Windows Phone Labyrinth

/*
* 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);
        }
    }
}