Merge pull request #61151 from akien-mga/rvo2-document-changes

10 files changed, 814 insertions, 588 deletions

diff --git a/thirdparty/README.md b/thirdparty/README.md
index 0b0583b1fc..0047f1c66c 100644
--- a/thirdparty/README.md
+++ b/thirdparty/README.md
@@ -566,17 +566,17 @@ Files extracted from upstream source:
 ## rvo2
 
 - Upstream: https://github.com/snape/RVO2-3D
-- Version: 1.0.1 (e3883f288a9e55ecfed3633a01af3e12778c6acf, 2016)
+- Version: git (bfc048670a4e85066e86a1f923d8ea92e3add3b2, 2021)
 - License: Apache 2.0
 
 Files extracted from upstream source:
 
-- All .cpp and .h files in the `src/` folder except for RVO.h, RVOSimulator.cpp and RVOSimulator.h
+- All .cpp and .h files in the `src/` folder except for Export.h, RVO.h, RVOSimulator.cpp and RVOSimulator.h
 - LICENSE
 
 Important: Some files have Godot-made changes; so to enrich the features
 originally proposed by this library and better integrate this library with
-Godot. Please check the file to know what's new.
+Godot. See the patch in the `patches` folder for details.
 
 
 ## spirv-reflect
diff --git a/thirdparty/rvo2/API.h b/thirdparty/rvo2/API.h
deleted file mode 100644
index c64efb452c..0000000000
--- a/thirdparty/rvo2/API.h
+++ /dev/null
@@ -1,45 +0,0 @@
-/*
- * 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_
-
-// -- GODOT start --
-#define RVO_API
-// -- GODOT end --
-
-#endif /* RVO_API_H_ */
diff --git a/thirdparty/rvo2/Agent.cpp b/thirdparty/rvo2/Agent.cpp
index 851d780758..b35eee9c12 100644
--- a/thirdparty/rvo2/Agent.cpp
+++ b/thirdparty/rvo2/Agent.cpp
@@ -8,7 +8,7 @@
  * 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
+ *     https://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,
@@ -27,40 +27,40 @@
  * Chapel Hill, N.C. 27599-3175
  * United States of America
  *
- * <http://gamma.cs.unc.edu/RVO2/>
+ * <https://gamma.cs.unc.edu/RVO2/>
  */
 
 #include "Agent.h"
 
-#include <algorithm>
 #include <cmath>
+#include <algorithm>
 
 #include "Definitions.h"
 #include "KdTree.h"
 
 namespace RVO {
-/**
+	/**
 	 * \brief   A sufficiently small positive number.
 	 */
-const float RVO_EPSILON = 0.00001f;
+	const float RVO3D_EPSILON = 0.00001f;
 
-/**
+	/**
 	 * \brief   Defines a directed line.
 	 */
-class Line {
-public:
-    /**
+	class Line {
+	public:
+		/**
 		 * \brief   The direction of the directed line.
 		 */
-    Vector3 direction;
+		Vector3 direction;
 
-    /**
+		/**
 		 * \brief   A point on the directed line.
 		 */
-    Vector3 point;
-};
+		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.
@@ -71,9 +71,9 @@ public:
 	 * \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);
+	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
@@ -83,9 +83,9 @@ bool linearProgram1(const std::vector<Plane> &planes, size_t planeNo, const Line
 	 * \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);
+	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.
@@ -94,332 +94,352 @@ bool linearProgram2(const std::vector<Plane> &planes, size_t planeNo, float radi
 	 * \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);
+	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);
+	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) {}
+	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_);
-    }
-}
+	void Agent::computeNeighbors(KdTree *kdTree_)
+	{
+		agentNeighbors_.clear();
+		if (maxNeighbors_ > 0) {
+			kdTree_->computeAgentNeighbors(this, neighborDist_ * neighborDist_);
+		}
+	}
 
+	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
 #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;
+				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 ww = relativeVelocity - t * relativePosition;
+					const float wwLength = abs(ww);
+					const Vector3 unitWW = ww / wwLength;
+
+					plane.normal = unitWW;
+					u = (combinedRadius * t - wwLength) * unitWW;
+				}
+			}
+			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 * t - wLength) * unitW;
+				u = (combinedRadius * invTimeStep - 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);
-    }
+			plane.point = velocity_ + 0.5f * u;
+			orcaPlanes_.push_back(plane);
+		}
 
-    const size_t planeFail = linearProgram3(orcaPlanes_, maxSpeed_, prefVelocity_, false, newVelocity_);
+		const size_t planeFail = linearProgram3(orcaPlanes_, maxSpeed_, prefVelocity_, false, newVelocity_);
 
-    if (planeFail < orcaPlanes_.size()) {
-        linearProgram4(orcaPlanes_, planeFail, maxSpeed_, newVelocity_);
-    }
+		if (planeFail < orcaPlanes_.size()) {
+			linearProgram4(orcaPlanes_, planeFail, maxSpeed_, newVelocity_);
+		}
 
-    if (ignore_y_) {
-        // Not 100% necessary, but better to have.
-        newVelocity_[1] = prefVelocity_[1];
-    }
-}
+		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_);
+	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));
-            }
+			if (distSq < rangeSq) {
+				if (agentNeighbors_.size() < maxNeighbors_) {
+					agentNeighbors_.push_back(std::make_pair(distSq, agent));
+				}
 
-            size_t i = agentNeighbors_.size() - 1;
+				size_t i = agentNeighbors_.size() - 1;
 
-            while (i != 0 && distSq < agentNeighbors_[i - 1].first) {
-                agentNeighbors_[i] = agentNeighbors_[i - 1];
-                --i;
-            }
+				while (i != 0 && distSq < agentNeighbors_[i - 1].first) {
+					agentNeighbors_[i] = agentNeighbors_[i - 1];
+					--i;
+				}
 
-            agentNeighbors_[i] = std::make_pair(distSq, agent);
+				agentNeighbors_[i] = std::make_pair(distSq, agent);
 
-            if (agentNeighbors_.size() == maxNeighbors_) {
-                rangeSq = agentNeighbors_.back().first;
+				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;
+	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) <= RVO3D_EPSILON) {
+				/* Lines line is (almost) parallel to plane i. */
+				if (numerator > 0.0f) {
+					return false;
+				}
+				else {
+					continue;
+				}
 			}
-        }
 
-        const float t = numerator / denominator;
+			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 (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 (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;
+			}
 		}
-    }
-
-    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;
+			}
 		}
-    } 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;
-}
+		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);
+	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;
-    }
+		if (planeDistSq > radiusSq) {
+			/* Max speed sphere fully invalidates plane planeNo. */
+			return false;
+		}
 
-    const float planeRadiusSq = radiusSq - planeDistSq;
+		const float planeRadiusSq = radiusSq - planeDistSq;
 
-    const Vector3 planeCenter = planeDist * planes[planeNo].normal;
+		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 (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;
+			if (planeOptVelocityLengthSq <= RVO3D_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;
+		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;
+
+		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) <= RVO3D_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;
 	}
 
-    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;
 
-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;
+				if (!linearProgram2(planes, i, radius, optVelocity, directionOpt, result)) {
+					result = tempResult;
+					return i;
+				}
 			}
 		}
-	}
 
-    return planes.size();
-}
+		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;
+	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) <= RVO3D_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);
 				}
 
-                plane.normal = normalize(planes[j].normal - planes[i].normal);
-                projPlanes.push_back(plane);
-            }
+				const Vector3 tempResult = result;
 
-            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;
+				}
 
-            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);
 			}
-
-            distance = planes[i].normal * (planes[i].point - result);
-        }
+		}
 	}
 }
-} // namespace RVO
diff --git a/thirdparty/rvo2/Agent.h b/thirdparty/rvo2/Agent.h
index 16f75a08f6..45fbead2f5 100644
--- a/thirdparty/rvo2/Agent.h
+++ b/thirdparty/rvo2/Agent.h
@@ -8,7 +8,7 @@
  * 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
+ *     https://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,
@@ -27,17 +27,15 @@
  * Chapel Hill, N.C. 27599-3175
  * United States of America
  *
- * <http://gamma.cs.unc.edu/RVO2/>
+ * <https://gamma.cs.unc.edu/RVO2/>
  */
 
 /**
  * \file    Agent.h
  * \brief   Contains the Agent class.
  */
-#ifndef RVO_AGENT_H_
-#define RVO_AGENT_H_
-
-#include "API.h"
+#ifndef RVO3D_AGENT_H_
+#define RVO3D_AGENT_H_
 
 #include <cstddef>
 #include <utility>
@@ -53,69 +51,68 @@
 // - 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 a plane.
+	 */
+	class Plane {
+	public:
+		/**
+		 * \brief   A point on the plane.
+		 */
+		Vector3 point;
 
-/**
-     * \brief   Defines an agent in the simulation.
-     */
-class Agent {
+		/**
+		 * \brief   The normal to the plane.
+		 */
+		Vector3 normal;
+	};
 
-public:
-    /**
+	/**
+	 * \brief   Defines an agent in the simulation.
+	 */
+	class Agent {
+	public:
+		/**
 		 * \brief   Constructs an agent instance.
 		 * \param   sim  The simulator instance.
 		 */
-    explicit Agent();
+		explicit Agent();
 
-    /**
+		/**
 		 * \brief   Computes the neighbors of this agent.
 		 */
-    void computeNeighbors(class KdTree *kdTree_);
+		void computeNeighbors(class KdTree *kdTree_);
 
-    /**
+		/**
 		 * \brief   Computes the new velocity of this agent.
 		 */
-    void computeNewVelocity(float timeStep);
+		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);
+		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_;
+		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
+		friend class KdTree;
+	};
+}
 
-#endif /* RVO_AGENT_H_ */
+#endif /* RVO3D_AGENT_H_ */
diff --git a/thirdparty/rvo2/Definitions.h b/thirdparty/rvo2/Definitions.h
index a73aca9908..707d3c897f 100644
--- a/thirdparty/rvo2/Definitions.h
+++ b/thirdparty/rvo2/Definitions.h
@@ -8,7 +8,7 @@
  * 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
+ *     https://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,
@@ -27,7 +27,7 @@
  * Chapel Hill, N.C. 27599-3175
  * United States of America
  *
- * <http://gamma.cs.unc.edu/RVO2/>
+ * <https://gamma.cs.unc.edu/RVO2/>
  */
 
 /**
@@ -35,10 +35,8 @@
  * \brief  Contains functions and constants used in multiple classes.
  */
 
-#ifndef RVO_DEFINITIONS_H_
-#define RVO_DEFINITIONS_H_
-
-#include "API.h"
+#ifndef RVO3D_DEFINITIONS_H_
+#define RVO3D_DEFINITIONS_H_
 
 namespace RVO {
 	/**
@@ -52,4 +50,4 @@ namespace RVO {
 	}
 }
 
-#endif /* RVO_DEFINITIONS_H_ */
+#endif /* RVO3D_DEFINITIONS_H_ */
diff --git a/thirdparty/rvo2/KdTree.cpp b/thirdparty/rvo2/KdTree.cpp
index bc224614f0..c857f299df 100644
--- a/thirdparty/rvo2/KdTree.cpp
+++ b/thirdparty/rvo2/KdTree.cpp
@@ -8,7 +8,7 @@
  * 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
+ *     https://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,
@@ -27,7 +27,7 @@
  * Chapel Hill, N.C. 27599-3175
  * United States of America
  *
- * <http://gamma.cs.unc.edu/RVO2/>
+ * <https://gamma.cs.unc.edu/RVO2/>
  */
 
 #include "KdTree.h"
@@ -38,115 +38,123 @@
 #include "Definitions.h"
 
 namespace RVO {
-const size_t RVO_MAX_LEAF_SIZE = 10;
+	const size_t RVO3D_MAX_LEAF_SIZE = 10;
 
-KdTree::KdTree() {}
+	KdTree::KdTree() { }
 
-void KdTree::buildAgentTree(std::vector<Agent *> agents) {
-    agents_.swap(agents);
+	void KdTree::buildAgentTree(std::vector<Agent *> agents)
+	{
+		agents_.swap(agents);
 
-    if (!agents_.empty()) {
-        agentTree_.resize(2 * agents_.size() - 1);
-        buildAgentTreeRecursive(0, agents_.size(), 0);
+		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;
+	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 > RVO3D_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;
 			}
 
-            if (left < right) {
-                std::swap(agents_[left], agents_[right - 1]);
-				++left;
-                --right;
+			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;
+			size_t leftSize = left - begin;
 
-        if (leftSize == 0) {
-            ++leftSize;
-            ++left;
-            ++right;
-		}
+			if (leftSize == 0) {
+				++leftSize;
+				++left;
+				++right;
+			}
 
-        agentTree_[node].left = node + 1;
-        agentTree_[node].right = node + 2 * leftSize;
+			agentTree_[node].left = node + 1;
+			agentTree_[node].right = node + 2 * leftSize;
 
-        buildAgentTreeRecursive(begin, left, agentTree_[node].left);
-        buildAgentTreeRecursive(left, end, agentTree_[node].right);
+			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::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);
+	void KdTree::queryAgentTreeRecursive(Agent *agent, float &rangeSq, size_t node) const
+	{
+		if (agentTree_[node].end - agentTree_[node].begin <= RVO3D_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]));
+		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]));
+			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 (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);
-                }
-            }
-        } else {
-            if (distSqRight < rangeSq) {
-                queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].right);
-
-                if (distSqLeft < rangeSq) {
-                    queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].left);
+
+					if (distSqLeft < rangeSq) {
+						queryAgentTreeRecursive(agent, rangeSq, agentTree_[node].left);
+					}
 				}
 			}
 		}
 	}
 }
-} // namespace RVO
diff --git a/thirdparty/rvo2/KdTree.h b/thirdparty/rvo2/KdTree.h
index 1dbad00ea4..69d8920ce0 100644
--- a/thirdparty/rvo2/KdTree.h
+++ b/thirdparty/rvo2/KdTree.h
@@ -8,7 +8,7 @@
  * 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
+ *     https://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,
@@ -27,16 +27,14 @@
  * Chapel Hill, N.C. 27599-3175
  * United States of America
  *
- * <http://gamma.cs.unc.edu/RVO2/>
+ * <https://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"
+#ifndef RVO3D_KD_TREE_H_
+#define RVO3D_KD_TREE_H_
 
 #include <cstddef>
 #include <vector>
@@ -47,78 +45,78 @@
 // - Removed `sim_`.
 // - KdTree things are public
 namespace RVO {
-class Agent;
-class RVOSimulator;
+	class Agent;
+	class RVOSimulator;
 
-/**
+	/**
 	 * \brief   Defines <i>k</i>d-trees for agents in the simulation.
 	 */
-class KdTree {
-public:
-    /**
+	class KdTree {
+	public:
+		/**
 		 * \brief   Defines an agent <i>k</i>d-tree node.
 		 */
-    class AgentTreeNode {
-    public:
-        /**
+		class AgentTreeNode {
+		public:
+			/**
 			 * \brief   The beginning node number.
 			 */
-        size_t begin;
+			size_t begin;
 
-        /**
+			/**
 			 * \brief   The ending node number.
 			 */
-        size_t end;
+			size_t end;
 
-        /**
+			/**
 			 * \brief   The left node number.
 			 */
-        size_t left;
+			size_t left;
 
-        /**
+			/**
 			 * \brief   The right node number.
 			 */
-        size_t right;
+			size_t right;
 
-        /**
+			/**
 			 * \brief   The maximum coordinates.
 			 */
-        Vector3 maxCoord;
+			Vector3 maxCoord;
 
-        /**
+			/**
 			 * \brief   The minimum coordinates.
 			 */
-        Vector3 minCoord;
-    };
+			Vector3 minCoord;
+		};
 
-    /**
+		/**
 		 * \brief   Constructs a <i>k</i>d-tree instance.
 		 * \param   sim  The simulator instance.
 		 */
-    explicit KdTree();
+		explicit KdTree();
 
-    /**
+		/**
 		 * \brief   Builds an agent <i>k</i>d-tree.
 		 */
-    void buildAgentTree(std::vector<Agent *> agents);
+		void buildAgentTree(std::vector<Agent *> agents);
 
-    void buildAgentTreeRecursive(size_t begin, size_t end, size_t node);
+		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 computeAgentNeighbors(Agent *agent, float rangeSq) const;
 
-    void queryAgentTreeRecursive(Agent *agent, float &rangeSq, size_t node) const;
+		void queryAgentTreeRecursive(Agent *agent, float &rangeSq, size_t node) const;
 
-    std::vector<Agent *> agents_;
-    std::vector<AgentTreeNode> agentTree_;
+		std::vector<Agent *> agents_;
+		std::vector<AgentTreeNode> agentTree_;
 
-    friend class Agent;
-    friend class RVOSimulator;
-};
-} // namespace RVO
+		friend class Agent;
+		friend class RVOSimulator;
+	};
+}
 
-#endif /* RVO_KD_TREE_H_ */
+#endif /* RVO3D_KD_TREE_H_ */
diff --git a/thirdparty/rvo2/README.md b/thirdparty/rvo2/README.md
deleted file mode 100644
index 96af597cb6..0000000000
--- a/thirdparty/rvo2/README.md
+++ /dev/null
@@ -1,32 +0,0 @@
-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/Vector3.h b/thirdparty/rvo2/Vector3.h
index 8c8835c865..f44e311f29 100644
--- a/thirdparty/rvo2/Vector3.h
+++ b/thirdparty/rvo2/Vector3.h
@@ -8,7 +8,7 @@
  * 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
+ *     https://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,
@@ -27,32 +27,32 @@
  * Chapel Hill, N.C. 27599-3175
  * United States of America
  *
- * <http://gamma.cs.unc.edu/RVO2/>
+ * <https://gamma.cs.unc.edu/RVO2/>
  */
 
 /**
  * \file    Vector3.h
  * \brief   Contains the Vector3 class.
  */
-#ifndef RVO_VECTOR3_H_
-#define RVO_VECTOR3_H_
-
-#include "API.h"
+#ifndef RVO3D_VECTOR3_H_
+#define RVO3D_VECTOR3_H_
 
 #include <cmath>
 #include <cstddef>
 #include <ostream>
 
+#define RVO3D_EXPORT
+
 namespace RVO {
 	/**
 	 * \brief  Defines a three-dimensional vector.
 	 */
-	class Vector3 {
+	class RVO3D_EXPORT Vector3 {
 	public:
 		/**
 		 * \brief   Constructs and initializes a three-dimensional vector instance to zero.
 		 */
-		RVO_API inline Vector3()
+		inline Vector3()
 		{
 			val_[0] = 0.0f;
 			val_[1] = 0.0f;
@@ -63,7 +63,7 @@ namespace RVO {
 		 * \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])
+		inline explicit Vector3(const float val[3])
 		{
 			val_[0] = val[0];
 			val_[1] = val[1];
@@ -76,7 +76,7 @@ namespace RVO {
 		 * \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)
+		inline Vector3(float x, float y, float z)
 		{
 			val_[0] = x;
 			val_[1] = y;
@@ -87,39 +87,39 @@ namespace RVO {
 		 * \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]; }
+		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]; }
+		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]; }
+		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]; }
+		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]; }
+		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
+		inline Vector3 operator-() const
 		{
 			return Vector3(-val_[0], -val_[1], -val_[2]);
 		}
@@ -129,7 +129,7 @@ namespace RVO {
 		 * \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
+		inline float operator*(const Vector3 &vector) const
 		{
 			return val_[0] * vector[0] + val_[1] * vector[1] + val_[2] * vector[2];
 		}
@@ -139,7 +139,7 @@ namespace RVO {
 		 * \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
+		inline Vector3 operator*(float scalar) const
 		{
 			return Vector3(val_[0] * scalar, val_[1] * scalar, val_[2] * scalar);
 		}
@@ -149,7 +149,7 @@ namespace RVO {
 		 * \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
+		inline Vector3 operator/(float scalar) const
 		{
 			const float invScalar = 1.0f / scalar;
 
@@ -161,7 +161,7 @@ namespace RVO {
 		 * \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
+		inline Vector3 operator+(const Vector3 &vector) const
 		{
 			return Vector3(val_[0] + vector[0], val_[1] + vector[1], val_[2] + vector[2]);
 		}
@@ -171,7 +171,7 @@ namespace RVO {
 		 * \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
+		inline Vector3 operator-(const Vector3 &vector) const
 		{
 			return Vector3(val_[0] - vector[0], val_[1] - vector[1], val_[2] - vector[2]);
 		}
@@ -181,7 +181,7 @@ namespace RVO {
 		 * \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
+		inline bool operator==(const Vector3 &vector) const
 		{
 			return val_[0] == vector[0] && val_[1] == vector[1] && val_[2] == vector[2];
 		}
@@ -191,7 +191,7 @@ namespace RVO {
 		 * \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
+		inline bool operator!=(const Vector3 &vector) const
 		{
 			return val_[0] != vector[0] || val_[1] != vector[1] || val_[2] != vector[2];
 		}
@@ -201,7 +201,7 @@ namespace RVO {
 		 * \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)
+		inline Vector3 &operator*=(float scalar)
 		{
 			val_[0] *= scalar;
 			val_[1] *= scalar;
@@ -215,7 +215,7 @@ namespace RVO {
 		 * \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)
+		inline Vector3 &operator/=(float scalar)
 		{
 			const float invScalar = 1.0f / scalar;
 
@@ -232,7 +232,7 @@ namespace RVO {
 		 * \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)
+		inline Vector3 &operator+=(const Vector3 &vector)
 		{
 			val_[0] += vector[0];
 			val_[1] += vector[1];
@@ -246,7 +246,7 @@ namespace RVO {
 		 * \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)
+		inline Vector3 &operator-=(const Vector3 &vector)
 		{
 			val_[0] -= vector[0];
 			val_[1] -= vector[1];
@@ -267,7 +267,7 @@ namespace RVO {
 	 * \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)
+	RVO3D_EXPORT inline Vector3 operator*(float scalar, const Vector3 &vector)
 	{
 		return Vector3(scalar * vector[0], scalar * vector[1], scalar * vector[2]);
 	}
@@ -279,7 +279,7 @@ namespace RVO {
 	 * \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)
+	RVO3D_EXPORT 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]);
 	}
@@ -291,7 +291,7 @@ namespace RVO {
 	 * \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)
+	RVO3D_EXPORT inline std::ostream &operator<<(std::ostream &os, const Vector3 &vector)
 	{
 		os << "(" << vector[0] << "," << vector[1] << "," << vector[2] << ")";
 
@@ -304,7 +304,7 @@ namespace RVO {
 	 * \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)
+	RVO3D_EXPORT inline float abs(const Vector3 &vector)
 	{
 		return std::sqrt(vector * vector);
 	}
@@ -315,7 +315,7 @@ namespace RVO {
 	 * \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)
+	RVO3D_EXPORT inline float absSq(const Vector3 &vector)
 	{
 		return vector * vector;
 	}
@@ -326,7 +326,7 @@ namespace RVO {
 	 * \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)
+	RVO3D_EXPORT inline Vector3 normalize(const Vector3 &vector)
 	{
 		return vector / abs(vector);
 	}
diff --git a/thirdparty/rvo2/patches/rvo2-godot-changes.patch b/thirdparty/rvo2/patches/rvo2-godot-changes.patch
new file mode 100644
index 0000000000..16dbc203ed
--- /dev/null
+++ b/thirdparty/rvo2/patches/rvo2-godot-changes.patch
@@ -0,0 +1,282 @@
+diff --git a/thirdparty/rvo2/Agent.cpp b/thirdparty/rvo2/Agent.cpp
+index 5e49a3554c..b35eee9c12 100644
+--- a/thirdparty/rvo2/Agent.cpp
++++ b/thirdparty/rvo2/Agent.cpp
+@@ -105,18 +105,17 @@ namespace RVO {
+ 	 */
+ 	void linearProgram4(const std::vector<Plane> &planes, size_t beginPlane, float radius, Vector3 &result);
+ 
+-	Agent::Agent(RVOSimulator *sim) : sim_(sim), id_(0), maxNeighbors_(0), maxSpeed_(0.0f), neighborDist_(0.0f), radius_(0.0f), timeHorizon_(0.0f) { }
++	Agent::Agent() : id_(0), maxNeighbors_(0), maxSpeed_(0.0f), neighborDist_(0.0f), radius_(0.0f), timeHorizon_(0.0f), ignore_y_(false) { }
+ 
+-	void Agent::computeNeighbors()
++	void Agent::computeNeighbors(KdTree *kdTree_)
+ 	{
+ 		agentNeighbors_.clear();
+-
+ 		if (maxNeighbors_ > 0) {
+-			sim_->kdTree_->computeAgentNeighbors(this, neighborDist_ * neighborDist_);
++			kdTree_->computeAgentNeighbors(this, neighborDist_ * neighborDist_);
+ 		}
+ 	}
+ 
+-	void Agent::computeNewVelocity()
++	void Agent::computeNewVelocity(float timeStep)
+ 	{
+ 		orcaPlanes_.clear();
+ 		const float invTimeHorizon = 1.0f / timeHorizon_;
+@@ -124,10 +123,24 @@ namespace RVO {
+ 		/* Create agent ORCA planes. */
+ 		for (size_t i = 0; i < agentNeighbors_.size(); ++i) {
+ 			const Agent *const other = agentNeighbors_[i].second;
+-			const Vector3 relativePosition = other->position_ - position_;
+-			const Vector3 relativeVelocity = velocity_ - other->velocity_;
+-			const float distSq = absSq(relativePosition);
++
++			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
++#define ABS(m_v) (((m_v) < 0) ? (-(m_v)) : (m_v))
++				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;
+@@ -165,7 +178,7 @@ namespace RVO {
+ 			}
+ 			else {
+ 				/* Collision. */
+-				const float invTimeStep = 1.0f / sim_->timeStep_;
++				const float invTimeStep = 1.0f / timeStep;
+ 				const Vector3 w = relativeVelocity - invTimeStep * relativePosition;
+ 				const float wLength = abs(w);
+ 				const Vector3 unitW = w / wLength;
+@@ -183,6 +196,11 @@ namespace RVO {
+ 		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)
+@@ -211,12 +229,6 @@ namespace RVO {
+ 		}
+ 	}
+ 
+-	void Agent::update()
+-	{
+-		velocity_ = newVelocity_;
+-		position_ += velocity_ * sim_->timeStep_;
+-	}
+-
+ 	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;
+diff --git a/thirdparty/rvo2/Agent.h b/thirdparty/rvo2/Agent.h
+index d3922ec645..45fbead2f5 100644
+--- a/thirdparty/rvo2/Agent.h
++++ b/thirdparty/rvo2/Agent.h
+@@ -41,30 +41,52 @@
+ #include <utility>
+ #include <vector>
+ 
+-#include "RVOSimulator.h"
+ #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 {
+-	private:
++	public:
+ 		/**
+ 		 * \brief   Constructs an agent instance.
+ 		 * \param   sim  The simulator instance.
+ 		 */
+-		explicit Agent(RVOSimulator *sim);
++		explicit Agent();
+ 
+ 		/**
+ 		 * \brief   Computes the neighbors of this agent.
+ 		 */
+-		void computeNeighbors();
++		void computeNeighbors(class KdTree *kdTree_);
+ 
+ 		/**
+ 		 * \brief   Computes the new velocity of this agent.
+ 		 */
+-		void computeNewVelocity();
++		void computeNewVelocity(float timeStep);
+ 
+ 		/**
+ 		 * \brief   Inserts an agent neighbor into the set of neighbors of this agent.
+@@ -73,16 +95,10 @@ namespace RVO {
+ 		 */
+ 		void insertAgentNeighbor(const Agent *agent, float &rangeSq);
+ 
+-		/**
+-		 * \brief   Updates the three-dimensional position and three-dimensional velocity of this agent.
+-		 */
+-		void update();
+-
+ 		Vector3 newVelocity_;
+ 		Vector3 position_;
+ 		Vector3 prefVelocity_;
+ 		Vector3 velocity_;
+-		RVOSimulator *sim_;
+ 		size_t id_;
+ 		size_t maxNeighbors_;
+ 		float maxSpeed_;
+@@ -91,9 +107,11 @@ namespace RVO {
+ 		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;
+-		friend class RVOSimulator;
+ 	};
+ }
+ 
+diff --git a/thirdparty/rvo2/KdTree.cpp b/thirdparty/rvo2/KdTree.cpp
+index 5e9e9777a6..c857f299df 100644
+--- a/thirdparty/rvo2/KdTree.cpp
++++ b/thirdparty/rvo2/KdTree.cpp
+@@ -36,16 +36,15 @@
+ 
+ #include "Agent.h"
+ #include "Definitions.h"
+-#include "RVOSimulator.h"
+ 
+ namespace RVO {
+ 	const size_t RVO3D_MAX_LEAF_SIZE = 10;
+ 
+-	KdTree::KdTree(RVOSimulator *sim) : sim_(sim) { }
++	KdTree::KdTree() { }
+ 
+-	void KdTree::buildAgentTree()
++	void KdTree::buildAgentTree(std::vector<Agent *> agents)
+ 	{
+-		agents_ = sim_->agents_;
++		agents_.swap(agents);
+ 
+ 		if (!agents_.empty()) {
+ 			agentTree_.resize(2 * agents_.size() - 1);
+diff --git a/thirdparty/rvo2/KdTree.h b/thirdparty/rvo2/KdTree.h
+index a09384c20f..69d8920ce0 100644
+--- a/thirdparty/rvo2/KdTree.h
++++ b/thirdparty/rvo2/KdTree.h
+@@ -41,6 +41,9 @@
+ 
+ #include "Vector3.h"
+ 
++// Note: Slightly modified to work better with Godot.
++// - Removed `sim_`.
++// - KdTree things are public
+ namespace RVO {
+ 	class Agent;
+ 	class RVOSimulator;
+@@ -49,7 +52,7 @@ namespace RVO {
+ 	 * \brief   Defines <i>k</i>d-trees for agents in the simulation.
+ 	 */
+ 	class KdTree {
+-	private:
++	public:
+ 		/**
+ 		 * \brief   Defines an agent <i>k</i>d-tree node.
+ 		 */
+@@ -90,12 +93,12 @@ namespace RVO {
+ 		 * \brief   Constructs a <i>k</i>d-tree instance.
+ 		 * \param   sim  The simulator instance.
+ 		 */
+-		explicit KdTree(RVOSimulator *sim);
++		explicit KdTree();
+ 
+ 		/**
+ 		 * \brief   Builds an agent <i>k</i>d-tree.
+ 		 */
+-		void buildAgentTree();
++		void buildAgentTree(std::vector<Agent *> agents);
+ 
+ 		void buildAgentTreeRecursive(size_t begin, size_t end, size_t node);
+ 
+@@ -110,7 +113,6 @@ namespace RVO {
+ 
+ 		std::vector<Agent *> agents_;
+ 		std::vector<AgentTreeNode> agentTree_;
+-		RVOSimulator *sim_;
+ 
+ 		friend class Agent;
+ 		friend class RVOSimulator;
+diff --git a/thirdparty/rvo2/Vector3.h b/thirdparty/rvo2/Vector3.h
+index 6c3223bb87..f44e311f29 100644
+--- a/thirdparty/rvo2/Vector3.h
++++ b/thirdparty/rvo2/Vector3.h
+@@ -41,7 +41,7 @@
+ #include <cstddef>
+ #include <ostream>
+ 
+-#include "Export.h"
++#define RVO3D_EXPORT
+ 
+ namespace RVO {
+ 	/**
+@@ -59,17 +59,6 @@ namespace RVO {
+ 			val_[2] = 0.0f;
+ 		}
+ 
+-		/**
+-		 * \brief   Constructs and initializes a three-dimensional vector from the specified three-dimensional vector.
+-		 * \param   vector  The three-dimensional vector containing the xyz-coordinates.
+-		 */
+-		inline Vector3(const Vector3 &vector)
+-		{
+-			val_[0] = vector[0];
+-			val_[1] = vector[1];
+-			val_[2] = vector[2];
+-		}
+-
+ 		/**
+ 		 * \brief   Constructs and initializes a three-dimensional vector from the specified three-element array.
+ 		 * \param   val  The three-element array containing the xyz-coordinates.