645 lines
26 KiB
C#
645 lines
26 KiB
C#
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// <copyright file="PointOctreeNode.cs">
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// Distributed under the BSD Licence (see LICENCE file).
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//
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// Copyright (c) 2014, Nition, http://www.momentstudio.co.nz/
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// Copyright (c) 2017, Máté Cserép, http://codenet.hu
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// All rights reserved.
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// </copyright>
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namespace Octree
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{
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using System.Collections.Generic;
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using System.Linq;
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public partial class PointOctree<T>
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{
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/// <summary>
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/// A node in a PointOctree
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/// </summary>
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private class Node
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{
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/// <summary>
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/// Center of this node
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/// </summary>
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public Point Center { get; private set; }
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/// <summary>
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/// Length of the sides of this node
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/// </summary>
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public double SideLength { get; private set; }
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/// <summary>
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/// Minimum size for a node in this octree
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/// </summary>
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private double _minSize;
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/// <summary>
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/// Bounding box that represents this node
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/// </summary>
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private BoundingBox _bounds = default(BoundingBox);
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/// <summary>
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/// Objects in this node
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/// </summary>
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private readonly List<OctreeObject> _objects = new List<OctreeObject>();
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/// <summary>
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/// Child nodes, if any
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/// </summary>
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private Node[] _children = null;
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/// <summary>
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/// Bounds of potential children to this node. These are actual size (with looseness taken into account), not base size
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/// </summary>
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private BoundingBox[] _childBounds;
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/// <summary>
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/// If there are already NumObjectsAllowed in a node, we split it into children
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/// </summary>
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/// <remarks>
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/// A generally good number seems to be something around 8-15
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/// </remarks>
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private const int NumObjectsAllowed = 8;
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/// <summary>
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/// For reverting the bounds size after temporary changes
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/// </summary>
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private Point _actualBoundsSize;
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/// <summary>
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/// Gets a value indicating whether this node has children
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/// </summary>
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private bool HasChildren
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{
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get { return _children != null; }
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}
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/// <summary>
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/// An object in the octree
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/// </summary>
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private class OctreeObject
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{
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/// <summary>
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/// Object content
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/// </summary>
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public T Obj;
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/// <summary>
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/// Object position
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/// </summary>
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public Point Pos;
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}
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/// <summary>
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/// Constructor.
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/// </summary>
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/// <param name="baseLengthVal">Length of this node, not taking looseness into account.</param>
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/// <param name="minSizeVal">Minimum size of nodes in this octree.</param>
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/// <param name="centerVal">Center position of this node.</param>
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public Node(double baseLengthVal, double minSizeVal, Point centerVal)
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{
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SetValues(baseLengthVal, minSizeVal, centerVal);
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}
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// #### PUBLIC METHODS ####
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/// <summary>
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/// Add an object.
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/// </summary>
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/// <param name="obj">Object to add.</param>
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/// <param name="objPos">Position of the object.</param>
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/// <returns></returns>
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public bool Add(T obj, Point objPos)
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{
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if (!Encapsulates(_bounds, objPos))
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{
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return false;
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}
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SubAdd(obj, objPos);
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return true;
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}
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/// <summary>
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/// Remove an object. Makes the assumption that the object only exists once in the tree.
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/// </summary>
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/// <param name="obj">Object to remove.</param>
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/// <returns>True if the object was removed successfully.</returns>
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public bool Remove(T obj)
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{
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bool removed = false;
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for (int i = 0; i < _objects.Count; i++)
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{
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if (_objects[i].Obj.Equals(obj))
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{
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removed = _objects.Remove(_objects[i]);
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break;
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}
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}
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if (!removed && _children != null)
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{
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for (int i = 0; i < 8; i++)
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{
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removed = _children[i].Remove(obj);
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if (removed) break;
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}
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}
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if (removed && _children != null)
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{
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// Check if we should merge nodes now that we've removed an item
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if (ShouldMerge())
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{
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Merge();
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}
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}
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return removed;
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}
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/// <summary>
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/// Removes the specified object at the given position. Makes the assumption that the object only exists once in the tree.
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/// </summary>
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/// <param name="obj">Object to remove.</param>
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/// <param name="objPos">Position of the object.</param>
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/// <returns>True if the object was removed successfully.</returns>
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public bool Remove(T obj, Point objPos)
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{
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if (!Encapsulates(_bounds, objPos))
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{
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return false;
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}
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return SubRemove(obj, objPos);
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}
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/// <summary>
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/// Return objects that are within <paramref name="maxDistance"/> of the specified ray.
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/// </summary>
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/// <param name="ray">The ray.</param>
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/// <param name="maxDistance">Maximum distance from the ray to consider.</param>
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/// <param name="result">List result.</param>
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/// <returns>Objects within range.</returns>
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public void GetNearby(ref Ray ray, double maxDistance, List<T> result)
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{
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// Does the ray hit this node at all?
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// Note: Expanding the bounds is not exactly the same as a real distance check, but it's fast.
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// TODO: Does someone have a fast AND accurate formula to do this check?
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_bounds.Expand(new Point(maxDistance * 2, maxDistance * 2, maxDistance * 2));
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bool intersected = _bounds.IntersectRay(ray);
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_bounds.Size = _actualBoundsSize;
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if (!intersected)
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{
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return;
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}
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// Check against any objects in this node
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for (int i = 0; i < _objects.Count; i++)
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{
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if (SqrDistanceToRay(ray, _objects[i].Pos) <= (maxDistance * maxDistance))
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{
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result.Add(_objects[i].Obj);
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}
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}
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// Check children
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if (_children != null)
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{
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for (int i = 0; i < 8; i++)
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{
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_children[i].GetNearby(ref ray, maxDistance, result);
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}
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}
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}
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/// <summary>
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/// Return objects that are within <paramref name="maxDistance"/> of the specified position.
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/// </summary>
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/// <param name="position">The position.</param>
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/// <param name="maxDistance">Maximum distance from the position to consider.</param>
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/// <param name="result">List result.</param>
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/// <returns>Objects within range.</returns>
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public void GetNearby(ref Point position, double maxDistance, List<T> result)
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{
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// Does the node contain this position at all?
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// Note: Expanding the bounds is not exactly the same as a real distance check, but it's fast.
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// TODO: Does someone have a fast AND accurate formula to do this check?
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_bounds.Expand(new Point(maxDistance * 2, maxDistance * 2, maxDistance * 2));
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bool contained = _bounds.Contains(position);
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_bounds.Size = _actualBoundsSize;
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if (!contained)
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{
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return;
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}
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// Check against any objects in this node
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for (int i = 0; i < _objects.Count; i++)
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{
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if (Point.Distance(position, _objects[i].Pos) <= maxDistance)
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{
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result.Add(_objects[i].Obj);
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}
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}
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// Check children
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if (_children != null)
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{
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for (int i = 0; i < 8; i++)
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{
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_children[i].GetNearby(ref position, maxDistance, result);
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}
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}
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}
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/// <summary>
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/// Return objects that are within <paramref name="maxDistance"/> of the specified position.
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/// </summary>
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/// <param name="position">The position.</param>
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/// <param name="maxDistance">Maximum distance from the position to consider.</param>
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/// <param name="result">List result.</param>
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/// <returns>Objects within range.</returns>
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public void GetObjectsSplitByPlane(ref Plane plane, List<T> front, List<T> onPlane, List<T> back)
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{
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double distance;
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// Is the plane at least partially in this node?
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if (!_bounds.IntersectPlane(plane, out distance))
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{
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if (distance > 0) GetAllObjects(front);
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else GetAllObjects(back);
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return;
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}
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// Check against any objects in this node
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for (int i = 0; i < _objects.Count; i++)
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{
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distance = Plane.Distance(plane, _objects[i].Pos);
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if (distance > 0) front.Add(_objects[i].Obj);
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else if (distance == 0) onPlane.Add(_objects[i].Obj);
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else back.Add(_objects[i].Obj);
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}
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// Check children
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if (_children != null)
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{
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for (int i = 0; i < 8; i++)
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{
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_children[i].GetObjectsSplitByPlane(ref plane, front, onPlane, back);
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}
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}
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}
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/// <summary>
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/// Return all objects in the tree.
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/// </summary>
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/// <returns>All objects.</returns>
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public void GetAll(List<T> result)
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{
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// add directly contained objects
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result.AddRange(_objects.Select(o => o.Obj));
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// add children objects
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if (_children != null)
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{
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for (int i = 0; i < 8; i++)
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{
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_children[i].GetAll(result);
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}
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}
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}
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/// <summary>
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/// Set the 8 children of this octree.
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/// </summary>
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/// <param name="childOctrees">The 8 new child nodes.</param>
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public void SetChildren(Node[] childOctrees)
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{
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if (childOctrees.Length != 8)
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{
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throw new System.Exception("Child octree array must be length 8. Was length: " + childOctrees.Length);
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}
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_children = childOctrees;
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}
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/// <summary>
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/// We can shrink the octree if:
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/// - This node is >= double minLength in length
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/// - All objects in the root node are within one octant
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/// - This node doesn't have children, or does but 7/8 children are empty
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/// We can also shrink it if there are no objects left at all!
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/// </summary>
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/// <param name="minLength">Minimum dimensions of a node in this octree.</param>
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/// <returns>The new root, or the existing one if we didn't shrink.</returns>
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public Node ShrinkIfPossible(double minLength)
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{
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if (SideLength < (2 * minLength))
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{
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return this;
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}
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if (_objects.Count == 0 && (_children == null || _children.Length == 0))
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{
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return this;
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}
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// Check objects in root
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int bestFit = -1;
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for (int i = 0; i < _objects.Count; i++)
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{
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OctreeObject curObj = _objects[i];
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int newBestFit = BestFitChild(curObj.Pos);
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if (i == 0 || newBestFit == bestFit)
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{
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if (bestFit < 0)
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{
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bestFit = newBestFit;
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}
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}
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else
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{
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return this; // Can't reduce - objects fit in different octants
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}
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}
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// Check objects in children if there are any
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if (_children != null)
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{
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bool childHadContent = false;
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for (int i = 0; i < _children.Length; i++)
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{
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if (_children[i].HasAnyObjects())
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{
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if (childHadContent)
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{
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return this; // Can't shrink - another child had content already
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}
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if (bestFit >= 0 && bestFit != i)
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{
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return this; // Can't reduce - objects in root are in a different octant to objects in child
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}
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childHadContent = true;
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bestFit = i;
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}
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}
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}
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|
|
|||
|
|
// Can reduce
|
|||
|
|
if (_children == null)
|
|||
|
|
{
|
|||
|
|
// We don't have any children, so just shrink this node to the new size
|
|||
|
|
// We already know that everything will still fit in it
|
|||
|
|
SetValues(SideLength / 2, _minSize, _childBounds[bestFit].Center);
|
|||
|
|
return this;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// We have children. Use the appropriate child as the new root node
|
|||
|
|
return _children[bestFit];
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Find which child node this object would be most likely to fit in.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="objPos">The object's position.</param>
|
|||
|
|
/// <returns>One of the eight child octants.</returns>
|
|||
|
|
public int BestFitChild(Point objPos)
|
|||
|
|
{
|
|||
|
|
return (objPos.X <= Center.X ? 0 : 1) + (objPos.Y >= Center.Y ? 0 : 4) + (objPos.Z <= Center.Z ? 0 : 2);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Checks if this node or anything below it has something in it.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <returns>True if this node or any of its children, grandchildren etc have something in them</returns>
|
|||
|
|
public bool HasAnyObjects()
|
|||
|
|
{
|
|||
|
|
if (_objects.Count > 0) return true;
|
|||
|
|
|
|||
|
|
if (_children != null)
|
|||
|
|
{
|
|||
|
|
for (int i = 0; i < 8; i++)
|
|||
|
|
{
|
|||
|
|
if (_children[i].HasAnyObjects()) return true;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return false;
|
|||
|
|
}
|
|||
|
|
public void GetAllObjects(List<T> objects)
|
|||
|
|
{
|
|||
|
|
foreach (var item in _objects)
|
|||
|
|
{
|
|||
|
|
objects.Add(item.Obj);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (_children != null)
|
|||
|
|
{
|
|||
|
|
for (int i = 0; i < 8; i++)
|
|||
|
|
{
|
|||
|
|
_children[i].GetAllObjects(objects);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Returns the squared distance to the given ray from a point.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="ray">The ray.</param>
|
|||
|
|
/// <param name="point">The point to check distance from the ray.</param>
|
|||
|
|
/// <returns>Squared distance from the point to the closest point of the ray.</returns>
|
|||
|
|
public static double SqrDistanceToRay(Ray ray, Point point)
|
|||
|
|
{
|
|||
|
|
return Point.Cross(ray.Direction, point - ray.Origin).SqrMagnitude;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// #### PRIVATE METHODS ####
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Set values for this node.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="baseLengthVal">Length of this node, not taking looseness into account.</param>
|
|||
|
|
/// <param name="minSizeVal">Minimum size of nodes in this octree.</param>
|
|||
|
|
/// <param name="centerVal">Centre position of this node.</param>
|
|||
|
|
private void SetValues(double baseLengthVal, double minSizeVal, Point centerVal)
|
|||
|
|
{
|
|||
|
|
SideLength = baseLengthVal;
|
|||
|
|
_minSize = minSizeVal;
|
|||
|
|
Center = centerVal;
|
|||
|
|
|
|||
|
|
// Create the bounding box.
|
|||
|
|
_actualBoundsSize = new Point(SideLength, SideLength, SideLength);
|
|||
|
|
_bounds = new BoundingBox(Center, _actualBoundsSize);
|
|||
|
|
|
|||
|
|
double quarter = SideLength / 4f;
|
|||
|
|
double childActualLength = SideLength / 2;
|
|||
|
|
Point childActualSize = new Point(childActualLength, childActualLength, childActualLength);
|
|||
|
|
_childBounds = new BoundingBox[8];
|
|||
|
|
_childBounds[0] = new BoundingBox(Center + new Point(-quarter, quarter, -quarter), childActualSize);
|
|||
|
|
_childBounds[1] = new BoundingBox(Center + new Point(quarter, quarter, -quarter), childActualSize);
|
|||
|
|
_childBounds[2] = new BoundingBox(Center + new Point(-quarter, quarter, quarter), childActualSize);
|
|||
|
|
_childBounds[3] = new BoundingBox(Center + new Point(quarter, quarter, quarter), childActualSize);
|
|||
|
|
_childBounds[4] = new BoundingBox(Center + new Point(-quarter, -quarter, -quarter), childActualSize);
|
|||
|
|
_childBounds[5] = new BoundingBox(Center + new Point(quarter, -quarter, -quarter), childActualSize);
|
|||
|
|
_childBounds[6] = new BoundingBox(Center + new Point(-quarter, -quarter, quarter), childActualSize);
|
|||
|
|
_childBounds[7] = new BoundingBox(Center + new Point(quarter, -quarter, quarter), childActualSize);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Private counterpart to the public Add method.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="obj">Object to add.</param>
|
|||
|
|
/// <param name="objPos">Position of the object.</param>
|
|||
|
|
private void SubAdd(T obj, Point objPos)
|
|||
|
|
{
|
|||
|
|
// We know it fits at this level if we've got this far
|
|||
|
|
|
|||
|
|
// We always put things in the deepest possible child
|
|||
|
|
// So we can skip checks and simply move down if there are children aleady
|
|||
|
|
if (!HasChildren)
|
|||
|
|
{
|
|||
|
|
// Just add if few objects are here, or children would be below min size
|
|||
|
|
if (_objects.Count < NumObjectsAllowed || (SideLength / 2) < _minSize)
|
|||
|
|
{
|
|||
|
|
OctreeObject newObj = new OctreeObject { Obj = obj, Pos = objPos };
|
|||
|
|
_objects.Add(newObj);
|
|||
|
|
return; // We're done. No children yet
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Enough objects in this node already: Create the 8 children
|
|||
|
|
int bestFitChild;
|
|||
|
|
if (_children == null)
|
|||
|
|
{
|
|||
|
|
Split();
|
|||
|
|
if (_children == null)
|
|||
|
|
{
|
|||
|
|
throw new System.Exception("Child creation failed for an unknown reason. Early exit.");
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Now that we have the new children, move this node's existing objects into them
|
|||
|
|
for (int i = _objects.Count - 1; i >= 0; i--)
|
|||
|
|
{
|
|||
|
|
OctreeObject existingObj = _objects[i];
|
|||
|
|
// Find which child the object is closest to based on where the
|
|||
|
|
// object's center is located in relation to the octree's center
|
|||
|
|
bestFitChild = BestFitChild(existingObj.Pos);
|
|||
|
|
_children[bestFitChild].SubAdd(existingObj.Obj, existingObj.Pos); // Go a level deeper
|
|||
|
|
_objects.Remove(existingObj); // Remove from here
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Handle the new object we're adding now
|
|||
|
|
int bestFit = BestFitChild(objPos);
|
|||
|
|
_children[bestFit].SubAdd(obj, objPos);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Private counterpart to the public <see cref="Remove(T, Point)"/> method.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="obj">Object to remove.</param>
|
|||
|
|
/// <param name="objPos">Position of the object.</param>
|
|||
|
|
/// <returns>True if the object was removed successfully.</returns>
|
|||
|
|
private bool SubRemove(T obj, Point objPos)
|
|||
|
|
{
|
|||
|
|
bool removed = false;
|
|||
|
|
|
|||
|
|
for (int i = 0; i < _objects.Count; i++)
|
|||
|
|
{
|
|||
|
|
if (_objects[i].Obj.Equals(obj))
|
|||
|
|
{
|
|||
|
|
removed = _objects.Remove(_objects[i]);
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (!removed && _children != null)
|
|||
|
|
{
|
|||
|
|
int bestFitChild = BestFitChild(objPos);
|
|||
|
|
removed = _children[bestFitChild].SubRemove(obj, objPos);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (removed && _children != null)
|
|||
|
|
{
|
|||
|
|
// Check if we should merge nodes now that we've removed an item
|
|||
|
|
if (ShouldMerge())
|
|||
|
|
{
|
|||
|
|
Merge();
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
return removed;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Splits the octree into eight children.
|
|||
|
|
/// </summary>
|
|||
|
|
private void Split()
|
|||
|
|
{
|
|||
|
|
double quarter = SideLength / 4f;
|
|||
|
|
double newLength = SideLength / 2;
|
|||
|
|
_children = new Node[8];
|
|||
|
|
_children[0] = new Node(newLength, _minSize, Center + new Point(-quarter, quarter, -quarter));
|
|||
|
|
_children[1] = new Node(newLength, _minSize, Center + new Point(quarter, quarter, -quarter));
|
|||
|
|
_children[2] = new Node(newLength, _minSize, Center + new Point(-quarter, quarter, quarter));
|
|||
|
|
_children[3] = new Node(newLength, _minSize, Center + new Point(quarter, quarter, quarter));
|
|||
|
|
_children[4] = new Node(newLength, _minSize, Center + new Point(-quarter, -quarter, -quarter));
|
|||
|
|
_children[5] = new Node(newLength, _minSize, Center + new Point(quarter, -quarter, -quarter));
|
|||
|
|
_children[6] = new Node(newLength, _minSize, Center + new Point(-quarter, -quarter, quarter));
|
|||
|
|
_children[7] = new Node(newLength, _minSize, Center + new Point(quarter, -quarter, quarter));
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Merge all children into this node - the opposite of Split.
|
|||
|
|
/// Note: We only have to check one level down since a merge will never happen if the children already have children,
|
|||
|
|
/// since THAT won't happen unless there are already too many objects to merge.
|
|||
|
|
/// </summary>
|
|||
|
|
private void Merge()
|
|||
|
|
{
|
|||
|
|
// Note: We know children != null or we wouldn't be merging
|
|||
|
|
for (int i = 0; i < 8; i++)
|
|||
|
|
{
|
|||
|
|
Node curChild = _children[i];
|
|||
|
|
int numObjects = curChild._objects.Count;
|
|||
|
|
for (int j = numObjects - 1; j >= 0; j--)
|
|||
|
|
{
|
|||
|
|
OctreeObject curObj = curChild._objects[j];
|
|||
|
|
_objects.Add(curObj);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
// Remove the child nodes (and the objects in them - they've been added elsewhere now)
|
|||
|
|
_children = null;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Checks if outerBounds encapsulates the given point.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <param name="outerBounds">Outer bounds.</param>
|
|||
|
|
/// <param name="point">Point.</param>
|
|||
|
|
/// <returns>True if innerBounds is fully encapsulated by outerBounds.</returns>
|
|||
|
|
private static bool Encapsulates(BoundingBox outerBounds, Point point)
|
|||
|
|
{
|
|||
|
|
return outerBounds.Contains(point);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/// <summary>
|
|||
|
|
/// Checks if there are few enough objects in this node and its children that the children should all be merged into this.
|
|||
|
|
/// </summary>
|
|||
|
|
/// <returns>True there are less or the same amount of objects in this and its children than <see cref="NumObjectsAllowed"/>.</returns>
|
|||
|
|
private bool ShouldMerge()
|
|||
|
|
{
|
|||
|
|
int totalObjects = _objects.Count;
|
|||
|
|
if (_children != null)
|
|||
|
|
{
|
|||
|
|
foreach (Node child in _children)
|
|||
|
|
{
|
|||
|
|
if (child._children != null)
|
|||
|
|
{
|
|||
|
|
// If any of the *children* have children, there are definitely too many to merge,
|
|||
|
|
// or the child would have been merged already
|
|||
|
|
return false;
|
|||
|
|
}
|
|||
|
|
totalObjects += child._objects.Count;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return totalObjects <= NumObjectsAllowed;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|