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Bobbing, KDTree implementation

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Xevion
2024-12-15 20:29:40 -06:00
parent a5a9d17565
commit d6b835fdd1
38 changed files with 2899 additions and 125 deletions
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Assets/Datastructures/Heap/BaseHeap.cs Normal file
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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
namespace DataStructures.ViliWonka.Heap {
// array start at index 1, optimisation reason
public abstract class BaseHeap {
protected int nodesCount;
protected int maxSize;
protected float[] heap;
protected BaseHeap(int initialSize) {
maxSize = initialSize;
heap = new float[initialSize + 1];
}
public int Count { get { return nodesCount; } }
public float HeadValue { get { return heap[1]; } }
public void Clear() {
nodesCount = 0;
}
protected int Parent(int index) { return (index >> 1); }
protected int Left (int index) { return (index << 1); }
protected int Right (int index) { return (index << 1) | 1; }
// bubble down, MaxHeap version
protected void BubbleDownMax(int index) {
int L = Left(index);
int R = Right(index);
// bubbling down, 2 kids
while (R <= nodesCount) {
// if heap property is violated between index and Left child
if(heap[index] < heap[L]) {
if (heap[L] < heap[R]) {
Swap(index, R); // left has bigger priority
index = R;
}
else {
Swap(index, L); // right has bigger priority
index = L;
}
}
else {
// if heap property is violated between index and R
if (heap[index] < heap[R]) {
Swap(index, R);
index = R;
}
else {
index = L;
L = Left(index);
break;
}
}
L = Left(index);
R = Right(index);
}
// only left & last children available to test and swap
if (L <= nodesCount && heap[index] < heap[L]) {
Swap(index, L);
}
}
// bubble up, MaxHeap version
protected void BubbleUpMax(int index) {
int P = Parent(index);
//swap, until Heap property isn't violated anymore
while (P > 0 && heap[P] < heap[index]) {
Swap(P, index);
index = P;
P = Parent(index);
}
}
// bubble down, MinHeap version
protected void BubbleDownMin(int index) {
int L = Left(index);
int R = Right(index);
// bubbling down, 2 kids
while(R <= nodesCount) {
// if heap property is violated between index and Left child
if(heap[index] > heap[L]) {
if(heap[L] > heap[R]) {
Swap(index, R); // right has smaller priority
index = R;
}
else {
Swap(index, L); // left has smaller priority
index = L;
}
}
else {
// if heap property is violated between index and R
if(heap[index] > heap[R]) {
Swap(index, R);
index = R;
}
else {
index = L;
L = Left(index);
break;
}
}
L = Left(index);
R = Right(index);
}
// only left & last children available to test and swap
if(L <= nodesCount && heap[index] > heap[L]) {
Swap(index, L);
}
}
// bubble up, MinHeap version
protected void BubbleUpMin(int index) {
int P = Parent(index);
//swap, until Heap property isn't violated anymore
while(P > 0 && heap[P] > heap[index]) {
Swap(P, index);
index = P;
P = Parent(index);
}
}
protected float tempHeap;
protected virtual void Swap(int A, int B) {
tempHeap = heap[A];
heap[A] = heap[B];
heap[B] = tempHeap;
}
protected virtual void UpsizeHeap() {
maxSize *= 2;
System.Array.Resize(ref heap, maxSize + 1);
}
public virtual void PushValue(float h) {
throw new System.NotImplementedException();
}
public virtual float PopValue() {
throw new System.NotImplementedException();
}
public void FlushHeapResult(List<float> heapList) {
for(int i = 1; i < Count; i++) {
heapList.Add(heap[i]);
}
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
namespace DataStructures.ViliWonka.Heap {
public class KSmallestHeap : BaseHeap {
public KSmallestHeap(int maxEntries) : base(maxEntries) {
}
public bool Full {
get {
return maxSize == nodesCount;
}
}
// in lots of cases, max head gets removed
public override void PushValue(float h) {
// if heap full
if(nodesCount == maxSize) {
// if Heads priority is smaller than input priority, then ignore that item
if(HeadValue < h) {
return;
}
else {
heap[1] = h; // remove top element
BubbleDownMax(1); // bubble it down
}
}
else {
nodesCount++;
heap[nodesCount] = h;
BubbleUpMax(nodesCount);
}
}
public override float PopValue() {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
float result = heap[1];
heap[1] = heap[nodesCount];
nodesCount--;
BubbleDownMax(1);
return result;
}
public void Print() {
UnityEngine.Debug.Log("HeapPropertyHolds? " + HeapPropertyHolds(1));
}
//should remove
public bool HeapPropertyHolds(int index, int depth = 0) {
if (index > nodesCount)
return true;
UnityEngine.Debug.Log(heap[index]);
int L = Left(index);
int R = Right(index);
bool bothHold = true;
if(L <= nodesCount) {
UnityEngine.Debug.Log(heap[index] + " => " + heap[L]);
if (heap[index] < heap[L])
bothHold = false;
}
// if L <= nodesCount, then R <= nodesCount can also happen
if (R <= nodesCount) {
UnityEngine.Debug.Log(heap[index] + " => " + heap[R]);
if (bothHold && heap[index] < heap[R])
bothHold = false;
}
return bothHold & HeapPropertyHolds(L, depth + 1) & HeapPropertyHolds(R, depth + 1);
}
}
// array start at index 1
// generic version
public class KSmallestHeap<T> : KSmallestHeap {
T[] objs; //objects
public KSmallestHeap(int maxEntries) : base(maxEntries) {
objs = new T[maxEntries + 1];
}
public T HeadHeapObject { get { return objs[1]; } }
T tempObjs;
protected override void Swap(int A, int B) {
tempHeap = heap[A];
tempObjs = objs[A];
heap[A] = heap[B];
objs[A] = objs[B];
heap[B] = tempHeap;
objs[B] = tempObjs;
}
public override void PushValue(float h) {
throw new System.ArgumentException("Use Push(T, float)!");
}
public void PushObj(T obj, float h) {
// if heap full
if(nodesCount == maxSize) {
// if Heads priority is smaller than input priority, then ignore that item
if(HeadValue < h) {
return;
}
else {
heap[1] = h; // remove top element
objs[1] = obj;
BubbleDownMax(1); // bubble it down
}
}
else {
nodesCount++;
heap[nodesCount] = h;
objs[nodesCount] = obj;
BubbleUpMax(nodesCount);
}
}
public override float PopValue() {
throw new System.ArgumentException("Use PopObj()!");
}
public T PopObj() {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
T result = objs[1];
heap[1] = heap[nodesCount];
objs[1] = objs[nodesCount];
nodesCount--;
BubbleDownMax(1);
return result;
}
public T PopObj(ref float heapValue) {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
heapValue = heap[1];
T result = PopObj();
return result;
}
//flush internal results, returns ordered data
public void FlushResult(List<T> resultList, List<float> heapList = null) {
int count = nodesCount + 1;
if(heapList == null) {
for(int i = 1; i < count; i++) {
resultList.Add(PopObj());
}
}
else {
float h = 0f;
for(int i = 1; i < count; i++) {
resultList.Add(PopObj(ref h));
heapList.Add(h);
}
}
}
}
}

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Assets/Datastructures/Heap/MaxHeap.cs Normal file
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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
namespace DataStructures.ViliWonka.Heap {
public class MaxHeap : BaseHeap {
public MaxHeap(int initialSize = 2048) : base(initialSize) {
}
public override void PushValue(float h) {
// if heap array is full
if(nodesCount == maxSize) {
UpsizeHeap();
}
nodesCount++;
heap[nodesCount] = h;
BubbleUpMax(nodesCount);
}
public override float PopValue() {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
float result = heap[1];
heap[1] = heap[nodesCount];
nodesCount--;
BubbleDownMax(1);
return result;
}
}
// generic version
public class MaxHeap<T> : MaxHeap {
T[] objs; // objects
public MaxHeap(int maxNodes) : base(maxNodes) {
objs = new T[maxNodes + 1];
}
public T HeadHeapObject { get { return objs[1]; } }
T tempObjs;
protected override void Swap(int A, int B) {
tempHeap = heap[A];
tempObjs = objs[A];
heap[A] = heap[B];
objs[A] = objs[B];
heap[B] = tempHeap;
objs[B] = tempObjs;
}
public override void PushValue(float h) {
throw new System.ArgumentException("Use PushObj(T, float)!");
}
public override float PopValue() {
throw new System.ArgumentException("Use Push(T, float)!");
}
public void PushObj(T obj, float h) {
// if heap array is full
if(nodesCount == maxSize) {
UpsizeHeap();
}
nodesCount++;
heap[nodesCount] = h;
objs[nodesCount] = obj;
BubbleUpMin(nodesCount);
}
public T PopObj() {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
T result = objs[1];
heap[1] = heap[nodesCount];
objs[1] = objs[nodesCount];
objs[nodesCount] = default(T);
nodesCount--;
BubbleDownMin(1);
return result;
}
public T PopObj(ref float heapValue) {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
heapValue = heap[1];
T result = PopObj();
return result;
}
protected override void UpsizeHeap() {
maxSize *= 2;
System.Array.Resize(ref heap, maxSize + 1);
System.Array.Resize(ref objs, maxSize + 1);
}
//flush internal results, returns ordered data
public void FlushResult(List<T> resultList, List<float> heapList = null) {
int count = nodesCount + 1;
if(heapList == null) {
for(int i = 1; i < count; i++) {
resultList.Add(PopObj());
}
}
else {
float h = 0f;
for(int i = 1; i < count; i++) {
resultList.Add(PopObj(ref h));
heapList.Add(h);
}
}
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
namespace DataStructures.ViliWonka.Heap {
public class MinHeap : BaseHeap {
public MinHeap(int initialSize = 2048) : base(initialSize) {
}
public override void PushValue(float h) {
// if heap array is full
if(nodesCount == maxSize) {
UpsizeHeap();
}
nodesCount++;
heap[nodesCount] = h;
BubbleUpMin(nodesCount);
}
public override float PopValue() {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
float result = heap[1];
heap[1] = heap[nodesCount];
nodesCount--;
if(nodesCount != 0)
BubbleDownMin(1);
return result;
}
}
// generic version
public class MinHeap<T> : MinHeap {
T[] objs; // objects
public MinHeap(int maxNodes = 2048) : base(maxNodes) {
objs = new T[maxNodes + 1];
}
public T HeadHeapObject { get { return objs[1]; } }
T tempObjs;
protected override void Swap(int A, int B) {
tempHeap = heap[A];
tempObjs = objs[A];
heap[A] = heap[B];
objs[A] = objs[B];
heap[B] = tempHeap;
objs[B] = tempObjs;
}
public override void PushValue(float h) {
throw new System.ArgumentException("Use Push(T, float)!");
}
public override float PopValue() {
throw new System.ArgumentException("Use Push(T, float)!");
}
public void PushObj(T obj, float h) {
// if heap array is full
if(nodesCount == maxSize) {
UpsizeHeap();
}
nodesCount++;
heap[nodesCount] = h;
objs[nodesCount] = obj;
BubbleUpMin(nodesCount);
}
public T PopObj() {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
T result = objs[1];
heap[1] = heap[nodesCount];
objs[1] = objs[nodesCount];
objs[nodesCount] = default(T);
nodesCount--;
if(nodesCount != 0)
BubbleDownMin(1);
return result;
}
public T PopObj(ref float heapValue) {
if(nodesCount == 0)
throw new System.ArgumentException("Heap is empty!");
heapValue = heap[1];
T result = PopObj();
return result;
}
protected override void UpsizeHeap() {
maxSize *= 2;
System.Array.Resize(ref heap, maxSize + 1);
System.Array.Resize(ref objs, maxSize + 1);
}
//flush internal array, returns ordered data
public void FlushResult(List<T> resultList, List<float> heapList = null) {
int count = nodesCount + 1;
if(heapList == null) {
for(int i = 1; i < count; i++) {
resultList.Add(PopObj());
}
}
else {
float h = 0f;
for(int i = 1; i < count; i++) {
resultList.Add(PopObj(ref h));
heapList.Add(h);
}
}
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using UnityEngine;
using UnityEditor;
namespace DataStructures.ViliWonka.KDTree {
public struct KDBounds {
public Vector3 min;
public Vector3 max;
public Vector3 size {
get {
return max - min;
}
}
// returns unity bounds
public Bounds Bounds {
get {
return new Bounds(
(min + max) / 2,
(max - min)
);
}
}
public Vector3 ClosestPoint(Vector3 point) {
// X axis
if(point.x < min.x) point.x = min.x;
else
if(point.x > max.x) point.x = max.x;
// Y axis
if(point.y < min.y) point.y = min.y;
else
if(point.y > max.y) point.y = max.y;
// Z axis
if(point.z < min.z) point.z = min.z;
else
if(point.z > max.z) point.z = max.z;
return point;
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections;
using System.Collections.Generic;
using UnityEngine;
namespace DataStructures.ViliWonka.KDTree {
public class KDNode {
public float partitionCoordinate;
public int partitionAxis = -1;
public KDNode negativeChild;
public KDNode positiveChild;
public int start;
public int end;
public int Count { get { return end - start; } }
public bool Leaf { get { return partitionAxis == -1; } }
public KDBounds bounds;
};
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
/*
The object used for querying. This object should be persistent - re-used for querying.
Contains internal array for pooling, so that it doesn't generate (too much) garbage.
The array never down-sizes, only up-sizes, so the more you use this object, less garbage will it make over time.
Should be used only by 1 thread,
which means each thread should have it's own KDQuery object in order for querying to be thread safe.
KDQuery can query different KDTrees.
*/
using System.Collections.Generic;
using UnityEngine;
using System;
namespace DataStructures.ViliWonka.KDTree {
public partial class KDQuery {
protected KDQueryNode[] queueArray; // queue array
protected Heap.MinHeap<KDQueryNode> minHeap; //heap for k-nearest
protected int count = 0; // size of queue
protected int queryIndex = 0; // current index at stack
/// <summary>
/// Returns initialized node from stack that also acts as a pool
/// The returned reference to node stays in stack
/// </summary>
/// <returns>Reference to pooled node</returns>
private KDQueryNode PushGetQueue() {
KDQueryNode node = null;
if (count < queueArray.Length) {
if (queueArray[count] == null)
queueArray[count] = node = new KDQueryNode();
else
node = queueArray[count];
}
else {
// automatic resize of pool
Array.Resize(ref queueArray, queueArray.Length * 2);
node = queueArray[count] = new KDQueryNode();
}
count++;
return node;
}
protected void PushToQueue(KDNode node, Vector3 tempClosestPoint) {
var queryNode = PushGetQueue();
queryNode.node = node;
queryNode.tempClosestPoint = tempClosestPoint;
}
protected void PushToHeap(KDNode node, Vector3 tempClosestPoint, Vector3 queryPosition) {
var queryNode = PushGetQueue();
queryNode.node = node;
queryNode.tempClosestPoint = tempClosestPoint;
float sqrDist = Vector3.SqrMagnitude(tempClosestPoint - queryPosition);
queryNode.distance = sqrDist;
minHeap.PushObj(queryNode, sqrDist);
}
protected int LeftToProcess {
get {
return count - queryIndex;
}
}
// just gets unprocessed node from stack
// increases queryIndex
protected KDQueryNode PopFromQueue() {
var node = queueArray[queryIndex];
queryIndex++;
return node;
}
protected KDQueryNode PopFromHeap() {
KDQueryNode heapNode = minHeap.PopObj();
queueArray[queryIndex]= heapNode;
queryIndex++;
return heapNode;
}
protected void Reset() {
count = 0;
queryIndex = 0;
minHeap.Clear();
}
public KDQuery(int queryNodesContainersInitialSize = 2048) {
queueArray = new KDQueryNode[queryNodesContainersInitialSize];
minHeap = new Heap.MinHeap<KDQueryNode>(queryNodesContainersInitialSize);
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#define KDTREE_VISUAL_DEBUG
using System.Collections.Generic;
using UnityEngine;
using System;
namespace DataStructures.ViliWonka.KDTree {
public partial class KDQuery {
// uses gizmos
public void DrawLastQuery() {
Color start = Color.red;
Color end = Color.green;
start.a = 0.25f;
end.a = 0.25f;
for(int i = 0; i < queryIndex; i++) {
float val = i / (float)queryIndex;
Gizmos.color = Color.Lerp(end, start, val);
Bounds b = queueArray[i].node.bounds.Bounds;
Gizmos.DrawWireCube(b.center, b.size);
}
}
}
}

11
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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using UnityEngine;
using UnityEditor;
namespace DataStructures.ViliWonka.KDTree {
public class KDQueryNode {
public KDNode node;
public Vector3 tempClosestPoint;
public float distance;
public KDQueryNode() {
}
public KDQueryNode(KDNode node, Vector3 tempClosestPoint) {
this.node = node;
this.tempClosestPoint = tempClosestPoint;
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
using UnityEngine;
using System;
namespace DataStructures.ViliWonka.KDTree {
using Heap;
public partial class KDQuery {
public void ClosestPoint(KDTree tree, Vector3 queryPosition, List<int> resultIndices, List<float> resultDistances = null) {
Reset();
Vector3[] points = tree.Points;
int[] permutation = tree.Permutation;
if (points.Length == 0) {
return;
}
int smallestIndex = 0;
/// Smallest Squared Radius
float SSR = Single.PositiveInfinity;
var rootNode = tree.RootNode;
Vector3 rootClosestPoint = rootNode.bounds.ClosestPoint(queryPosition);
PushToHeap(rootNode, rootClosestPoint, queryPosition);
KDQueryNode queryNode = null;
KDNode node = null;
int partitionAxis;
float partitionCoord;
Vector3 tempClosestPoint;
// searching
while(minHeap.Count > 0) {
queryNode = PopFromHeap();
if(queryNode.distance > SSR)
continue;
node = queryNode.node;
if(!node.Leaf) {
partitionAxis = node.partitionAxis;
partitionCoord = node.partitionCoordinate;
tempClosestPoint = queryNode.tempClosestPoint;
if((tempClosestPoint[partitionAxis] - partitionCoord) < 0) {
// we already know we are on the side of negative bound/node,
// so we don't need to test for distance
// push to stack for later querying
PushToHeap(node.negativeChild, tempClosestPoint, queryPosition);
// project the tempClosestPoint to other bound
tempClosestPoint[partitionAxis] = partitionCoord;
if(node.positiveChild.Count != 0) {
PushToHeap(node.positiveChild, tempClosestPoint, queryPosition);
}
}
else {
// we already know we are on the side of positive bound/node,
// so we don't need to test for distance
// push to stack for later querying
PushToHeap(node.positiveChild, tempClosestPoint, queryPosition);
// project the tempClosestPoint to other bound
tempClosestPoint[partitionAxis] = partitionCoord;
if(node.positiveChild.Count != 0) {
PushToHeap(node.negativeChild, tempClosestPoint, queryPosition);
}
}
}
else {
float sqrDist;
// LEAF
for(int i = node.start; i < node.end; i++) {
int index = permutation[i];
sqrDist = Vector3.SqrMagnitude(points[index] - queryPosition);
if(sqrDist <= SSR) {
SSR = sqrDist;
smallestIndex = index;
}
}
}
}
resultIndices.Add(smallestIndex);
if(resultDistances != null) {
resultDistances.Add(SSR);
}
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
using UnityEngine;
using System;
namespace DataStructures.ViliWonka.KDTree {
public partial class KDQuery {
public void Interval(KDTree tree, Vector3 min, Vector3 max, List<int> resultIndices) {
Reset();
Vector3[] points = tree.Points;
int[] permutation = tree.Permutation;
var rootNode = tree.RootNode;
PushToQueue(
rootNode,
rootNode.bounds.ClosestPoint((min + max) / 2)
);
KDQueryNode queryNode = null;
KDNode node = null;
// KD search with pruning (don't visit areas which distance is more away than range)
// Recursion done on Stack
while(LeftToProcess > 0) {
queryNode = PopFromQueue();
node = queryNode.node;
if(!node.Leaf) {
int partitionAxis = node.partitionAxis;
float partitionCoord = node.partitionCoordinate;
Vector3 tempClosestPoint = queryNode.tempClosestPoint;
if((tempClosestPoint[partitionAxis] - partitionCoord) < 0) {
// we already know we are inside negative bound/node,
// so we don't need to test for distance
// push to stack for later querying
// tempClosestPoint is inside negative side
// assign it to negativeChild
PushToQueue(node.negativeChild, tempClosestPoint);
tempClosestPoint[partitionAxis] = partitionCoord;
// testing other side
if(node.positiveChild.Count != 0
&& tempClosestPoint[partitionAxis] <= max[partitionAxis]) {
PushToQueue(node.positiveChild, tempClosestPoint);
}
}
else {
// we already know we are inside positive bound/node,
// so we don't need to test for distance
// push to stack for later querying
// tempClosestPoint is inside positive side
// assign it to positiveChild
PushToQueue(node.positiveChild, tempClosestPoint);
// project the tempClosestPoint to other bound
tempClosestPoint[partitionAxis] = partitionCoord;
// testing other side
if(node.negativeChild.Count != 0
&& tempClosestPoint[partitionAxis] >= min[partitionAxis]) {
PushToQueue(node.negativeChild, tempClosestPoint);
}
}
}
else {
// LEAF
// testing if node bounds are inside the query interval
if(node.bounds.min[0] >= min[0]
&& node.bounds.min[1] >= min[1]
&& node.bounds.min[2] >= min[2]
&& node.bounds.max[0] <= max[0]
&& node.bounds.max[1] <= max[1]
&& node.bounds.max[2] <= max[2]) {
for(int i = node.start; i < node.end; i++) {
resultIndices.Add(permutation[i]);
}
}
// node is not inside query interval, need to do test on each point separately
else {
for(int i = node.start; i < node.end; i++) {
int index = permutation[i];
Vector3 v = points[index];
if(v[0] >= min[0]
&& v[1] >= min[1]
&& v[2] >= min[2]
&& v[0] <= max[0]
&& v[1] <= max[1]
&& v[2] <= max[2]) {
resultIndices.Add(index);
}
}
}
}
}
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#define KDTREE_VISUAL_DEBUG
using System.Collections.Generic;
using UnityEngine;
using System;
namespace DataStructures.ViliWonka.KDTree {
using Heap;
public partial class KDQuery {
SortedList<int, KSmallestHeap<int>> _heaps = new SortedList<int, KSmallestHeap<int>>();
/// <summary>
/// Returns indices to k closest points, and optionaly can return distances
/// </summary>
/// <param name="tree">Tree to do search on</param>
/// <param name="queryPosition">Position</param>
/// <param name="k">Max number of points</param>
/// <param name="resultIndices">List where resulting indices will be stored</param>
/// <param name="resultDistances">Optional list where resulting distances will be stored</param>
public void KNearest(KDTree tree, Vector3 queryPosition, int k, List<int> resultIndices, List<float> resultDistances = null) {
// pooled heap arrays
KSmallestHeap<int> kHeap;
_heaps.TryGetValue(k, out kHeap);
if(kHeap == null) {
kHeap = new KSmallestHeap<int>(k);
_heaps.Add(k, kHeap);
}
kHeap.Clear();
Reset();
Vector3[] points = tree.Points;
int[] permutation = tree.Permutation;
///Biggest Smallest Squared Radius
float BSSR = Single.PositiveInfinity;
var rootNode = tree.RootNode;
Vector3 rootClosestPoint = rootNode.bounds.ClosestPoint(queryPosition);
PushToHeap(rootNode, rootClosestPoint, queryPosition);
KDQueryNode queryNode = null;
KDNode node = null;
int partitionAxis;
float partitionCoord;
Vector3 tempClosestPoint;
// searching
while(minHeap.Count > 0) {
queryNode = PopFromHeap();
if(queryNode.distance > BSSR)
continue;
node = queryNode.node;
if(!node.Leaf) {
partitionAxis = node.partitionAxis;
partitionCoord = node.partitionCoordinate;
tempClosestPoint = queryNode.tempClosestPoint;
if((tempClosestPoint[partitionAxis] - partitionCoord) < 0) {
// we already know we are on the side of negative bound/node,
// so we don't need to test for distance
// push to stack for later querying
PushToHeap(node.negativeChild, tempClosestPoint, queryPosition);
// project the tempClosestPoint to other bound
tempClosestPoint[partitionAxis] = partitionCoord;
if(node.positiveChild.Count != 0) {
PushToHeap(node.positiveChild, tempClosestPoint, queryPosition);
}
}
else {
// we already know we are on the side of positive bound/node,
// so we don't need to test for distance
// push to stack for later querying
PushToHeap(node.positiveChild, tempClosestPoint, queryPosition);
// project the tempClosestPoint to other bound
tempClosestPoint[partitionAxis] = partitionCoord;
if(node.positiveChild.Count != 0) {
PushToHeap(node.negativeChild, tempClosestPoint, queryPosition);
}
}
}
else {
float sqrDist;
// LEAF
for(int i = node.start; i < node.end; i++) {
int index = permutation[i];
sqrDist = Vector3.SqrMagnitude(points[index] - queryPosition);
if(sqrDist <= BSSR) {
kHeap.PushObj(index, sqrDist);
if(kHeap.Full) {
BSSR = kHeap.HeadValue;
}
}
}
}
}
kHeap.FlushResult(resultIndices, resultDistances);
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
using System.Collections.Generic;
using UnityEngine;
using System;
namespace DataStructures.ViliWonka.KDTree {
public partial class KDQuery {
/// <summary>
/// Search by radius method.
/// </summary>
/// <param name="tree">Tree to do search on</param>
/// <param name="queryPosition">Position</param>
/// <param name="queryRadius">Radius</param>
/// <param name="resultIndices">Initialized list, cleared.</param>
public void Radius(KDTree tree, Vector3 queryPosition, float queryRadius, List<int> resultIndices) {
Reset();
Vector3[] points = tree.Points;
int[] permutation = tree.Permutation;
float squaredRadius = queryRadius * queryRadius;
var rootNode = tree.RootNode;
PushToQueue(rootNode, rootNode.bounds.ClosestPoint(queryPosition));
KDQueryNode queryNode = null;
KDNode node = null;
// KD search with pruning (don't visit areas which distance is more away than range)
// Recursion done on Stack
while(LeftToProcess > 0) {
queryNode = PopFromQueue();
node = queryNode.node;
if(!node.Leaf) {
int partitionAxis = node.partitionAxis;
float partitionCoord = node.partitionCoordinate;
Vector3 tempClosestPoint = queryNode.tempClosestPoint;
if((tempClosestPoint[partitionAxis] - partitionCoord) < 0) {
// we already know we are inside negative bound/node,
// so we don't need to test for distance
// push to stack for later querying
// tempClosestPoint is inside negative side
// assign it to negativeChild
PushToQueue(node.negativeChild, tempClosestPoint);
tempClosestPoint[partitionAxis] = partitionCoord;
float sqrDist = Vector3.SqrMagnitude(tempClosestPoint - queryPosition);
// testing other side
if(node.positiveChild.Count != 0
&& sqrDist <= squaredRadius) {
PushToQueue(node.positiveChild, tempClosestPoint);
}
}
else {
// we already know we are inside positive bound/node,
// so we don't need to test for distance
// push to stack for later querying
// tempClosestPoint is inside positive side
// assign it to positiveChild
PushToQueue(node.positiveChild, tempClosestPoint);
// project the tempClosestPoint to other bound
tempClosestPoint[partitionAxis] = partitionCoord;
float sqrDist = Vector3.SqrMagnitude(tempClosestPoint - queryPosition);
// testing other side
if(node.negativeChild.Count != 0
&& sqrDist <= squaredRadius) {
PushToQueue(node.negativeChild, tempClosestPoint);
}
}
}
else {
// LEAF
for(int i = node.start; i < node.end; i++) {
int index = permutation[i];
if(Vector3.SqrMagnitude(points[index] - queryPosition) <= squaredRadius) {
resultIndices.Add(index);
}
}
}
}
}
}
}

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/*MIT License
Copyright(c) 2018 Vili Volčini / viliwonka
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
// change to !KDTREE_DUPLICATES
// if you know for sure you will not use duplicate coordinates (all unique)
#define KDTREE_DUPLICATES
using System.Collections;
using System.Collections.Generic;
using System;
using UnityEngine;
namespace DataStructures.ViliWonka.KDTree {
public class KDTree {
public KDNode RootNode { get; private set; }
public Vector3[] Points { get { return points; } } // points on which kd-tree will build on. This array will stay unchanged when re/building kdtree!
private Vector3[] points;
public int[] Permutation { get { return permutation; } } // index aray, that will be permuted
private int[] permutation;
public int Count { get; private set; }
private int maxPointsPerLeafNode = 32;
private KDNode[] kdNodesStack;
private int kdNodesCount = 0;
public KDTree(int maxPointsPerLeafNode = 32) {
Count = 0;
points = new Vector3[0];
permutation = new int[0];
kdNodesStack = new KDNode[64];
this.maxPointsPerLeafNode = maxPointsPerLeafNode;
}
public KDTree(Vector3[] points, int maxPointsPerLeafNode = 32) {
this.points = points;
this.permutation = new int[points.Length];
Count = points.Length;
kdNodesStack = new KDNode[64];
this.maxPointsPerLeafNode = maxPointsPerLeafNode;
Rebuild();
}
public void Build(Vector3[] newPoints, int maxPointsPerLeafNode = -1) {
SetCount(newPoints.Length);
for(int i = 0; i < Count; i++) {
points[i] = newPoints[i];
}
Rebuild(maxPointsPerLeafNode);
}
public void Build(List<Vector3> newPoints, int maxPointsPerLeafNode = -1) {
SetCount(newPoints.Count);
for(int i = 0; i < Count; i++) {
points[i] = newPoints[i];
}
Rebuild(maxPointsPerLeafNode);
}
public void Rebuild(int maxPointsPerLeafNode = -1) {
for(int i = 0; i < Count; i++) {
permutation[i] = i;
}
if(maxPointsPerLeafNode > 0) {
this.maxPointsPerLeafNode = maxPointsPerLeafNode;
}
BuildTree();
}
public void SetCount(int newSize) {
Count = newSize;
// upsize internal arrays
if(Count > points.Length) {
Array.Resize(ref points, Count);
Array.Resize(ref permutation, Count);
}
}
void BuildTree() {
ResetKDNodeStack();
RootNode = GetKDNode();
RootNode.bounds = MakeBounds();
RootNode.start = 0;
RootNode.end = Count;
SplitNode(RootNode);
}
KDNode GetKDNode() {
KDNode node = null;
if(kdNodesCount < kdNodesStack.Length) {
if(kdNodesStack[kdNodesCount] == null) {
kdNodesStack[kdNodesCount] = node = new KDNode();
}
else {
node = kdNodesStack[kdNodesCount];
node.partitionAxis = -1;
}
}
else {
// automatic resize of KDNode pool array
Array.Resize(ref kdNodesStack, kdNodesStack.Length * 2);
node = kdNodesStack[kdNodesCount] = new KDNode();
}
kdNodesCount++;
return node;
}
void ResetKDNodeStack() {
kdNodesCount = 0;
}
/// <summary>
/// For calculating root node bounds
/// </summary>
/// <returns>Boundary of all Vector3 points</returns>
KDBounds MakeBounds() {
Vector3 max = new Vector3(float.MinValue, float.MinValue, float.MinValue);
Vector3 min = new Vector3(float.MaxValue, float.MaxValue, float.MaxValue);
int even = Count & ~1; // calculate even Length
// min, max calculations
// 3n/2 calculations instead of 2n
for (int i0 = 0; i0 < even; i0 += 2) {
int i1 = i0 + 1;
// X Coords
if (points[i0].x > points[i1].x) {
// i0 is bigger, i1 is smaller
if (points[i1].x < min.x)
min.x = points[i1].x;
if (points[i0].x > max.x)
max.x = points[i0].x;
}
else {
// i1 is smaller, i0 is bigger
if (points[i0].x < min.x)
min.x = points[i0].x;
if (points[i1].x > max.x)
max.x = points[i1].x;
}
// Y Coords
if (points[i0].y > points[i1].y) {
// i0 is bigger, i1 is smaller
if (points[i1].y < min.y)
min.y = points[i1].y;
if (points[i0].y > max.y)
max.y = points[i0].y;
}
else {
// i1 is smaller, i0 is bigger
if (points[i0].y < min.y)
min.y = points[i0].y;
if (points[i1].y > max.y)
max.y = points[i1].y;
}
// Z Coords
if (points[i0].z > points[i1].z) {
// i0 is bigger, i1 is smaller
if (points[i1].z < min.z)
min.z = points[i1].z;
if (points[i0].z > max.z)
max.z = points[i0].z;
}
else {
// i1 is smaller, i0 is bigger
if (points[i0].z < min.z)
min.z = points[i0].z;
if (points[i1].z > max.z)
max.z = points[i1].z;
}
}
// if array was odd, calculate also min/max for the last element
if(even != Count) {
// X
if (min.x > points[even].x)
min.x = points[even].x;
if (max.x < points[even].x)
max.x = points[even].x;
// Y
if (min.y > points[even].y)
min.y = points[even].y;
if (max.y < points[even].y)
max.y = points[even].y;
// Z
if (min.z > points[even].z)
min.z = points[even].z;
if (max.z < points[even].z)
max.z = points[even].z;
}
KDBounds b = new KDBounds();
b.min = min;
b.max = max;
return b;
}
/// <summary>
/// Recursive splitting procedure
/// </summary>
/// <param name="parent">This is where root node goes</param>
/// <param name="depth"></param>
///
void SplitNode(KDNode parent) {
// center of bounding box
KDBounds parentBounds = parent.bounds;
Vector3 parentBoundsSize = parentBounds.size;
// Find axis where bounds are largest
int splitAxis = 0;
float axisSize = parentBoundsSize.x;
if (axisSize < parentBoundsSize.y) {
splitAxis = 1;
axisSize = parentBoundsSize.y;
}
if (axisSize < parentBoundsSize.z) {
splitAxis = 2;
}
// Our axis min-max bounds
float boundsStart = parentBounds.min[splitAxis];
float boundsEnd = parentBounds.max[splitAxis];
// Calculate the spliting coords
float splitPivot = CalculatePivot(parent.start, parent.end, boundsStart, boundsEnd, splitAxis);
parent.partitionAxis = splitAxis;
parent.partitionCoordinate = splitPivot;
// 'Spliting' array to two subarrays
int splittingIndex = Partition(parent.start, parent.end, splitPivot, splitAxis);
// Negative / Left node
Vector3 negMax = parentBounds.max;
negMax[splitAxis] = splitPivot;
KDNode negNode = GetKDNode();
negNode.bounds = parentBounds;
negNode.bounds.max = negMax;
negNode.start = parent.start;
negNode.end = splittingIndex;
parent.negativeChild = negNode;
// Positive / Right node
Vector3 posMin = parentBounds.min;
posMin[splitAxis] = splitPivot;
KDNode posNode = GetKDNode();
posNode.bounds = parentBounds;
posNode.bounds.min = posMin;
posNode.start = splittingIndex;
posNode.end = parent.end;
parent.positiveChild = posNode;
// check if we are actually splitting it anything
// this if check enables duplicate coordinates, but makes construction a bit slower
#if KDTREE_DUPLICATES
if(negNode.Count != 0 && posNode.Count != 0) {
#endif
// Constraint function deciding if split should be continued
if(ContinueSplit(negNode))
SplitNode(negNode);
if(ContinueSplit(posNode))
SplitNode(posNode);
#if KDTREE_DUPLICATES
}
#endif
}
/// <summary>
/// Sliding midpoint splitting pivot calculation
/// 1. First splits node to two equal parts (midPoint)
/// 2. Checks if elements are in both sides of splitted bounds
/// 3a. If they are, just return midPoint
/// 3b. If they are not, then points are only on left or right bound.
/// 4. Move the splitting pivot so that it shrinks part with points completely (calculate min or max dependent) and return.
/// </summary>
/// <param name="start"></param>
/// <param name="end"></param>
/// <param name="boundsStart"></param>
/// <param name="boundsEnd"></param>
/// <param name="axis"></param>
/// <returns></returns>
float CalculatePivot(int start, int end, float boundsStart, float boundsEnd, int axis) {
//! sliding midpoint rule
float midPoint = (boundsStart + boundsEnd) / 2f;
bool negative = false;
bool positive = false;
float negMax = Single.MinValue;
float posMin = Single.MaxValue;
// this for loop section is used both for sorted and unsorted data
for (int i = start; i < end; i++) {
if (points[permutation[i]][axis] < midPoint)
negative = true;
else
positive = true;
if (negative == true && positive == true)
return midPoint;
}
if (negative) {
for (int i = start; i < end; i++)
if (negMax < points[permutation[i]][axis])
negMax = points[permutation[i]][axis];
return negMax;
}
else {
for (int i = start; i < end; i++)
if (posMin > points[permutation[i]][axis])
posMin = points[permutation[i]][axis];
return posMin;
}
}
/// <summary>
/// Similar to Hoare partitioning algorithm (used in Quick Sort)
/// Modification: pivot is not left-most element but is instead argument of function
/// Calculates splitting index and partially sorts elements (swaps them until they are on correct side - depending on pivot)
/// Complexity: O(n)
/// </summary>
/// <param name="start">Start index</param>
/// <param name="end">End index</param>
/// <param name="partitionPivot">Pivot that decides boundary between left and right</param>
/// <param name="axis">Axis of this pivoting</param>
/// <returns>
/// Returns splitting index that subdivides array into 2 smaller arrays
/// left = [start, pivot),
/// right = [pivot, end)
/// </returns>
int Partition(int start, int end, float partitionPivot, int axis) {
// note: increasing right pointer is actually decreasing!
int LP = start - 1; // left pointer (negative side)
int RP = end; // right pointer (positive side)
int temp; // temporary var for swapping permutation indexes
while (true) {
do {
// move from left to the right until "out of bounds" value is found
LP++;
}
while (LP < RP && points[permutation[LP]][axis] < partitionPivot);
do {
// move from right to the left until "out of bounds" value found
RP--;
}
while (LP < RP && points[permutation[RP]][axis] >= partitionPivot);
if (LP < RP) {
// swap
temp = permutation[LP];
permutation[LP] = permutation[RP];
permutation[RP] = temp;
}
else {
return LP;
}
}
}
/// <summary>
/// Constraint function. You can add custom constraints here - if you have some other data/classes binded to Vector3 points
/// Can hardcode it into
/// </summary>
/// <param name="node"></param>
/// <returns></returns>
bool ContinueSplit(KDNode node) {
return (node.Count > maxPointsPerLeafNode);
}
}
}

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