assimp/code/SpatialSort.cpp

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/** @file Implementation of the helper class to quickly find vertices close to a given position */

#include "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

// ------------------------------------------------------------------------------------------------
// Constructs a spatially sorted representation from the given position array.
SpatialSort::SpatialSort( const aiVector3D* pPositions, unsigned int pNumPositions,
    unsigned int pElementOffset)

    // 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.
    : mPlaneNormal(0.8523f, 0.34321f, 0.5736f)
{
    mPlaneNormal.Normalize();
    Fill(pPositions,pNumPositions,pElementOffset);
}

// ------------------------------------------------------------------------------------------------
SpatialSort :: SpatialSort()
: mPlaneNormal(0.8523f, 0.34321f, 0.5736f)
{
    mPlaneNormal.Normalize();
}

// ------------------------------------------------------------------------------------------------
// Destructor
SpatialSort::~SpatialSort()
{
    // nothing to do here, everything destructs automatically
}

// ------------------------------------------------------------------------------------------------
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);
        #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.

        // Two's complement?
        if( (-42 == (~42 + 1)) && (binValue & 0x80000000))
            return BinFloat(1 << (CHAR_BIT * sizeof(BinFloat) - 1)) - binValue;
        // One's complement?
        else if( (-42 == ~42) && (binValue & 0x80000000))
            return BinFloat(-0) - binValue;
        // Sign-magnitude?
        else if( (-42 == (42 | (-0))) && (binValue & 0x80000000)) // -0 = 1000... binary
            return binValue;
        else
            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 aray
    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;
}