void KdTreeAccel::buildTree(KdAccelNode* node, const Bounds3f &bound, vector<int> &prims,
int depth, BoundEdge* edges[3])
{
node->bbox = bound;
int np = prims.size();
//If not enough primitives or reach max depth of a tree
//Create a leaf node
if (np <= maxPrims || depth == 0)
{
node->initLeaf(prims);
return;
}
//Interior node parameters
int bestAxis = -1, bestOffest = -1;//Split axis and split index*2
Float bestCost = INFINITY;
Float oldCost = np;
Float totalSA = bound.surfaceArea();
Float invTotalSA = 1.0 / totalSA;
Vector3f bbDiag = bound.pMax - bound.pMin;
//choose max extension axis of bounding box
int axis = bound.maxExtent();//axis is the longest edge of bounding box
int retries = 0;
RETRY_SPLIT:
//
//Calculate surface cost
for (int i = 0; i < np; ++i)
{
int prmIdx = prims[i];
const Bounds3f tmpBox = primitives[prmIdx]->ObjBound;
edges[axis][i * 2] = BoundEdge(tmpBox.pMin[axis], prmIdx, true);
edges[axis][i * 2 + 1] = BoundEdge(tmpBox.pMax[axis], prmIdx, false);
}
sort(&edges[axis][0], &edges[axis][2 * np]);
int nBelow(0), nAbove(np);
for (int i = 0; i < 2 * np; ++i)
{
if (edges[axis][i].type == BoundEdge::END)
{
--nAbove;
}
Float edget = edges[axis][i].t;
//when t is in between the boundary
if (edget > bound.pMin[axis] && edget < bound.pMax[axis])
{
//Compute cost for split at ith edge
//get other two axes
int axis0 = (axis + 1) % 3, axis1 = (axis + 2) % 3;
Float belowSA = 2 * (bbDiag[axis0] * bbDiag[axis1] +
(edget - bound.pMin[axis]) *
(bbDiag[axis0] + bbDiag[axis1]));
Float aboveSA = 2 * (bbDiag[axis0] * bbDiag[axis1] +
(bound.pMax[axis] - edget) *
(bbDiag[axis0] + bbDiag[axis1]));
Float pBelow = belowSA * invTotalSA;
Float pAbove = aboveSA * invTotalSA;
Float eb = (nAbove == 0 || nBelow == 0) ? emptyBonus : 0;
Float cost = (1.0 - eb) * (pBelow * nBelow + pAbove * nAbove);
//cout << "cost at i:" << i << " is " << cost << endl;
if (cost < bestCost)
{
bestCost = cost;
bestAxis = axis;
bestOffest = i;// edges[axis][i].type ? i + 1 : i;//When end use next node
}
}
if (edges[axis][i].type == BoundEdge::START)
{
++nBelow;
}
}
if (retries < 2)//(bestAxis == -1 && retries < 2)//
{
++retries;
axis = (axis + 1) % 3;
goto RETRY_SPLIT;
}
//if no good split, init as leaf
if (bestAxis == -1)
{
node->initLeaf(prims);
return;
}
//recursively build subtree
vector<int> primsBelow;
vector<int> primsAbove;
//Store indices of below primitives
for (int i = 0; i < bestOffest; ++i)
{
if (edges[bestAxis][i].type == BoundEdge::START)
{
primsBelow.push_back(edges[bestAxis][i].primNum);
}
}
//Store indices of above primitives
for (int i = bestOffest + 1; i < np * 2; ++i)
{
if (edges[bestAxis][i].type == BoundEdge::END)
{
primsAbove.push_back(edges[bestAxis][i].primNum);
}
}
Float tsplit = edges[bestAxis][bestOffest].t;
node->initInterior(bestAxis, tsplit);
/*for (int i = 0; i < 2 * np; ++i)
{
cout << edges[bestAxis][i].primNum << ": "
<< edges[bestAxis][i].t << "; Start/End: " << edges[bestAxis][i].type << endl;
}
cout << "Split on axis " << axisChar[bestAxis] << " at " << tsplit << endl;
cout << "Best offset: " << bestOffest << endl;
cout << "Prims above: ";
for (int i = 0; i < primsAbove.size(); ++i)
{
cout << primsAbove[i] << " ";
}cout << endl;
cout << "Prims below: ";
for (int i = 0; i < primsBelow.size(); ++i)
{
cout << primsBelow[i] << " ";
}cout << endl;
cout << "////////////////////////" << endl;*/
Bounds3f belowBound = bound, aboveBound = bound;
belowBound.pMax[bestAxis] = aboveBound.pMin[bestAxis] = tsplit;
buildTree(node->belowNode, belowBound, primsBelow, depth - 1, edges);
buildTree(node->aboveNode, aboveBound, primsAbove, depth - 1, edges);
}
void KdTreeAccel::buildTree(int nodeNum,
const BBox &nodeBounds,
const vector<BBox> &allPrimBounds, int *primNums,
int nPrims, int depth, BoundEdge *edges[3],
int *prims0, int *prims1, int badRefines) {
Assert(nodeNum == nextFreeNode); // NOBOOK
// Get next free node from _nodes_ array
if (nextFreeNode == nAllocedNodes) {
int nAlloc = max(2 * nAllocedNodes, 512);
KdAccelNode *n = (KdAccelNode *)AllocAligned(nAlloc *
sizeof(KdAccelNode));
if (nAllocedNodes > 0) {
memcpy(n, nodes,
nAllocedNodes * sizeof(KdAccelNode));
FreeAligned(nodes);
}
nodes = n;
nAllocedNodes = nAlloc;
}
++nextFreeNode;
// Initialize leaf node if termination criteria met
if (nPrims <= maxPrims || depth == 0) {
nodes[nodeNum].initLeaf(primNums, nPrims,
mailboxPrims, arena);
return;
}
// Initialize interior node and continue recursion
// Choose split axis position for interior node
int bestAxis = -1, bestOffset = -1;
float bestCost = INFINITY;
float oldCost = isectCost * float(nPrims);
Vector d = nodeBounds.pMax - nodeBounds.pMin;
float totalSA = (2.f * (d.x*d.y + d.x*d.z + d.y*d.z));
float invTotalSA = 1.f / totalSA;
// Choose which axis to split along
int axis;
if (d.x > d.y && d.x > d.z) axis = 0;
else axis = (d.y > d.z) ? 1 : 2;
int retries = 0;
retrySplit:
// Initialize edges for _axis_
for (int i = 0; i < nPrims; ++i) {
int pn = primNums[i];
const BBox &bbox = allPrimBounds[pn];
edges[axis][2*i] =
BoundEdge(bbox.pMin[axis], pn, true);
edges[axis][2*i+1] =
BoundEdge(bbox.pMax[axis], pn, false);
}
sort(&edges[axis][0], &edges[axis][2*nPrims]);
// Compute cost of all splits for _axis_ to find best
int nBelow = 0, nAbove = nPrims;
for (int i = 0; i < 2*nPrims; ++i) {
if (edges[axis][i].type == BoundEdge::END) --nAbove;
float edget = edges[axis][i].t;
if (edget > nodeBounds.pMin[axis] &&
edget < nodeBounds.pMax[axis]) {
// Compute cost for split at _i_th edge
int otherAxis[3][2] = { {1,2}, {0,2}, {0,1} };
int otherAxis0 = otherAxis[axis][0];
int otherAxis1 = otherAxis[axis][1];
float belowSA = 2 * (d[otherAxis0] * d[otherAxis1] +
(edget - nodeBounds.pMin[axis]) *
(d[otherAxis0] + d[otherAxis1]));
float aboveSA = 2 * (d[otherAxis0] * d[otherAxis1] +
(nodeBounds.pMax[axis] - edget) *
(d[otherAxis0] + d[otherAxis1]));
float pBelow = belowSA * invTotalSA;
float pAbove = aboveSA * invTotalSA;
float eb = (nAbove == 0 || nBelow == 0) ? emptyBonus : 0.f;
float cost = traversalCost + isectCost * (1.f - eb) *
(pBelow * nBelow + pAbove * nAbove);
// Update best split if this is lowest cost so far
if (cost < bestCost) {
bestCost = cost;
bestAxis = axis;
bestOffset = i;
}
}
if (edges[axis][i].type == BoundEdge::START) ++nBelow;
}
Assert(nBelow == nPrims && nAbove == 0); // NOBOOK
// Create leaf if no good splits were found
if (bestAxis == -1 && retries < 2) {
++retries;
axis = (axis+1) % 3;
goto retrySplit;
}
if (bestCost > oldCost) ++badRefines;
if ((bestCost > 4.f * oldCost && nPrims < 16) ||
bestAxis == -1 || badRefines == 3) {
nodes[nodeNum].initLeaf(primNums, nPrims,
mailboxPrims, arena);
return;
}
// Classify primitives with respect to split
int n0 = 0, n1 = 0;
for (int i = 0; i < bestOffset; ++i)
if (edges[bestAxis][i].type == BoundEdge::START)
prims0[n0++] = edges[bestAxis][i].primNum;
for (int i = bestOffset+1; i < 2*nPrims; ++i)
if (edges[bestAxis][i].type == BoundEdge::END)
prims1[n1++] = edges[bestAxis][i].primNum;
// Recursively initialize children nodes
float tsplit = edges[bestAxis][bestOffset].t;
nodes[nodeNum].initInterior(bestAxis, tsplit);
BBox bounds0 = nodeBounds, bounds1 = nodeBounds;
bounds0.pMax[bestAxis] = bounds1.pMin[bestAxis] = tsplit;
buildTree(nodeNum+1, bounds0,
allPrimBounds, prims0, n0, depth-1, edges,
prims0, prims1 + nPrims, badRefines);
nodes[nodeNum].aboveChild = nextFreeNode;
buildTree(nodes[nodeNum].aboveChild, bounds1, allPrimBounds,
prims1, n1, depth-1, edges,
prims0, prims1 + nPrims, badRefines);
}
void KdTreeAccelerator::initializeInteriorNode(int node, const BBox& nodeBounds,
const std::vector<BBox>& primitiveBounds, uint* overlappingPrimitives,
int numOverlappingPrimitives, int depth, BoundEdge* edges[3],
uint* prims0, uint* prims1, int badRefines)
{
// Choose split axis and position for interior node
int bestAxis = -1;
int bestOffset = -1;
float bestCost = INFINITY;
float oldCost = m_intersectionCost * float(numOverlappingPrimitives);
float totalSA = nodeBounds.getSurfaceArea();
float invTotalSA = 1.f / totalSA;
glm::vec3 d = nodeBounds.getMax() - nodeBounds.getMin();
uint axis = nodeBounds.getAxisMaximumExtent();
int retries = 0;
// label for jump to choose another split
retrySplit:
// Initialize edges for choosen axis
for(int i = 0; i < numOverlappingPrimitives; ++i)
{
int primitive = overlappingPrimitives[i];
const BBox& bbox = primitiveBounds[primitive];
edges[axis][2 * i + 0] = BoundEdge(bbox.getMin()[axis], primitive, true);
edges[axis][2 * i + 1] = BoundEdge(bbox.getMax()[axis], primitive, false);
}
std::sort(&edges[axis][0], &edges[axis][2*numOverlappingPrimitives]);
// Compute cost of all splits for the choosen axis to find best
int nBelow = 0;
int nAbove = numOverlappingPrimitives;
for(int i = 0; i < 2 * numOverlappingPrimitives; ++i)
{
if(edges[axis][i].m_type == BoundEdge::END) --nAbove;
float split = edges[axis][i].m_t;
if(split > nodeBounds.getMin()[axis] && split < nodeBounds.getMax()[axis])
{
// compute cost of split at i-th edge
uint oA0 = (axis + 1) % 3; // first other axis
uint oA1 = (axis + 2) % 3; // second other axis
float belowSA = 2 * (d[oA0] * d[oA1] + (split - nodeBounds.getMin()[axis]) * (d[oA0] + d[oA1]));
float aboveSA = 2 * (d[oA0] * d[oA1] + (nodeBounds.getMax()[axis] - split) * (d[oA0] + d[oA1]));
float pBelow = belowSA * invTotalSA;
float pAbove = aboveSA * invTotalSA;
float bonus = (nAbove==0 || nBelow==0) ? m_emptyBonus : 0.f;
float cost = m_intersectionCost * (1.f - bonus) * (pBelow * nBelow + pAbove * nAbove)
+ m_traversalCost;
// update best split if this split has lower costs
if(cost < bestCost)
{
bestCost = cost;
bestAxis = axis;
bestOffset = i;
}
}
if(edges[axis][i].m_type == BoundEdge::START) ++nBelow;
}
// try another axis of no good slit was found
if(bestAxis == -1 && retries < 2)
{
++retries;
axis = (axis + 1) % 3;
goto retrySplit;
}
// Create lead if no good splits were found
if (bestCost > oldCost) ++badRefines;
if ((bestCost > 4.f * oldCost && numOverlappingPrimitives < 16) ||
bestAxis == -1 || badRefines == 3) {
m_nodes[node].initLeaf(overlappingPrimitives, numOverlappingPrimitives);
return;
}
// Classify overlapping primitives with respect to split
int n0 = 0, n1 = 0;
for (int i = 0; i < bestOffset; ++i) {
if (edges[bestAxis][i].m_type == BoundEdge::START) {
prims0[n0++] = edges[bestAxis][i].m_primitive;
}
}
for (int i = bestOffset+1; i < 2*numOverlappingPrimitives; ++i) {
if (edges[bestAxis][i].m_type == BoundEdge::END) {
prims1[n1++] = edges[bestAxis][i].m_primitive;
}
}
// Recursively initialize child nodes
float split = edges[bestAxis][bestOffset].m_t;
glm::vec3 min = nodeBounds.getMax();
glm::vec3 max = nodeBounds.getMin();
min[bestAxis] = split;
max[bestAxis] = split;
BBox bounds0 = nodeBounds;
BBox bounds1 = nodeBounds;
bounds0.setMax(max);
bounds1.setMin(min);
buildTreeRecursive(node + 1, bounds0, primitiveBounds, prims0, n0, depth - 1,
edges, prims0, prims1 + numOverlappingPrimitives, badRefines);
uint aboveChild = m_nextFreeNode;
m_nodes[node].initInterior(bestAxis, aboveChild, split);
buildTreeRecursive(aboveChild, bounds1, primitiveBounds, prims1, n1, depth - 1,
edges, prims0, prims1 + numOverlappingPrimitives, badRefines);
}