (i != 0 && distSq < agentNeighbors_[i - 1].first) {
+                agentNeighbors_[i] = agentNeighbors_[i - 1];
+                --i;
+            }
+
+            agentNeighbors_[i] = std::make_pair(distSq, agent);
+
+            if (agentNeighbors_.size() == maxNeighbors_) {
+                rangeSq = agentNeighbors_.back().first;
+			}
+		}
+	}
+}
+
+bool linearProgram1(const std::vector<Plane> &planes, size_t planeNo, const Line &line, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result) {
+    const float dotProduct = line.point * line.direction;
+    const float discriminant = sqr(dotProduct) + sqr(radius) - absSq(line.point);
+
+    if (discriminant < 0.0f) {
+        /* Max speed sphere fully invalidates line. */
+        return false;
+    }
+
+    const float sqrtDiscriminant = std::sqrt(discriminant);
+    float tLeft = -dotProduct - sqrtDiscriminant;
+    float tRight = -dotProduct + sqrtDiscriminant;
+
+    for (size_t i = 0; i < planeNo; ++i) {
+        const float numerator = (planes[i].point - line.point) * planes[i].normal;
+        const float denominator = line.direction * planes[i].normal;
+
+        if (sqr(denominator) <= RVO_EPSILON) {
+            /* Lines line is (almost) parallel to plane i. */
+            if (numerator > 0.0f) {
+                return false;
+            } else {
+                continue;
+			}
+        }
+
+        const float t = numerator / denominator;
+
+        if (denominator >= 0.0f) {
+            /* Plane i bounds line on the left. */
+            tLeft = std::max(tLeft, t);
+        } else {
+            /* Plane i bounds line on the right. */
+            tRight = std::min(tRight, t);
+		}
+
+        if (tLeft > tRight) {
+            return false;
+		}
+    }
+
+    if (directionOpt) {
+        /* Optimize direction. */
+        if (optVelocity * line.direction > 0.0f) {
+            /* Take right extreme. */
+            result = line.point + tRight * line.direction;
+        } else {
+            /* Take left extreme. */
+            result = line.point + tLeft * line.direction;
+		}
+    } else {
+        /* Optimize closest point. */
+        const float t = line.direction * (optVelocity - line.point);
+
+        if (t < tLeft) {
+            result = line.point + tLeft * line.direction;
+        } else if (t > tRight) {
+            result = line.point + tRight * line.direction;
+        } else {
+            result = line.point + t * line.direction;
+        }
+	}
+
+    return true;
+}
+
+bool linearProgram2(const std::vector<Plane> &planes, size_t planeNo, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result) {
+    const float planeDist = planes[planeNo].point * planes[planeNo].normal;
+    const float planeDistSq = sqr(planeDist);
+    const float radiusSq = sqr(radius);
+
+    if (planeDistSq > radiusSq) {
+        /* Max speed sphere fully invalidates plane planeNo. */
+        return false;
+    }
+
+    const float planeRadiusSq = radiusSq - planeDistSq;
+
+    const Vector3 planeCenter = planeDist * planes[planeNo].normal;
+
+    if (directionOpt) {
+        /* Project direction optVelocity on plane planeNo. */
+        const Vector3 planeOptVelocity = optVelocity - (optVelocity * planes[planeNo].normal) * planes[planeNo].normal;
+        const float planeOptVelocityLengthSq = absSq(planeOptVelocity);
+
+        if (planeOptVelocityLengthSq <= RVO_EPSILON) {
+            result = planeCenter;
+        } else {
+            result = planeCenter + std::sqrt(planeRadiusSq / planeOptVelocityLengthSq) * planeOptVelocity;
+		}
+    } else {
+        /* Project point optVelocity on plane planeNo. */
+        result = optVelocity + ((planes[planeNo].point - optVelocity) * planes[planeNo].normal) * planes[planeNo].normal;
+
+        /* If outside planeCircle, project on planeCircle. */
+        if (absSq(result) > radiusSq) {
+            const Vector3 planeResult = result - planeCenter;
+            const float planeResultLengthSq = absSq(planeResult);
+            result = planeCenter + std::sqrt(planeRadiusSq / planeResultLengthSq) * planeResult;
+		}
+    }
+
+    for (size_t i = 0; i < planeNo; ++i) {
+        if (planes[i].normal * (planes[i].point - result) > 0.0f) {
+            /* Result does not satisfy constraint i. Compute new optimal result. */
+            /* Compute intersection line of plane i and plane planeNo. */
+            Vector3 crossProduct = cross(planes[i].normal, planes[planeNo].normal);
+
+            if (absSq(crossProduct) <= RVO_EPSILON) {
+                /* Planes planeNo and i are (almost) parallel, and plane i fully invalidates plane planeNo. */
+                return false;
+            }
+
+            Line line;
+            line.direction = normalize(crossProduct);
+            const Vector3 lineNormal = cross(line.direction, planes[planeNo].normal);
+            line.point = planes[planeNo].point + (((planes[i].point - planes[planeNo].point) * planes[i].normal) / (lineNormal * planes[i].normal)) * lineNormal;
+
+            if (!linearProgram1(planes, i, line, radius, optVelocity, directionOpt, result)) {
+                return false;
+			}
+		}
+	}
+
+    return true;
+}
+
+size_t linearProgram3(const std::vector<Plane> &planes, float radius, const Vector3 &optVelocity, bool directionOpt, Vector3 &result) {
+    if (directionOpt) {
+        /* Optimize direction. Note that the optimization velocity is of unit length in this case. */
+        result = optVelocity * radius;
+    } else if (absSq(optVelocity) > sqr(radius)) {
+        /* Optimize closest point and outside circle. */
+        result = normalize(optVelocity) * radius;
+    } else {
+        /* Optimize closest point and inside circle. */
+        result = optVelocity;
+    }
+
+    for (size_t i = 0; i < planes.size(); ++i) {
+        if (planes[i].normal * (planes[i].point - result) > 0.0f) {
+            /* Result does not satisfy constraint i. Compute new optimal result. */
+            const Vector3 tempResult = result;
+
+            if (!linearProgram2(planes, i, radius, optVelocity, directionOpt, result)) {
+                result = tempResult;
+                return i;
+			}
+		}
+	}
+
+    return planes.size();
+}
+
+void linearProgram4(const std::vector<Plane> &planes, size_t beginPlane, float radius, Vector3 &result) {
+    float distance = 0.0f;
+
+    for (size_t i = beginPlane; i < planes.size(); ++i) {
+        if (planes[i].normal * (planes[i].point - result) > distance) {
+            /* Result does not satisfy constraint of plane i. */
+            std::vector<Plane> projPlanes;
+
+            for (size_t j = 0; j < i; ++j) {
+                Plane plane;
+
+                const Vector3 crossProduct = cross(planes[j].normal, planes[i].normal);
+
+                if (absSq(crossProduct) <= RVO_EPSILON) {
+                    /* Plane i and plane j are (almost) parallel. */
+                    if (planes[i].normal * planes[j].normal > 0.0f) {
+                        /* Plane i and plane j point in the same direction. */
+                        continue;
+                    } else {
+                        /* Plane i and plane j point in opposite direction. */
+                        plane.point = 0.5f * (planes[i].point + planes[j].point);
+                    }
+                } else {
+                    /* Plane.point is point on line of intersection between plane i and plane j. */
+                    const Vector3 lineNormal = cross(crossProduct, planes[i].normal);
+                    plane.point = planes[i].point + (((planes[j].point - planes[i].point) * planes[j].normal) / (lineNormal * planes[j].normal)) * lineNormal;
+				}
+
+                plane.normal = normalize(planes[j].normal - planes[i].normal);
+                projPlanes.push_back(plane);
+            }
+
+            const Vector3 tempResult = result;
+
+            if (linearProgram3(projPlanes, radius, planes[i].normal, true, result) < projPlanes.size()) {
+                /* 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 = planes[i].normal * (planes[i].point - result);
+        }
+	}
+}
+} // namespace RVO
diff --git a/thirdparty/rvo2/src/Agent.h b/thirdparty/rvo2/src/Agent.h
new file mode 100644
index 0000000000..16f75a08f6
--- /dev/null
+++ b/thirdparty/rvo2/src/Agent.h
@@ -0,0 +1,121 @@
+/*
+ * Agent.h
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+/**
+ * \file    Agent.h
+ * \brief   Contains the Agent class.
+ */
+#ifndef RVO_AGENT_H_
+#define RVO_AGENT_H_
+
+#include "API.h"
+
+#include <cstddef>
+#include <utility>
+#include <vector>
+
+#include "Vector3.h"
+
+// Note: Slightly modified to work better in Godot.
+// - The agent can be created by anyone.
+// - The simulator pointer is removed.
+// - The update function is removed.
+// - The compute velocity function now need the timeStep.
+// - Moved the `Plane` class here.
+// - Added a new parameter `ignore_y_` in the `Agent`. This parameter is used to control a godot feature that allows to avoid collisions by moving on the horizontal plane.
+namespace RVO {
+/**
+     * \brief   Defines a plane.
+     */
+class Plane {
+public:
+    /**
+         * \brief   A point on the plane.
+         */
+    Vector3 point;
+
+    /**
+         * \brief   The normal to the plane.
+         */
+    Vector3 normal;
+};
+
+/**
+     * \brief   Defines an agent in the simulation.
+     */
+class Agent {
+
+public:
+    /**
+		 * \brief   Constructs an agent instance.
+		 * \param   sim  The simulator instance.
+		 */
+    explicit Agent();
+
+    /**
+		 * \brief   Computes the neighbors of this agent.
+		 */
+    void computeNeighbors(class KdTree *kdTree_);
+
+    /**
+		 * \brief   Computes the new velocity of this agent.
+		 */
+    void computeNewVelocity(float timeStep);
+
+    /**
+		 * \brief   Inserts an agent neighbor into the set of neighbors of this agent.
+		 * \param   agent    A pointer to the agent to be inserted.
+		 * \param   rangeSq  The squared range around this agent.
+		 */
+    void insertAgentNeighbor(const Agent *agent, float &rangeSq);
+
+    Vector3 newVelocity_;
+    Vector3 position_;
+    Vector3 prefVelocity_;
+    Vector3 velocity_;
+    size_t id_;
+    size_t maxNeighbors_;
+    float maxSpeed_;
+    float neighborDist_;
+    float radius_;
+    float timeHorizon_;
+    std::vector<std::pair<float, const Agent *> > agentNeighbors_;
+    std::vector<Plane> orcaPlanes_;
+    /// This is a godot feature that allows the Agent to avoid collision by mooving
+    /// on the horizontal plane.
+    bool ignore_y_;
+
+    friend class KdTree;
+};
+} // namespace RVO
+
+#endif /* RVO_AGENT_H_ */
diff --git a/thirdparty/rvo2/src/Definitions.h b/thirdparty/rvo2/src/Definitions.h
new file mode 100644
index 0000000000..a73aca9908
--- /dev/null
+++ b/thirdparty/rvo2/src/Definitions.h
@@ -0,0 +1,55 @@
+/*
+ * Definitions.h
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+/**
+ * \file   Definitions.h
+ * \brief  Contains functions and constants used in multiple classes.
+ */
+
+#ifndef RVO_DEFINITIONS_H_
+#define RVO_DEFINITIONS_H_
+
+#include "API.h"
+
+namespace RVO {
+	/**
+	 * \brief   Computes the square of a float.
+	 * \param   scalar  The float to be squared.
+	 * \return  The square of the float.
+	 */
+	inline float sqr(float scalar)
+	{
+		return scalar * scalar;
+	}
+}
+
+#endif /* RVO_DEFINITIONS_H_ */
diff --git a/thirdparty/rvo2/src/KdTree.cpp b/thirdparty/rvo2/src/KdTree.cpp
new file mode 100644
index 0000000000..bc224614f0
--- /dev/null
+++ b/thirdparty/rvo2/src/KdTree.cpp
@@ -0,0 +1,152 @@
+/*
+ * KdTree.cpp
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+#include "KdTree.h"
+
+#include <algorithm>
+
+#include "Agent.h"
+#include "Definitions.h"
+
+namespace RVO {
+const size_t RVO_MAX_LEAF_SIZE = 10;
+
+KdTree::KdTree() {}
+
+void KdTree::buildAgentTree(std::vector<Agent *> agents) {
+    agents_.swap(agents);
+
+    if (!agents_.empty()) {
+        agentTree_.resize(2 * agents_.size() - 1);
+        buildAgentTreeRecursive(0, agents_.size(), 0);
+	}
+}
+
+void KdTree::buildAgentTreeRecursive(size_t begin, size_t end, size_t node) {
+    agentTree_[node].begin = begin;
+    agentTree_[node].end = end;
+    agentTree_[node].minCoord = agents_[begin]->position_;
+    agentTree_[node].maxCoord = agents_[begin]->position_;
+
+    for (size_t i = begin + 1; i < end; ++i) {
+        agentTree_[node].maxCoord[0] = std::max(agentTree_[node].maxCoord[0], agents_[i]->position_.x());
+        agentTree_[node].minCoord[0] = std::min(agentTree_[node].minCoord[0], agents_[i]->position_.x());
+        agentTree_[node].maxCoord[1] = std::max(agentTree_[node].maxCoord[1], agents_[i]->position_.y());
+        agentTree_[node].minCoord[1] = std::min(agentTree_[node].minCoord[1], agents_[i]->position_.y());
+        agentTree_[node].maxCoord[2] = std::max(agentTree_[node].maxCoord[2], agents_[i]->position_.z());
+        agentTree_[node].minCoord[2] = std::min(agentTree_[node].minCoord[2], agents_[i]->position_.z());
+    }
+
+    if (end - begin > RVO_MAX_LEAF_SIZE) {
+        /* No leaf node. */
+        size_t coord;
+
+        if (agentTree_[node].maxCoord[0] - agentTree_[node].minCoord[0] > agentTree_[node].maxCoord[1] - agentTree_[node].minCoord[1] && agentTree_[node].maxCoord[0] - agentTree_[node].minCoord[0] > agentTree_[node].maxCoord[2] - agentTree_[node].minCoord[2]) {
+            coord = 0;
+        } else if (agentTree_[node].maxCoord[1] - agentTree_[node].minCoord[1] > agentTree_[node].maxCoord[2] - agentTree_[node].minCoord[2]) {
+            coord = 1;
+        } else {
+            coord = 2;
+        }
+
+        const float splitValue = 0.5f * (agentTree_[node].maxCoord[coord] + agentTree_[node].minCoord[coord]);
+
+        size_t left = begin;
+
+        size_t right = end;
+
+        while (left < right) {
+            while (left < right && agents_[left]->position_[coord] < splitValue) {
+                ++left;
+            }
+
+            while (right > left && agents_[right - 1]->position_[coord] >= splitValue) {
+                --right;
+			}
+
+            if (left < right) {
+                std::swap(agents_[left], agents_[right - 1]);
+				++left;
+                --right;
+			}
+        }
+
+        size_t leftSize = left - begin;
+
+        if (leftSize == 0) {
+            ++leftSize;
+            ++left;
+            ++right;
+		}
+
+        agentTree_[node].left = node + 1;
+        agentTree_[node].right = node + 2 * leftSize;
+
+        buildAgentTreeRecursive(begin, left, agentTree_[node].left);
+        buildAgentTreeRecursive(left, end, agentTree_[node].right);
+	}
+}
+
+void KdTree::computeAgentNeighbors(Agent *agent, float rangeSq) const {
+    queryAgentTreeRecursive(agent, rangeSq, 0);
+}
+
+void KdTree::queryAgentTreeRecursive(Agent *agent, float &rangeSq, size_t node) const {
+    if (agentTree_[node].end - agentTree_[node].begin <= RVO_MAX_LEAF_SIZE) {
+        for (size_t i = agentTree_[node].begin; i < agentTree_[node].end; ++i) {
+            agent->insertAgentNeighbor(agents_[i], rangeSq);
+		}
+    } else {
+        const float distSqLeft = sqr(std::max(0.0f, agentTree_[agentTree_[node].left].minCoord[0] - agent->position_.x())) + sqr(std::max(0.0f, agent->position_.x() - agentTree_[agentTree_[node].left].maxCoord[0])) + sqr(std::max(0.0f, agentTree_[agentTree_[node].left].minCoord[1] - agent->position_.y())) + sqr(std::max(0.0f, agent->position_.y() - agentTree_[agentTree_[node].left].maxCoord[1])) + sqr(std::max(0.0f, agentTree_[agentTree_[node].left].minCoord[2] - agent->position_.z())) + sqr(std::max(0.0f, agent->position_.z() - agentTree_[agentTree_[node].left].maxCoord[2]));
+
+        const float distSqRight = sqr(std::max(0.0f, agentTree_[agentTree_[node].right].minCoord[0] - agent->position_.x())) + sqr(std::max(0.0f, agent->position_.x() - agentTree_[agentTree_[node].right].maxCoord[0])) + sqr(std::max(0.0f, agentTree_[agentTree_[node].right].minCoord[1] - agent->position_.y())) + sqr(std::max(0.0f, agent->position_.y() - agentTree_[agentTree_[node].right].maxCoord[1])) + sqr(std::max(0.0f, agentTree_[agentTree_[node].right].minCoord[2] - agent->position_.z())) + sqr(std::max(0.0f, agent->position_.z() - agentTree_[agentTree_[node].right].maxCoord[2]));
+
+        if (distSqLeft < distSqRight) {
+            if (distSqLeft < rangeSq) {
+                queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].left);
+
+				if (distSqRight < rangeSq) {
+					queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].right);
+                }
+            }
+        } else {
+            if (distSqRight < rangeSq) {
+                queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].right);
+
+                if (distSqLeft < rangeSq) {
+                    queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].left);
+				}
+			}
+		}
+	}
+}
+} // namespace RVO
diff --git a/thirdparty/rvo2/src/KdTree.h b/thirdparty/rvo2/src/KdTree.h
new file mode 100644
index 0000000000..1dbad00ea4
--- /dev/null
+++ b/thirdparty/rvo2/src/KdTree.h
@@ -0,0 +1,124 @@
+/*
+ * KdTree.h
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+/**
+ * \file    KdTree.h
+ * \brief   Contains the KdTree class.
+ */
+#ifndef RVO_KD_TREE_H_
+#define RVO_KD_TREE_H_
+
+#include "API.h"
+
+#include <cstddef>
+#include <vector>
+
+#include "Vector3.h"
+
+// Note: Slightly modified to work better with Godot.
+// - Removed `sim_`.
+// - KdTree things are public
+namespace RVO {
+class Agent;
+class RVOSimulator;
+
+/**
+	 * \brief   Defines <i>k</i>d-trees for agents in the simulation.
+	 */
+class KdTree {
+public:
+    /**
+		 * \brief   Defines an agent <i>k</i>d-tree node.
+		 */
+    class AgentTreeNode {
+    public:
+        /**
+			 * \brief   The beginning node number.
+			 */
+        size_t begin;
+
+        /**
+			 * \brief   The ending node number.
+			 */
+        size_t end;
+
+        /**
+			 * \brief   The left node number.
+			 */
+        size_t left;
+
+        /**
+			 * \brief   The right node number.
+			 */
+        size_t right;
+
+        /**
+			 * \brief   The maximum coordinates.
+			 */
+        Vector3 maxCoord;
+
+        /**
+			 * \brief   The minimum coordinates.
+			 */
+        Vector3 minCoord;
+    };
+
+    /**
+		 * \brief   Constructs a <i>k</i>d-tree instance.
+		 * \param   sim  The simulator instance.
+		 */
+    explicit KdTree();
+
+    /**
+		 * \brief   Builds an agent <i>k</i>d-tree.
+		 */
+    void buildAgentTree(std::vector<Agent *> agents);
+
+    void buildAgentTreeRecursive(size_t begin, size_t end, size_t node);
+
+    /**
+		 * \brief   Computes the agent neighbors of the specified agent.
+		 * \param   agent    A pointer to the agent for which agent neighbors are to be computed.
+		 * \param   rangeSq  The squared range around the agent.
+		 */
+    void computeAgentNeighbors(Agent *agent, float rangeSq) const;
+
+    void queryAgentTreeRecursive(Agent *agent, float &rangeSq, size_t node) const;
+
+    std::vector<Agent *> agents_;
+    std::vector<AgentTreeNode> agentTree_;
+
+    friend class Agent;
+    friend class RVOSimulator;
+};
+} // namespace RVO
+
+#endif /* RVO_KD_TREE_H_ */
diff --git a/thirdparty/rvo2/src/RVO.h b/thirdparty/rvo2/src/RVO.h
new file mode 100644
index 0000000000..81c9cbd8d3
--- /dev/null
+++ b/thirdparty/rvo2/src/RVO.h
@@ -0,0 +1,406 @@
+/*
+ * RVO.h
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+#ifndef RVO_RVO_H_
+#define RVO_RVO_H_
+
+#include "API.h"
+#include "RVOSimulator.h"
+#include "Vector3.h"
+
+/**
+
+ \file       RVO.h
+ \brief      Includes all public headers in the library.
+
+ \namespace	 RVO
+ \brief      Contains all classes, functions, and constants used in the library.
+
+ \mainpage   RVO2-3D Library
+
+ \author     Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, and Dinesh Manocha
+
+ <b>RVO2-3D Library</b> is an easy-to-use C++ implementation of the
+ <a href="http://gamma.cs.unc.edu/CA/">Optimal Reciprocal Collision Avoidance</a>
+ (ORCA) formulation for multi-agent simulation in three dimensions. <b>RVO2-3D Library</b>
+ automatically uses parallelism for computing the motion of the agents if your machine
+ has multiple processors and your compiler supports <a href="http://www.openmp.org/">
+ OpenMP</a>.
+
+ Please follow the following steps to install and use <b>RVO2-3D Library</b>.
+
+ - \subpage  whatsnew
+ - \subpage  building
+ - \subpage  using
+ - \subpage  params
+
+ See the documentation of the RVO::RVOSimulator class for an exhaustive list of
+ public functions of <b>RVO2-3D Library</b>.
+
+ <b>RVO2-3D Library</b>, accompanying example code, and this documentation is
+ released for educational, research, and non-profit purposes under the following
+ \subpage terms "terms and conditions".
+
+
+ \page       whatsnew    What Is New in RVO2-3D Library
+
+ \section    localca     Three Dimensions
+
+ In contrast to RVO2 Library, <b>RVO2-3D Library</b> operates in 3D workspaces. It uses
+ a three dimensional implementation of <a href="http://gamma.cs.unc.edu/CA/">Optimal
+ Reciprocal Collision Avoidance</a> (ORCA) for local collision avoidance. <b>RVO2-3D
+ Library</b> does not replace RVO2 Library; for 2D applications, RVO2 Library should
+ be used.
+
+ \section    structure   Structure of RVO2-3D Library
+
+ The structure of <b>RVO2-3D Library</b> is similar to that of RVO2 Library.
+ Users familiar with RVO2 Library should find little trouble in using <b>RVO2-3D
+ Library</b>. <b>RVO2-3D Library</b> currently does not support static obstacles.
+
+ \page       building    Building RVO2-3D Library
+
+ We assume that you have downloaded <b>RVO2-3D Library</b> and unpacked the ZIP
+ archive to a path <tt>$RVO_ROOT</tt>.
+
+ \section    xcode       Apple Xcode 4.x
+
+ Open <tt>$RVO_ROOT/RVO.xcodeproj</tt> and select the <tt>Static Library</tt> scheme. A static library <tt>libRVO.a</tt> will be built in the default build directory.
+
+ \section    cmake       CMake
+
+ Create and switch to your chosen build directory, e.g. <tt>$RVO_ROOT/build</tt>.
+ Run <tt>cmake</tt> inside the build directory on the source directory, e.g.
+ <tt>cmake $RVO_ROOT/src</tt>. Build files for the default generator for your
+ platform will be generated in the build directory.
+
+ \section    make        GNU Make
+
+ Switch to the source directory <tt>$RVO_ROOT/src</tt> and run <tt>make</tt>.
+ Public header files (<tt>API.h</tt>, <tt>RVO.h</tt>, <tt>RVOSimulator.h</tt>, and <tt>Vector3.h</tt>) will be copied to the <tt>$RVO_ROOT/include</tt> directory and a static library <tt>libRVO.a</tt> will be compiled into the
+ <tt>$RVO_ROOT/lib</tt> directory.
+
+ \section    visual      Microsoft Visual Studio 2010
+
+ Open <tt>$RVO_ROOT/RVO.sln</tt> and select the <tt>RVOStatic</tt> project and a
+ configuration (<tt>Debug</tt>  or <tt>Release</tt>). Public header files (<tt>API.h</tt>, <tt>RVO.h</tt>, <tt>RVOSimulator.h</tt>, and <tt>Vector3.h</tt>) will be copied to the <tt>$RVO_ROOT/include</tt> directory and a static library, e.g. <tt>RVO.lib</tt>, will be compiled into the
+ <tt>$RVO_ROOT/lib</tt> directory.
+
+
+ \page       using       Using RVO2-3D Library
+
+ \section    structure   Structure
+
+ A program performing an <b>RVO2-3D Library</b> simulation has the following global
+ structure.
+
+ \code
+ #include <RVO.h>
+
+ std::vector<RVO::Vector3> goals;
+
+ int main()
+ {
+ // Create a new simulator instance.
+ RVO::RVOSimulator* sim = new RVO::RVOSimulator();
+
+ // Set up the scenario.
+ setupScenario(sim);
+
+ // Perform (and manipulate) the simulation.
+ do {
+ updateVisualization(sim);
+ setPreferredVelocities(sim);
+ sim->doStep();
+ } while (!reachedGoal(sim));
+
+ delete sim;
+ }
+ \endcode
+
+ In order to use <b>RVO2-3D Library</b>, the user needs to include RVO.h. The first
+ step is then to create an instance of RVO::RVOSimulator. Then, the process
+ consists of two stages. The first stage is specifying the simulation scenario
+ and its parameters. In the above example program, this is done in the method
+ setupScenario(...), which we will discuss below. The second stage is the actual
+ performing of the simulation.
+
+ In the above example program, simulation steps are taken until all
+ the agents have reached some predefined goals. Prior to each simulation step,
+ we set the preferred velocity for each agent, i.e. the
+ velocity the agent would have taken if there were no other agents around, in the
+ method setPreferredVelocities(...). The simulator computes the actual velocities
+ of the agents and attempts to follow the preferred velocities as closely as
+ possible while guaranteeing collision avoidance at the same time. During the
+ simulation, the user may want to retrieve information from the simulation for
+ instance to visualize the simulation. In the above example program, this is done
+ in the method updateVisualization(...), which we will discuss below. It is also
+ possible to manipulate the simulation during the simulation, for instance by
+ changing positions, radii, velocities, etc. of the agents.
+
+ \section    spec        Setting up the Simulation Scenario
+
+ A scenario that is to be simulated can be set up as follows. A scenario consists
+ of a set of agents that can be manually specified. Agents may be added anytime
+ before or during the simulation. The user may also want to define goal positions
+ of the agents, or a roadmap to guide the agents around obstacles. This is not done
+ in <b>RVO2-3D Library</b>, but needs to be taken care of in the user's external
+ application.
+
+ The following example creates a scenario with eight agents exchanging positions.
+
+ \code
+ void setupScenario(RVO::RVOSimulator* sim) {
+ // Specify global time step of the simulation.
+ sim->setTimeStep(0.25f);
+
+ // Specify default parameters for agents that are subsequently added.
+ sim->setAgentDefaults(15.0f, 10, 10.0f, 2.0f, 2.0f);
+
+ // Add agents, specifying their start position.
+ sim->addAgent(RVO::Vector3(-50.0f, -50.0f, -50.0f));
+ sim->addAgent(RVO::Vector3(50.0f, -50.0f, -50.0f));
+ sim->addAgent(RVO::Vector3(50.0f, 50.0f, -50.0f));
+ sim->addAgent(RVO::Vector3(-50.0f, 50.0f, -50.0f));
+ sim->addAgent(RVO::Vector3(-50.0f, -50.0f, 50.0f));
+ sim->addAgent(RVO::Vector3(50.0f, -50.0f, 50.0f));
+ sim->addAgent(RVO::Vector3(50.0f, 50.0f, 50.0f));
+ sim->addAgent(RVO::Vector3(-50.0f, 50.0f, 50.0f));
+
+ // Create goals (simulator is unaware of these).
+ for (size_t i = 0; i < sim->getNumAgents(); ++i) {
+ goals.push_back(-sim->getAgentPosition(i));
+ }
+ }
+ \endcode
+
+ See the documentation on RVO::RVOSimulator for a full overview of the
+ functionality to specify scenarios.
+
+ \section    ret         Retrieving Information from the Simulation
+
+ During the simulation, the user can extract information from the simulation for
+ instance for visualization purposes, or to determine termination conditions of
+ the simulation. In the example program above, visualization is done in the
+ updateVisualization(...) method. Below we give an example that simply writes
+ the positions of each agent in each time step to the standard output. The
+ termination condition is checked in the reachedGoal(...) method. Here we give an
+ example that returns true if all agents are within one radius of their goals.
+
+ \code
+ void updateVisualization(RVO::RVOSimulator* sim) {
+ // Output the current global time.
+ std::cout << sim->getGlobalTime() << " ";
+
+ // Output the position for all the agents.
+ for (size_t i = 0; i < sim->getNumAgents(); ++i) {
+ std::cout << sim->getAgentPosition(i) << " ";
+ }
+
+ std::cout << std::endl;
+ }
+ \endcode
+
+ \code
+ bool reachedGoal(RVO::RVOSimulator* sim) {
+ // Check whether all agents have arrived at their goals.
+ for (size_t i = 0; i < sim->getNumAgents(); ++i) {
+ if (absSq(goals[i] - sim->getAgentPosition(i)) > sim->getAgentRadius(i) * sim->getAgentRadius(i)) {
+ // Agent is further away from its goal than one radius.
+ return false;
+ }
+ }
+ return true;
+ }
+ \endcode
+
+ Using similar functions as the ones used in this example, the user can access
+ information about other parameters of the agents, as well as the global
+ parameters, and the obstacles. See the documentation of the class
+ RVO::RVOSimulator for an exhaustive list of public functions for retrieving
+ simulation information.
+
+ \section    manip       Manipulating the Simulation
+
+ During the simulation, the user can manipulate the simulation, for instance by
+ changing the global parameters, or changing the parameters of the agents
+ (potentially causing abrupt different behavior). It is also possible to give the
+ agents a new position, which make them jump through the scene.
+ New agents can be added to the simulation at any time.
+
+ See the documentation of the class RVO::RVOSimulator for an exhaustive list of
+ public functions for manipulating the simulation.
+
+ To provide global guidance to the agents, the preferred velocities of the agents
+ can be changed ahead of each simulation step. In the above example program, this
+ happens in the method setPreferredVelocities(...). Here we give an example that
+ simply sets the preferred velocity to the unit vector towards the agent's goal
+ for each agent (i.e., the preferred speed is 1.0).
+
+ \code
+ void setPreferredVelocities(RVO::RVOSimulator* sim) {
+ // Set the preferred velocity for each agent.
+ for (size_t i = 0; i < sim->getNumAgents(); ++i) {
+ if (absSq(goals[i] - sim->getAgentPosition(i)) < sim->getAgentRadius(i) * sim->getAgentRadius(i) ) {
+ // Agent is within one radius of its goal, set preferred velocity to zero
+ sim->setAgentPrefVelocity(i, RVO::Vector3());
+ } else {
+ // Agent is far away from its goal, set preferred velocity as unit vector towards agent's goal.
+ sim->setAgentPrefVelocity(i, normalize(goals[i] - sim->getAgentPosition(i)));
+ }
+ }
+ }
+ \endcode
+
+ \section    example     Example Programs
+
+ <b>RVO2-3D Library</b> is accompanied by one example program, which can be found in the
+ <tt>$RVO_ROOT/examples</tt> directory. The example is named Sphere, and
+ contains the following demonstration scenario:
+ <table border="0" cellpadding="3" width="100%">
+ <tr>
+ <td valign="top" width="100"><b>Sphere</b></td>
+ <td valign="top">A scenario in which 812 agents, initially positioned evenly
+ distributed on a sphere, move to the antipodal position on the
+ sphere. </td>
+ </tr>
+ </table>
+
+
+ \page       params      Parameter Overview
+
+ \section    globalp     Global Parameters
+
+ <table border="0" cellpadding="3" width="100%">
+ <tr>
+ <td valign="top" width="150"><strong>Parameter</strong></td>
+ <td valign="top" width="150"><strong>Type (unit)</strong></td>
+ <td valign="top"><strong>Meaning</strong></td>
+ </tr>
+ <tr>
+ <td valign="top">timeStep</td>
+ <td valign="top">float (time)</td>
+ <td valign="top">The time step of the simulation. Must be positive.</td>
+ </tr>
+ </table>
+
+ \section    agent       Agent Parameters
+
+ <table border="0" cellpadding="3" width="100%">
+ <tr>
+ <td valign="top" width="150"><strong>Parameter</strong></td>
+ <td valign="top" width="150"><strong>Type (unit)</strong></td>
+ <td valign="top"><strong>Meaning</strong></td>
+ </tr>
+ <tr>
+ <td valign="top">maxNeighbors</td>
+ <td valign="top">size_t</td>
+ <td valign="top">The maximum number of other agents the agent takes into
+ account in the navigation. The larger this number, the
+ longer the running time of the simulation. If the number is
+ too low, the simulation will not be safe.</td>
+ </tr>
+ <tr>
+ <td valign="top">maxSpeed</td>
+ <td valign="top">float (distance/time)</td>
+ <td valign="top">The maximum speed of the agent. Must be non-negative.</td>
+ </tr>
+ <tr>
+ <td valign="top">neighborDist</td>
+ <td valign="top">float (distance)</td>
+ <td valign="top">The maximum distance (center point to center point) to
+ other agents the agent takes into account in the
+ navigation. The larger this number, the longer the running
+ time of the simulation. If the number is too low, the
+ simulation will not be safe. Must be non-negative.</td>
+ </tr>
+ <tr>
+ <td valign="top" width="150">position</td>
+ <td valign="top" width="150">RVO::Vector3 (distance, distance)</td>
+ <td valign="top">The current position of the agent.</td>
+ </tr>
+ <tr>
+ <td valign="top" width="150">prefVelocity</td>
+ <td valign="top" width="150">RVO::Vector3 (distance/time, distance/time)
+ </td>
+ <td valign="top">The current preferred velocity of the agent. This is the
+ velocity the agent would take if no other agents or
+ obstacles were around. The simulator computes an actual
+ velocity for the agent that follows the preferred velocity
+ as closely as possible, but at the same time guarantees
+ collision avoidance.</td>
+ </tr>
+ <tr>
+ <td valign="top">radius</td>
+ <td valign="top">float (distance)</td>
+ <td valign="top">The radius of the agent. Must be non-negative.</td>
+ </tr>
+ <tr>
+ <td valign="top" width="150">timeHorizon</td>
+ <td valign="top" width="150">float (time)</td>
+ <td valign="top">The minimum amount of time for which the agent's velocities
+ that are computed by the simulation are safe with respect
+ to other agents. The larger this number, the sooner this
+ agent will respond to the presence of other agents, but the
+ less freedom the agent has in choosing its velocities.
+ Must be positive. </td>
+ </tr>
+ <tr>
+ <td valign="top" width="150">velocity</td>
+ <td valign="top" width="150">RVO::Vector3 (distance/time, distance/time)
+ </td>
+ <td valign="top">The (current) velocity of the agent.</td>
+ </tr>
+ </table>
+
+
+ \page       terms       Terms and Conditions
+
+ <b>RVO2-3D Library</b>
+
+ Copyright 2008 University of North Carolina at Chapel Hill
+
+ Licensed under the Apache License, Version 2.0 (the "License");
+ you may not use this file except in compliance with the License.
+ You may obtain a copy of the License at
+
+     http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+
+ */
+
+#endif /* RVO_RVO_H_ */
diff --git a/thirdparty/rvo2/src/Vector3.h b/thirdparty/rvo2/src/Vector3.h
new file mode 100644
index 0000000000..8c8835c865
--- /dev/null
+++ b/thirdparty/rvo2/src/Vector3.h
@@ -0,0 +1,335 @@
+/*
+ * Vector3.h
+ * RVO2-3D Library
+ *
+ * Copyright 2008 University of North Carolina at Chapel Hill
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ *
+ * Please send all bug reports to <geom@cs.unc.edu>.
+ *
+ * The authors may be contacted via:
+ *
+ * Jur van den Berg, Stephen J. Guy, Jamie Snape, Ming C. Lin, Dinesh Manocha
+ * Dept. of Computer Science
+ * 201 S. Columbia St.
+ * Frederick P. Brooks, Jr. Computer Science Bldg.
+ * Chapel Hill, N.C. 27599-3175
+ * United States of America
+ *
+ * <http://gamma.cs.unc.edu/RVO2/>
+ */
+
+/**
+ * \file    Vector3.h
+ * \brief   Contains the Vector3 class.
+ */
+#ifndef RVO_VECTOR3_H_
+#define RVO_VECTOR3_H_
+
+#include "API.h"
+
+#include <cmath>
+#include <cstddef>
+#include <ostream>
+
+namespace RVO {
+	/**
+	 * \brief  Defines a three-dimensional vector.
+	 */
+	class Vector3 {
+	public:
+		/**
+		 * \brief   Constructs and initializes a three-dimensional vector instance to zero.
+		 */
+		RVO_API inline Vector3()
+		{
+			val_[0] = 0.0f;
+			val_[1] = 0.0f;
+			val_[2] = 0.0f;
+		}
+
+		/**
+		 * \brief   Constructs and initializes a three-dimensional vector from the specified three-element array.
+		 * \param   val  The three-element array containing the xyz-coordinates.
+		 */
+		RVO_API inline explicit Vector3(const float val[3])
+		{
+			val_[0] = val[0];
+			val_[1] = val[1];
+			val_[2] = val[2];
+		}
+
+		/**
+		 * \brief   Constructs and initializes a three-dimensional vector from the specified xyz-coordinates.
+		 * \param   x  The x-coordinate of the three-dimensional vector.
+		 * \param   y  The y-coordinate of the three-dimensional vector.
+		 * \param   z  The z-coordinate of the three-dimensional vector.
+		 */
+		RVO_API inline Vector3(float x, float y, float z)
+		{
+			val_[0] = x;
+			val_[1] = y;
+			val_[2] = z;
+		}
+
+		/**
+		 * \brief   Returns the x-coordinate of this three-dimensional vector.
+		 * \return  The x-coordinate of the three-dimensional vector.
+		 */
+		RVO_API inline float x() const { return val_[0]; }
+
+		/**
+		 * \brief   Returns the y-coordinate of this three-dimensional vector.
+		 * \return  The y-coordinate of the three-dimensional vector.
+		 */
+		RVO_API inline float y() const { return val_[1]; }
+
+		/**
+		 * \brief   Returns the z-coordinate of this three-dimensional vector.
+		 * \return  The z-coordinate of the three-dimensional vector.
+		 */
+		RVO_API inline float z() const { return val_[2]; }
+
+		/**
+		 * \brief   Returns the specified coordinate of this three-dimensional vector.
+		 * \param   i  The coordinate that should be returned (0 <= i < 3).
+		 * \return  The specified coordinate of the three-dimensional vector.
+		 */
+		RVO_API inline float operator[](size_t i) const { return val_[i]; }
+
+		/**
+		 * \brief   Returns a reference to the specified coordinate of this three-dimensional vector.
+		 * \param   i  The coordinate to which a reference should be returned (0 <= i < 3).
+		 * \return  A reference to the specified coordinate of the three-dimensional vector.
+		 */
+		RVO_API inline float &operator[](size_t i) { return val_[i]; }
+
+		/**
+		 * \brief   Computes the negation of this three-dimensional vector.
+		 * \return  The negation of this three-dimensional vector.
+		 */
+		RVO_API inline Vector3 operator-() const
+		{
+			return Vector3(-val_[0], -val_[1], -val_[2]);
+		}
+
+		/**
+		 * \brief   Computes the dot product of this three-dimensional vector with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which the dot product should be computed.
+		 * \return  The dot product of this three-dimensional vector with a specified three-dimensional vector.
+		 */
+		RVO_API inline float operator*(const Vector3 &vector) const
+		{
+			return val_[0] * vector[0] + val_[1] * vector[1] + val_[2] * vector[2];
+		}
+
+		/**
+		 * \brief   Computes the scalar multiplication of this three-dimensional vector with the specified scalar value.
+		 * \param   scalar  The scalar value with which the scalar multiplication should be computed.
+		 * \return  The scalar multiplication of this three-dimensional vector with a specified scalar value.
+		 */
+		RVO_API inline Vector3 operator*(float scalar) const
+		{
+			return Vector3(val_[0] * scalar, val_[1] * scalar, val_[2] * scalar);
+		}
+
+		/**
+		 * \brief   Computes the scalar division of this three-dimensional vector with the specified scalar value.
+		 * \param   scalar  The scalar value with which the scalar division should be computed.
+		 * \return  The scalar division of this three-dimensional vector with a specified scalar value.
+		 */
+		RVO_API inline Vector3 operator/(float scalar) const
+		{
+			const float invScalar = 1.0f / scalar;
+
+			return Vector3(val_[0] * invScalar, val_[1] * invScalar, val_[2] * invScalar);
+		}
+
+		/**
+		 * \brief   Computes the vector sum of this three-dimensional vector with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which the vector sum should be computed.
+		 * \return 	The vector sum of this three-dimensional vector with a specified three-dimensional vector.
+		 */
+		RVO_API inline Vector3 operator+(const Vector3 &vector) const
+		{
+			return Vector3(val_[0] + vector[0], val_[1] + vector[1], val_[2] + vector[2]);
+		}
+
+		/**
+		 * \brief   Computes the vector difference of this three-dimensional vector with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which the vector difference should be computed.
+		 * \return  The vector difference of this three-dimensional vector with a specified three-dimensional vector.
+		 */
+		RVO_API inline Vector3 operator-(const Vector3 &vector) const
+		{
+			return Vector3(val_[0] - vector[0], val_[1] - vector[1], val_[2] - vector[2]);
+		}
+
+		/**
+		 * \brief   Tests this three-dimensional vector for equality with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which to test for equality.
+		 * \return  True if the three-dimensional vectors are equal.
+		 */
+		RVO_API inline bool operator==(const Vector3 &vector) const
+		{
+			return val_[0] == vector[0] && val_[1] == vector[1] && val_[2] == vector[2];
+		}
+
+		/**
+		 * \brief   Tests this three-dimensional vector for inequality with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which to test for inequality.
+		 * \return  True if the three-dimensional vectors are not equal.
+		 */
+		RVO_API inline bool operator!=(const Vector3 &vector) const
+		{
+			return val_[0] != vector[0] || val_[1] != vector[1] || val_[2] != vector[2];
+		}
+
+		/**
+		 * \brief   Sets the value of this three-dimensional vector to the scalar multiplication of itself with the specified scalar value.
+		 * \param   scalar  The scalar value with which the scalar multiplication should be computed.
+		 * \return  A reference to this three-dimensional vector.
+		 */
+		RVO_API inline Vector3 &operator*=(float scalar)
+		{
+			val_[0] *= scalar;
+			val_[1] *= scalar;
+			val_[2] *= scalar;
+
+			return *this;
+		}
+
+		/**
+		 * \brief   Sets the value of this three-dimensional vector to the scalar division of itself with the specified scalar value.
+		 * \param   scalar  The scalar value with which the scalar division should be computed.
+		 * \return  A reference to this three-dimensional vector.
+		 */
+		RVO_API inline Vector3 &operator/=(float scalar)
+		{
+			const float invScalar = 1.0f / scalar;
+
+			val_[0] *= invScalar;
+			val_[1] *= invScalar;
+			val_[2] *= invScalar;
+
+			return *this;
+		}
+
+		/**
+		 * \brief   Sets the value of this three-dimensional vector to the vector
+		 *             sum of itself with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which the vector sum should be computed.
+		 * \return  A reference to this three-dimensional vector.
+		 */
+		RVO_API inline Vector3 &operator+=(const Vector3 &vector)
+		{
+			val_[0] += vector[0];
+			val_[1] += vector[1];
+			val_[2] += vector[2];
+
+			return *this;
+		}
+
+		/**
+		 * \brief   Sets the value of this three-dimensional vector to the vector difference of itself with the specified three-dimensional vector.
+		 * \param   vector  The three-dimensional vector with which the vector difference should be computed.
+		 * \return  A reference to this three-dimensional vector.
+		 */
+		RVO_API inline Vector3 &operator-=(const Vector3 &vector)
+		{
+			val_[0] -= vector[0];
+			val_[1] -= vector[1];
+			val_[2] -= vector[2];
+
+			return *this;
+		}
+
+	private:
+		float val_[3];
+	};
+
+
+	/**
+	 * \relates  Vector3
+	 * \brief    Computes the scalar multiplication of the specified three-dimensional vector with the specified scalar value.
+	 * \param    scalar  The scalar value with which the scalar multiplication should be computed.
+	 * \param    vector  The three-dimensional vector with which the scalar multiplication should be computed.
+	 * \return   The scalar multiplication of the three-dimensional vector with the scalar value.
+	 */
+	inline Vector3 operator*(float scalar, const Vector3 &vector)
+	{
+		return Vector3(scalar * vector[0], scalar * vector[1], scalar * vector[2]);
+	}
+
+	/**
+	 * \relates  Vector3
+	 * \brief    Computes the cross product of the specified three-dimensional vectors.
+	 * \param    vector1  The first vector with which the cross product should be computed.
+	 * \param    vector2  The second vector with which the cross product should be computed.
+	 * \return   The cross product of the two specified vectors.
+	 */
+	inline Vector3 cross(const Vector3 &vector1, const Vector3 &vector2)
+	{
+		return Vector3(vector1[1] * vector2[2] - vector1[2] * vector2[1], vector1[2] * vector2[0] - vector1[0] * vector2[2], vector1[0] * vector2[1] - vector1[1] * vector2[0]);
+	}
+
+	/**
+	 * \relates  Vector3
+	 * \brief    Inserts the specified three-dimensional vector into the specified output stream.
+	 * \param    os      The output stream into which the three-dimensional vector should be inserted.
+	 * \param    vector  The three-dimensional vector which to insert into the output stream.
+	 * \return   A reference to the output stream.
+	 */
+	inline std::ostream &operator<<(std::ostream &os, const Vector3 &vector)
+	{
+		os << "(" << vector[0] << "," << vector[1] << "," << vector[2] << ")";
+
+		return os;
+	}
+
+	/**
+	 * \relates  Vector3
+	 * \brief    Computes the length of a specified three-dimensional vector.
+	 * \param    vector  The three-dimensional vector whose length is to be computed.
+	 * \return   The length of the three-dimensional vector.
+	 */
+	inline float abs(const Vector3 &vector)
+	{
+		return std::sqrt(vector * vector);
+	}
+
+	/**
+	 * \relates  Vector3
+	 * \brief    Computes the squared length of a specified three-dimensional vector.
+	 * \param    vector  The three-dimensional vector whose squared length is to be computed.
+	 * \return   The squared length of the three-dimensional vector.
+	 */
+	inline float absSq(const Vector3 &vector)
+	{
+		return vector * vector;
+	}
+
+	/**
+	 * \relates  Vector3
+	 * \brief    Computes the normalization of the specified three-dimensional vector.
+	 * \param    vector  The three-dimensional vector whose normalization is to be computed.
+	 * \return   The normalization of the three-dimensional vector.
+	 */
+	inline Vector3 normalize(const Vector3 &vector)
+	{
+		return vector / abs(vector);
+	}
+}
+
+#endif