/*
 * ***** BEGIN GPL LICENSE BLOCK *****
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software Foundation,
 * Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
 *
 * The Original Code is Copyright (C) 2006 by NaN Holding BV.
 * All rights reserved.
 *
 * The Original Code is: all of this file.
 *
 * Contributor(s): Daniel Genrich, Andre Pinto
 *
 * ***** END GPL LICENSE BLOCK *****
 */

/** \file blender/blenlib/intern/BLI_kdopbvh.c
 *  \ingroup bli
 *  \brief BVH-tree implementation.
 *
 * KD-Overlap-BVH, implements a bvh-tree structure with support for:
 *
 * - Ray-cast:
 *   #BLI_bvhtree_ray_cast, #BVHRayCastData
 * - Nearest point on surface:
 *   #BLI_bvhtree_find_nearest, #BVHNearestData
 * - Overlapping 2 trees:
 *   #BLI_bvhtree_overlap, #BVHOverlapData_Shared, #BVHOverlapData_Thread
 */

#include <assert.h>

#include "MEM_guardedalloc.h"

#include "BLI_utildefines.h"
#include "BLI_alloca.h"
#include "BLI_stack.h"
#include "BLI_kdopbvh.h"
#include "BLI_math.h"
#include "BLI_strict_flags.h"

#ifdef _OPENMP
#include <omp.h>
#endif

/* used for iterative_raycast */
// #define USE_SKIP_LINKS

#define MAX_TREETYPE 32

/* Setting zero so we can catch bugs in OpenMP/KDOPBVH.
 * TODO(sergey): Deduplicate the limits with PBVH from BKE.
 */
#ifdef _OPENMP
#  ifdef DEBUG
#    define KDOPBVH_OMP_LIMIT 0
#  else
#    define KDOPBVH_OMP_LIMIT 1024
#  endif
#endif

typedef unsigned char axis_t;

typedef struct BVHNode {
	struct BVHNode **children;
	struct BVHNode *parent; /* some user defined traversed need that */
#ifdef USE_SKIP_LINKS
	struct BVHNode *skip[2];
#endif
	float *bv;      /* Bounding volume of all nodes, max 13 axis */
	int index;      /* face, edge, vertex index */
	char totnode;   /* how many nodes are used, used for speedup */
	char main_axis; /* Axis used to split this node */
} BVHNode;

/* keep under 26 bytes for speed purposes */
struct BVHTree {
	BVHNode **nodes;
	BVHNode *nodearray;     /* pre-alloc branch nodes */
	BVHNode **nodechild;    /* pre-alloc childs for nodes */
	float   *nodebv;        /* pre-alloc bounding-volumes for nodes */
	float epsilon;          /* epslion is used for inflation of the k-dop	   */
	int totleaf;            /* leafs */
	int totbranch;
	axis_t start_axis, stop_axis;  /* KDOP_AXES array indices according to axis */
	axis_t axis;                   /* kdop type (6 => OBB, 7 => AABB, ...) */
	char tree_type;                /* type of tree (4 => quadtree) */
};

/* optimization, ensure we stay small */
BLI_STATIC_ASSERT((sizeof(void *) == 8 && sizeof(BVHTree) <= 48) ||
                  (sizeof(void *) == 4 && sizeof(BVHTree) <= 32),
                  "over sized")

/* avoid duplicating vars in BVHOverlapData_Thread */
typedef struct BVHOverlapData_Shared {
	const BVHTree *tree1, *tree2;
	axis_t start_axis, stop_axis;

	/* use for callbacks */
	BVHTree_OverlapCallback callback;
	void *userdata;
} BVHOverlapData_Shared;

typedef struct BVHOverlapData_Thread {
	BVHOverlapData_Shared *shared;
	struct BLI_Stack *overlap;  /* store BVHTreeOverlap */
	/* use for callbacks */
	int thread;
} BVHOverlapData_Thread;

typedef struct BVHNearestData {
	BVHTree *tree;
	const float *co;
	BVHTree_NearestPointCallback callback;
	void    *userdata;
	float proj[13];         /* coordinates projection over axis */
	BVHTreeNearest nearest;

} BVHNearestData;

typedef struct BVHRayCastData {
	BVHTree *tree;

	BVHTree_RayCastCallback callback;
	void    *userdata;


	BVHTreeRay ray;

#ifdef USE_KDOPBVH_WATERTIGHT
	struct IsectRayPrecalc isect_precalc;
#endif

	/* initialized by bvhtree_ray_cast_data_precalc */
	float ray_dot_axis[13];
	float idot_axis[13];
	int index[6];

	BVHTreeRayHit hit;
} BVHRayCastData;


/**
 * Bounding Volume Hierarchy Definition
 *
 * Notes: From OBB until 26-DOP --> all bounding volumes possible, just choose type below
 * Notes: You have to choose the type at compile time ITM
 * Notes: You can choose the tree type --> binary, quad, octree, choose below
 */

static const float KDOP_AXES[13][3] = {
	{1.0, 0, 0}, {0, 1.0, 0}, {0, 0, 1.0}, {1.0, 1.0, 1.0}, {1.0, -1.0, 1.0}, {1.0, 1.0, -1.0},
	{1.0, -1.0, -1.0}, {1.0, 1.0, 0}, {1.0, 0, 1.0}, {0, 1.0, 1.0}, {1.0, -1.0, 0}, {1.0, 0, -1.0},
	{0, 1.0, -1.0}
};

MINLINE axis_t min_axis(axis_t a, axis_t b)
{
	return (a < b) ? a : b;
}
#if 0
MINLINE axis_t max_axis(axis_t a, axis_t b)
{
	return (b < a) ? a : b;
}
#endif

#if 0

/*
 * Generic push and pop heap
 */
#define PUSH_HEAP_BODY(HEAP_TYPE, PRIORITY, heap, heap_size)                  \
	{                                                                         \
		HEAP_TYPE element = heap[heap_size - 1];                              \
		int child = heap_size - 1;                                            \
		while (child != 0) {                                                  \
			int parent = (child - 1) / 2;                                     \
			if (PRIORITY(element, heap[parent])) {                            \
				heap[child] = heap[parent];                                   \
				child = parent;                                               \
			}                                                                 \
			else {                                                            \
				break;                                                        \
			}                                                                 \
		}                                                                     \
		heap[child] = element;                                                \
	} (void)0

#define POP_HEAP_BODY(HEAP_TYPE, PRIORITY, heap, heap_size)                   \
	{                                                                         \
		HEAP_TYPE element = heap[heap_size - 1];                              \
		int parent = 0;                                                       \
		while (parent < (heap_size - 1) / 2) {                                \
			int child2 = (parent + 1) * 2;                                    \
			if (PRIORITY(heap[child2 - 1], heap[child2])) {                   \
				child2--;                                                     \
			}                                                                 \
			if (PRIORITY(element, heap[child2])) {                            \
				break;                                                        \
			}                                                                 \
			heap[parent] = heap[child2];                                      \
			parent = child2;                                                  \
		}                                                                     \
		heap[parent] = element;                                               \
	} (void)0

static bool ADJUST_MEMORY(void *local_memblock, void **memblock, int new_size, int *max_size, int size_per_item)
{
	int new_max_size = *max_size * 2;
	void *new_memblock = NULL;

	if (new_size <= *max_size) {
		return true;
	}

	if (*memblock == local_memblock) {
		new_memblock = malloc(size_per_item * new_max_size);
		memcpy(new_memblock, *memblock, size_per_item * *max_size);
	}
	else {
		new_memblock = realloc(*memblock, size_per_item * new_max_size);
	}

	if (new_memblock) {
		*memblock = new_memblock;
		*max_size = new_max_size;
		return true;
	}
	else {
		return false;
	}
}
#endif

/**
 * Introsort
 * with permission deriven from the following Java code:
 * http://ralphunden.net/content/tutorials/a-guide-to-introsort/
 * and he derived it from the SUN STL
 */

//static int size_threshold = 16;

#if 0
/**
 * Common methods for all algorithms
 */
static int floor_lg(int a)
{
	return (int)(floor(log(a) / log(2)));
}
#endif

static void node_minmax_init(const BVHTree *tree, BVHNode *node)
{
	axis_t axis_iter;
	float (*bv)[2] = (float (*)[2])node->bv;

	for (axis_iter = tree->start_axis; axis_iter != tree->stop_axis; axis_iter++) {
		bv[axis_iter][0] =  FLT_MAX;
		bv[axis_iter][1] = -FLT_MAX;
	}
}

/**
 * Insertion sort algorithm
 */
static void bvh_insertionsort(BVHNode **a, int lo, int hi, int axis)
{
	int i, j;
	BVHNode *t;
	for (i = lo; i < hi; i++) {
		j = i;
		t = a[i];
		while ((j != lo) && (t->bv[axis] < (a[j - 1])->bv[axis])) {
			a[j] = a[j - 1];
			j--;
		}
		a[j] = t;
	}
}

static int bvh_partition(BVHNode **a, int lo, int hi, BVHNode *x, int axis)
{
	int i = lo, j = hi;
	while (1) {
		while ((a[i])->bv[axis] < x->bv[axis]) i++;
		j--;
		while (x->bv[axis] < (a[j])->bv[axis]) j--;
		if (!(i < j))
			return i;
		SWAP(BVHNode *, a[i], a[j]);
		i++;
	}
}

#if 0
/**
 * Heapsort algorithm
 */
static void bvh_downheap(BVHNode **a, int i, int n, int lo, int axis)
{
	BVHNode *d = a[lo + i - 1];
	int child;
	while (i <= n / 2) {
		child = 2 * i;
		if ((child < n) && ((a[lo + child - 1])->bv[axis] < (a[lo + child])->bv[axis])) {
			child++;
		}
		if (!(d->bv[axis] < (a[lo + child - 1])->bv[axis])) break;
		a[lo + i - 1] = a[lo + child - 1];
		i = child;
	}
	a[lo + i - 1] = d;
}

static void bvh_heapsort(BVHNode **a, int lo, int hi, int axis)
{
	int n = hi - lo, i;
	for (i = n / 2; i >= 1; i = i - 1) {
		bvh_downheap(a, i, n, lo, axis);
	}
	for (i = n; i > 1; i = i - 1) {
		SWAP(BVHNode *, a[lo], a[lo + i - 1]);
		bvh_downheap(a, 1, i - 1, lo, axis);
	}
}
#endif

static BVHNode *bvh_medianof3(BVHNode **a, int lo, int mid, int hi, int axis)  /* returns Sortable */
{
	if ((a[mid])->bv[axis] < (a[lo])->bv[axis]) {
		if ((a[hi])->bv[axis] < (a[mid])->bv[axis])
			return a[mid];
		else {
			if ((a[hi])->bv[axis] < (a[lo])->bv[axis])
				return a[hi];
			else
				return a[lo];
		}
	}
	else {
		if ((a[hi])->bv[axis] < (a[mid])->bv[axis]) {
			if ((a[hi])->bv[axis] < (a[lo])->bv[axis])
				return a[lo];
			else
				return a[hi];
		}
		else
			return a[mid];
	}
}

#if 0
/*
 * Quicksort algorithm modified for Introsort
 */
static void bvh_introsort_loop(BVHNode **a, int lo, int hi, int depth_limit, int axis)
{
	int p;

	while (hi - lo > size_threshold) {
		if (depth_limit == 0) {
			bvh_heapsort(a, lo, hi, axis);
			return;
		}
		depth_limit = depth_limit - 1;
		p = bvh_partition(a, lo, hi, bvh_medianof3(a, lo, lo + ((hi - lo) / 2) + 1, hi - 1, axis), axis);
		bvh_introsort_loop(a, p, hi, depth_limit, axis);
		hi = p;
	}
}

static void sort(BVHNode **a0, int begin, int end, int axis)
{
	if (begin < end) {
		BVHNode **a = a0;
		bvh_introsort_loop(a, begin, end, 2 * floor_lg(end - begin), axis);
		bvh_insertionsort(a, begin, end, axis);
	}
}

static void sort_along_axis(BVHTree *tree, int start, int end, int axis)
{
	sort(tree->nodes, start, end, axis);
}
#endif

/**
 * \note after a call to this function you can expect one of:
 * - every node to left of a[n] are smaller or equal to it
 * - every node to the right of a[n] are greater or equal to it */
static int partition_nth_element(BVHNode **a, int _begin, int _end, int n, int axis)
{
	int begin = _begin, end = _end, cut;
	while (end - begin > 3) {
		cut = bvh_partition(a, begin, end, bvh_medianof3(a, begin, (begin + end) / 2, end - 1, axis), axis);
		if (cut <= n)
			begin = cut;
		else
			end = cut;
	}
	bvh_insertionsort(a, begin, end, axis);

	return n;
}

#ifdef USE_SKIP_LINKS
static void build_skip_links(BVHTree *tree, BVHNode *node, BVHNode *left, BVHNode *right)
{
	int i;
	
	node->skip[0] = left;
	node->skip[1] = right;
	
	for (i = 0; i < node->totnode; i++) {
		if (i + 1 < node->totnode)
			build_skip_links(tree, node->children[i], left, node->children[i + 1]);
		else
			build_skip_links(tree, node->children[i], left, right);

		left = node->children[i];
	}
}
#endif

/*
 * BVHTree bounding volumes functions
 */
static void create_kdop_hull(BVHTree *tree, BVHNode *node, const float *co, int numpoints, int moving)
{
	float newminmax;
	float *bv = node->bv;
	int k;
	axis_t axis_iter;
	
	/* don't init boudings for the moving case */
	if (!moving) {
		node_minmax_init(tree, node);
	}

	for (k = 0; k < numpoints; k++) {
		/* for all Axes. */
		for (axis_iter = tree->start_axis; axis_iter < tree->stop_axis; axis_iter++) {
			newminmax = dot_v3v3(&co[k * 3], KDOP_AXES[axis_iter]);
			if (newminmax < bv[2 * axis_iter])
				bv[2 * axis_iter] = newminmax;
			if (newminmax > bv[(2 * axis_iter) + 1])
				bv[(2 * axis_iter) + 1] = newminmax;
		}
	}
}

/**
 * \note depends on the fact that the BVH's for each face is already build
 */
static void refit_kdop_hull(BVHTree *tree, BVHNode *node, int start, int end)
{
	float newmin, newmax;
	float *bv = node->bv;
	int j;
	axis_t axis_iter;

	node_minmax_init(tree, node);

	for (j = start; j < end; j++) {
		/* for all Axes. */
		for (axis_iter = tree->start_axis; axis_iter < tree->stop_axis; axis_iter++) {
			newmin = tree->nodes[j]->bv[(2 * axis_iter)];
			if ((newmin < bv[(2 * axis_iter)]))
				bv[(2 * axis_iter)] = newmin;

			newmax = tree->nodes[j]->bv[(2 * axis_iter) + 1];
			if ((newmax > bv[(2 * axis_iter) + 1]))
				bv[(2 * axis_iter) + 1] = newmax;
		}
	}

}

/**
 * only supports x,y,z axis in the moment
 * but we should use a plain and simple function here for speed sake */
static char get_largest_axis(const float *bv)
{
	float middle_point[3];

	middle_point[0] = (bv[1]) - (bv[0]); /* x axis */
	middle_point[1] = (bv[3]) - (bv[2]); /* y axis */
	middle_point[2] = (bv[5]) - (bv[4]); /* z axis */
	if (middle_point[0] > middle_point[1]) {
		if (middle_point[0] > middle_point[2])
			return 1;  /* max x axis */
		else
			return 5;  /* max z axis */
	}
	else {
		if (middle_point[1] > middle_point[2])
			return 3;  /* max y axis */
		else
			return 5;  /* max z axis */
	}
}

/**
 * bottom-up update of bvh node BV
 * join the children on the parent BV */
static void node_join(BVHTree *tree, BVHNode *node)
{
	int i;
	axis_t axis_iter;

	node_minmax_init(tree, node);
	
	for (i = 0; i < tree->tree_type; i++) {
		if (node->children[i]) {
			for (axis_iter = tree->start_axis; axis_iter < tree->stop_axis; axis_iter++) {
				/* update minimum */
				if (node->children[i]->bv[(2 * axis_iter)] < node->bv[(2 * axis_iter)])
					node->bv[(2 * axis_iter)] = node->children[i]->bv[(2 * axis_iter)];

				/* update maximum */
				if (node->children[i]->bv[(2 * axis_iter) + 1] > node->bv[(2 * axis_iter) + 1])
					node->bv[(2 * axis_iter) + 1] = node->children[i]->bv[(2 * axis_iter) + 1];
			}
		}
		else
			break;
	}
}

/*
 * Debug and information functions
 */
#if 0
static void bvhtree_print_tree(BVHTree *tree, BVHNode *node, int depth)
{
	int i;
	axis_t axis_iter;

	for (i = 0; i < depth; i++) printf(" ");
	printf(" - %d (%ld): ", node->index, (long int)(node - tree->nodearray));
	for (axis_iter = (axis_t)(2 * tree->start_axis);
	     axis_iter < (axis_t)(2 * tree->stop_axis);
	     axis_iter++)
	{
		printf("%.3f ", node->bv[axis_iter]);
	}
	printf("\n");

	for (i = 0; i < tree->tree_type; i++)
		if (node->children[i])
			bvhtree_print_tree(tree, node->children[i], depth + 1);
}

static void bvhtree_info(BVHTree *tree)
{
	printf("BVHTree info\n");
	printf("tree_type = %d, axis = %d, epsilon = %f\n", tree->tree_type, tree->axis, tree->epsilon);
	printf("nodes = %d, branches = %d, leafs = %d\n", tree->totbranch + tree->totleaf,  tree->totbranch, tree->totleaf);
	printf("Memory per node = %ldbytes\n", sizeof(BVHNode) + sizeof(BVHNode *) * tree->tree_type + sizeof(float) * tree->axis);
	printf("BV memory = %dbytes\n", (int)MEM_allocN_len(tree->nodebv));

	printf("Total memory = %ldbytes\n", sizeof(BVHTree) +
	       MEM_allocN_len(tree->nodes) +
	       MEM_allocN_len(tree->nodearray) +
	       MEM_allocN_len(tree->nodechild) +
	       MEM_allocN_len(tree->nodebv));

//	bvhtree_print_tree(tree, tree->nodes[tree->totleaf], 0);
}
#endif

#if 0


static void verify_tree(BVHTree *tree)
{
	int i, j, check = 0;
	
	/* check the pointer list */
	for (i = 0; i < tree->totleaf; i++) {
		if (tree->nodes[i]->parent == NULL) {
			printf("Leaf has no parent: %d\n", i);
		}
		else {
			for (j = 0; j < tree->tree_type; j++) {
				if (tree->nodes[i]->parent->children[j] == tree->nodes[i])
					check = 1;
			}
			if (!check) {
				printf("Parent child relationship doesn't match: %d\n", i);
			}
			check = 0;
		}
	}
	
	/* check the leaf list */
	for (i = 0; i < tree->totleaf; i++) {
		if (tree->nodearray[i].parent == NULL) {
			printf("Leaf has no parent: %d\n", i);
		}
		else {
			for (j = 0; j < tree->tree_type; j++) {
				if (tree->nodearray[i].parent->children[j] == &tree->nodearray[i])
					check = 1;
			}
			if (!check) {
				printf("Parent child relationship doesn't match: %d\n", i);
			}
			check = 0;
		}
	}
	
	printf("branches: %d, leafs: %d, total: %d\n", tree->totbranch, tree->totleaf, tree->totbranch + tree->totleaf);
}
#endif

/* Helper data and structures to build a min-leaf generalized implicit tree
 * This code can be easily reduced (basicly this is only method to calculate pow(k, n) in O(1).. and stuff like that) */
typedef struct BVHBuildHelper {
	int tree_type;              /* */
	int totleafs;               /* */

	int leafs_per_child[32];    /* Min number of leafs that are archievable from a node at depth N */
	int branches_on_level[32];  /* Number of nodes at depth N (tree_type^N) */

	int remain_leafs;           /* Number of leafs that are placed on the level that is not 100% filled */

} BVHBuildHelper;

static void build_implicit_tree_helper(BVHTree *tree, BVHBuildHelper *data)
{
	int depth = 0;
	int remain;
	int nnodes;

	data->totleafs = tree->totleaf;
	data->tree_type = tree->tree_type;

	/* Calculate the smallest tree_type^n such that tree_type^n >= num_leafs */
	for (data->leafs_per_child[0] = 1;
	     data->leafs_per_child[0] <  data->totleafs;
	     data->leafs_per_child[0] *= data->tree_type)
	{
		/* pass */
	}

	data->branches_on_level[0] = 1;

	for (depth = 1; (depth < 32) && data->leafs_per_child[depth - 1]; depth++) {
		data->branches_on_level[depth] = data->branches_on_level[depth - 1] * data->tree_type;
		data->leafs_per_child[depth] = data->leafs_per_child[depth - 1] / data->tree_type;
	}

	remain = data->totleafs - data->leafs_per_child[1];
	nnodes = (remain + data->tree_type - 2) / (data->tree_type - 1);
	data->remain_leafs = remain + nnodes;
}

// return the min index of all the leafs archivable with the given branch
static int implicit_leafs_index(BVHBuildHelper *data, int depth, int child_index)
{
	int min_leaf_index = child_index * data->leafs_per_child[depth - 1];
	if (min_leaf_index <= data->remain_leafs)
		return min_leaf_index;
	else if (data->leafs_per_child[depth])
		return data->totleafs - (data->branches_on_level[depth - 1] - child_index) * data->leafs_per_child[depth];
	else
		return data->remain_leafs;
}

/**
 * Generalized implicit tree build
 *
 * An implicit tree is a tree where its structure is implied, thus there is no need to store child pointers or indexs.
 * Its possible to find the position of the child or the parent with simple maths (multiplication and adittion). This type
 * of tree is for example used on heaps.. where node N has its childs at indexs N*2 and N*2+1.
 *
 * Although in this case the tree type is general.. and not know until runtime.
 * tree_type stands for the maximum number of childs that a tree node can have.
 * All tree types >= 2 are supported.
 *
 * Advantages of the used trees include:
 *  - No need to store child/parent relations (they are implicit);
 *  - Any node child always has an index greater than the parent;
 *  - Brother nodes are sequential in memory;
 *
 *
 * Some math relations derived for general implicit trees:
 *
 *   K = tree_type, ( 2 <= K )
 *   ROOT = 1
 *   N child of node A = A * K + (2 - K) + N, (0 <= N < K)
 *
 * Util methods:
 *   TODO...
 *    (looping elements, knowing if its a leaf or not.. etc...)
 */

/* This functions returns the number of branches needed to have the requested number of leafs. */
static int implicit_needed_branches(int tree_type, int leafs)
{
	return max_ii(1, (leafs + tree_type - 3) / (tree_type - 1));
}

/**
 * This function handles the problem of "sorting" the leafs (along the split_axis).
 *
 * It arranges the elements in the given partitions such that:
 *  - any element in partition N is less or equal to any element in partition N+1.
 *  - if all elements are different all partition will get the same subset of elements
 *    as if the array was sorted.
 *
 * partition P is described as the elements in the range ( nth[P], nth[P+1] ]
 *
 * TODO: This can be optimized a bit by doing a specialized nth_element instead of K nth_elements
 */
static void split_leafs(BVHNode **leafs_array, int *nth, int partitions, int split_axis)
{
	int i;
	for (i = 0; i < partitions - 1; i++) {
		if (nth[i] >= nth[partitions])
			break;

		partition_nth_element(leafs_array, nth[i], nth[partitions], nth[i + 1], split_axis);
	}
}

/**
 * This functions builds an optimal implicit tree from the given leafs.
 * Where optimal stands for:
 *  - The resulting tree will have the smallest number of branches;
 *  - At most only one branch will have NULL childs;
 *  - All leafs will be stored at level N or N+1.
 *
 * This function creates an implicit tree on branches_array, the leafs are given on the leafs_array.
 *
 * The tree is built per depth levels. First branches at depth 1.. then branches at depth 2.. etc..
 * The reason is that we can build level N+1 from level N without any data dependencies.. thus it allows
 * to use multithread building.
 *
 * To archive this is necessary to find how much leafs are accessible from a certain branch, BVHBuildHelper
 * implicit_needed_branches and implicit_leafs_index are auxiliary functions to solve that "optimal-split".
 */
static void non_recursive_bvh_div_nodes(BVHTree *tree, BVHNode *branches_array, BVHNode **leafs_array, int num_leafs)
{
	int i;

	const int tree_type   = tree->tree_type;
	const int tree_offset = 2 - tree->tree_type; /* this value is 0 (on binary trees) and negative on the others */
	const int num_branches = implicit_needed_branches(tree_type, num_leafs);

	BVHBuildHelper data;
	int depth;
	
	/* set parent from root node to NULL */
	BVHNode *tmp = branches_array + 0;
	tmp->parent = NULL;

	/* Most of bvhtree code relies on 1-leaf trees having at least one branch
	 * We handle that special case here */
	if (num_leafs == 1) {
		BVHNode *root = branches_array + 0;
		refit_kdop_hull(tree, root, 0, num_leafs);
		root->main_axis = get_largest_axis(root->bv) / 2;
		root->totnode = 1;
		root->children[0] = leafs_array[0];
		root->children[0]->parent = root;
		return;
	}

	branches_array--;  /* Implicit trees use 1-based indexs */

	build_implicit_tree_helper(tree, &data);

	/* Loop tree levels (log N) loops */
	for (i = 1, depth = 1; i <= num_branches; i = i * tree_type + tree_offset, depth++) {
		const int first_of_next_level = i * tree_type + tree_offset;
		const int end_j = min_ii(first_of_next_level, num_branches + 1);  /* index of last branch on this level */
		int j;

		/* Loop all branches on this level */

#pragma omp parallel for private(j) schedule(static) if (num_leafs > KDOPBVH_OMP_LIMIT)
		for (j = i; j < end_j; j++) {
			int k;
			const int parent_level_index = j - i;
			BVHNode *parent = branches_array + j;
			int nth_positions[MAX_TREETYPE + 1];
			char split_axis;

			int parent_leafs_begin = implicit_leafs_index(&data, depth, parent_level_index);
			int parent_leafs_end   = implicit_leafs_index(&data, depth, parent_level_index + 1);

			/* This calculates the bounding box of this branch
			 * and chooses the largest axis as the axis to divide leafs */
			refit_kdop_hull(tree, parent, parent_leafs_begin, parent_leafs_end);
			split_axis = get_largest_axis(parent->bv);

			/* Save split axis (this can be used on raytracing to speedup the query time) */
			parent->main_axis = split_axis / 2;

			/* Split the childs along the split_axis, note: its not needed to sort the whole leafs array
			 * Only to assure that the elements are partitioned on a way that each child takes the elements
			 * it would take in case the whole array was sorted.
			 * Split_leafs takes care of that "sort" problem. */
			nth_positions[0] = parent_leafs_begin;
			nth_positions[tree_type] = parent_leafs_end;
			for (k = 1; k < tree_type; k++) {
				int child_index = j * tree_type + tree_offset + k;
				int child_level_index = child_index - first_of_next_level; /* child level index */
				nth_positions[k] = implicit_leafs_index(&data, depth + 1, child_level_index);
			}

			split_leafs(leafs_array, nth_positions, tree_type, split_axis);


			/* Setup children and totnode counters
			 * Not really needed but currently most of BVH code relies on having an explicit children structure */
			for (k = 0; k < tree_type; k++) {
				int child_index = j * tree_type + tree_offset + k;
				int child_level_index = child_index - first_of_next_level; /* child level index */

				int child_leafs_begin = implicit_leafs_index(&data, depth + 1, child_level_index);
				int child_leafs_end   = implicit_leafs_index(&data, depth + 1, child_level_index + 1);

				if (child_leafs_end - child_leafs_begin > 1) {
					parent->children[k] = branches_array + child_index;
					parent->children[k]->parent = parent;
				}
				else if (child_leafs_end - child_leafs_begin == 1) {
					parent->children[k] = leafs_array[child_leafs_begin];
					parent->children[k]->parent = parent;
				}
				else {
					break;
				}

				parent->totnode = (char)(k + 1);
			}
		}
	}
}

/* -------------------------------------------------------------------- */
/* BLI_bvhtree api */

/**
 * \note many callers don't check for ``NULL`` return.
 */
BVHTree *BLI_bvhtree_new(int maxsize, float epsilon, char tree_type, char axis)
{
	BVHTree *tree;
	int numnodes, i;

	BLI_assert(tree_type >= 2 && tree_type <= MAX_TREETYPE);

	tree = MEM_callocN(sizeof(BVHTree), "BVHTree");

	/* tree epsilon must be >= FLT_EPSILON
	 * so that tangent rays can still hit a bounding volume..
	 * this bug would show up when casting a ray aligned with a kdop-axis and with an edge of 2 faces */
	epsilon = max_ff(FLT_EPSILON, epsilon);

	if (tree) {
		tree->epsilon = epsilon;
		tree->tree_type = tree_type;
		tree->axis = axis;

		if (axis == 26) {
			tree->start_axis = 0;
			tree->stop_axis = 13;
		}
		else if (axis == 18) {
			tree->start_axis = 7;
			tree->stop_axis = 13;
		}
		else if (axis == 14) {
			tree->start_axis = 0;
			tree->stop_axis = 7;
		}
		else if (axis == 8) { /* AABB */
			tree->start_axis = 0;
			tree->stop_axis = 4;
		}
		else if (axis == 6) { /* OBB */
			tree->start_axis = 0;
			tree->stop_axis = 3;
		}
		else {
			/* should never happen! */
			BLI_assert(0);

			goto fail;
		}


		/* Allocate arrays */
		numnodes = maxsize + implicit_needed_branches(tree_type, maxsize) + tree_type;

		tree->nodes = MEM_callocN(sizeof(BVHNode *) * (size_t)numnodes, "BVHNodes");
		tree->nodebv = MEM_callocN(sizeof(float) * (size_t)(axis * numnodes), "BVHNodeBV");
		tree->nodechild = MEM_callocN(sizeof(BVHNode *) * (size_t)(tree_type * numnodes), "BVHNodeBV");
		tree->nodearray = MEM_callocN(sizeof(BVHNode) * (size_t)numnodes, "BVHNodeArray");
		
		if (UNLIKELY((!tree->nodes) ||
		             (!tree->nodebv) ||
		             (!tree->nodechild) ||
		             (!tree->nodearray)))
		{
			goto fail;
		}

		/* link the dynamic bv and child links */
		for (i = 0; i < numnodes; i++) {
			tree->nodearray[i].bv = &tree->nodebv[i * axis];
			tree->nodearray[i].children = &tree->nodechild[i * tree_type];
		}
		
	}
	return tree;


fail:
	MEM_SAFE_FREE(tree->nodes);
	MEM_SAFE_FREE(tree->nodebv);
	MEM_SAFE_FREE(tree->nodechild);
	MEM_SAFE_FREE(tree->nodearray);

	MEM_freeN(tree);

	return NULL;
}

void BLI_bvhtree_free(BVHTree *tree)
{
	if (tree) {
		MEM_freeN(tree->nodes);
		MEM_freeN(tree->nodearray);
		MEM_freeN(tree->nodebv);
		MEM_freeN(tree->nodechild);
		MEM_freeN(tree);
	}
}

void BLI_bvhtree_balance(BVHTree *tree)
{
	int i;

	BVHNode *branches_array = tree->nodearray + tree->totleaf;
	BVHNode **leafs_array    = tree->nodes;

	/* This function should only be called once (some big bug goes here if its being called more than once per tree) */
	BLI_assert(tree->totbranch == 0);

	/* Build the implicit tree */
	non_recursive_bvh_div_nodes(tree, branches_array, leafs_array, tree->totleaf);

	/* current code expects the branches to be linked to the nodes array
	 * we perform that linkage here */
	tree->totbranch = implicit_needed_branches(tree->tree_type, tree->totleaf);
	for (i = 0; i < tree->totbranch; i++)
		tree->nodes[tree->totleaf + i] = branches_array + i;

#ifdef USE_SKIP_LINKS
	build_skip_links(tree, tree->nodes[tree->totleaf], NULL, NULL);
#endif

	/* bvhtree_info(tree); */
}

void BLI_bvhtree_insert(BVHTree *tree, int index, const float co[3], int numpoints)
{
	axis_t axis_iter;
	BVHNode *node = NULL;

	/* insert should only possible as long as tree->totbranch is 0 */
	BLI_assert(tree->totbranch <= 0);
	BLI_assert((size_t)tree->totleaf < MEM_allocN_len(tree->nodes) / sizeof(*(tree->nodes)));

	node = tree->nodes[tree->totleaf] = &(tree->nodearray[tree->totleaf]);
	tree->totleaf++;

	create_kdop_hull(tree, node, co, numpoints, 0);
	node->index = index;

	/* inflate the bv with some epsilon */
	for (axis_iter = tree->start_axis; axis_iter < tree->stop_axis; axis_iter++) {
		node->bv[(2 * axis_iter)] -= tree->epsilon; /* minimum */
		node->bv[(2 * axis_iter) + 1] += tree->epsilon; /* maximum */
	}
}


/* call before BLI_bvhtree_update_tree() */
bool BLI_bvhtree_update_node(BVHTree *tree, int index, const float co[3], const float co_moving[3], int numpoints)
{
	BVHNode *node = NULL;
	axis_t axis_iter;
	
	/* check if index exists */
	if (index > tree->totleaf)
		return false;
	
	node = tree->nodearray + index;
	
	create_kdop_hull(tree, node, co, numpoints, 0);
	
	if (co_moving)
		create_kdop_hull(tree, node, co_moving, numpoints, 1);
	
	/* inflate the bv with some epsilon */
	for (axis_iter = tree->start_axis; axis_iter < tree->stop_axis; axis_iter++) {
		node->bv[(2 * axis_iter)]     -= tree->epsilon; /* minimum */
		node->bv[(2 * axis_iter) + 1] += tree->epsilon; /* maximum */
	}

	return true;
}

/* call BLI_bvhtree_update_node() first for every node/point/triangle */
void BLI_bvhtree_update_tree(BVHTree *tree)
{
	/* Update bottom=>top
	 * TRICKY: the way we build the tree all the childs have an index greater than the parent
	 * This allows us todo a bottom up update by starting on the bigger numbered branch */

	BVHNode **root  = tree->nodes + tree->totleaf;
	BVHNode **index = tree->nodes + tree->totleaf + tree->totbranch - 1;

	for (; index >= root; index--)
		node_join(tree, *index);
}

float BLI_bvhtree_getepsilon(const BVHTree *tree)
{
	return tree->epsilon;
}


/* -------------------------------------------------------------------- */
/* BLI_bvhtree_overlap */

/**
 * overlap - is it possible for 2 bv's to collide ?
 */
static bool tree_overlap_test(const BVHNode *node1, const BVHNode *node2, axis_t start_axis, axis_t stop_axis)
{
	const float *bv1     = node1->bv + (start_axis << 1);
	const float *bv2     = node2->bv + (start_axis << 1);
	const float *bv1_end = node1->bv + (stop_axis  << 1);
	
	/* test all axis if min + max overlap */
	for (; bv1 != bv1_end; bv1 += 2, bv2 += 2) {
		if ((bv1[0] > bv2[1]) || (bv2[0] > bv1[1])) {
			return 0;
		}
	}

	return 1;
}

static void tree_overlap_traverse(
        BVHOverlapData_Thread *data_thread,
        const BVHNode *node1, const BVHNode *node2)
{
	BVHOverlapData_Shared *data = data_thread->shared;
	int j;

	if (tree_overlap_test(node1, node2, data->start_axis, data->stop_axis)) {
		/* check if node1 is a leaf */
		if (!node1->totnode) {
			/* check if node2 is a leaf */
			if (!node2->totnode) {
				BVHTreeOverlap *overlap;

				if (UNLIKELY(node1 == node2)) {
					return;
				}

				/* both leafs, insert overlap! */
				overlap = BLI_stack_push_r(data_thread->overlap);
				overlap->indexA = node1->index;
				overlap->indexB = node2->index;
			}
			else {
				for (j = 0; j < data->tree2->tree_type; j++) {
					if (node2->children[j]) {
						tree_overlap_traverse(data_thread, node1, node2->children[j]);
					}
				}
			}
		}
		else {
			for (j = 0; j < data->tree2->tree_type; j++) {
				if (node1->children[j]) {
					tree_overlap_traverse(data_thread, node1->children[j], node2);
				}
			}
		}
	}
}

/**
 * a version of #tree_overlap_traverse that runs a callback to check if the nodes really intersect.
 */
static void tree_overlap_traverse_cb(
        BVHOverlapData_Thread *data_thread,
        const BVHNode *node1, const BVHNode *node2)
{
	BVHOverlapData_Shared *data = data_thread->shared;
	int j;

	if (tree_overlap_test(node1, node2, data->start_axis, data->stop_axis)) {
		/* check if node1 is a leaf */
		if (!node1->totnode) {
			/* check if node2 is a leaf */
			if (!node2->totnode) {
				BVHTreeOverlap *overlap;

				if (UNLIKELY(node1 == node2)) {
					return;
				}

				/* only difference to tree_overlap_traverse! */
				if (data->callback(data->userdata, node1->index, node2->index, data_thread->thread)) {
					/* both leafs, insert overlap! */
					overlap = BLI_stack_push_r(data_thread->overlap);
					overlap->indexA = node1->index;
					overlap->indexB = node2->index;
				}
			}
			else {
				for (j = 0; j < data->tree2->tree_type; j++) {
					if (node2->children[j]) {
						tree_overlap_traverse_cb(data_thread, node1, node2->children[j]);
					}
				}
			}
		}
		else {
			for (j = 0; j < data->tree2->tree_type; j++) {
				if (node1->children[j]) {
					tree_overlap_traverse_cb(data_thread, node1->children[j], node2);
				}
			}
		}
	}
}

/**
 * Use to check the total number of threads #BLI_bvhtree_overlap will use.
 *
 * \warning Must be the first tree passed to #BLI_bvhtree_overlap!
 */
int BLI_bvhtree_overlap_thread_num(const BVHTree *tree)
{
	return (int)MIN2(tree->tree_type, tree->nodes[tree->totleaf]->totnode);
}

BVHTreeOverlap *BLI_bvhtree_overlap(
        const BVHTree *tree1, const BVHTree *tree2, unsigned int *r_overlap_tot,
        /* optional callback to test the overlap before adding (must be thread-safe!) */
        BVHTree_OverlapCallback callback, void *userdata)
{
	const int thread_num = BLI_bvhtree_overlap_thread_num(tree1);
	int j;
	size_t total = 0;
	BVHTreeOverlap *overlap = NULL, *to = NULL;
	BVHOverlapData_Shared data_shared;
	BVHOverlapData_Thread *data = BLI_array_alloca(data, (size_t)thread_num);
	axis_t start_axis, stop_axis;
	
	/* check for compatibility of both trees (can't compare 14-DOP with 18-DOP) */
	if (UNLIKELY((tree1->axis != tree2->axis) &&
	             (tree1->axis == 14 || tree2->axis == 14) &&
	             (tree1->axis == 18 || tree2->axis == 18)))
	{
		BLI_assert(0);
		return NULL;
	}

	start_axis = min_axis(tree1->start_axis, tree2->start_axis);
	stop_axis  = min_axis(tree1->stop_axis,  tree2->stop_axis);
	
	/* fast check root nodes for collision before doing big splitting + traversal */
	if (!tree_overlap_test(tree1->nodes[tree1->totleaf], tree2->nodes[tree2->totleaf], start_axis, stop_axis)) {
		return NULL;
	}

	data_shared.tree1 = tree1;
	data_shared.tree2 = tree2;
	data_shared.start_axis = start_axis;
	data_shared.stop_axis = stop_axis;

	/* can be NULL */
	data_shared.callback = callback;
	data_shared.userdata = userdata;

	for (j = 0; j < thread_num; j++) {
		/* init BVHOverlapData_Thread */
		data[j].shared = &data_shared;
		data[j].overlap = BLI_stack_new(sizeof(BVHTreeOverlap), __func__);

		/* for callback */
		data[j].thread = j;
	}

#pragma omp parallel for private(j) schedule(static)  if (tree1->totleaf > KDOPBVH_OMP_LIMIT)
	for (j = 0; j < thread_num; j++) {
		if (callback) {
			tree_overlap_traverse_cb(&data[j], tree1->nodes[tree1->totleaf]->children[j], tree2->nodes[tree2->totleaf]);
		}
		else {
			tree_overlap_traverse(&data[j], tree1->nodes[tree1->totleaf]->children[j], tree2->nodes[tree2->totleaf]);
		}
	}
	
	for (j = 0; j < thread_num; j++)
		total += BLI_stack_count(data[j].overlap);
	
	to = overlap = MEM_mallocN(sizeof(BVHTreeOverlap) * total, "BVHTreeOverlap");
	
	for (j = 0; j < thread_num; j++) {
		unsigned int count = (unsigned int)BLI_stack_count(data[j].overlap);
		BLI_stack_pop_n(data[j].overlap, to, count);
		BLI_stack_free(data[j].overlap);
		to += count;
	}

	*r_overlap_tot = (unsigned int)total;
	return overlap;
}

/* Determines the nearest point of the given node BV. Returns the squared distance to that point. */
static float calc_nearest_point_squared(const float proj[3], BVHNode *node, float nearest[3])
{
	int i;
	const float *bv = node->bv;

	/* nearest on AABB hull */
	for (i = 0; i != 3; i++, bv += 2) {
		if (bv[0] > proj[i])
			nearest[i] = bv[0];
		else if (bv[1] < proj[i])
			nearest[i] = bv[1];
		else
			nearest[i] = proj[i]; 
	}

#if 0
	/* nearest on a general hull */
	copy_v3_v3(nearest, data->co);
	for (i = data->tree->start_axis; i != data->tree->stop_axis; i++, bv += 2) {
		float proj = dot_v3v3(nearest, KDOP_AXES[i]);
		float dl = bv[0] - proj;
		float du = bv[1] - proj;

		if (dl > 0) {
			madd_v3_v3fl(nearest, KDOP_AXES[i], dl);
		}
		else if (du < 0) {
			madd_v3_v3fl(nearest, KDOP_AXES[i], du);
		}
	}
#endif

	return len_squared_v3v3(proj, nearest);
}

/* TODO: use a priority queue to reduce the number of nodes looked on */
static void dfs_find_nearest_dfs(BVHNearestData *data, BVHNode *node)
{
	if (node->totnode == 0) {
		if (data->callback)
			data->callback(data->userdata, node->index, data->co, &data->nearest);
		else {
			data->nearest.index = node->index;
			data->nearest.dist_sq = calc_nearest_point_squared(data->proj, node, data->nearest.co);
		}
	}
	else {
		/* Better heuristic to pick the closest node to dive on */
		int i;
		float nearest[3];

		if (data->proj[node->main_axis] <= node->children[0]->bv[node->main_axis * 2 + 1]) {

			for (i = 0; i != node->totnode; i++) {
				if (calc_nearest_point_squared(data->proj, node->children[i], nearest) >= data->nearest.dist_sq)
					continue;
				dfs_find_nearest_dfs(data, node->children[i]);
			}
		}
		else {
			for (i = node->totnode - 1; i >= 0; i--) {
				if (calc_nearest_point_squared(data->proj, node->children[i], nearest) >= data->nearest.dist_sq)
					continue;
				dfs_find_nearest_dfs(data, node->children[i]);
			}
		}
	}
}

static void dfs_find_nearest_begin(BVHNearestData *data, BVHNode *node)
{
	float nearest[3], dist_sq;
	dist_sq = calc_nearest_point_squared(data->proj, node, nearest);
	if (dist_sq >= data->nearest.dist_sq) {
		return;
	}
	dfs_find_nearest_dfs(data, node);
}


#if 0

typedef struct NodeDistance {
	BVHNode *node;
	float dist;

} NodeDistance;

#define DEFAULT_FIND_NEAREST_HEAP_SIZE 1024

#define NodeDistance_priority(a, b) ((a).dist < (b).dist)

static void NodeDistance_push_heap(NodeDistance *heap, int heap_size)
PUSH_HEAP_BODY(NodeDistance, NodeDistance_priority, heap, heap_size)

static void NodeDistance_pop_heap(NodeDistance *heap, int heap_size)
POP_HEAP_BODY(NodeDistance, NodeDistance_priority, heap, heap_size)

/* NN function that uses an heap.. this functions leads to an optimal number of min-distance
 * but for normal tri-faces and BV 6-dop.. a simple dfs with local heuristics (as implemented
 * in source/blender/blenkernel/intern/shrinkwrap.c) works faster.
 *
 * It may make sense to use this function if the callback queries are very slow.. or if its impossible
 * to get a nice heuristic
 *
 * this function uses "malloc/free" instead of the MEM_* because it intends to be openmp safe */
static void bfs_find_nearest(BVHNearestData *data, BVHNode *node)
{
	int i;
	NodeDistance default_heap[DEFAULT_FIND_NEAREST_HEAP_SIZE];
	NodeDistance *heap = default_heap, current;
	int heap_size = 0, max_heap_size = sizeof(default_heap) / sizeof(default_heap[0]);
	float nearest[3];

	int callbacks = 0, push_heaps = 0;

	if (node->totnode == 0) {
		dfs_find_nearest_dfs(data, node);
		return;
	}

	current.node = node;
	current.dist = calc_nearest_point(data->proj, node, nearest);

	while (current.dist < data->nearest.dist) {
//		printf("%f : %f\n", current.dist, data->nearest.dist);
		for (i = 0; i < current.node->totnode; i++) {
			BVHNode *child = current.node->children[i];
			if (child->totnode == 0) {
				callbacks++;
				dfs_find_nearest_dfs(data, child);
			}
			else {
				/* adjust heap size */
				if ((heap_size >= max_heap_size) &&
				    ADJUST_MEMORY(default_heap, (void **)&heap, heap_size + 1, &max_heap_size, sizeof(heap[0])) == false)
				{
					printf("WARNING: bvh_find_nearest got out of memory\n");

					if (heap != default_heap)
						free(heap);

					return;
				}

				heap[heap_size].node = current.node->children[i];
				heap[heap_size].dist = calc_nearest_point(data->proj, current.node->children[i], nearest);

				if (heap[heap_size].dist >= data->nearest.dist) continue;
				heap_size++;

				NodeDistance_push_heap(heap, heap_size);
				//			PUSH_HEAP_BODY(NodeDistance, NodeDistance_priority, heap, heap_size);
				push_heaps++;
			}
		}
		
		if (heap_size == 0) break;

		current = heap[0];
		NodeDistance_pop_heap(heap, heap_size);
//		POP_HEAP_BODY(NodeDistance, NodeDistance_priority, heap, heap_size);
		heap_size--;
	}

//	printf("hsize=%d, callbacks=%d, pushs=%d\n", heap_size, callbacks, push_heaps);

	if (heap != default_heap)
		free(heap);
}
#endif


int BLI_bvhtree_find_nearest(BVHTree *tree, const float co[3], BVHTreeNearest *nearest,
                             BVHTree_NearestPointCallback callback, void *userdata)
{
	axis_t axis_iter;

	BVHNearestData data;
	BVHNode *root = tree->nodes[tree->totleaf];

	/* init data to search */
	data.tree = tree;
	data.co = co;

	data.callback = callback;
	data.userdata = userdata;

	for (axis_iter = data.tree->start_axis; axis_iter != data.tree->stop_axis; axis_iter++) {
		data.proj[axis_iter] = dot_v3v3(data.co, KDOP_AXES[axis_iter]);
	}

	if (nearest) {
		memcpy(&data.nearest, nearest, sizeof(*nearest));
	}
	else {
		data.nearest.index = -1;
		data.nearest.dist_sq = FLT_MAX;
	}

	/* dfs search */
	if (root)
		dfs_find_nearest_begin(&data, root);

	/* copy back results */
	if (nearest) {
		memcpy(nearest, &data.nearest, sizeof(*nearest));
	}

	return data.nearest.index;
}


/**
 * Raycast - BLI_bvhtree_ray_cast
 *
 * raycast is done by performing a DFS on the BVHTree and saving the closest hit
 */


/* Determines the distance that the ray must travel to hit the bounding volume of the given node */
static float ray_nearest_hit(BVHRayCastData *data, const float bv[6])
{
	int i;

	float low = 0, upper = data->hit.dist;

	for (i = 0; i != 3; i++, bv += 2) {
		if (data->ray_dot_axis[i] == 0.0f) {
			/* axis aligned ray */
			if (data->ray.origin[i] < bv[0] - data->ray.radius ||
			    data->ray.origin[i] > bv[1] + data->ray.radius)
			{
				return FLT_MAX;
			}
		}
		else {
			float ll = (bv[0] - data->ray.radius - data->ray.origin[i]) / data->ray_dot_axis[i];
			float lu = (bv[1] + data->ray.radius - data->ray.origin[i]) / data->ray_dot_axis[i];

			if (data->ray_dot_axis[i] > 0.0f) {
				if (ll > low) low = ll;
				if (lu < upper) upper = lu;
			}
			else {
				if (lu > low) low = lu;
				if (ll < upper) upper = ll;
			}
	
			if (low > upper) return FLT_MAX;
		}
	}
	return low;
}

/**
 * Determines the distance that the ray must travel to hit the bounding volume of the given node
 * Based on Tactical Optimization of Ray/Box Intersection, by Graham Fyffe
 * [http://tog.acm.org/resources/RTNews/html/rtnv21n1.html#art9]
 *
 * TODO this doesn't take data->ray.radius into consideration */
static float fast_ray_nearest_hit(const BVHRayCastData *data, const BVHNode *node)
{
	const float *bv = node->bv;
	
	float t1x = (bv[data->index[0]] - data->ray.origin[0]) * data->idot_axis[0];
	float t2x = (bv[data->index[1]] - data->ray.origin[0]) * data->idot_axis[0];
	float t1y = (bv[data->index[2]] - data->ray.origin[1]) * data->idot_axis[1];
	float t2y = (bv[data->index[3]] - data->ray.origin[1]) * data->idot_axis[1];
	float t1z = (bv[data->index[4]] - data->ray.origin[2]) * data->idot_axis[2];
	float t2z = (bv[data->index[5]] - data->ray.origin[2]) * data->idot_axis[2];

	if ((t1x > t2y || t2x < t1y || t1x > t2z || t2x < t1z || t1y > t2z || t2y < t1z) ||
	    (t2x < 0.0f || t2y < 0.0f || t2z < 0.0f) ||
	    (t1x > data->hit.dist || t1y > data->hit.dist || t1z > data->hit.dist))
	{
		return FLT_MAX;
	}
	else {
		return max_fff(t1x, t1y, t1z);
	}
}

static void dfs_raycast(BVHRayCastData *data, BVHNode *node)
{
	int i;

	/* ray-bv is really fast.. and simple tests revealed its worth to test it
	 * before calling the ray-primitive functions */
	/* XXX: temporary solution for particles until fast_ray_nearest_hit supports ray.radius */
	float dist = (data->ray.radius == 0.0f) ? fast_ray_nearest_hit(data, node) : ray_nearest_hit(data, node->bv);
	if (dist >= data->hit.dist) return;

	if (node->totnode == 0) {
		if (data->callback) {
			data->callback(data->userdata, node->index, &data->ray, &data->hit);
		}
		else {
			data->hit.index = node->index;
			data->hit.dist  = dist;
			madd_v3_v3v3fl(data->hit.co, data->ray.origin, data->ray.direction, dist);
		}
	}
	else {
		/* pick loop direction to dive into the tree (based on ray direction and split axis) */
		if (data->ray_dot_axis[node->main_axis] > 0.0f) {
			for (i = 0; i != node->totnode; i++) {
				dfs_raycast(data, node->children[i]);
			}
		}
		else {
			for (i = node->totnode - 1; i >= 0; i--) {
				dfs_raycast(data, node->children[i]);
			}
		}
	}
}

static void dfs_raycast_all(BVHRayCastData *data, BVHNode *node)
{
	int i;

	/* ray-bv is really fast.. and simple tests revealed its worth to test it
	 * before calling the ray-primitive functions */
	/* XXX: temporary solution for particles until fast_ray_nearest_hit supports ray.radius */
	float dist = (data->ray.radius == 0.0f) ? fast_ray_nearest_hit(data, node) : ray_nearest_hit(data, node->bv);

	if (node->totnode == 0) {
		if (data->callback) {
			data->hit.index = -1;
			data->hit.dist = FLT_MAX;
			data->callback(data->userdata, node->index, &data->ray, &data->hit);
		}
		else {
			data->hit.index = node->index;
			data->hit.dist  = dist;
			madd_v3_v3v3fl(data->hit.co, data->ray.origin, data->ray.direction, dist);
		}
	}
	else {
		/* pick loop direction to dive into the tree (based on ray direction and split axis) */
		if (data->ray_dot_axis[node->main_axis] > 0.0f) {
			for (i = 0; i != node->totnode; i++) {
				dfs_raycast_all(data, node->children[i]);
			}
		}
		else {
			for (i = node->totnode - 1; i >= 0; i--) {
				dfs_raycast_all(data, node->children[i]);
			}
		}
	}
}

#if 0
static void iterative_raycast(BVHRayCastData *data, BVHNode *node)
{
	while (node) {
		float dist = fast_ray_nearest_hit(data, node);
		if (dist >= data->hit.dist) {
			node = node->skip[1];
			continue;
		}

		if (node->totnode == 0) {
			if (data->callback) {
				data->callback(data->userdata, node->index, &data->ray, &data->hit);
			}
			else {
				data->hit.index = node->index;
				data->hit.dist  = dist;
				madd_v3_v3v3fl(data->hit.co, data->ray.origin, data->ray.direction, dist);
			}
			
			node = node->skip[1];
		}
		else {
			node = node->children[0];
		}
	}
}
#endif

static void bvhtree_ray_cast_data_precalc(BVHRayCastData *data, int flag)
{
	int i;

	for (i = 0; i < 3; i++) {
		data->ray_dot_axis[i] = dot_v3v3(data->ray.direction, KDOP_AXES[i]);
		data->idot_axis[i] = 1.0f / data->ray_dot_axis[i];

		if (fabsf(data->ray_dot_axis[i]) < FLT_EPSILON) {
			data->ray_dot_axis[i] = 0.0;
		}
		data->index[2 * i] = data->idot_axis[i] < 0.0f ? 1 : 0;
		data->index[2 * i + 1] = 1 - data->index[2 * i];
		data->index[2 * i]   += 2 * i;
		data->index[2 * i + 1] += 2 * i;
	}

#ifdef USE_KDOPBVH_WATERTIGHT
	if (flag & BVH_RAYCAST_WATERTIGHT) {
		isect_ray_tri_watertight_v3_precalc(&data->isect_precalc, data->ray.direction);
		data->ray.isect_precalc = &data->isect_precalc;
	}
	else {
		data->ray.isect_precalc = NULL;
	}
#else
	UNUSED_VARS(flag);
#endif
}

int BLI_bvhtree_ray_cast_ex(
        BVHTree *tree, const float co[3], const float dir[3], float radius, BVHTreeRayHit *hit,
        BVHTree_RayCastCallback callback, void *userdata,
        int flag)
{
	BVHRayCastData data;
	BVHNode *root = tree->nodes[tree->totleaf];

	BLI_ASSERT_UNIT_V3(dir);

	data.tree = tree;

	data.callback = callback;
	data.userdata = userdata;

	copy_v3_v3(data.ray.origin,    co);
	copy_v3_v3(data.ray.direction, dir);
	data.ray.radius = radius;

	bvhtree_ray_cast_data_precalc(&data, flag);

	if (hit) {
		memcpy(&data.hit, hit, sizeof(*hit));
	}
	else {
		data.hit.index = -1;
		data.hit.dist = FLT_MAX;
	}

	if (root) {
		dfs_raycast(&data, root);
//		iterative_raycast(&data, root);
	}


	if (hit)
		memcpy(hit, &data.hit, sizeof(*hit));

	return data.hit.index;
}

int BLI_bvhtree_ray_cast(
        BVHTree *tree, const float co[3], const float dir[3], float radius, BVHTreeRayHit *hit,
        BVHTree_RayCastCallback callback, void *userdata)
{
	return BLI_bvhtree_ray_cast_ex(tree, co, dir, radius, hit, callback, userdata, BVH_RAYCAST_DEFAULT);
}

float BLI_bvhtree_bb_raycast(const float bv[6], const float light_start[3], const float light_end[3], float pos[3])
{
	BVHRayCastData data;
	float dist;

	data.hit.dist = FLT_MAX;
	
	/* get light direction */
	sub_v3_v3v3(data.ray.direction, light_end, light_start);
	
	data.ray.radius = 0.0;
	
	copy_v3_v3(data.ray.origin, light_start);

	normalize_v3(data.ray.direction);
	copy_v3_v3(data.ray_dot_axis, data.ray.direction);
	
	dist = ray_nearest_hit(&data, bv);

	madd_v3_v3v3fl(pos, light_start, data.ray.direction, dist);

	return dist;
	
}

/**
 * Calls the callback for every ray intersection
 */
int BLI_bvhtree_ray_cast_all_ex(
        BVHTree *tree, const float co[3], const float dir[3], float radius,
        BVHTree_RayCastCallback callback, void *userdata,
        int flag)
{
	BVHRayCastData data;
	BVHNode *root = tree->nodes[tree->totleaf];

	BLI_ASSERT_UNIT_V3(dir);

	data.tree = tree;

	data.callback = callback;
	data.userdata = userdata;

	copy_v3_v3(data.ray.origin,    co);
	copy_v3_v3(data.ray.direction, dir);
	data.ray.radius = radius;

	bvhtree_ray_cast_data_precalc(&data, flag);

	data.hit.index = -1;
	data.hit.dist = FLT_MAX;

	if (root) {
		dfs_raycast_all(&data, root);
	}

	return data.hit.index;
}

int BLI_bvhtree_ray_cast_all(
        BVHTree *tree, const float co[3], const float dir[3], float radius,
        BVHTree_RayCastCallback callback, void *userdata)
{
	return BLI_bvhtree_ray_cast_all_ex(tree, co, dir, radius, callback, userdata, BVH_RAYCAST_DEFAULT);
}

/**
 * Range Query - as request by broken :P
 *
 * Allocs and fills an array with the indexs of node that are on the given spherical range (center, radius) 
 * Returns the size of the array.
 */
typedef struct RangeQueryData {
	BVHTree *tree;
	const float *center;
	float radius_sq;  /* squared radius */

	int hits;

	BVHTree_RangeQuery callback;
	void *userdata;


} RangeQueryData;


static void dfs_range_query(RangeQueryData *data, BVHNode *node)
{
	if (node->totnode == 0) {
#if 0   /*UNUSED*/
		/* Calculate the node min-coords (if the node was a point then this is the point coordinates) */
		float co[3];
		co[0] = node->bv[0];
		co[1] = node->bv[2];
		co[2] = node->bv[4];
#endif
	}
	else {
		int i;
		for (i = 0; i != node->totnode; i++) {
			float nearest[3];
			float dist_sq = calc_nearest_point_squared(data->center, node->children[i], nearest);
			if (dist_sq < data->radius_sq) {
				/* Its a leaf.. call the callback */
				if (node->children[i]->totnode == 0) {
					data->hits++;
					data->callback(data->userdata, node->children[i]->index, dist_sq);
				}
				else
					dfs_range_query(data, node->children[i]);
			}
		}
	}
}

int BLI_bvhtree_range_query(BVHTree *tree, const float co[3], float radius, BVHTree_RangeQuery callback, void *userdata)
{
	BVHNode *root = tree->nodes[tree->totleaf];

	RangeQueryData data;
	data.tree = tree;
	data.center = co;
	data.radius_sq = radius * radius;
	data.hits = 0;

	data.callback = callback;
	data.userdata = userdata;

	if (root != NULL) {
		float nearest[3];
		float dist_sq = calc_nearest_point_squared(data.center, root, nearest);
		if (dist_sq < data.radius_sq) {
			/* Its a leaf.. call the callback */
			if (root->totnode == 0) {
				data.hits++;
				data.callback(data.userdata, root->index, dist_sq);
			}
			else
				dfs_range_query(&data, root);
		}
	}

	return data.hits;
}
