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-/*
----------------------------------------------------------------------------
-Open Asset Import Library (assimp)
----------------------------------------------------------------------------
-
-Copyright (c) 2006-2022, assimp team
-
-All rights reserved.
-
-Redistribution and use of this software in source and binary forms,
-with or without modification, are permitted provided that the following
-conditions are met:
-
-* Redistributions of source code must retain the above
- copyright notice, this list of conditions and the
- following disclaimer.
-
-* Redistributions in binary form must reproduce the above
- copyright notice, this list of conditions and the
- following disclaimer in the documentation and/or other
- materials provided with the distribution.
-
-* Neither the name of the assimp team, nor the names of its
- contributors may be used to endorse or promote products
- derived from this software without specific prior
- written permission of the assimp team.
-
-THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
----------------------------------------------------------------------------
-*/
-
-/** @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 axes
-// 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),
- mFinalized(false) {
- mPlaneNormal.Normalize();
- Fill(pPositions, pNumPositions, pElementOffset);
-}
-
-// ------------------------------------------------------------------------------------------------
-SpatialSort::SpatialSort() :
- mPlaneNormal(PlaneInit),
- mFinalized(false) {
- mPlaneNormal.Normalize();
-}
-
-// ------------------------------------------------------------------------------------------------
-// Destructor
-SpatialSort::~SpatialSort() {
- // empty
-}
-
-// ------------------------------------------------------------------------------------------------
-void SpatialSort::Fill(const aiVector3D *pPositions, unsigned int pNumPositions,
- unsigned int pElementOffset,
- bool pFinalize /*= true */) {
- mPositions.clear();
- mFinalized = false;
- Append(pPositions, pNumPositions, pElementOffset, pFinalize);
- mFinalized = pFinalize;
-}
-
-// ------------------------------------------------------------------------------------------------
-ai_real SpatialSort::CalculateDistance(const aiVector3D &pPosition) const {
- return (pPosition - mCentroid) * mPlaneNormal;
-}
-
-// ------------------------------------------------------------------------------------------------
-void SpatialSort::Finalize() {
- const ai_real scale = 1.0f / mPositions.size();
- for (unsigned int i = 0; i < mPositions.size(); i++) {
- mCentroid += scale * mPositions[i].mPosition;
- }
- for (unsigned int i = 0; i < mPositions.size(); i++) {
- mPositions[i].mDistance = CalculateDistance(mPositions[i].mPosition);
- }
- std::sort(mPositions.begin(), mPositions.end());
- mFinalized = true;
-}
-
-// ------------------------------------------------------------------------------------------------
-void SpatialSort::Append(const aiVector3D *pPositions, unsigned int pNumPositions,
- unsigned int pElementOffset,
- bool pFinalize /*= true */) {
- ai_assert(!mFinalized && "You cannot add positions to the SpatialSort object after it has been finalized.");
- // store references to all given positions along with their distance to the reference plane
- const size_t initial = mPositions.size();
- mPositions.reserve(initial + pNumPositions);
- 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);
- mPositions.push_back(Entry(static_cast<unsigned int>(a + initial), *vec));
- }
-
- 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 {
- ai_assert(mFinalized && "The SpatialSort object must be finalized before FindPositions can be called.");
- const ai_real dist = CalculateDistance(pPosition);
- 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 array
- 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 {
- ai_assert(mFinalized && "The SpatialSort object must be finalized before FindIdenticalPositions can be called.");
- // 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(CalculateDistance(pPosition)) - 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 {
- ai_assert(mFinalized && "The SpatialSort object must be finalized before GenerateMappingTable can be called.");
- 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 - mCentroid) * 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;
-}