654 lines
22 KiB
C#
654 lines
22 KiB
C#
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/*
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* Farseer Physics Engine based on Box2D.XNA port:
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* Copyright (c) 2010 Ian Qvist
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*
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* Box2D.XNA port of Box2D:
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* Copyright (c) 2009 Brandon Furtwangler, Nathan Furtwangler
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*
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* Original source Box2D:
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* Copyright (c) 2006-2009 Erin Catto http://www.gphysics.com
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*
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* This software is provided 'as-is', without any express or implied
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* warranty. In no event will the authors be held liable for any damages
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* arising from the use of this software.
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* Permission is granted to anyone to use this software for any purpose,
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* including commercial applications, and to alter it and redistribute it
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* freely, subject to the following restrictions:
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* 1. The origin of this software must not be misrepresented; you must not
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* claim that you wrote the original software. If you use this software
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* in a product, an acknowledgment in the product documentation would be
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* appreciated but is not required.
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* 2. Altered source versions must be plainly marked as such, and must not be
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* misrepresented as being the original software.
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* 3. This notice may not be removed or altered from any source distribution.
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*/
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using System;
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using System.Collections.Generic;
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using System.Diagnostics;
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using FarseerPhysics.Common;
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using Microsoft.Xna.Framework;
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namespace FarseerPhysics.Collision
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{
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/// <summary>
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/// A node in the dynamic tree. The client does not interact with this directly.
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/// </summary>
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internal struct DynamicTreeNode<T>
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{
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/// <summary>
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/// This is the fattened AABB.
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/// </summary>
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internal AABB AABB;
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internal int Child1;
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internal int Child2;
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internal int LeafCount;
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internal int ParentOrNext;
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internal T UserData;
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internal bool IsLeaf()
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{
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return Child1 == DynamicTree<T>.NullNode;
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}
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}
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/// <summary>
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/// A dynamic tree arranges data in a binary tree to accelerate
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/// queries such as volume queries and ray casts. Leafs are proxies
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/// with an AABB. In the tree we expand the proxy AABB by Settings.b2_fatAABBFactor
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/// so that the proxy AABB is bigger than the client object. This allows the client
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/// object to move by small amounts without triggering a tree update.
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///
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/// Nodes are pooled and relocatable, so we use node indices rather than pointers.
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/// </summary>
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public class DynamicTree<T>
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{
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internal const int NullNode = -1;
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private static Stack<int> _stack = new Stack<int>(256);
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private int _freeList;
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private int _insertionCount;
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private int _nodeCapacity;
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private int _nodeCount;
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private DynamicTreeNode<T>[] _nodes;
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/// <summary>
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/// This is used incrementally traverse the tree for re-balancing.
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/// </summary>
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private int _path;
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private int _root;
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/// <summary>
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/// Constructing the tree initializes the node pool.
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/// </summary>
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public DynamicTree()
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{
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_root = NullNode;
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_nodeCapacity = 16;
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_nodes = new DynamicTreeNode<T>[_nodeCapacity];
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// Build a linked list for the free list.
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for (int i = 0; i < _nodeCapacity - 1; ++i)
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{
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_nodes[i].ParentOrNext = i + 1;
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}
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_nodes[_nodeCapacity - 1].ParentOrNext = NullNode;
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}
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/// <summary>
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/// Create a proxy in the tree as a leaf node. We return the index
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/// of the node instead of a pointer so that we can grow
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/// the node pool.
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/// /// </summary>
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/// <param name="aabb">The aabb.</param>
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/// <param name="userData">The user data.</param>
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/// <returns>Index of the created proxy</returns>
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public int AddProxy(ref AABB aabb, T userData)
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{
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int proxyId = AllocateNode();
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// Fatten the aabb.
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Vector2 r = new Vector2(Settings.AABBExtension, Settings.AABBExtension);
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_nodes[proxyId].AABB.LowerBound = aabb.LowerBound - r;
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_nodes[proxyId].AABB.UpperBound = aabb.UpperBound + r;
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_nodes[proxyId].UserData = userData;
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_nodes[proxyId].LeafCount = 1;
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InsertLeaf(proxyId);
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return proxyId;
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}
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/// <summary>
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/// Destroy a proxy. This asserts if the id is invalid.
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/// </summary>
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/// <param name="proxyId">The proxy id.</param>
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public void RemoveProxy(int proxyId)
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{
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Debug.Assert(0 <= proxyId && proxyId < _nodeCapacity);
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Debug.Assert(_nodes[proxyId].IsLeaf());
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RemoveLeaf(proxyId);
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FreeNode(proxyId);
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}
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/// <summary>
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/// Move a proxy with a swepted AABB. If the proxy has moved outside of its fattened AABB,
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/// then the proxy is removed from the tree and re-inserted. Otherwise
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/// the function returns immediately.
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/// </summary>
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/// <param name="proxyId">The proxy id.</param>
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/// <param name="aabb">The aabb.</param>
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/// <param name="displacement">The displacement.</param>
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/// <returns>true if the proxy was re-inserted.</returns>
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public bool MoveProxy(int proxyId, ref AABB aabb, Vector2 displacement)
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{
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Debug.Assert(0 <= proxyId && proxyId < _nodeCapacity);
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Debug.Assert(_nodes[proxyId].IsLeaf());
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if (_nodes[proxyId].AABB.Contains(ref aabb))
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{
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return false;
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}
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RemoveLeaf(proxyId);
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// Extend AABB.
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AABB b = aabb;
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Vector2 r = new Vector2(Settings.AABBExtension, Settings.AABBExtension);
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b.LowerBound = b.LowerBound - r;
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b.UpperBound = b.UpperBound + r;
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// Predict AABB displacement.
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Vector2 d = Settings.AABBMultiplier * displacement;
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if (d.X < 0.0f)
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{
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b.LowerBound.X += d.X;
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}
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else
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{
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b.UpperBound.X += d.X;
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}
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if (d.Y < 0.0f)
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{
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b.LowerBound.Y += d.Y;
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}
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else
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{
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b.UpperBound.Y += d.Y;
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}
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_nodes[proxyId].AABB = b;
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InsertLeaf(proxyId);
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return true;
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}
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/// <summary>
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/// Perform some iterations to re-balance the tree.
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/// </summary>
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/// <param name="iterations">The iterations.</param>
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public void Rebalance(int iterations)
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{
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if (_root == NullNode)
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{
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return;
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}
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// Rebalance the tree by removing and re-inserting leaves.
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for (int i = 0; i < iterations; ++i)
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{
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int node = _root;
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int bit = 0;
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while (_nodes[node].IsLeaf() == false)
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{
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// Child selector based on a bit in the path
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int selector = (_path >> bit) & 1;
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// Select the child nod
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node = (selector == 0) ? _nodes[node].Child1 : _nodes[node].Child2;
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// Keep bit between 0 and 31 because _path has 32 bits
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// bit = (bit + 1) % 31
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bit = (bit + 1) & 0x1F;
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}
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++_path;
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RemoveLeaf(node);
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InsertLeaf(node);
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}
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}
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/// <summary>
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/// Get proxy user data.
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/// </summary>
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/// <typeparam name="T"></typeparam>
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/// <param name="proxyId">The proxy id.</param>
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/// <returns>the proxy user data or 0 if the id is invalid.</returns>
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public T GetUserData(int proxyId)
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{
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Debug.Assert(0 <= proxyId && proxyId < _nodeCapacity);
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return _nodes[proxyId].UserData;
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}
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/// <summary>
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/// Get the fat AABB for a proxy.
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/// </summary>
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/// <param name="proxyId">The proxy id.</param>
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/// <param name="fatAABB">The fat AABB.</param>
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public void GetFatAABB(int proxyId, out AABB fatAABB)
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{
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Debug.Assert(0 <= proxyId && proxyId < _nodeCapacity);
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fatAABB = _nodes[proxyId].AABB;
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}
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/// <summary>
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/// Compute the height of the binary tree in O(N) time. Should not be
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/// called often.
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/// </summary>
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/// <returns></returns>
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public int ComputeHeight()
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{
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return ComputeHeight(_root);
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}
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/// <summary>
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/// Query an AABB for overlapping proxies. The callback class
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/// is called for each proxy that overlaps the supplied AABB.
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/// </summary>
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/// <param name="callback">The callback.</param>
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/// <param name="aabb">The aabb.</param>
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public void Query(Func<int, bool> callback, ref AABB aabb)
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{
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_stack.Clear();
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_stack.Push(_root);
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while (_stack.Count > 0)
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{
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int nodeId = _stack.Pop();
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if (nodeId == NullNode)
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{
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continue;
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}
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DynamicTreeNode<T> node = _nodes[nodeId];
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if (AABB.TestOverlap(ref node.AABB, ref aabb))
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{
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if (node.IsLeaf())
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{
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bool proceed = callback(nodeId);
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if (proceed == false)
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{
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return;
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}
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}
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else
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{
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_stack.Push(node.Child1);
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_stack.Push(node.Child2);
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}
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}
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}
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}
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/// <summary>
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/// Ray-cast against the proxies in the tree. This relies on the callback
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/// to perform a exact ray-cast in the case were the proxy contains a Shape.
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/// The callback also performs the any collision filtering. This has performance
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/// roughly equal to k * log(n), where k is the number of collisions and n is the
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/// number of proxies in the tree.
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/// </summary>
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/// <param name="callback">A callback class that is called for each proxy that is hit by the ray.</param>
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/// <param name="input">The ray-cast input data. The ray extends from p1 to p1 + maxFraction * (p2 - p1).</param>
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public void RayCast(Func<RayCastInput, int, float> callback, ref RayCastInput input)
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{
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Vector2 p1 = input.Point1;
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Vector2 p2 = input.Point2;
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Vector2 r = p2 - p1;
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Debug.Assert(r.LengthSquared() > 0.0f);
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r.Normalize();
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// v is perpendicular to the segment.
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Vector2 absV = MathUtils.Abs(new Vector2(-r.Y, r.X));
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// Separating axis for segment (Gino, p80).
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// |dot(v, p1 - c)| > dot(|v|, h)
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float maxFraction = input.MaxFraction;
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// Build a bounding box for the segment.
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AABB segmentAABB = new AABB();
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{
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Vector2 t = p1 + maxFraction * (p2 - p1);
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Vector2.Min(ref p1, ref t, out segmentAABB.LowerBound);
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Vector2.Max(ref p1, ref t, out segmentAABB.UpperBound);
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}
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_stack.Clear();
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_stack.Push(_root);
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while (_stack.Count > 0)
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{
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int nodeId = _stack.Pop();
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if (nodeId == NullNode)
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{
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continue;
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}
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DynamicTreeNode<T> node = _nodes[nodeId];
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if (AABB.TestOverlap(ref node.AABB, ref segmentAABB) == false)
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{
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continue;
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}
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// Separating axis for segment (Gino, p80).
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// |dot(v, p1 - c)| > dot(|v|, h)
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Vector2 c = node.AABB.Center;
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Vector2 h = node.AABB.Extents;
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float separation = Math.Abs(Vector2.Dot(new Vector2(-r.Y, r.X), p1 - c)) - Vector2.Dot(absV, h);
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if (separation > 0.0f)
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{
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continue;
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}
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if (node.IsLeaf())
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{
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RayCastInput subInput;
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subInput.Point1 = input.Point1;
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subInput.Point2 = input.Point2;
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subInput.MaxFraction = maxFraction;
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float value = callback(subInput, nodeId);
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|
|
if (value == 0.0f)
|
|||
|
|
{
|
|||
|
|
// the client has terminated the raycast.
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (value > 0.0f)
|
|||
|
|
{
|
|||
|
|
// Update segment bounding box.
|
|||
|
|
maxFraction = value;
|
|||
|
|
Vector2 t = p1 + maxFraction * (p2 - p1);
|
|||
|
|
segmentAABB.LowerBound = Vector2.Min(p1, t);
|
|||
|
|
segmentAABB.UpperBound = Vector2.Max(p1, t);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
_stack.Push(node.Child1);
|
|||
|
|
_stack.Push(node.Child2);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private int CountLeaves(int nodeId)
|
|||
|
|
{
|
|||
|
|
if (nodeId == NullNode)
|
|||
|
|
{
|
|||
|
|
return 0;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
Debug.Assert(0 <= nodeId && nodeId < _nodeCapacity);
|
|||
|
|
DynamicTreeNode<T> node = _nodes[nodeId];
|
|||
|
|
|
|||
|
|
if (node.IsLeaf())
|
|||
|
|
{
|
|||
|
|
Debug.Assert(node.LeafCount == 1);
|
|||
|
|
return 1;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
int count1 = CountLeaves(node.Child1);
|
|||
|
|
int count2 = CountLeaves(node.Child2);
|
|||
|
|
int count = count1 + count2;
|
|||
|
|
Debug.Assert(count == node.LeafCount);
|
|||
|
|
return count;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private void Validate()
|
|||
|
|
{
|
|||
|
|
CountLeaves(_root);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private int AllocateNode()
|
|||
|
|
{
|
|||
|
|
// Expand the node pool as needed.
|
|||
|
|
if (_freeList == NullNode)
|
|||
|
|
{
|
|||
|
|
Debug.Assert(_nodeCount == _nodeCapacity);
|
|||
|
|
|
|||
|
|
// The free list is empty. Rebuild a bigger pool.
|
|||
|
|
DynamicTreeNode<T>[] oldNodes = _nodes;
|
|||
|
|
_nodeCapacity *= 2;
|
|||
|
|
_nodes = new DynamicTreeNode<T>[_nodeCapacity];
|
|||
|
|
Array.Copy(oldNodes, _nodes, _nodeCount);
|
|||
|
|
|
|||
|
|
// Build a linked list for the free list. The parent
|
|||
|
|
// pointer becomes the "next" pointer.
|
|||
|
|
for (int i = _nodeCount; i < _nodeCapacity - 1; ++i)
|
|||
|
|
{
|
|||
|
|
_nodes[i].ParentOrNext = i + 1;
|
|||
|
|
}
|
|||
|
|
_nodes[_nodeCapacity - 1].ParentOrNext = NullNode;
|
|||
|
|
_freeList = _nodeCount;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Peel a node off the free list.
|
|||
|
|
int nodeId = _freeList;
|
|||
|
|
_freeList = _nodes[nodeId].ParentOrNext;
|
|||
|
|
_nodes[nodeId].ParentOrNext = NullNode;
|
|||
|
|
_nodes[nodeId].Child1 = NullNode;
|
|||
|
|
_nodes[nodeId].Child2 = NullNode;
|
|||
|
|
_nodes[nodeId].LeafCount = 0;
|
|||
|
|
++_nodeCount;
|
|||
|
|
return nodeId;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private void FreeNode(int nodeId)
|
|||
|
|
{
|
|||
|
|
Debug.Assert(0 <= nodeId && nodeId < _nodeCapacity);
|
|||
|
|
Debug.Assert(0 < _nodeCount);
|
|||
|
|
_nodes[nodeId].ParentOrNext = _freeList;
|
|||
|
|
_freeList = nodeId;
|
|||
|
|
--_nodeCount;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private void InsertLeaf(int leaf)
|
|||
|
|
{
|
|||
|
|
++_insertionCount;
|
|||
|
|
|
|||
|
|
if (_root == NullNode)
|
|||
|
|
{
|
|||
|
|
_root = leaf;
|
|||
|
|
_nodes[_root].ParentOrNext = NullNode;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Find the best sibling for this node
|
|||
|
|
AABB leafAABB = _nodes[leaf].AABB;
|
|||
|
|
int sibling = _root;
|
|||
|
|
while (_nodes[sibling].IsLeaf() == false)
|
|||
|
|
{
|
|||
|
|
int child1 = _nodes[sibling].Child1;
|
|||
|
|
int child2 = _nodes[sibling].Child2;
|
|||
|
|
|
|||
|
|
// Expand the node's AABB.
|
|||
|
|
_nodes[sibling].AABB.Combine(ref leafAABB);
|
|||
|
|
_nodes[sibling].LeafCount += 1;
|
|||
|
|
|
|||
|
|
float siblingArea = _nodes[sibling].AABB.Perimeter;
|
|||
|
|
AABB parentAABB = new AABB();
|
|||
|
|
parentAABB.Combine(ref _nodes[sibling].AABB, ref leafAABB);
|
|||
|
|
float parentArea = parentAABB.Perimeter;
|
|||
|
|
float cost1 = 2.0f * parentArea;
|
|||
|
|
|
|||
|
|
float inheritanceCost = 2.0f * (parentArea - siblingArea);
|
|||
|
|
|
|||
|
|
float cost2;
|
|||
|
|
if (_nodes[child1].IsLeaf())
|
|||
|
|
{
|
|||
|
|
AABB aabb = new AABB();
|
|||
|
|
aabb.Combine(ref leafAABB, ref _nodes[child1].AABB);
|
|||
|
|
cost2 = aabb.Perimeter + inheritanceCost;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
AABB aabb = new AABB();
|
|||
|
|
aabb.Combine(ref leafAABB, ref _nodes[child1].AABB);
|
|||
|
|
float oldArea = _nodes[child1].AABB.Perimeter;
|
|||
|
|
float newArea = aabb.Perimeter;
|
|||
|
|
cost2 = (newArea - oldArea) + inheritanceCost;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
float cost3;
|
|||
|
|
if (_nodes[child2].IsLeaf())
|
|||
|
|
{
|
|||
|
|
AABB aabb = new AABB();
|
|||
|
|
aabb.Combine(ref leafAABB, ref _nodes[child2].AABB);
|
|||
|
|
cost3 = aabb.Perimeter + inheritanceCost;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
AABB aabb = new AABB();
|
|||
|
|
aabb.Combine(ref leafAABB, ref _nodes[child2].AABB);
|
|||
|
|
float oldArea = _nodes[child2].AABB.Perimeter;
|
|||
|
|
float newArea = aabb.Perimeter;
|
|||
|
|
cost3 = newArea - oldArea + inheritanceCost;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Descend according to the minimum cost.
|
|||
|
|
if (cost1 < cost2 && cost1 < cost3)
|
|||
|
|
{
|
|||
|
|
break;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Expand the node's AABB to account for the new leaf.
|
|||
|
|
_nodes[sibling].AABB.Combine(ref leafAABB);
|
|||
|
|
|
|||
|
|
// Descend
|
|||
|
|
if (cost2 < cost3)
|
|||
|
|
{
|
|||
|
|
sibling = child1;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
sibling = child2;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
// Create a new parent for the siblings.
|
|||
|
|
int oldParent = _nodes[sibling].ParentOrNext;
|
|||
|
|
int newParent = AllocateNode();
|
|||
|
|
_nodes[newParent].ParentOrNext = oldParent;
|
|||
|
|
_nodes[newParent].UserData = default(T);
|
|||
|
|
_nodes[newParent].AABB.Combine(ref leafAABB, ref _nodes[sibling].AABB);
|
|||
|
|
_nodes[newParent].LeafCount = _nodes[sibling].LeafCount + 1;
|
|||
|
|
|
|||
|
|
if (oldParent != NullNode)
|
|||
|
|
{
|
|||
|
|
// The sibling was not the root.
|
|||
|
|
if (_nodes[oldParent].Child1 == sibling)
|
|||
|
|
{
|
|||
|
|
_nodes[oldParent].Child1 = newParent;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
_nodes[oldParent].Child2 = newParent;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
_nodes[newParent].Child1 = sibling;
|
|||
|
|
_nodes[newParent].Child2 = leaf;
|
|||
|
|
_nodes[sibling].ParentOrNext = newParent;
|
|||
|
|
_nodes[leaf].ParentOrNext = newParent;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
// The sibling was the root.
|
|||
|
|
_nodes[newParent].Child1 = sibling;
|
|||
|
|
_nodes[newParent].Child2 = leaf;
|
|||
|
|
_nodes[sibling].ParentOrNext = newParent;
|
|||
|
|
_nodes[leaf].ParentOrNext = newParent;
|
|||
|
|
_root = newParent;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private void RemoveLeaf(int leaf)
|
|||
|
|
{
|
|||
|
|
if (leaf == _root)
|
|||
|
|
{
|
|||
|
|
_root = NullNode;
|
|||
|
|
return;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
int parent = _nodes[leaf].ParentOrNext;
|
|||
|
|
int grandParent = _nodes[parent].ParentOrNext;
|
|||
|
|
int sibling;
|
|||
|
|
if (_nodes[parent].Child1 == leaf)
|
|||
|
|
{
|
|||
|
|
sibling = _nodes[parent].Child2;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
sibling = _nodes[parent].Child1;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
if (grandParent != NullNode)
|
|||
|
|
{
|
|||
|
|
// Destroy parent and connect sibling to grandParent.
|
|||
|
|
if (_nodes[grandParent].Child1 == parent)
|
|||
|
|
{
|
|||
|
|
_nodes[grandParent].Child1 = sibling;
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
_nodes[grandParent].Child2 = sibling;
|
|||
|
|
}
|
|||
|
|
_nodes[sibling].ParentOrNext = grandParent;
|
|||
|
|
FreeNode(parent);
|
|||
|
|
|
|||
|
|
// Adjust ancestor bounds.
|
|||
|
|
parent = grandParent;
|
|||
|
|
while (parent != NullNode)
|
|||
|
|
{
|
|||
|
|
_nodes[parent].AABB.Combine(ref _nodes[_nodes[parent].Child1].AABB,
|
|||
|
|
ref _nodes[_nodes[parent].Child2].AABB);
|
|||
|
|
|
|||
|
|
Debug.Assert(_nodes[parent].LeafCount > 0);
|
|||
|
|
_nodes[parent].LeafCount -= 1;
|
|||
|
|
|
|||
|
|
parent = _nodes[parent].ParentOrNext;
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
else
|
|||
|
|
{
|
|||
|
|
_root = sibling;
|
|||
|
|
_nodes[sibling].ParentOrNext = NullNode;
|
|||
|
|
FreeNode(parent);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
private int ComputeHeight(int nodeId)
|
|||
|
|
{
|
|||
|
|
if (nodeId == NullNode)
|
|||
|
|
{
|
|||
|
|
return 0;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
Debug.Assert(0 <= nodeId && nodeId < _nodeCapacity);
|
|||
|
|
DynamicTreeNode<T> node = _nodes[nodeId];
|
|||
|
|
int height1 = ComputeHeight(node.Child1);
|
|||
|
|
int height2 = ComputeHeight(node.Child2);
|
|||
|
|
return 1 + Math.Max(height1, height2);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
}
|