assimp/code/Common/SpatialSort.cpp

327 lines
14 KiB
C++

/*
---------------------------------------------------------------------------
Open Asset Import Library (assimp)
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*/
/** @file Implementation of the helper class to quickly find vertices close to a given position */
#include <assimp/SpatialSort.h>
#include <assimp/ai_assert.h>
using namespace Assimp;
// CHAR_BIT seems to be defined under MVSC, but not under GCC. Pray that the correct value is 8.
#ifndef CHAR_BIT
#define CHAR_BIT 8
#endif
const aiVector3D PlaneInit(0.8523f, 0.34321f, 0.5736f);
// ------------------------------------------------------------------------------------------------
// Constructs a spatially sorted representation from the given position array.
// define the reference plane. We choose some arbitrary vector away from all basic axises
// in the hope that no model spreads all its vertices along this plane.
SpatialSort::SpatialSort(const aiVector3D *pPositions, unsigned int pNumPositions, unsigned int pElementOffset) :
mPlaneNormal(PlaneInit) {
mPlaneNormal.Normalize();
Fill(pPositions, pNumPositions, pElementOffset);
}
// ------------------------------------------------------------------------------------------------
SpatialSort::SpatialSort() :
mPlaneNormal(PlaneInit) {
mPlaneNormal.Normalize();
}
// ------------------------------------------------------------------------------------------------
// Destructor
SpatialSort::~SpatialSort() {
// empty
}
// ------------------------------------------------------------------------------------------------
void SpatialSort::Fill(const aiVector3D *pPositions, unsigned int pNumPositions,
unsigned int pElementOffset,
bool pFinalize /*= true */) {
mPositions.clear();
Append(pPositions, pNumPositions, pElementOffset, pFinalize);
}
// ------------------------------------------------------------------------------------------------
void SpatialSort::Finalize() {
std::sort(mPositions.begin(), mPositions.end());
}
// ------------------------------------------------------------------------------------------------
void SpatialSort::Append(const aiVector3D *pPositions, unsigned int pNumPositions,
unsigned int pElementOffset,
bool pFinalize /*= true */) {
// store references to all given positions along with their distance to the reference plane
const size_t initial = mPositions.size();
mPositions.reserve(initial + (pFinalize ? pNumPositions : pNumPositions * 2));
for (unsigned int a = 0; a < pNumPositions; a++) {
const char *tempPointer = reinterpret_cast<const char *>(pPositions);
const aiVector3D *vec = reinterpret_cast<const aiVector3D *>(tempPointer + a * pElementOffset);
// store position by index and distance
ai_real distance = *vec * mPlaneNormal;
mPositions.push_back(Entry(static_cast<unsigned int>(a + initial), *vec, distance));
}
if (pFinalize) {
// now sort the array ascending by distance.
Finalize();
}
}
// ------------------------------------------------------------------------------------------------
// Returns an iterator for all positions close to the given position.
void SpatialSort::FindPositions(const aiVector3D &pPosition,
ai_real pRadius, std::vector<unsigned int> &poResults) const {
const ai_real dist = pPosition * mPlaneNormal;
const ai_real minDist = dist - pRadius, maxDist = dist + pRadius;
// clear the array
poResults.clear();
// quick check for positions outside the range
if (mPositions.size() == 0)
return;
if (maxDist < mPositions.front().mDistance)
return;
if (minDist > mPositions.back().mDistance)
return;
// do a binary search for the minimal distance to start the iteration there
unsigned int index = (unsigned int)mPositions.size() / 2;
unsigned int binaryStepSize = (unsigned int)mPositions.size() / 4;
while (binaryStepSize > 1) {
if (mPositions[index].mDistance < minDist)
index += binaryStepSize;
else
index -= binaryStepSize;
binaryStepSize /= 2;
}
// depending on the direction of the last step we need to single step a bit back or forth
// to find the actual beginning element of the range
while (index > 0 && mPositions[index].mDistance > minDist)
index--;
while (index < (mPositions.size() - 1) && mPositions[index].mDistance < minDist)
index++;
// Mow start iterating from there until the first position lays outside of the distance range.
// Add all positions inside the distance range within the given radius to the result aray
std::vector<Entry>::const_iterator it = mPositions.begin() + index;
const ai_real pSquared = pRadius * pRadius;
while (it->mDistance < maxDist) {
if ((it->mPosition - pPosition).SquareLength() < pSquared)
poResults.push_back(it->mIndex);
++it;
if (it == mPositions.end())
break;
}
// that's it
}
namespace {
// Binary, signed-integer representation of a single-precision floating-point value.
// IEEE 754 says: "If two floating-point numbers in the same format are ordered then they are
// ordered the same way when their bits are reinterpreted as sign-magnitude integers."
// This allows us to convert all floating-point numbers to signed integers of arbitrary size
// and then use them to work with ULPs (Units in the Last Place, for high-precision
// computations) or to compare them (integer comparisons are faster than floating-point
// comparisons on many platforms).
typedef ai_int BinFloat;
// --------------------------------------------------------------------------------------------
// Converts the bit pattern of a floating-point number to its signed integer representation.
BinFloat ToBinary(const ai_real &pValue) {
// If this assertion fails, signed int is not big enough to store a float on your platform.
// Please correct the declaration of BinFloat a few lines above - but do it in a portable,
// #ifdef'd manner!
static_assert(sizeof(BinFloat) >= sizeof(ai_real), "sizeof(BinFloat) >= sizeof(ai_real)");
#if defined(_MSC_VER)
// If this assertion fails, Visual C++ has finally moved to ILP64. This means that this
// code has just become legacy code! Find out the current value of _MSC_VER and modify
// the #if above so it evaluates false on the current and all upcoming VC versions (or
// on the current platform, if LP64 or LLP64 are still used on other platforms).
static_assert(sizeof(BinFloat) == sizeof(ai_real), "sizeof(BinFloat) == sizeof(ai_real)");
// This works best on Visual C++, but other compilers have their problems with it.
const BinFloat binValue = reinterpret_cast<BinFloat const &>(pValue);
//::memcpy(&binValue, &pValue, sizeof(pValue));
//return binValue;
#else
// On many compilers, reinterpreting a float address as an integer causes aliasing
// problems. This is an ugly but more or less safe way of doing it.
union {
ai_real asFloat;
BinFloat asBin;
} conversion;
conversion.asBin = 0; // zero empty space in case sizeof(BinFloat) > sizeof(float)
conversion.asFloat = pValue;
const BinFloat binValue = conversion.asBin;
#endif
// floating-point numbers are of sign-magnitude format, so find out what signed number
// representation we must convert negative values to.
// See http://en.wikipedia.org/wiki/Signed_number_representations.
const BinFloat mask = BinFloat(1) << (CHAR_BIT * sizeof(BinFloat) - 1);
// Two's complement?
const bool DefaultValue = ((-42 == (~42 + 1)) && (binValue & mask));
const bool OneComplement = ((-42 == ~42) && (binValue & mask));
if (DefaultValue)
return mask - binValue;
// One's complement?
else if (OneComplement)
return BinFloat(-0) - binValue;
// Sign-magnitude? -0 = 1000... binary
return binValue;
}
} // namespace
// ------------------------------------------------------------------------------------------------
// Fills an array with indices of all positions identical to the given position. In opposite to
// FindPositions(), not an epsilon is used but a (very low) tolerance of four floating-point units.
void SpatialSort::FindIdenticalPositions(const aiVector3D &pPosition, std::vector<unsigned int> &poResults) const {
// Epsilons have a huge disadvantage: they are of constant precision, while floating-point
// values are of log2 precision. If you apply e=0.01 to 100, the epsilon is rather small, but
// if you apply it to 0.001, it is enormous.
// The best way to overcome this is the unit in the last place (ULP). A precision of 2 ULPs
// tells us that a float does not differ more than 2 bits from the "real" value. ULPs are of
// logarithmic precision - around 1, they are 1*(2^24) and around 10000, they are 0.00125.
// For standard C math, we can assume a precision of 0.5 ULPs according to IEEE 754. The
// incoming vertex positions might have already been transformed, probably using rather
// inaccurate SSE instructions, so we assume a tolerance of 4 ULPs to safely identify
// identical vertex positions.
static const int toleranceInULPs = 4;
// An interesting point is that the inaccuracy grows linear with the number of operations:
// multiplying to numbers, each inaccurate to four ULPs, results in an inaccuracy of four ULPs
// plus 0.5 ULPs for the multiplication.
// To compute the distance to the plane, a dot product is needed - that is a multiplication and
// an addition on each number.
static const int distanceToleranceInULPs = toleranceInULPs + 1;
// The squared distance between two 3D vectors is computed the same way, but with an additional
// subtraction.
static const int distance3DToleranceInULPs = distanceToleranceInULPs + 1;
// Convert the plane distance to its signed integer representation so the ULPs tolerance can be
// applied. For some reason, VC won't optimize two calls of the bit pattern conversion.
const BinFloat minDistBinary = ToBinary(pPosition * mPlaneNormal) - distanceToleranceInULPs;
const BinFloat maxDistBinary = minDistBinary + 2 * distanceToleranceInULPs;
// clear the array in this strange fashion because a simple clear() would also deallocate
// the array which we want to avoid
poResults.resize(0);
// do a binary search for the minimal distance to start the iteration there
unsigned int index = (unsigned int)mPositions.size() / 2;
unsigned int binaryStepSize = (unsigned int)mPositions.size() / 4;
while (binaryStepSize > 1) {
// Ugly, but conditional jumps are faster with integers than with floats
if (minDistBinary > ToBinary(mPositions[index].mDistance))
index += binaryStepSize;
else
index -= binaryStepSize;
binaryStepSize /= 2;
}
// depending on the direction of the last step we need to single step a bit back or forth
// to find the actual beginning element of the range
while (index > 0 && minDistBinary < ToBinary(mPositions[index].mDistance))
index--;
while (index < (mPositions.size() - 1) && minDistBinary > ToBinary(mPositions[index].mDistance))
index++;
// Now start iterating from there until the first position lays outside of the distance range.
// Add all positions inside the distance range within the tolerance to the result array
std::vector<Entry>::const_iterator it = mPositions.begin() + index;
while (ToBinary(it->mDistance) < maxDistBinary) {
if (distance3DToleranceInULPs >= ToBinary((it->mPosition - pPosition).SquareLength()))
poResults.push_back(it->mIndex);
++it;
if (it == mPositions.end())
break;
}
// that's it
}
// ------------------------------------------------------------------------------------------------
unsigned int SpatialSort::GenerateMappingTable(std::vector<unsigned int> &fill, ai_real pRadius) const {
fill.resize(mPositions.size(), UINT_MAX);
ai_real dist, maxDist;
unsigned int t = 0;
const ai_real pSquared = pRadius * pRadius;
for (size_t i = 0; i < mPositions.size();) {
dist = mPositions[i].mPosition * mPlaneNormal;
maxDist = dist + pRadius;
fill[mPositions[i].mIndex] = t;
const aiVector3D &oldpos = mPositions[i].mPosition;
for (++i; i < fill.size() && mPositions[i].mDistance < maxDist && (mPositions[i].mPosition - oldpos).SquareLength() < pSquared; ++i) {
fill[mPositions[i].mIndex] = t;
}
++t;
}
#ifdef ASSIMP_BUILD_DEBUG
// debug invariant: mPositions[i].mIndex values must range from 0 to mPositions.size()-1
for (size_t i = 0; i < fill.size(); ++i) {
ai_assert(fill[i] < mPositions.size());
}
#endif
return t;
}