axiosengine/axios/Collision/DynamicTree.cs
2012-03-19 18:57:59 -05:00

654 lines
22 KiB
C#

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