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octree.h
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/*
MIT License
Copyright (c) 2021 Attila Csikós
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/
#ifndef ORTHOTREE_GUARD
#define ORTHOTREE_GUARD
#include <algorithm>
#include <concepts>
#include <execution>
#include <functional>
#include <iterator>
#include <numeric>
#include <optional>
#include <stdexcept>
#include <type_traits>
#include <array>
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <span>
#include <tuple>
#include <unordered_map>
#include <vector>
#include <ratio>
#include <assert.h>
#include <math.h>
#ifndef autoc
#define autoc auto const
#define undef_autoc
#endif
#ifndef autoce
#define autoce auto constexpr
#define undef_autoce
#endif
#if defined(__clang__)
#define LOOPIVDEP
#elif defined(__INTEL_COMPILER)
#define LOOPIVDEP _Pragma("ivdep")
#elif defined(__GNUC__)
#define LOOPIVDEP _Pragma("GCC ivdep")
#elif defined(_MSC_VER)
#define LOOPIVDEP _Pragma("loop(ivdep)")
#else
#define LOOPIVDEP
#endif
namespace OrthoTree
{
#ifdef __clang__
#pragma clang diagnostic push
#pragma clang diagnostic ignored "-Wreturn-type"
#endif
#ifdef __GNUC__
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wreturn-type"
#endif
#ifdef _MSC_VER
#pragma warning(disable : 4715)
#endif
// Crash the program if out_of_range exception is raised
template<typename container_type>
inline auto& cont_at(container_type& container, typename std::remove_reference_t<container_type>::key_type const& id) noexcept
{
return container.at(id);
}
#ifdef _MSC_VER
#pragma warning(default : 4715)
#endif
#ifdef __clang__
#pragma clang diagnostic pop
#endif
#ifdef __GNUC__
#pragma GCC diagnostic pop
#endif
template<uint8_t e>
consteval std::size_t pow2_ce()
{
constexpr auto bitSize = sizeof(std::size_t) * CHAR_BIT;
static_assert(e >= 0 && e < bitSize);
return std::size_t{ 1 } << e;
}
constexpr int32_t pow2(int32_t e)
{
assert(e >= 0 && e < 31);
return int32_t(1) << e;
}
// Type of the dimension
using dim_t = int;
// Type of depth
using depth_t = int;
// Grid id
using GridID = uint32_t;
// Enum of relation with Planes
enum class PlaneRelation : char
{
Negative,
Hit,
Positive
};
// Adaptor concepts
template<class TAdapter, typename TVector, typename TBox, typename TRay, typename TPlane, typename TGeometry = double>
concept AdaptorBasicsConcept = requires(TVector& point, dim_t dimensionID, TGeometry value) {
{
TAdapter::SetPointC(point, dimensionID, value)
};
} && requires(TVector const& point, dim_t dimensionID) {
{
TAdapter::GetPointC(point, dimensionID)
} -> std::convertible_to<TGeometry>;
} && requires(TBox& box, dim_t dimensionID, TGeometry value) {
{
TAdapter::SetBoxMinC(box, dimensionID, value)
};
} && requires(TBox& box, dim_t dimensionID, TGeometry value) {
{
TAdapter::SetBoxMaxC(box, dimensionID, value)
};
} && requires(TBox const& box, dim_t dimensionID) {
{
TAdapter::GetBoxMinC(box, dimensionID)
} -> std::convertible_to<TGeometry>;
} && requires(TBox const& box, dim_t dimensionID) {
{
TAdapter::GetBoxMaxC(box, dimensionID)
} -> std::convertible_to<TGeometry>;
} && requires(TRay const& ray) {
{
TAdapter::GetRayOrigin(ray)
} -> std::convertible_to<TVector>;
} && requires(TRay const& ray) {
{
TAdapter::GetRayDirection(ray)
} -> std::convertible_to<TVector>;
} && requires(TPlane const& plane) {
{
TAdapter::GetPlaneNormal(plane)
} -> std::convertible_to<TVector>;
} && requires(TPlane const& plane) {
{
TAdapter::GetPlaneOrigoDistance(plane)
} -> std::convertible_to<TGeometry>;
};
template<class TAdapter, typename TVector, typename TBox, typename TRay, typename TPlane, typename TGeometry = double>
concept AdaptorConcept =
requires { AdaptorBasicsConcept<TAdapter, TVector, TBox, TRay, TPlane, TGeometry>; } && requires(TBox const& box, TVector const& point) {
{
TAdapter::DoesBoxContainPoint(box, point)
} -> std::convertible_to<bool>;
} && requires(TBox const& e1, TBox const& e2, bool e1_must_contain_e2) {
{
TAdapter::AreBoxesOverlapped(e1, e2, e1_must_contain_e2)
} -> std::convertible_to<bool>;
} && requires(TBox const& e1, TBox const& e2) {
{
TAdapter::AreBoxesOverlappedStrict(e1, e2)
} -> std::convertible_to<bool>;
} && requires(std::span<TVector const> const& points) {
{
TAdapter::GetBoxOfPoints(points)
} -> std::convertible_to<TBox>;
} && requires(std::span<TBox const> const& boxes) {
{
TAdapter::GetBoxOfBoxes(boxes)
} -> std::convertible_to<TBox>;
} && requires(TVector const& box, TGeometry distanceOfOrigo, TVector const& planeNormal, TGeometry tolerance) {
{
TAdapter::GetPointPlaneRelation(box, distanceOfOrigo, planeNormal, tolerance)
} -> std::convertible_to<PlaneRelation>;
} && requires(TBox const& box, TGeometry distanceOfOrigo, TVector const& planeNormal, TGeometry tolerance) {
{
TAdapter::GetBoxPlaneRelation(box, distanceOfOrigo, planeNormal, tolerance)
} -> std::convertible_to<PlaneRelation>;
} && requires(TBox const& box, TVector const& rayBasePoint, TVector const& rayHeading, TGeometry tolerance) {
{
TAdapter::IsRayHit(box, rayBasePoint, rayHeading, tolerance)
} -> std::convertible_to<std::optional<double>>;
} && requires(TBox const& box, TRay const& ray, TGeometry tolerance) {
{
TAdapter::IsRayHit(box, ray, tolerance)
} -> std::convertible_to<std::optional<double>>;
};
// Adaptors
template<dim_t DIMENSION_NO, typename TVector, typename TBox, typename TRay, typename TPlane, typename TGeometry = double>
struct AdaptorGeneralBasics
{
static constexpr TGeometry GetPointC(TVector const& point, dim_t dimensionID) noexcept { return point[dimensionID]; }
static constexpr void SetPointC(TVector& point, dim_t dimensionID, TGeometry value) noexcept { point[dimensionID] = value; }
static constexpr TGeometry GetBoxMinC(TBox const& box, dim_t dimensionID) noexcept { return box.Min[dimensionID]; }
static constexpr TGeometry GetBoxMaxC(TBox const& box, dim_t dimensionID) noexcept { return box.Max[dimensionID]; }
static constexpr void SetBoxMinC(TBox& box, dim_t dimensionID, TGeometry value) noexcept { box.Min[dimensionID] = value; }
static constexpr void SetBoxMaxC(TBox& box, dim_t dimensionID, TGeometry value) noexcept { box.Max[dimensionID] = value; }
static constexpr TVector const& GetRayDirection(TRay const& ray) noexcept { return ray.Direction; }
static constexpr TVector const& GetRayOrigin(TRay const& ray) noexcept { return ray.Origin; }
static constexpr TVector const& GetPlaneNormal(TPlane const& plane) noexcept { return plane.Normal; }
static constexpr TGeometry GetPlaneOrigoDistance(TPlane const& plane) noexcept { return plane.OrigoDistance; }
};
template<dim_t DIMENSION_NO, std::array CONTINUOUS_DIMENSIONS, class RATIO, typename TVector, typename TBox, typename TRay, typename TPlane, typename TGeometry, typename TAdaptorBasics>
//template<dim_t DIMENSION_NO, typename TVector, typename TBox, typename TRay, typename TPlane, typename TGeometry, typename TAdaptorBasics>
struct AdaptorGeneralBase : TAdaptorBasics
{
using Base = TAdaptorBasics;
static_assert(AdaptorBasicsConcept<Base, TVector, TBox, TRay, TPlane, TGeometry>);
// jump3
static constexpr TGeometry Size2(TVector const& point) noexcept
{
auto d2 = TGeometry{ 0 };
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
autoc d = Base::GetPointC(point, dimensionID);
d2 += d * d;
}
return d2;
}
static constexpr TGeometry Size(TVector const& point) noexcept { return std::sqrt(Size2(point)); }
static constexpr TGeometry pose_size(TVector const& pt) noexcept
{
auto d2 = TGeometry{ 0 };
auto angle_dis = TGeometry{ 0 };
for (dim_t iDim = 0; iDim < DIMENSION_NO; ++iDim)
{
if (!CONTINUOUS_DIMENSIONS[iDim])
{
autoc d = Base::GetPointC(pt, iDim);
d2 += d * d;
}
else
{
autoc angle = Base::GetPointC(pt, iDim);
angle_dis += angle * angle;
}
}
autoc translation_part = sqrt(d2);
autoc orientation_part = (180 * (sqrt(angle_dis) / 4.6389)) * (RATIO::num/RATIO::den);
return translation_part + orientation_part;
}
static constexpr TGeometry pose_distance(TVector const& ptL, TVector const& ptR) noexcept
{
autoc pt = TVector{Subtract(ptL, ptR)};
auto d2 = TGeometry{ 0 };
auto angle_dis = TGeometry{ 0 };
for (dim_t iDim = 0; iDim < DIMENSION_NO; ++iDim)
{
if (!CONTINUOUS_DIMENSIONS[iDim])
{
autoc d = Base::GetPointC(pt, iDim);
d2 += d * d;
}
else
{
autoc angle = std::min(abs(Base::GetPointC(ptL, iDim) -
Base::GetPointC(ptR, iDim)), (2 * std::numbers::pi) -
(abs(Base::GetPointC(ptL, iDim) - Base::GetPointC(ptR, iDim))));
angle_dis += angle * angle;
// Bloated expression for std::min(abs(a - b), (2 * std::numbers::pi) - (abs(a - b)))
// Where a, b are ptL[iDim], ptR[iDim]
}
}
autoc translation_part = sqrt(d2);
autoc orientation_part = (180 * (sqrt(angle_dis) / 4.6389)) * (RATIO::num/RATIO::den);
return (translation_part + orientation_part);
}
static constexpr TVector Add(TVector const& ptL, TVector const& ptR) noexcept
{
auto point = TVector{};
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
Base::SetPointC(point, dimensionID, Base::GetPointC(ptL, dimensionID) + Base::GetPointC(ptR, dimensionID));
return point;
}
static constexpr TVector Subtract(TVector const& ptL, TVector const& ptR) noexcept
{
auto point = TVector{};
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
Base::SetPointC(point, dimensionID, Base::GetPointC(ptL, dimensionID) - Base::GetPointC(ptR, dimensionID));
return point;
}
static constexpr TVector Multiply(TVector const& ptL, double rScalarR) noexcept
{
auto point = TVector{};
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
Base::SetPointC(point, dimensionID, TGeometry(Base::GetPointC(ptL, dimensionID) * rScalarR));
return point;
}
static constexpr TGeometry Dot(TVector const& ptL, TVector const& ptR) noexcept
{
auto value = TGeometry{};
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
value += Base::GetPointC(ptL, dimensionID) * Base::GetPointC(ptR, dimensionID);
return value;
}
static constexpr TGeometry Distance(TVector const& ptL, TVector const& ptR) noexcept { return Size(Subtract(ptL, ptR)); }
static constexpr TGeometry Distance2(TVector const& ptL, TVector const& ptR) noexcept { return Size2(Subtract(ptL, ptR)); }
static constexpr bool ArePointsEqual(TVector const& ptL, TVector const& ptR, TGeometry rAccuracy) noexcept
{
return Distance2(ptL, ptR) <= rAccuracy * rAccuracy;
}
static constexpr bool IsNormalizedVector(TVector const& normal) noexcept { return std::abs(Size2(normal) - 1.0) < 0.000001; }
static constexpr bool DoesBoxContainPoint(TBox const& box, TVector const& point, TGeometry tolerance = 0) noexcept
{
if (tolerance != 0.0)
{
assert(tolerance > 0);
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
if (!(Base::GetBoxMinC(box, dimensionID) - tolerance < Base::GetPointC(point, dimensionID) &&
Base::GetPointC(point, dimensionID) < Base::GetBoxMaxC(box, dimensionID) + tolerance))
return false;
}
else
{
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
if (!(Base::GetBoxMinC(box, dimensionID) <= Base::GetPointC(point, dimensionID) &&
Base::GetPointC(point, dimensionID) <= Base::GetBoxMaxC(box, dimensionID)))
return false;
}
return true;
}
static constexpr bool DoesBoxContainPointStrict(TBox const& box, TVector const& point) noexcept
{
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
if (!(Base::GetBoxMinC(box, dimensionID) < Base::GetPointC(point, dimensionID) &&
Base::GetPointC(point, dimensionID) < Base::GetBoxMaxC(box, dimensionID)))
return false;
return true;
}
enum class EBoxRelation
{
Overlapped = -1,
Adjecent = 0,
Separated = 1
};
static constexpr EBoxRelation GetBoxRelation(TBox const& e1, TBox const& e2) noexcept
{
enum EBoxRelationCandidate : uint8_t
{
OverlappedC = 0x1,
AdjecentC = 0x2,
SeparatedC = 0x4
};
uint8_t rel = 0;
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
if (Base::GetBoxMinC(e1, dimensionID) < Base::GetBoxMaxC(e2, dimensionID) && Base::GetBoxMaxC(e1, dimensionID) > Base::GetBoxMinC(e2, dimensionID))
rel |= EBoxRelationCandidate::OverlappedC;
else if (Base::GetBoxMinC(e1, dimensionID) == Base::GetBoxMaxC(e2, dimensionID) || Base::GetBoxMaxC(e1, dimensionID) == Base::GetBoxMinC(e2, dimensionID))
rel |= EBoxRelationCandidate::AdjecentC;
else if (Base::GetBoxMinC(e1, dimensionID) > Base::GetBoxMaxC(e2, dimensionID) || Base::GetBoxMaxC(e1, dimensionID) < Base::GetBoxMinC(e2, dimensionID))
return EBoxRelation::Separated;
}
return (rel & EBoxRelationCandidate::AdjecentC) == EBoxRelationCandidate::AdjecentC ? EBoxRelation::Adjecent : EBoxRelation::Overlapped;
}
static constexpr bool AreBoxesOverlappedStrict(TBox const& e1, TBox const& e2) noexcept
{
return GetBoxRelation(e1, e2) == EBoxRelation::Overlapped;
}
static constexpr bool AreBoxesOverlapped(TBox const& e1, TBox const& e2, bool e1_must_contain_e2 = true, bool fOverlapPtTouchAllowed = false) noexcept
{
if (e1_must_contain_e2)
{
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
if (Base::GetBoxMinC(e1, dimensionID) > Base::GetBoxMinC(e2, dimensionID) || Base::GetBoxMinC(e2, dimensionID) > Base::GetBoxMaxC(e1, dimensionID))
return false;
if (Base::GetBoxMinC(e1, dimensionID) > Base::GetBoxMaxC(e2, dimensionID) || Base::GetBoxMaxC(e2, dimensionID) > Base::GetBoxMaxC(e1, dimensionID))
return false;
}
return true;
}
else
{
autoc rel = GetBoxRelation(e1, e2);
if (fOverlapPtTouchAllowed)
return rel == EBoxRelation::Adjecent || rel == EBoxRelation::Overlapped;
else
return rel == EBoxRelation::Overlapped;
}
}
static inline TBox BoxInvertedInit() noexcept
{
auto ext = TBox{};
LOOPIVDEP
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
Base::SetBoxMinC(ext, dimensionID, std::numeric_limits<TGeometry>::max());
Base::SetBoxMaxC(ext, dimensionID, std::numeric_limits<TGeometry>::lowest());
}
return ext;
}
static TBox GetBoxOfPoints(std::span<TVector const> const& points) noexcept
{
auto ext = BoxInvertedInit();
for (autoc& point : points)
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
if (Base::GetBoxMinC(ext, dimensionID) > Base::GetPointC(point, dimensionID))
Base::SetBoxMinC(ext, dimensionID, Base::GetPointC(point, dimensionID));
if (Base::GetBoxMaxC(ext, dimensionID) < Base::GetPointC(point, dimensionID))
Base::SetBoxMaxC(ext, dimensionID, Base::GetPointC(point, dimensionID));
}
return ext;
}
static TBox GetBoxOfBoxes(std::span<TBox const> const& vExtent) noexcept
{
auto ext = BoxInvertedInit();
for (autoc& e : vExtent)
{
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
if (Base::GetBoxMinC(ext, dimensionID) > Base::GetBoxMinC(e, dimensionID))
Base::SetBoxMinC(ext, dimensionID, Base::GetBoxMinC(e, dimensionID));
if (Base::GetBoxMaxC(ext, dimensionID) < Base::GetBoxMaxC(e, dimensionID))
Base::SetBoxMaxC(ext, dimensionID, Base::GetBoxMaxC(e, dimensionID));
}
}
return ext;
}
static void MoveBox(TBox& box, TVector const& moveVector) noexcept
{
LOOPIVDEP
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
Base::SetBoxMinC(box, dimensionID, Base::GetBoxMinC(box, dimensionID) + Base::GetPointC(moveVector, dimensionID));
Base::SetBoxMaxC(box, dimensionID, Base::GetBoxMaxC(box, dimensionID) + Base::GetPointC(moveVector, dimensionID));
}
}
static constexpr std::optional<double> IsRayHit(TBox const& box, TVector const& rayBasePoint, TVector const& rayHeading, TGeometry tolerance) noexcept
{
if (DoesBoxContainPoint(box, rayBasePoint, tolerance))
return 0.0;
autoce inf = std::numeric_limits<double>::infinity();
auto minDistances = std::array<double, DIMENSION_NO>{};
auto maxDistances = std::array<double, DIMENSION_NO>{};
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
autoc hComp = Base::GetPointC(rayHeading, dimensionID);
if (hComp == 0)
{
if (tolerance != 0.0)
{
assert(tolerance > 0);
if (Base::GetBoxMaxC(box, dimensionID) + tolerance <= Base::GetPointC(rayBasePoint, dimensionID))
return std::nullopt;
if (Base::GetBoxMinC(box, dimensionID) - tolerance >= Base::GetPointC(rayBasePoint, dimensionID))
return std::nullopt;
}
else
{
if (Base::GetBoxMaxC(box, dimensionID) < Base::GetPointC(rayBasePoint, dimensionID))
return std::nullopt;
if (Base::GetBoxMinC(box, dimensionID) > Base::GetPointC(rayBasePoint, dimensionID))
return std::nullopt;
}
minDistances[dimensionID] = -inf;
maxDistances[dimensionID] = +inf;
continue;
}
minDistances[dimensionID] = ((hComp > 0.0 ? (Base::GetBoxMinC(box, dimensionID) - tolerance) : (Base::GetBoxMaxC(box, dimensionID) + tolerance)) -
Base::GetPointC(rayBasePoint, dimensionID)) /
hComp;
maxDistances[dimensionID] = ((hComp < 0.0 ? (Base::GetBoxMinC(box, dimensionID) - tolerance) : (Base::GetBoxMaxC(box, dimensionID) + tolerance)) -
Base::GetPointC(rayBasePoint, dimensionID)) /
hComp;
}
autoc rMin = *std::ranges::max_element(minDistances);
autoc rMax = *std::ranges::min_element(maxDistances);
if (rMin > rMax || rMax < 0.0)
return std::nullopt;
return rMin < 0 ? rMax : rMin;
}
static constexpr std::optional<double> IsRayHit(TBox const& box, TRay const& ray, TGeometry tolerance) noexcept
{
return IsRayHit(box, Base::GetRayOrigin(ray), Base::GetRayDirection(ray), tolerance);
}
// Get point-Hyperplane relation (Plane equation: dotProduct(planeNormal, point) = distanceOfOrigo)
static constexpr PlaneRelation GetPointPlaneRelation(TVector const& point, TGeometry distanceOfOrigo, TVector const& planeNormal, TGeometry tolerance) noexcept
{
assert(IsNormalizedVector(planeNormal));
autoc pointProjected = Dot(planeNormal, point);
if (pointProjected < distanceOfOrigo - tolerance)
return PlaneRelation::Negative;
if (pointProjected > distanceOfOrigo + tolerance)
return PlaneRelation::Positive;
return PlaneRelation::Hit;
}
// Get box-Hyperplane relation (Plane equation: dotProduct(planeNormal, point) = distanceOfOrigo)
static constexpr PlaneRelation GetBoxPlaneRelation(TBox const& box, TGeometry distanceOfOrigo, TVector const& planeNormal, TGeometry tolerance) noexcept
{
assert(IsNormalizedVector(planeNormal));
TVector center, radius;
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
autoc minComponent = Base::GetBoxMinC(box, dimensionID);
autoc maxComponent = Base::GetBoxMaxC(box, dimensionID);
autoc centerComponent = static_cast<TGeometry>((minComponent + maxComponent) * 0.5);
Base::SetPointC(center, dimensionID, centerComponent);
Base::SetPointC(radius, dimensionID, centerComponent - minComponent);
}
auto radiusProjected = double(tolerance);
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
radiusProjected += Base::GetPointC(radius, dimensionID) * std::abs(Base::GetPointC(planeNormal, dimensionID));
autoc centerProjected = Dot(planeNormal, center);
if (centerProjected + radiusProjected < distanceOfOrigo)
return PlaneRelation::Negative;
if (centerProjected - radiusProjected > distanceOfOrigo)
return PlaneRelation::Positive;
return PlaneRelation::Hit;
}
};
template<dim_t DIMENSION_NO, std::array CONTINUOUS_DIMENSIONS, class RATIO, typename TVector, typename TBox, typename TRay, typename TPlane, typename TGeometry = double>
using AdaptorGeneral =
AdaptorGeneralBase<DIMENSION_NO, CONTINUOUS_DIMENSIONS, RATIO, TVector, TBox, TRay, TPlane, TGeometry, AdaptorGeneralBasics<DIMENSION_NO, TVector, TBox, TRay, TPlane, TGeometry>>;
// Bitset helpers for higher dimensions
template<std::size_t N>
using bitset_arithmetic = std::bitset<N>;
template<std::size_t N>
bitset_arithmetic<N> operator+(bitset_arithmetic<N> const& lhs, bitset_arithmetic<N> const& rhs) noexcept
{
bool carry = false;
auto ans = bitset_arithmetic<N>();
for (std::size_t i = 0; i < N; ++i)
{
autoc sum = (lhs[i] ^ rhs[i]) ^ carry;
carry = (lhs[i] && rhs[i]) || (lhs[i] && carry) || (rhs[i] && carry);
ans[i] = sum;
}
assert(!carry); // unhandled overflow
return ans;
}
template<std::size_t N>
bitset_arithmetic<N> operator+(bitset_arithmetic<N> const& lhs, std::size_t rhs) noexcept
{
return lhs + bitset_arithmetic<N>(rhs);
}
template<std::size_t N>
bitset_arithmetic<N> operator-(bitset_arithmetic<N> const& lhs, bitset_arithmetic<N> const& rhs) noexcept
{
assert(lhs >= rhs);
auto ret = lhs;
bool borrow = false;
for (std::size_t i = 0; i < N; ++i)
{
if (borrow)
{
if (ret[i])
{
ret[i] = rhs[i];
borrow = rhs[i];
}
else
{
ret[i] = !rhs[i];
borrow = true;
}
}
else
{
if (ret[i])
{
ret[i] = !rhs[i];
borrow = false;
}
else
{
ret[i] = rhs[i];
borrow = rhs[i];
}
}
}
return ret;
}
template<std::size_t N>
bitset_arithmetic<N> operator-(bitset_arithmetic<N> const& lhs, std::size_t rhs) noexcept
{
return lhs - bitset_arithmetic<N>(rhs);
}
template<std::size_t N>
bitset_arithmetic<N> operator*(bitset_arithmetic<N> const& lhs, bitset_arithmetic<N> const& rhs) noexcept
{
auto ret = bitset_arithmetic<N>{};
if (lhs.count() < rhs.count())
{
for (std::size_t i = 0; i < N; ++i)
if (lhs[i])
ret = ret + (rhs << i);
}
else
{
for (std::size_t i = 0; i < N; ++i)
if (rhs[i])
ret = ret + (lhs << i);
}
return ret;
}
template<std::size_t N>
bitset_arithmetic<N> operator*(bitset_arithmetic<N> const& lhs, std::size_t rhs) noexcept
{
return lhs * bitset_arithmetic<N>(rhs);
}
template<std::size_t N>
bitset_arithmetic<N> operator*(std::size_t rhs, bitset_arithmetic<N> const& lhs) noexcept
{
return lhs * bitset_arithmetic<N>(rhs);
}
template<std::size_t N>
static std::tuple<bitset_arithmetic<N>, bitset_arithmetic<N>> gf2_div(bitset_arithmetic<N> const& dividend, bitset_arithmetic<N> divisor) noexcept
{
if (divisor.none())
{
assert(false);
return {};
}
if (dividend.none())
return {};
auto quotent = bitset_arithmetic<N>{ 0 };
if (dividend == divisor)
return { bitset_arithmetic<N>(1), quotent };
if (dividend < divisor)
return { quotent, dividend };
std::size_t sig_dividend = 0;
for (std::size_t i = 0, id = N - 1; i < N; ++i, --id)
if (dividend[id])
{
sig_dividend = id;
break;
}
std::size_t sig_divisor = 0;
for (std::size_t i = 0, id = N - 1; i < N; ++i, --id)
if (divisor[id])
{
sig_divisor = id;
break;
}
std::size_t nAlignment = (sig_dividend - sig_divisor);
divisor <<= nAlignment;
nAlignment += 1;
auto remainder = dividend;
while (nAlignment--)
{
if (divisor <= remainder)
{
quotent[nAlignment] = true;
remainder = remainder - divisor;
}
divisor >>= 1;
}
return { quotent, remainder };
}
template<std::size_t N>
bitset_arithmetic<N> operator/(bitset_arithmetic<N> const& dividend, bitset_arithmetic<N> const& divisor) noexcept
{
return std::get<0>(gf2_div(dividend, divisor));
}
template<std::size_t N>
auto operator<=>(bitset_arithmetic<N> const& lhs, bitset_arithmetic<N> const& rhs) noexcept
{
using R = std::strong_ordering;
for (std::size_t i = 0, id = N - 1; i < N; ++i, --id)
if (lhs[id] ^ rhs[id])
return lhs[id] ? R::greater : R::less;
return R::equal;
}
struct bitset_arithmetic_compare final
{
template<std::size_t N>
bool operator()(bitset_arithmetic<N> const& lhs, bitset_arithmetic<N> const& rhs) const noexcept
{
return lhs < rhs;
}
};
// NTrees
// NTreeLinear: Non-owning Base container which spatially organize data ids in N dimension space into a hash-table by Morton Z order.
template<
dim_t DIMENSION_NO,
typename TVector_,
typename TBox_,
typename TRay_,
typename TPlane_,
typename TGeometry_ = double,
typename TAdapter = AdaptorGeneral<DIMENSION_NO, {0,0}, std::ratio<1,1>, TVector_, TBox_, TRay_, TPlane_, TGeometry_>>
class OrthoTreeBase
{
public:
struct UpdateID
{
enum : std::size_t
{
ERASE = std::numeric_limits<std::size_t>::max()
};
};
static autoce IS_LINEAR_TREE = DIMENSION_NO < 15;
// Max value: 2 ^ DIMENSION_NO
using ChildID = std::conditional < DIMENSION_NO<4, uint32_t, uint64_t>::type;
// Max value: 2 ^ nDepth ^ DIMENSION_NO * 2 (signal bit)
using LinearMortonGridID = ChildID;
using NonLinearMortonGridID = bitset_arithmetic<DIMENSION_NO * 4 + 1>;
using MortonGridID = typename std::conditional<IS_LINEAR_TREE, LinearMortonGridID, NonLinearMortonGridID>::type;
using MortonNodeID = MortonGridID; // same as the MortonGridID, but depth is signed by a sentinel bit.
using MortonGridIDCR = typename std::conditional<IS_LINEAR_TREE, MortonNodeID const, MortonNodeID const&>::type;
using MortonNodeIDCR = MortonGridIDCR;
using TGeometry = TGeometry_;
using TVector = TVector_;
using TBox = TBox_;
using TRay = TRay_;
using TPlane = TPlane_;
using AD = TAdapter;
static_assert(AdaptorConcept<AD, TVector, TBox, TRay, TPlane, TGeometry>);
static_assert(0 < DIMENSION_NO && DIMENSION_NO < 64);
protected:
// Max number of children
static autoce CHILD_NO = pow2_ce<DIMENSION_NO>();
// Type system determined maximal depth.
static autoce MAX_THEORETICAL_DEPTH = depth_t((CHAR_BIT * sizeof(MortonNodeID) - 1 /*sentinal bit*/) / DIMENSION_NO);
public:
class Node
{
private:
std::vector<MortonNodeID> m_children;
public: // Public members
std::vector<std::size_t> Entities = {};
TBox Box = {};
public:
constexpr void AddChild(MortonNodeIDCR childKey) noexcept { m_children.emplace_back(childKey); }
constexpr void AddChildInOrder(MortonNodeIDCR childKey) noexcept
{
auto it = std::end(m_children);
if constexpr (IS_LINEAR_TREE)
it = std::lower_bound(m_children.begin(), m_children.end(), childKey);
else
it = std::lower_bound(m_children.begin(), m_children.end(), childKey, bitset_arithmetic_compare{});
if (it != m_children.end() && *it == childKey)
return;
m_children.insert(it, childKey);
}
constexpr bool HasChild(MortonNodeIDCR childKey) const noexcept
{
if constexpr (IS_LINEAR_TREE)
return std::ranges::binary_search(m_children, childKey);
else
return std::ranges::binary_search(m_children, childKey, bitset_arithmetic_compare{});
}
constexpr bool IsChildNodeEnabled(ChildID childID) const noexcept
{
autoc childMortonID = MortonNodeID(childID);
return std::find_if(m_children.begin(), m_children.end(), [childMortonID](autoc& childKey) {
return (childKey & childMortonID) == childMortonID;
});
}
constexpr void RemoveChild(MortonNodeIDCR childKey) noexcept
{
auto it = std::end(m_children);
if constexpr (IS_LINEAR_TREE)
it = std::lower_bound(m_children.begin(), m_children.end(), childKey);
else
it = std::lower_bound(m_children.begin(), m_children.end(), childKey, bitset_arithmetic_compare{});
if (it == std::end(m_children))
return;
m_children.erase(it);
}
constexpr bool IsAnyChildExist() const noexcept { return !m_children.empty(); }
constexpr std::vector<MortonNodeID> const& GetChildren() const noexcept { return m_children; }
};
protected: // Aid struct to partitioning and distance ordering
struct ItemDistance
{
TGeometry Distance;
auto operator<=>(ItemDistance const& rhs) const = default;
};
struct EntityDistance : ItemDistance
{
std::size_t EntityID;
auto operator<=>(EntityDistance const& rhs) const = default;
};
struct BoxDistance : ItemDistance
{
MortonNodeID NodeKey;
Node const& NodeReference;
};
template<typename T>
using DimArray = std::array<T, DIMENSION_NO>;
template<typename TData>
using LinearUnderlyingContainer = std::unordered_map<MortonNodeID, TData>;
template<typename TData>
using NonLinearUnderlyingContainer = std::map<MortonNodeID, TData, bitset_arithmetic_compare>;
template<typename TData>
using UnderlyingContainer = typename std::conditional<IS_LINEAR_TREE, LinearUnderlyingContainer<TData>, NonLinearUnderlyingContainer<TData>>::type;
protected: // Member variables
UnderlyingContainer<Node> m_nodes;
TBox m_boxSpace = {};
depth_t m_maxDepthNo = {};
GridID m_maxRasterResolution = {};
GridID m_maxRasterID = {};
std::size_t m_maxElementNo = 11;
double m_volumeOfOverallSpace = {};
DimArray<double> m_rasterizerFactors;
DimArray<double> m_sizeInDimensions;
DimArray<double> m_minInDimensions;
protected: // Aid functions
static inline ChildID castMortonIdToChildId(NonLinearMortonGridID const& bs) noexcept
{
assert(bs <= NonLinearMortonGridID(std::numeric_limits<std::size_t>::max()));
return bs.to_ullong();
}
static constexpr ChildID castMortonIdToChildId(LinearMortonGridID morton) noexcept { return morton; }
protected: // Grid functions
struct RasterInfo
{
DimArray<double> rasterizerFactors;
DimArray<double> sizeInDimensions;
};
static constexpr RasterInfo getGridRasterizer(TBox const& box, GridID subDivisionNo) noexcept
{
auto ri = RasterInfo{};
autoc subDivisionNoFactor = static_cast<double>(subDivisionNo);
for (dim_t dimensionID = 0; dimensionID < DIMENSION_NO; ++dimensionID)
{
ri.sizeInDimensions[dimensionID] = static_cast<double>(AD::GetBoxMaxC(box, dimensionID) - AD::GetBoxMinC(box, dimensionID));
ri.rasterizerFactors[dimensionID] = ri.sizeInDimensions[dimensionID] == 0 ? 1.0 : (subDivisionNoFactor / ri.sizeInDimensions[dimensionID]);
}
return ri;
}
constexpr DimArray<GridID> getGridIdPoint(TVector const& point) const noexcept
{