assimp/code/SpatialSort.cpp

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

#include "AssimpPCH.h"
#include "SpatialSort.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
		float distance = *vec * mPlaneNormal;
		mPositions.push_back( Entry( 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, 
	float pRadius, std::vector<unsigned int>& poResults) const
{
	const float dist = pPosition * mPlaneNormal;
	const float minDist = dist - pRadius, maxDist = dist + pRadius;

	// clear the array in this strange fashion because a simple clear() would also deallocate
    // the array which we want to avoid
	poResults.erase( poResults.begin(), poResults.end());

	// 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 float 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 signed int BinFloat;

	// --------------------------------------------------------------------------------------------
	// Converts the bit pattern of a floating-point number to its signed integer representation.
	BinFloat ToBinary( const float & 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!
		BOOST_STATIC_ASSERT( sizeof(BinFloat) >= sizeof(float));

		#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).
			BOOST_STATIC_ASSERT( sizeof(BinFloat) == sizeof(float));

			// 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 {
				float		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 indentical 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.erase( poResults.begin(), poResults.end());

	// 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,float pRadius) const
{
	fill.resize(mPositions.size(),UINT_MAX);
	float dist, maxDist;

	unsigned int t=0;
	const float 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 _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;
}