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octree.hpp
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octree.hpp
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#pragma once
#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <cstdint>
#include <limits>
#include <vector>
#ifdef Z_ORDER_OCTREE_DEBUG
#include <cstdio>
#define log_debug(...) do { std::printf(__VA_ARGS__); std::printf("\n"); } while (0)
#else
#define log_debug(...)
#endif
template <class Element, class Float = float, class ZIndex = std::uint64_t>
class ZOrderOctree {
public:
// Note: "should" also work with 1 more bit but something is broken
static constexpr size_t MAX_ROOT_LEVEL = std::numeric_limits<ZIndex>::digits / 3 - 1;
using Vector3 = std::array<Float, 3>;
struct Parameters {
Vector3 origin = { 0, 0, 0 };
Float leafSize = 1.0;
bool stableSort = false;
bool sortKnnResponse = false;
size_t rootLevel = MAX_ROOT_LEVEL;
};
ZOrderOctree(const Parameters ¶ms) :
params(params)
{
assert(params.rootLevel <= MAX_ROOT_LEVEL);
}
void clear() {
zindices.clear();
elements.clear();
}
void addData(const Element* elementsBegin, size_t nElements) {
// log_debug("minCorner %g,%g,%g", minCorner[0], minCorner[1], minCorner[2]);
tmp.clear();
tmp.reserve(nElements + zindices.size());
assert(zindices.size() == elements.size());
// add existing data (note: it could be faster to do a custom merge-sort)
for (size_t i = 0; i < zindices.size(); ++i) {
tmp.zindices.push_back(zindices.at(i));
tmp.elements.push_back(elements.at(i));
tmp.order.push_back(tmp.order.size());
}
zindices.clear();
elements.clear();
for (const auto *itr = elementsBegin; itr != (elementsBegin + nElements); ++itr) {
tmp.elements.push_back(&*itr);
tmp.zindices.push_back(getZIndex(*itr));
tmp.order.push_back(tmp.order.size());
}
assert(tmp.order.size() == tmp.zindices.size());
const auto cmp = [this](size_t a, size_t b) -> int {
return tmp.zindices.at(a) < tmp.zindices.at(b);
};
if (params.stableSort) {
std::stable_sort(tmp.order.begin(), tmp.order.end(), cmp);
} else {
std::sort(tmp.order.begin(), tmp.order.end(), cmp);
}
elements.reserve(tmp.elements.size());
zindices.reserve(tmp.zindices.size());
for (size_t idx : tmp.order) {
const auto zidx = tmp.zindices.at(idx);
if (zidx == INVALID_COORD) break;
else assert(zidx < INVALID_COORD);
// log_debug("order: %zu (zindex %lx)", idx, zidx);
zindices.push_back(tmp.zindices.at(idx));
elements.push_back(tmp.elements.at(idx));
}
}
template <class Predicate> void removeData(const Predicate &func) {
auto zIdxIn = zindices.begin();
auto elemIn = elements.begin();
auto zIdxOut = zIdxIn;
auto elemOut = elemIn;
while (elemIn != elements.end()) {
if (!func(**elemIn)) {
*elemOut++ = *elemIn;
*zIdxOut++ = *zIdxIn;
}
elemIn++;
zIdxIn++;
}
const size_t nLeft = elemOut - elements.begin();
elements.resize(nLeft);
zindices.resize(nLeft);
}
void clearWorkspace() {
tmp = {}; // should deallocate
}
class ElementRange {
public:
using Iterator = const Element * const *;
Iterator begin() const { return b; }
Iterator end() const { return e; }
size_t size() const {
return e - b;
}
ElementRange(Iterator b, Iterator e) : b(b), e(e) {}
private:
Iterator b = nullptr, e = nullptr;
};
class NodeRange;
struct Node {
Node(const ZOrderOctree &t, ZIndex zidx, int level) :
tree(&t),
level(level),
zindex(zidx)
{
ZIndex mask = levelMask(level);
zindex = zindex & mask;
elementsBegin = tree->findRange(zindex, mask, true);
elementsEnd = tree->findRange(zindex, mask, false);
// log_debug("node %lx at level %d, elements %zu to %zu", zindex, level, elementsBegin, elementsEnd);
}
// "end node" marker
Node() :
tree(nullptr),
level(-1),
zindex(0),
elementsBegin(0),
elementsEnd(0)
{}
int getLevel() const {
return level;
}
bool isLeaf() const {
return level == 0 || isEndNode() || empty();
}
Node firstChild() const {
assert(!isLeaf());
return Node(*tree, tree->zindices.at(elementsBegin), level - 1);
}
bool isLastAtThisLevel() const {
if (isEndNode()) return true;
return elementsEnd == tree->zindices.size();
}
bool isLastSibling() const {
if (isLastAtThisLevel()) return true;
ZIndex parentMask = levelMask(level + 1);
return (zindex & parentMask) != (tree->zindices.at(elementsEnd) & parentMask);
}
Node nextAtThisLevel() const {
assert(!isLastAtThisLevel());
return Node(*tree, tree->zindices.at(elementsEnd), level);
}
Node nextSibling() const {
assert(!isLastSibling());
return nextAtThisLevel();
}
bool isEndNode() const {
return tree == nullptr;
}
bool operator==(const Node &other) const {
if (isEndNode()) return other.isEndNode();
return tree == other.tree &&
level == other.level &&
zindex == other.zindex;
}
NodeRange children() const {
assert(!isLeaf());
Node child = firstChild();
assert(!child.empty());
return NodeRange(child, true);
}
ElementRange elements() const {
assert(!isEndNode());
return tree->buildRange(elementsBegin, elementsEnd);
}
bool empty() const {
return elementsEnd == elementsBegin;
}
Vector3 minCorner() const {
return tree->zIndexToPoint(zindex, level, 0);
}
Vector3 maxCorner() const {
return tree->zIndexToPoint(zindex, level, 1);
}
Vector3 center() const {
return tree->zIndexToPoint(zindex, level, 0.5);
}
Float sideLength() const {
return tree->params.leafSize * (1 << level);
}
bool isRoot() const {
return level == tree->params.rootLevel;
}
// internal, do not use directly
const ZOrderOctree *tree;
int level;
ZIndex zindex;
size_t elementsBegin, elementsEnd;
};
class LevelIterator {
public:
LevelIterator(const Node &node, bool siblingsOnly) : node(node), siblings(siblingsOnly) {}
const Node &operator*() const {
assert(!node.isEndNode());
return node;
}
LevelIterator &operator++() { // prefix OP, ++itr
if ((siblings && node.isLastSibling()) ||
(!siblings && node.isLastAtThisLevel())) {
node = Node();
} else {
node = node.nextAtThisLevel();
}
return *this;
}
bool operator==(const LevelIterator &other) const {
return node == other.node && siblings == other.siblings;
}
bool operator!=(const LevelIterator &other) const {
return !(*this == other);
}
private:
Node node;
const bool siblings;
};
class NodeRange {
private:
LevelIterator b, e;
public:
NodeRange(Node beginNode, bool siblingsOnly) :
b(beginNode, siblingsOnly),
e(Node(), siblingsOnly)
{}
LevelIterator begin() const { return b; }
LevelIterator end() const { return e; }
bool empty() const { return b == e; }
};
template<class Point> Node lookup(const Point &point, int level) const {
assert(level >= 0 && level < int(params.rootLevel));
ZIndex zindex = getZIndex(point);
if (zindex == INVALID_COORD) return Node();
return Node(*this, zindex, level);
}
Node root() const {
return Node(*this, zindices.empty() ? 0 : *zindices.begin(), params.rootLevel);
}
NodeRange nodesAtLevel(int level) const {
assert(level >= 0 && level < int(params.rootLevel));
return NodeRange(Node(*this, zindices.empty() ? 0 : *zindices.begin(), level), false);
}
class RadiusSearchIterator {
public:
const Element *operator*() const {
assert(currentNodeIdx < nodeCount);
return nodes[currentNodeIdx].tree->elements.at(currentElementIdx);
}
RadiusSearchIterator &operator++() { // prefix OP, ++itr
assert(currentNodeIdx < nodeCount && currentNodeIdx < 8);
findNext(false);
return *this;
}
// note: do not compare these from two unrelated ranges
bool operator==(const RadiusSearchIterator &other) const {
return currentNodeIdx == other.currentNodeIdx &&
currentElementIdx == other.currentElementIdx;
}
bool operator!=(const RadiusSearchIterator &other) const {
return !(*this == other);
}
RadiusSearchIterator(
size_t nodeCount,
bool end = true,
Float searchRadius = 0,
const Vector3 *searchCenter = nullptr,
Node *nodesPtr = nullptr)
:
currentNodeIdx(nodeCount),
currentElementIdx(0),
nodeCount(nodeCount)
{
assert(nodeCount <= 8);
if (!end) {
searchRadiusSquared = searchRadius*searchRadius;
this->searchCenter = *searchCenter;
for (size_t i = 0; i < nodeCount; ++i) nodes[i] = nodesPtr[i];
currentNodeIdx = 0;
if (nodeCount > 0) {
currentElementIdx = nodes[currentNodeIdx].elementsBegin;
findNext(true);
}
}
// log_debug("iterator %zu/%zu, %zu", currentNodeIdx, nodeCount, currentElementIdx);
}
size_t getNodeCount() const {
return nodeCount;
}
bool containsAllElements() const {
if (nodeCount == 0) return false;
assert(nodes[0].tree);
const auto &tree = *nodes[0].tree;
if (nodeCount == 1) return nodes[0].level == int(tree.params.rootLevel);
if (nodeCount == 8) return nodes[0].level == int(tree.params.rootLevel) - 1;
return false;
}
private:
void findNext(bool checkFirst) {
if (currentNodeIdx >= nodeCount) return; // alerady at end
bool checkCurrent = checkFirst;
while (true) {
//log_debug("search %zu/%zu, %zu in %zu - %zu %s", currentNodeIdx, nodeCount, currentElementIdx,
// nodes[currentNodeIdx].elementsBegin, nodes[currentNodeIdx].elementsEnd, checkCurrent ? " cur" : "");
if (checkCurrent && currentElementIdx < nodes[currentNodeIdx].elementsEnd) {
const Element &el = *nodes[currentNodeIdx].tree->elements.at(currentElementIdx);
Float r2 = 0;
for (int c = 0; c < 3; ++c) {
Float d = el[c] - searchCenter[c];
r2 += d*d;
}
// log_debug("%g/%g (%g, %g, %g)", std::sqrt(r2), std::sqrt(searchRadiusSquared), el[0], el[1], el[2]);
if (r2 < searchRadiusSquared) break;
}
checkCurrent = true;
if (++currentElementIdx >= nodes[currentNodeIdx].elementsEnd) {
if (++currentNodeIdx < nodeCount) {
currentElementIdx = nodes[currentNodeIdx].elementsBegin;
} else {
// end node
currentElementIdx = 0;
break;
}
}
}
}
size_t currentNodeIdx, currentElementIdx;
size_t nodeCount;
Node nodes[8];
Vector3 searchCenter;
Float searchRadiusSquared;
};
class RadiusSearchRange {
private:
RadiusSearchIterator b, e;
public:
RadiusSearchRange(RadiusSearchIterator begin) :
b(begin), e(begin.getNodeCount())
{}
RadiusSearchIterator begin() const { return b; }
RadiusSearchIterator end() const { return e; }
bool empty() const { return b == e; }
bool containsAllElements() const { return b.containsAllElements(); }
};
template<class Point> RadiusSearchRange searchWithRadius(const Point &point, Float radius) const {
size_t searchLevel = 0;
const Vector3 searchCenter = { point[0], point[1], point[2] };
while (nodeCountWithinBox(searchCenter, radius, searchLevel) > 8) {
assert(searchLevel < params.rootLevel);
searchLevel++;
}
Node nodes[8];
size_t nodeCount = 0;
for (int dx = -1; dx <= 1; dx += 2) {
for (int dy = -1; dy <= 1; dy += 2) {
for (int dz = -1; dz <= 1; dz += 2) {
Vector3 corner = searchCenter;
corner[0] += dx * radius;
corner[1] += dy * radius;
corner[2] += dz * radius;
ZIndex zindex = getZIndex(corner, true) & levelMask(searchLevel);
// log_debug("corner (%g, %g, %g) zindex %lx", corner[0], corner[1], corner[2], zindex);
for (size_t j = 0; j < nodeCount; ++j) {
if (zindex == nodes[j].zindex) {
// log_debug("equal to corner %zu", j);
goto NEXT_CORNER;
}
}
assert(nodeCount < 8);
nodes[nodeCount++] = Node(*this, zindex, searchLevel);
NEXT_CORNER: (void)0;
}
}
}
// assert(nodeCount == nodeCountWithinBox(searchCenter, radius, searchLevel));
return RadiusSearchRange(RadiusSearchIterator(nodeCount, false, radius, &searchCenter, nodes));
}
// note: not thread-safe & modifies workspace
template <class Point> void kNearestNeighbors(const Point ¢er, size_t k, std::vector<const Element *> &result, Float maxRadius = -1) {
result.clear();
if (k == 0) return;
auto &heap = tmp.knnHeap;
heap.clear();
Float searchRadius = params.leafSize * 0.5;
while (true) {
if (maxRadius > 0 && searchRadius > maxRadius) searchRadius = maxRadius;
HeapElement heapEl;
auto search = searchWithRadius(center, searchRadius);
for (const Element *el : search) {
heapEl.r2 = 0;
for (int c = 0; c < 3; ++c) {
Float d = (*el)[c] - center[c];
heapEl.r2 += d*d;
}
heapEl.element = el;
if (heap.size() < k) {
heap.push_back(heapEl);
if (heap.size() == k) std::make_heap(heap.begin(), heap.end());
} else if (!(heap.front() < heapEl)) {
std::pop_heap(heap.begin(), heap.end());
heap.back() = heapEl;
std::push_heap(heap.begin(), heap.end());
}
}
// log_debug("radius %g, heap size %zu", searchRadius, heap.size());
if (search.containsAllElements() || heap.size() == k || searchRadius == maxRadius) break;
searchRadius *= 2;
}
if (params.sortKnnResponse) {
if (params.stableSort) std::stable_sort(heap.begin(), heap.end());
else std::sort(heap.begin(), heap.end());
}
result.reserve(heap.size());
for (const auto &e : heap) result.push_back(e.element);
}
private:
struct HeapElement {
const Element *element;
Float r2;
bool operator<(const HeapElement &other) const {
return r2 < other.r2;
}
};
struct Workspace {
std::vector<size_t> order;
std::vector<ZIndex> zindices;
std::vector<const Element*> elements;
std::vector<HeapElement> knnHeap;
void clear() {
order.clear();
zindices.clear();
elements.clear();
}
void reserve(size_t n) {
order.reserve(n);
zindices.reserve(n);
elements.reserve(n);
}
} tmp;
ElementRange buildRange(size_t elementsBegin, size_t elementsEnd) const {
return ElementRange(
elements.data() + elementsBegin,
elements.data() + elementsEnd);
}
static ZIndex levelMask(int level) {
ZIndex mask = 0;
for (int l = 0; l < level; ++l) {
mask = (mask << 3l) | 0x7l;
}
return std::numeric_limits<ZIndex>::max() ^ mask;
}
static Vector3 saxpy(Float alpha, const Vector3 &x, const Vector3 &y) {
Vector3 r;
for (size_t i = 0; i < 3; ++i) r[i] = alpha * x[i] + y[i];
return r;
}
static constexpr ZIndex INVALID_COORD = std::numeric_limits<ZIndex>::max();
size_t findRange(ZIndex target, ZIndex mask, bool findBegin) const {
// binary search
size_t begin = 0;
size_t end = zindices.size();
while (end > begin) {
size_t mid = begin + (end - begin) / 2;
ZIndex cur = zindices[mid] & mask;
// log_debug("findRange [%zu, %zu, %zu] -> [?, %lx, ?]", begin, mid, end, cur);
if ((findBegin && (cur < target)) || (!findBegin && (cur <= target))) {
if (begin == mid) mid++;
begin = mid;
} else {
end = mid;
}
}
return end;
}
inline int maxCoord() const {
return 1 << params.rootLevel;
}
inline int halfMaxCoord() const {
return (1 << params.rootLevel) / 2;
}
inline int floatToCoord(Float c, int dim, bool capped) const {
const int max = maxCoord();
Float rel = (c - params.origin[dim]) / params.leafSize;
const Float maxF = max; // avoid integer overflow issues
rel = std::min(rel, maxF);
rel = std::max(rel, -maxF);
int coord = std::floor(rel) + halfMaxCoord();
if (coord < 0) {
if (capped) return 0;
return -1;
} else if (coord >= max) {
if (capped) return max - 1;
return -1;
}
return coord;
}
Vector3 zIndexToPoint(ZIndex zindex, int level, Float cellOffset) const {
int coords[3] = { 0, 0, 0 };
for (int l = params.rootLevel; l >= level; --l) {
for (int d = 0; d < 3; ++d) {
int bit = (zindex >> (3*l + d)) & 0x1;
if (bit) coords[d] += 1 << l;
}
}
Vector3 v;
const Float offs = params.leafSize * (1 << level) * cellOffset;
for (int d = 0; d < 3; ++d) {
v[d] = (coords[d] - halfMaxCoord()) * params.leafSize + params.origin[d] + offs;
}
return v;
}
template <class Point> ZIndex getZIndex(const Point &xyz, bool capped = false) const {
ZIndex zindex = 0;
for (int d = 0; d < 3; ++d) {
int coord = floatToCoord(xyz[d], d, capped);
if (coord < 0) return INVALID_COORD;
zindex |= interleaveBits(coord) << d;
}
// log_debug("getZIndex -> %lx", zindex);
return zindex;
}
size_t nodeCountWithinBox(const Vector3 ¢er, Float radius, int level) const {
size_t count = 1;
for (int d = 0; d < 3; ++d) {
int range = 1;
for (int sign = -1; sign <= 1; sign += 2) {
int coord = floatToCoord(center[d] + sign*radius, d, true);
assert(coord >= 0);
coord = coord >> level;
range += coord * sign;
}
assert(range >= 0);
count *= range;
}
// log_debug("nodeCountWithinBox %g, %d -> %zu", radius, level, count);
return count;
}
static ZIndex interleaveBits(ZIndex coord) {
auto x = static_cast<std::uint64_t>(coord);
// https://stackoverflow.com/a/18528775/1426569
x &= 0x1fffff;
x = (x | x << 32) & 0x1f00000000ffffll;
x = (x | x << 16) & 0x1f0000ff0000ffll;
x = (x | x << 8) & 0x100f00f00f00f00fll;
x = (x | x << 4) & 0x10c30c30c30c30c3ll;
x = (x | x << 2) & 0x1249249249249249ll;
return static_cast<ZIndex>(x);
}
const Parameters params;
std::vector<size_t> zindices;
std::vector<const Element*> elements;
};